POPL 2018 – Author Index 
Contents 
Abstracts 
Authors

A B C D E F G H I J K L M N O P R S T U V W Y Z
Abel, Andreas 
POPL '18: "Decidability of Conversion ..."
Decidability of Conversion for Type Theory in Type Theory
Andreas Abel, Joakim Öhman , and Andrea Vezzosi (University of Gothenburg, Sweden; IMDEA Software Institute, Spain; Chalmers University of Technology, Sweden) Type theory should be able to handle its own metatheory, both to justify its foundational claims and to obtain a verified implementation. At the core of a type checker for intensional type theory lies an algorithm to check equality of types, or in other words, to check whether two types are convertible. We have formalized in Agda a practical conversion checking algorithm for a dependent type theory with one universe à la Russell, natural numbers, and ηequality for Π types. We prove the algorithm correct via a Kripke logical relation parameterized by a suitable notion of equivalence of terms. We then instantiate the parameterized fundamental lemma twice: once to obtain canonicity and injectivity of type formers, and once again to prove the completeness of the algorithm. Our proof relies on inductiverecursive definitions, but not on the uniqueness of identity proofs. Thus, it is valid in variants of intensional MartinLöf Type Theory as long as they support inductionrecursion, for instance, Extensional, Observational, or Homotopy Type Theory. @Article{POPL18p23, author = {Andreas Abel and Joakim Öhman and Andrea Vezzosi}, title = {Decidability of Conversion for Type Theory in Type Theory}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {23}, numpages = {29}, doi = {10.1145/3158111}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Abraham, Ittai 
POPL '18: "Online Detection of Effectively ..."
Online Detection of Effectively Callback Free Objects with Applications to Smart Contracts
Shelly Grossman, Ittai Abraham, Guy GolanGueta, Yan Michalevsky, Noam Rinetzky, Mooly Sagiv, and Yoni Zohar (Tel Aviv University, Israel; VMware, USA; Stanford University, USA) Callbacks are essential in many programming environments, but drastically complicate program understanding and reasoning because they allow to mutate object's local states by external objects in unexpected fashions, thus breaking modularity. The famous DAO bug in the cryptocurrency framework Ethereum, employed callbacks to steal $150M. We define the notion of Effectively Callback Free (ECF) objects in order to allow callbacks without preventing modular reasoning. An object is ECF in a given execution trace if there exists an equivalent execution trace without callbacks to this object. An object is ECF if it is ECF in every possible execution trace. We study the decidability of dynamically checking ECF in a given execution trace and statically checking if an object is ECF. We also show that dynamically checking ECF in Ethereum is feasible and can be done online. By running the history of all execution traces in Ethereum, we were able to verify that virtually all existing contract executions, excluding these of the DAO or of contracts with similar known vulnerabilities, are ECF. Finally, we show that ECF, whether it is verified dynamically or statically, enables modular reasoning about objects with encapsulated state. @Article{POPL18p48, author = {Shelly Grossman and Ittai Abraham and Guy GolanGueta and Yan Michalevsky and Noam Rinetzky and Mooly Sagiv and Yoni Zohar}, title = {Online Detection of Effectively Callback Free Objects with Applications to Smart Contracts}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {48}, numpages = {28}, doi = {10.1145/3158136}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Agrawal, Sheshansh 
POPL '18: "Lexicographic Ranking Supermartingales: ..."
Lexicographic Ranking Supermartingales: An Efficient Approach to Termination of Probabilistic Programs
Sheshansh Agrawal, Krishnendu Chatterjee , and Petr Novotný (IIT Bombay, India; IST Austria, Austria) Probabilistic programs extend classical imperative programs with realvalued random variables and random branching. The most basic liveness property for such programs is the termination property. The qualitative (aka almostsure) termination problem asks whether a given program program terminates with probability 1. While ranking functions provide a sound and complete method for nonprobabilistic programs, the extension of them to probabilistic programs is achieved via ranking supermartingales (RSMs). Although deep theoretical results have been established about RSMs, their application to probabilistic programs with nondeterminism has been limited only to programs of restricted controlflow structure. For nonprobabilistic programs, lexicographic ranking functions provide a compositional and practical approach for termination analysis of realworld programs. In this work we introduce lexicographic RSMs and show that they present a sound method for almostsure termination of probabilistic programs with nondeterminism. We show that lexicographic RSMs provide a tool for compositional reasoning about almostsure termination, and for probabilistic programs with linear arithmetic they can be synthesized efficiently (in polynomial time). We also show that with additional restrictions even asymptotic bounds on expected termination time can be obtained through lexicographic RSMs. Finally, we present experimental results on benchmarks adapted from previous work to demonstrate the effectiveness of our approach. @Article{POPL18p34, author = {Sheshansh Agrawal and Krishnendu Chatterjee and Petr Novotný}, title = {Lexicographic Ranking Supermartingales: An Efficient Approach to Termination of Probabilistic Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {34}, numpages = {32}, doi = {10.1145/3158122}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Ahman, Danel 
POPL '18: "Recalling a Witness: Foundations ..."
Recalling a Witness: Foundations and Applications of Monotonic State
Danel Ahman, Cédric Fournet, Cătălin Hriţcu, Kenji Maillard , Aseem Rastogi, and Nikhil Swamy (Inria, France; Microsoft Research, UK; ENS Paris, France; Microsoft Research, India; Microsoft Research, USA) We provide a way to ease the verification of programs whose state evolves monotonically. The main idea is that a property witnessed in a prior state can be soundly recalled in the current state, provided (1) state evolves according to a given preorder, and (2) the property is preserved by this preorder. In many scenarios, such monotonic reasoning yields concise modular proofs, saving the need for explicit program invariants. We distill our approach into the monotonicstate monad, a general yet compact interface for Hoarestyle reasoning about monotonic state in a dependently typed language. We prove the soundness of the monotonicstate monad and use it as a unified foundation for reasoning about monotonic state in the F^{⋆} verification system. Based on this foundation, we build libraries for various mutable data structures like monotonic references and apply these libraries at scale to the verification of several distributed applications. @Article{POPL18p65, author = {Danel Ahman and Cédric Fournet and Cătălin Hriţcu and Kenji Maillard and Aseem Rastogi and Nikhil Swamy}, title = {Recalling a Witness: Foundations and Applications of Monotonic State}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {65}, numpages = {30}, doi = {10.1145/3158153}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional POPL '18: "Handling Fibred Algebraic ..." Handling Fibred Algebraic Effects Danel Ahman (Inria, France) We study algebraic computational effects and their handlers in the dependently typed setting. We describe computational effects using a generalisation of Plotkin and Pretnar's effect theories, whose dependently typed operations allow us to capture precise notions of computation, e.g., state with locationdependent store types and dependently typed update monads. Our treatment of handlers is based on an observation that their conventional termlevel definition leads to unsound program equivalences being derivable in languages that include a notion of homomorphism. We solve this problem by giving handlers a novel typebased treatment via a new computation type, the userdefined algebra type, which pairs a value type (the carrier) with a set of value terms (the operations), capturing Plotkin and Pretnar's insight that effect handlers denote algebras. We then show that the conventional presentation of handlers can be routinely derived, and demonstrate that this typebased treatment of handlers provides a useful mechanism for reasoning about effectful computations. We also equip the resulting language with a sound denotational semantics based on families fibrations. @Article{POPL18p7, author = {Danel Ahman}, title = {Handling Fibred Algebraic Effects}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {7}, numpages = {29}, doi = {10.1145/3158095}, year = {2018}, } Publisher's Version Article Search 

Ahmed, Amal 
POPL '18: "Correctness of Speculative ..."
Correctness of Speculative Optimizations with Dynamic Deoptimization
Olivier Flückiger , Gabriel Scherer , MingHo Yee, Aviral Goel, Amal Ahmed, and Jan Vitek (Northeastern University, USA; Inria, France; Czech Technical University, Czechia) Highperformance dynamic language implementations make heavy use of speculative optimizations to achieve speeds close to statically compiled languages. These optimizations are typically performed by a justintime compiler that generates code under a set of assumptions about the state of the program and its environment. In certain cases, a program may execute code compiled under assumptions that are no longer valid. The implementation must then deoptimize the program onthefly; this entails finding semantically equivalent code that does not rely on invalid assumptions, translating program state to that expected by the target code, and transferring control. This paper looks at the interaction between optimization and deoptimization, and shows that reasoning about speculation is surprisingly easy when assumptions are made explicit in the program representation. This insight is demonstrated on a compiler intermediate representation, named sourir, modeled after the highlevel representation for a dynamic language. Traditional compiler optimizations such as constant folding, unreachable code elimination, and function inlining are shown to be correct in the presence of assumptions. Furthermore, the paper establishes the correctness of compiler transformations specific to deoptimization: namely unrestricted deoptimization, predicate hoisting, and assume composition. @Article{POPL18p49, author = {Olivier Flückiger and Gabriel Scherer and MingHo Yee and Aviral Goel and Amal Ahmed and Jan Vitek}, title = {Correctness of Speculative Optimizations with Dynamic Deoptimization}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {49}, numpages = {28}, doi = {10.1145/3158137}, year = {2018}, } Publisher's Version Article Search POPL '18: "TypePreserving CPS Translation ..." TypePreserving CPS Translation of Σ and Π Types Is Not Not Possible William J. Bowman, Youyou Cong, Nick Rioux, and Amal Ahmed (Northeastern University, USA; Ochanomizu University, Japan) Dependently typed languages such as Coq are used to specify and prove functional correctness of source programs, but what we ultimately need are guarantees about correctness of compiled code. By preserving dependent types through each compiler pass, we could preserve sourcelevel specifications and correctness proofs into the generated targetlanguage programs. Unfortunately, typepreserving compilation of dependent types is hard. In 2002, Barthe and Uustalu showed that typepreserving CPS is not possible for languages such as Coq. Specifically, they showed that for strong dependent pairs (Σ types), the standard typed callbyname CPS is not type preserving. They further proved that for dependent case analysis on sums, a class of typed CPS translations—including the standard translation—is not possible. In 2016, Morrisett noticed a similar problem with the standard callbyvalue CPS translation for dependent functions (Π types). In essence, the problem is that the standard typed CPS translation by doublenegation, in which computations are assigned types of the form (A → ⊥) → ⊥, disrupts the term/type equivalence that is used during type checking in a dependently typed language. In this paper, we prove that typepreserving CPS translation for dependently typed languages is not not possible. We develop both callbyname and callbyvalue CPS translations from the Calculus of Constructions with both Π and Σ types (CC) to a dependently typed target language, and prove type preservation and compiler correctness of each translation. Our target language is CC extended with an additional equivalence rule and an additional typing rule, which we prove consistent by giving a model in the extensional Calculus of Constructions. Our key observation is that we can use a CPS translation that employs answertype polymorphism, where CPStranslated computations have type ∀ α. (A → α) → α. This type justifies, by a free theorem, the new equality rule in our target language and allows us to recover the term/type equivalences that CPS translation disrupts. Finally, we conjecture that our translation extends to dependent case analysis on sums, despite the impossibility result, and provide a proof sketch. @Article{POPL18p22, author = {William J. Bowman and Youyou Cong and Nick Rioux and Amal Ahmed}, title = {TypePreserving CPS Translation of Σ and Π Types Is Not Not Possible}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {22}, numpages = {33}, doi = {10.1145/3158110}, year = {2018}, } Publisher's Version Article Search Info 

Aiken, Alex 
POPL '18: "On Automatically Proving the ..."
On Automatically Proving the Correctness of math.h Implementations
Wonyeol Lee, Rahul Sharma, and Alex Aiken (Stanford University, USA; Microsoft Research, India) Industry standard implementations of math.h claim (often without formal proof) tight bounds on floatingpoint errors. We demonstrate a novel static analysis that proves these bounds and verifies the correctness of these implementations. Our key insight is a reduction of this verification task to a set of mathematical optimization problems that can be solved by offtheshelf computer algebra systems. We use this analysis to prove the correctness of implementations in Intel's math library automatically. Prior to this work, these implementations could only be verified with significant manual effort. @Article{POPL18p47, author = {Wonyeol Lee and Rahul Sharma and Alex Aiken}, title = {On Automatically Proving the Correctness of math.h Implementations}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {47}, numpages = {32}, doi = {10.1145/3158135}, year = {2018}, } Publisher's Version Article Search 

Albarghouthi, Aws 
POPL '18: "Synthesizing Coupling Proofs ..."
Synthesizing Coupling Proofs of Differential Privacy
Aws Albarghouthi and Justin Hsu (University of WisconsinMadison, USA; University College London, UK) Differential privacy has emerged as a promising probabilistic formulation of privacy, generating intense interest within academia and industry. We present a pushbutton, automated technique for verifying εdifferential privacy of sophisticated randomized algorithms. We make several conceptual, algorithmic, and practical contributions: (i) Inspired by the recent advances on approximate couplings and randomness alignment, we present a new proof technique called coupling strategies, which casts differential privacy proofs as a winning strategy in a game where we have finite privacy resources to expend. (ii) To discover a winning strategy, we present a constraintbased formulation of the problem as a set of Horn modulo couplings (HMC) constraints, a novel combination of firstorder Horn clauses and probabilistic constraints. (iii) We present a technique for solving HMC constraints by transforming probabilistic constraints into logical constraints with uninterpreted functions. (iv) Finally, we implement our technique in the FairSquare verifier and provide the first automated privacy proofs for a number of challenging algorithms from the differential privacy literature, including Report Noisy Max, the Exponential Mechanism, and the Sparse Vector Mechanism. @Article{POPL18p58, author = {Aws Albarghouthi and Justin Hsu}, title = {Synthesizing Coupling Proofs of Differential Privacy}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {58}, numpages = {30}, doi = {10.1145/3158146}, year = {2018}, } Publisher's Version Article Search 

Amin, Nada 
POPL '18: "Collapsing Towers of Interpreters ..."
Collapsing Towers of Interpreters
Nada Amin and Tiark Rompf (University of Cambridge, UK; Purdue University, USA) Given a tower of interpreters, i.e., a sequence of multiple interpreters interpreting one another as input programs, we aim to collapse this tower into a compiler that removes all interpretive overhead and runs in a single pass. In the real world, a use case might be Python code executed by an x86 runtime, on a CPU emulated in a JavaScript VM, running on an ARM CPU. Collapsing such a tower can not only exponentially improve runtime performance, but also enable the use of baselanguage tools for interpreted programs, e.g., for analysis and verification. In this paper, we lay the foundations in an idealized but realistic setting. We present a multilevel lambda calculus that features staging constructs and stage polymorphism: based on runtime parameters, an evaluator either executes source code (thereby acting as an interpreter) or generates code (thereby acting as a compiler). We identify stage polymorphism, a programming model from the domain of highperformance program generators, as the key mechanism to make such interpreters compose in a collapsible way. We present Pink, a metacircular Lisplike evaluator on top of this calculus, and demonstrate that we can collapse arbitrarily many levels of selfinterpretation, including levels with semantic modifications. We discuss several examples: compiling regular expressions through an interpreter to base code, building program transformers from modi ed interpreters, and others. We develop these ideas further to include reflection and reification, culminating in Purple, a reflective language inspired by Brown, Blond, and Black, which realizes a conceptually infinite tower, where every aspect of the semantics can change dynamically. Addressing an open challenge, we show how user programs can be compiled and recompiled under usermodified semantics. @Article{POPL18p52, author = {Nada Amin and Tiark Rompf}, title = {Collapsing Towers of Interpreters}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {52}, numpages = {33}, doi = {10.1145/3158140}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Bach Poulsen, Casper 
POPL '18: "IntrinsicallyTyped Definitional ..."
IntrinsicallyTyped Definitional Interpreters for Imperative Languages
Casper Bach Poulsen , Arjen Rouvoet , Andrew Tolmach, Robbert Krebbers , and Eelco Visser (Delft University of Technology, Netherlands; Portland State University, USA) A definitional interpreter defines the semantics of an object language in terms of the (wellknown) semantics of a host language, enabling understanding and validation of the semantics through execution. Combining a definitional interpreter with a separate type system requires a separate type safety proof. An alternative approach, at least for pure object languages, is to use a dependentlytyped language to encode the object language type system in the definition of the abstract syntax. Using such intrinsicallytyped abstract syntax definitions allows the host language type checker to verify automatically that the interpreter satisfies type safety. Does this approach scale to larger and more realistic object languages, and in particular to languages with mutable state and objects? In this paper, we describe and demonstrate techniques and libraries in Agda that successfully scale up intrinsicallytyped definitional interpreters to handle rich object languages with nontrivial binding structures and mutable state. While the resulting interpreters are certainly more complex than the simplytyped λcalculus interpreter we start with, we claim that they still meet the goals of being concise, comprehensible, and executable, while guaranteeing type safety for more elaborate object languages. We make the following contributions: (1) A dependentpassing style technique for hiding the weakening of indexed values as they propagate through monadic code. (2) An Agda library for programming with scope graphs and frames, which provides a uniform approach to dealing with name binding in intrinsicallytyped interpreters. (3) Case studies of intrinsicallytyped definitional interpreters for the simplytyped λcalculus with references (STLC+Ref) and for a large subset of Middleweight Java (MJ). @Article{POPL18p16, author = {Casper Bach Poulsen and Arjen Rouvoet and Andrew Tolmach and Robbert Krebbers and Eelco Visser}, title = {IntrinsicallyTyped Definitional Interpreters for Imperative Languages}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {16}, numpages = {34}, doi = {10.1145/3158104}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Bao, Wenlei 
POPL '18: "Analytical Modeling of Cache ..."
Analytical Modeling of Cache Behavior for Affine Programs
Wenlei Bao, Sriram Krishnamoorthy, LouisNoel Pouchet, and P. Sadayappan (Ohio State University, USA; Pacific Northwest National Laboratory, USA; Colorado State University, USA) Optimizing compilers implement program transformation strategies aimed at reducing data movement to or from main memory by exploiting the datacache hierarchy. However, instead of attempting to minimize the number of cache misses, very approximate cost models are used, due to the lack of precise compiletime models for misses for hierarchical caches. The current state of practice for cache miss analysis is based on accurate simulation. However, simulation requires time proportional to the dataset/problem size, as well as the number of distinct cache configurations of interest to be evaluated. This paper takes a fundamentally different approach, by focusing on polyhedral programs with static control flow. Instead of relying on costly simulation, a closedform solution for modeling of misses in a set associative cache hierarchy is developed. This solution can enable program transformation choice at compile time to optimize cache misses. A tool implementing the approach has been developed and used for validation of the framework. @Article{POPL18p32, author = {Wenlei Bao and Sriram Krishnamoorthy and LouisNoel Pouchet and P. Sadayappan}, title = {Analytical Modeling of Cache Behavior for Affine Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {32}, numpages = {26}, doi = {10.1145/3158120}, year = {2018}, } Publisher's Version Article Search 

Barthe, Gilles 
POPL '18: "Monadic Refinements for Relational ..."
Monadic Refinements for Relational Cost Analysis
Ivan Radiček, Gilles Barthe , Marco Gaboardi, Deepak Garg , and Florian Zuleger (Vienna University of Technology, Austria; IMDEA Software Institute, Spain; SUNY Buffalo, USA; MPISWS, Germany) Formal frameworks for cost analysis of programs have been widely studied in the unary setting and, to a limited extent, in the relational setting. However, many of these frameworks focus only on the cost aspect, largely sidelining functional properties that are often a prerequisite for cost analysis, thus leaving many interesting programs out of their purview. In this paper, we show that elegant, simple, expressive proof systems combining cost analysis and functional properties can be built by combining already known ingredients: higherorder refinements and cost monads. Specifically, we derive two syntaxdirected proof systems, U^{C} and R^{C}, for unary and relational cost analysis, by adding a cost monad to a (syntaxdirected) logic of higherorder programs. We study the metatheory of the systems, show that several nontrivial examples can be verified in them, and prove that existing frameworks for cost analysis (RelCost and RAML) can be embedded in them. @Article{POPL18p36, author = {Ivan Radiček and Gilles Barthe and Marco Gaboardi and Deepak Garg and Florian Zuleger}, title = {Monadic Refinements for Relational Cost Analysis}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {36}, numpages = {32}, doi = {10.1145/3158124}, year = {2018}, } Publisher's Version Article Search POPL '18: "Proving Expected Sensitivity ..." Proving Expected Sensitivity of Probabilistic Programs Gilles Barthe , Thomas Espitau, Benjamin Grégoire, Justin Hsu , and PierreYves Strub (IMDEA Software Institute, Spain; UPMC, France; Inria, France; University College London, UK; École Polytechnique, France) Program sensitivity, also known as Lipschitz continuity, describes how small changes in a program’s input lead to bounded changes in the output. We propose an average notion of program sensitivity for probabilistic programs—expected sensitivity—that averages a distance function over a probabilistic coupling of two output distributions from two similar inputs. By varying the distance, expected sensitivity recovers useful notions of probabilistic function sensitivity, including stability of machine learning algorithms and convergence of Markov chains. Furthermore, expected sensitivity satisfies clean compositional properties and is amenable to formal verification. We develop a relational program logic called EpRHL for proving expected sensitivity properties. Our logic features two key ideas. First, relational preconditions and postconditions are expressed using distances, a realvalued generalization of typical booleanvalued (relational) assertions. Second, judgments are interpreted in terms of expectation coupling, a novel, quantitative generalization of probabilistic couplings which supports compositional reasoning. We demonstrate our logic on examples beyond the reach of prior relational logics. Our main example formalizes uniform stability of the stochastic gradient method. Furthermore, we prove rapid mixing for a probabilistic model of population dynamics. We also extend our logic with a transitivity principle for expectation couplings to capture the path coupling proof technique by Bubley and Dyer, and formalize rapid mixing of the Glauber dynamics from statistical physics. @Article{POPL18p57, author = {Gilles Barthe and Thomas Espitau and Benjamin Grégoire and Justin Hsu and PierreYves Strub}, title = {Proving Expected Sensitivity of Probabilistic Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {57}, numpages = {29}, doi = {10.1145/3158145}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Bernardy, JeanPhilippe 
POPL '18: "Linear Haskell: Practical ..."
Linear Haskell: Practical Linearity in a HigherOrder Polymorphic Language
JeanPhilippe Bernardy, Mathieu Boespflug, Ryan R. Newton, Simon Peyton Jones, and Arnaud Spiwack (University of Gothenburg, Sweden; Tweag I/O, France; Indiana University, USA; Microsoft Research, UK) Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind: backwardscompatibility and code reuse across linear and nonlinear users of a library. Only then can the benefits of linear types permeate conventional functional programming. Rather than bifurcate types into linear and nonlinear counterparts, we instead attach linearity to function arrows. Linear functions can receive inputs from linearlybound values, but can also operate over unrestricted, regular values. To demonstrate the efficacy of our linear type system — both how easy it can be integrated in an existing language implementation and how streamlined it makes it to write programs with linear types — we implemented our type system in ghc, the leading Haskell compiler, and demonstrate two kinds of applications of linear types: mutable data with pure interfaces; and enforcing protocols in I/Operforming functions. @Article{POPL18p5, author = {JeanPhilippe Bernardy and Mathieu Boespflug and Ryan R. Newton and Simon Peyton Jones and Arnaud Spiwack}, title = {Linear Haskell: Practical Linearity in a HigherOrder Polymorphic Language}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {5}, numpages = {29}, doi = {10.1145/3158093}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Biboudis, Aggelos 
POPL '18: "Simplicitly: Foundations and ..."
Simplicitly: Foundations and Applications of Implicit Function Types
Martin Odersky, Olivier Blanvillain, Fengyun Liu, Aggelos Biboudis, Heather Miller, and Sandro Stucki (EPFL, Switzerland; Northeastern University, USA) Understanding a program entails understanding its context; dependencies, configurations and even implementations are all forms of contexts. Modern programming languages and theorem provers offer an array of constructs to define contexts, implicitly. Scala offers implicit parameters which are used pervasively, but which cannot be abstracted over. This paper describes a generalization of implicit parameters to implicit function types, a powerful way to abstract over the context in which some piece of code is run. We provide a formalization based on bidirectional typechecking that closely follows the semantics implemented by the Scala compiler. To demonstrate their range of abstraction capabilities, we present several applications that make use of implicit function types. We show how to encode the builder pattern, tagless interpreters, reader and free monads and we assess the performance of the monadic structures presented. @Article{POPL18p42, author = {Martin Odersky and Olivier Blanvillain and Fengyun Liu and Aggelos Biboudis and Heather Miller and Sandro Stucki}, title = {Simplicitly: Foundations and Applications of Implicit Function Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {42}, numpages = {29}, doi = {10.1145/3158130}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Biernacki, Dariusz 
POPL '18: "Handle with Care: Relational ..."
Handle with Care: Relational Interpretation of Algebraic Effects and Handlers
Dariusz Biernacki, Maciej Piróg, Piotr Polesiuk, and Filip Sieczkowski (University of Wrocław, Poland) Algebraic effects and handlers have received a lot of attention recently, both from the theoretical point of view and in practical language design. This stems from the fact that algebraic effects give the programmer unprecedented freedom to define, combine, and interpret computational effects. This plentyofrope, however, demands not only a deep understanding of the underlying semantics, but also access to practical means of reasoning about effectful code, including correctness and program equivalence. In this paper we tackle this problem by constructing a stepindexed relational interpretation of a callbyvalue calculus with algebraic effect handlers and a rowbased polymorphic typeandeffect system. Our calculus, while striving for simplicity, enjoys desirable theoretical properties, and is close to the cores of programming languages with algebraic effects used in the wild, while the logical relation we build for it can be used to reason about nontrivial properties, such as contextual equivalence and contextual approximation of programs. Our development has been fully formalised in the Coq proof assistant. @Article{POPL18p8, author = {Dariusz Biernacki and Maciej Piróg and Piotr Polesiuk and Filip Sieczkowski}, title = {Handle with Care: Relational Interpretation of Algebraic Effects and Handlers}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {8}, numpages = {30}, doi = {10.1145/3158096}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Birkedal, Lars 
POPL '18: "A Logical Relation for Monadic ..."
A Logical Relation for Monadic Encapsulation of State: Proving Contextual Equivalences in the Presence of runST
Amin Timany, Léo Stefanesco, Morten KroghJespersen, and Lars Birkedal (KU Leuven, Belgium; IRIF, France; CNRS, France; University of Paris Diderot, France; Aarhus University, Denmark) We present a logical relations model of a higherorder functional programming language with impredicative polymorphism, recursive types, and a Haskellstyle ST monad type with runST. We use our logical relations model to show that runST provides proper encapsulation of state, by showing that effectful computations encapsulated by runST are heap independent. Furthermore, we show that contextual refinements and equivalences that are expected to hold for pure computations do indeed hold in the presence of runST. This is the first time such relational results have been proven for a language with monadic encapsulation of state. We have formalized all the technical development and results in Coq. @Article{POPL18p64, author = {Amin Timany and Léo Stefanesco and Morten KroghJespersen and Lars Birkedal}, title = {A Logical Relation for Monadic Encapsulation of State: Proving Contextual Equivalences in the Presence of runST}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {64}, numpages = {28}, doi = {10.1145/3158152}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Blanvillain, Olivier 
POPL '18: "Simplicitly: Foundations and ..."
Simplicitly: Foundations and Applications of Implicit Function Types
Martin Odersky, Olivier Blanvillain, Fengyun Liu, Aggelos Biboudis, Heather Miller, and Sandro Stucki (EPFL, Switzerland; Northeastern University, USA) Understanding a program entails understanding its context; dependencies, configurations and even implementations are all forms of contexts. Modern programming languages and theorem provers offer an array of constructs to define contexts, implicitly. Scala offers implicit parameters which are used pervasively, but which cannot be abstracted over. This paper describes a generalization of implicit parameters to implicit function types, a powerful way to abstract over the context in which some piece of code is run. We provide a formalization based on bidirectional typechecking that closely follows the semantics implemented by the Scala compiler. To demonstrate their range of abstraction capabilities, we present several applications that make use of implicit function types. We show how to encode the builder pattern, tagless interpreters, reader and free monads and we assess the performance of the monadic structures presented. @Article{POPL18p42, author = {Martin Odersky and Olivier Blanvillain and Fengyun Liu and Aggelos Biboudis and Heather Miller and Sandro Stucki}, title = {Simplicitly: Foundations and Applications of Implicit Function Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {42}, numpages = {29}, doi = {10.1145/3158130}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Bodik, Rastislav 
POPL '18: "Bonsai: SynthesisBased Reasoning ..."
Bonsai: SynthesisBased Reasoning for Type Systems
Kartik Chandra and Rastislav Bodik (Henry M. Gunn High School, USA; Stanford University, USA; University of Washington, USA) When designing a type system, we may want to mechanically check the design to guide its further development. We describe algorithms that perform symbolic reasoning about executable models of type systems. The algorithms support three queries. First, they check type soundness and synthesize a counterexample program if such a soundness bug is found. Second, they compare two versions of a type system, synthesizing a program accepted by one but rejected by the other. Third, they minimize the size of synthesized counterexample programs. These algorithms symbolically evaluate typecheckers and interpreters, producing formulas that characterize the set of programs that fail or succeed in the typechecker and the interpreter. However, symbolically evaluating interpreters poses efficiency challenges, which are caused by having to merge execution paths of the various possible input programs. Our main contribution is the bonsai tree, a novel symbolic representation of programs and program states that addresses these challenges. Bonsai trees encode complex syntactic information in terms of logical constraints, enabling more efficient merging. We implement these algorithms in the Bonsai tool, an assistant for type system designers. We perform case studies on how Bonsai helps test and explore a variety of type systems. Bonsai efficiently synthesizes counterexamples for soundness bugs previously inaccessible to automatic tools and is the first automated tool to find a counterexample for the recently discovered Scala soundness bug SI9633. @Article{POPL18p62, author = {Kartik Chandra and Rastislav Bodik}, title = {Bonsai: SynthesisBased Reasoning for Type Systems}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {62}, numpages = {34}, doi = {10.1145/3158150}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Boespflug, Mathieu 
POPL '18: "Linear Haskell: Practical ..."
Linear Haskell: Practical Linearity in a HigherOrder Polymorphic Language
JeanPhilippe Bernardy, Mathieu Boespflug, Ryan R. Newton, Simon Peyton Jones, and Arnaud Spiwack (University of Gothenburg, Sweden; Tweag I/O, France; Indiana University, USA; Microsoft Research, UK) Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind: backwardscompatibility and code reuse across linear and nonlinear users of a library. Only then can the benefits of linear types permeate conventional functional programming. Rather than bifurcate types into linear and nonlinear counterparts, we instead attach linearity to function arrows. Linear functions can receive inputs from linearlybound values, but can also operate over unrestricted, regular values. To demonstrate the efficacy of our linear type system — both how easy it can be integrated in an existing language implementation and how streamlined it makes it to write programs with linear types — we implemented our type system in ghc, the leading Haskell compiler, and demonstrate two kinds of applications of linear types: mutable data with pure interfaces; and enforcing protocols in I/Operforming functions. @Article{POPL18p5, author = {JeanPhilippe Bernardy and Mathieu Boespflug and Ryan R. Newton and Simon Peyton Jones and Arnaud Spiwack}, title = {Linear Haskell: Practical Linearity in a HigherOrder Polymorphic Language}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {5}, numpages = {29}, doi = {10.1145/3158093}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Bowman, William J. 
POPL '18: "TypePreserving CPS Translation ..."
TypePreserving CPS Translation of Σ and Π Types Is Not Not Possible
William J. Bowman, Youyou Cong, Nick Rioux, and Amal Ahmed (Northeastern University, USA; Ochanomizu University, Japan) Dependently typed languages such as Coq are used to specify and prove functional correctness of source programs, but what we ultimately need are guarantees about correctness of compiled code. By preserving dependent types through each compiler pass, we could preserve sourcelevel specifications and correctness proofs into the generated targetlanguage programs. Unfortunately, typepreserving compilation of dependent types is hard. In 2002, Barthe and Uustalu showed that typepreserving CPS is not possible for languages such as Coq. Specifically, they showed that for strong dependent pairs (Σ types), the standard typed callbyname CPS is not type preserving. They further proved that for dependent case analysis on sums, a class of typed CPS translations—including the standard translation—is not possible. In 2016, Morrisett noticed a similar problem with the standard callbyvalue CPS translation for dependent functions (Π types). In essence, the problem is that the standard typed CPS translation by doublenegation, in which computations are assigned types of the form (A → ⊥) → ⊥, disrupts the term/type equivalence that is used during type checking in a dependently typed language. In this paper, we prove that typepreserving CPS translation for dependently typed languages is not not possible. We develop both callbyname and callbyvalue CPS translations from the Calculus of Constructions with both Π and Σ types (CC) to a dependently typed target language, and prove type preservation and compiler correctness of each translation. Our target language is CC extended with an additional equivalence rule and an additional typing rule, which we prove consistent by giving a model in the extensional Calculus of Constructions. Our key observation is that we can use a CPS translation that employs answertype polymorphism, where CPStranslated computations have type ∀ α. (A → α) → α. This type justifies, by a free theorem, the new equality rule in our target language and allows us to recover the term/type equivalences that CPS translation disrupts. Finally, we conjecture that our translation extends to dependent case analysis on sums, despite the impossibility result, and provide a proof sketch. @Article{POPL18p22, author = {William J. Bowman and Youyou Cong and Nick Rioux and Amal Ahmed}, title = {TypePreserving CPS Translation of Σ and Π Types Is Not Not Possible}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {22}, numpages = {33}, doi = {10.1145/3158110}, year = {2018}, } Publisher's Version Article Search Info 

Breck, Jason 
POPL '18: "Nonlinear Reasoning for Invariant ..."
Nonlinear Reasoning for Invariant Synthesis
Zachary Kincaid , John Cyphert, Jason Breck, and Thomas Reps (Princeton University, USA; University of WisconsinMadison, USA; GrammaTech, USA) Automatic generation of nonlinear loop invariants is a longstanding challenge in program analysis, with many applications. For instance, reasoning about exponentials provides a way to find invariants of digitalfilter programs, and reasoning about polynomials and/or logarithms is needed for establishing invariants that describe the time or memory usage of many wellknown algorithms. An appealing approach to this challenge is to exploit the powerful recurrencesolving techniques that have been developed in the field of computer algebra, which can compute exact characterizations of nonlinear repetitive behavior. However, there is a gap between the capabilities of recurrence solvers and the needs of program analysis: (1) loop bodies are not merely systems of recurrence relationsthey may contain conditional branches, nested loops, nondeterministic assignments, etc., and (2) a client program analyzer must be able to reason about the closedform solutions produced by a recurrence solver (e.g., to prove assertions). This paper presents a method for generating nonlinear invariants of general loops based on analyzing recurrence relations. The key components are an abstract domain for reasoning about nonlinear arithmetic, a semanticsbased method for extracting recurrence relations from loop bodies, and a recurrence solver that avoids closed forms that involve complex or irrational numbers. Our technique has been implemented in a program analyzer that can analyze general loops and mutually recursive procedures. Our experiments show that our technique shows promise for nonlinear assertionchecking and resourcebound generation. @Article{POPL18p54, author = {Zachary Kincaid and John Cyphert and Jason Breck and Thomas Reps}, title = {Nonlinear Reasoning for Invariant Synthesis}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {54}, numpages = {33}, doi = {10.1145/3158142}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Brown, Matt 
POPL '18: "JonesOptimal Partial Evaluation ..."
JonesOptimal Partial Evaluation by SpecializationSafe Normalization
Matt Brown and Jens Palsberg (University of California at Los Angeles, USA) We present partial evaluation by specializationsafe normalization, a novel partial evaluation technique that is Jonesoptimal, that can be selfapplied to achieve the Futamura projections and that can be typechecked to ensure it always generates code with the correct type. Jonesoptimality is the goldstandard for nontrivial partial evaluation and guarantees that a specializer can remove an entire layer of interpretation. We achieve Jonesoptimality by using a novel affinevariable static analysis that directs specializationsafe normalization to always decrease a program’s runtime. We demonstrate the robustness of our approach by showing Jonesoptimality in a variety of settings. We have formally proved that our partial evaluator is Jonesoptimal for callbyvalue reduction, and we have experimentally shown that it is Jonesoptimal for callbyvalue, normalorder, and memoized normalorder. Each of our experiments tests Jonesoptimality with three different selfinterpreters. We implemented our partial evaluator in F_{ω}^{µ i}, a recent language for typed selfapplicable metaprogramming. It is the first Jonesoptimal and selfapplicable partial evaluator whose type guarantees that it always generates typecorrect code. @Article{POPL18p14, author = {Matt Brown and Jens Palsberg}, title = {JonesOptimal Partial Evaluation by SpecializationSafe Normalization}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {14}, numpages = {28}, doi = {10.1145/3158102}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Cai, Yufei 
POPL '18: "Denotational Validation of ..."
Denotational Validation of HigherOrder Bayesian Inference
Adam Ścibior, Ohad Kammar, Matthijs Vákár, Sam Staton, Hongseok Yang, Yufei Cai, Klaus Ostermann , Sean K. Moss, Chris Heunen , and Zoubin Ghahramani (University of Cambridge, UK; MPI Tübingen, Germany; University of Oxford, UK; KAIST, South Korea; University of Tübingen, Germany; University of Edinburgh, UK; Uber AI Labs, USA) We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higherorder functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higherorder functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasiBorel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasiBorel counterpart to the MetropolisHastingsGreen theorem. @Article{POPL18p60, author = {Adam Ścibior and Ohad Kammar and Matthijs Vákár and Sam Staton and Hongseok Yang and Yufei Cai and Klaus Ostermann and Sean K. Moss and Chris Heunen and Zoubin Ghahramani}, title = {Denotational Validation of HigherOrder Bayesian Inference}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {60}, numpages = {29}, doi = {10.1145/3158148}, year = {2018}, } Publisher's Version Article Search Info 

Campora, John Peter 
POPL '18: "Migrating Gradual Types ..."
Migrating Gradual Types
John Peter Campora, Sheng Chen, Martin Erwig, and Eric Walkingshaw (University of Louisiana at Lafayette, USA; Oregon State University, USA) Gradual typing allows programs to enjoy the benefits of both static typing and dynamic typing. While it is often desirable to migrate a program from more dynamicallytyped to more staticallytyped or vice versa, gradual typing itself does not provide a way to facilitate this migration. This places the burden on programmers who have to manually add or remove type annotations. Besides the general challenge of adding type annotations to dynamically typed code, there are subtle interactions between these annotations in gradually typed code that exacerbate the situation. For example, to migrate a program to be as static as possible, in general, all possible combinations of adding or removing type annotations from parameters must be tried out and compared. In this paper, we address this problem by developing migrational typing, which efficiently types all possible ways of adding or removing type annotations from a gradually typed program. The typing result supports automatically migrating a program to be as static as possible, or introducing the least number of dynamic types necessary to remove a type error. The approach can be extended to support userdefined criteria about which annotations to modify. We have implemented migrational typing and evaluated it on large programs. The results show that migrational typing scales linearly with the size of the program and takes only 2–4 times longer than plain gradual typing. @Article{POPL18p15, author = {John Peter Campora and Sheng Chen and Martin Erwig and Eric Walkingshaw}, title = {Migrating Gradual Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {15}, numpages = {29}, doi = {10.1145/3158103}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Capriotti, Paolo 
POPL '18: "Univalent Higher Categories ..."
Univalent Higher Categories via Complete SemiSegal Types
Paolo Capriotti and Nicolai Kraus (University of Nottingham, UK) Category theory in homotopy type theory is intricate as categorical laws can only be stated ”up to homotopy”, and thus require coherences. The established notion of a univalent category (as introduced by Ahrens et al.) solves this by considering only truncated types, roughly corresponding to an ordinary category. This fails to capture many naturally occurring structures, stemming from the fact that the naturally occurring structures in homotopy type theory are not ordinary, but rather higher categories. Out of the large variety of approaches to higher category theory that mathematicians have proposed, we believe that, for type theory, the simplicial strategy is best suited. Work by Lurie and Harpaz motivates the following definition. Given the first (n+3) levels of a semisimplicial type S, we can equip S with three properties: first, contractibility of the types of certain horn fillers; second, a completeness property; and third, a truncation condition. We call this a complete semiSegal ntype. This is very similar to an earlier suggestion by Schreiber. The definition of a univalent (1) category by Ahrens et al. can easily be extended or restricted to the definition of a univalent ncategory (more precisely, (n,1)category) for n ∈ {0,1,2}, and we show that the type of complete semiSegal ntypes is equivalent to the type of univalent ncategories in these cases. Thus, we believe that the notion of a complete semiSegal ntype can be taken as the definition of a univalent ncategory. We provide a formalisation in the proof assistant Agda using a completely explicit representation of semisimplicial types for levels up to 4. @Article{POPL18p44, author = {Paolo Capriotti and Nicolai Kraus}, title = {Univalent Higher Categories via Complete SemiSegal Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {44}, numpages = {29}, doi = {10.1145/3158132}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Cathcart Burn, Toby 
POPL '18: "HigherOrder Constrained Horn ..."
HigherOrder Constrained Horn Clauses for Verification
Toby Cathcart Burn, C.H. Luke Ong, and Steven J. Ramsay (University of Oxford, UK; University of Bristol, UK) Motivated by applications in automated verification of higherorder functional programs, we develop a notion of constrained Horn clauses in higherorder logic and a decision problem concerning their satisfiability. We show that, although satisfiable systems of higherorder clauses do not generally have least models, there is a notion of canonical model obtained through a reduction to a problem concerning a kind of monotone logic program. Following work in higherorder program verification, we develop a refinement type system in order to reason about and automate the search for models. This provides a sound but incomplete method for solving the decision problem. Finally, we show that there is a sense in which we can use refinement types to express properties of terms whilst staying within the higherorder constrained Horn clause framework. @Article{POPL18p11, author = {Toby Cathcart Burn and C.H. Luke Ong and Steven J. Ramsay}, title = {HigherOrder Constrained Horn Clauses for Verification}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {11}, numpages = {28}, doi = {10.1145/3158099}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Chalupa, Marek 
POPL '18: "DataCentric Dynamic Partial ..."
DataCentric Dynamic Partial Order Reduction
Marek Chalupa, Krishnendu Chatterjee , Andreas Pavlogiannis, Nishant Sinha, and Kapil Vaidya (Masaryk University, Czechia; IST Austria, Austria; Kena Labs, India; IIT Bombay, India) We present a new dynamic partialorder reduction method for stateless model checking of concurrent programs. A common approach for exploring program behaviors relies on enumerating the traces of the program, without storing the visited states (aka stateless exploration). As the number of distinct traces grows exponentially, dynamic partialorder reduction (DPOR) techniques have been successfully used to partition the space of traces into equivalence classes (Mazurkiewicz partitioning), with the goal of exploring only few representative traces from each class. We introduce a new equivalence on traces under sequential consistency semantics, which we call the observation equivalence. Two traces are observationally equivalent if every read event observes the same write event in both traces. While the traditional Mazurkiewicz equivalence is controlcentric, our new definition is datacentric. We show that our observation equivalence is coarser than the Mazurkiewicz equivalence, and in many cases even exponentially coarser. We devise a DPOR exploration of the trace space, called datacentric DPOR, based on the observation equivalence. For acyclic architectures, our algorithm is guaranteed to explore exactly one representative trace from each observation class, while spending polynomial time per class. Hence, our algorithm is optimal wrt the observation equivalence, and in several cases explores exponentially fewer traces than any enumerative method based on the Mazurkiewicz equivalence. For cyclic architectures, we consider an equivalence between traces which is finer than the observation equivalence; but coarser than the Mazurkiewicz equivalence, and in some cases is exponentially coarser. Our datacentric DPOR algorithm remains optimal under this trace equivalence. Finally, we perform a basic experimental comparison between the existing Mazurkiewiczbased DPOR and our datacentric DPOR on a set of academic benchmarks. Our results show a significant reduction in both running time and the number of explored equivalence classes. @Article{POPL18p31, author = {Marek Chalupa and Krishnendu Chatterjee and Andreas Pavlogiannis and Nishant Sinha and Kapil Vaidya}, title = {DataCentric Dynamic Partial Order Reduction}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {31}, numpages = {30}, doi = {10.1145/3158119}, year = {2018}, } Publisher's Version Article Search 

Chandra, Kartik 
POPL '18: "Bonsai: SynthesisBased Reasoning ..."
Bonsai: SynthesisBased Reasoning for Type Systems
Kartik Chandra and Rastislav Bodik (Henry M. Gunn High School, USA; Stanford University, USA; University of Washington, USA) When designing a type system, we may want to mechanically check the design to guide its further development. We describe algorithms that perform symbolic reasoning about executable models of type systems. The algorithms support three queries. First, they check type soundness and synthesize a counterexample program if such a soundness bug is found. Second, they compare two versions of a type system, synthesizing a program accepted by one but rejected by the other. Third, they minimize the size of synthesized counterexample programs. These algorithms symbolically evaluate typecheckers and interpreters, producing formulas that characterize the set of programs that fail or succeed in the typechecker and the interpreter. However, symbolically evaluating interpreters poses efficiency challenges, which are caused by having to merge execution paths of the various possible input programs. Our main contribution is the bonsai tree, a novel symbolic representation of programs and program states that addresses these challenges. Bonsai trees encode complex syntactic information in terms of logical constraints, enabling more efficient merging. We implement these algorithms in the Bonsai tool, an assistant for type system designers. We perform case studies on how Bonsai helps test and explore a variety of type systems. Bonsai efficiently synthesizes counterexamples for soundness bugs previously inaccessible to automatic tools and is the first automated tool to find a counterexample for the recently discovered Scala soundness bug SI9633. @Article{POPL18p62, author = {Kartik Chandra and Rastislav Bodik}, title = {Bonsai: SynthesisBased Reasoning for Type Systems}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {62}, numpages = {34}, doi = {10.1145/3158150}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Chang, Stephen 
POPL '18: "Symbolic Types for Lenient ..."
Symbolic Types for Lenient Symbolic Execution
Stephen Chang, Alex Knauth, and Emina Torlak (Northeastern University, USA; University of Washington, USA) We present lambda_sym, a typed λcalculus for lenient symbolic execution, where some language constructs do not recognize symbolic values. Its type system, however, ensures safe behavior of all symbolic values in a program. Our calculus extends a base occurrence typing system with symbolic types and mutable state, making it a suitable model for both functional and imperative symbolically executed languages. Naively allowing mutation in this mixed setting introduces soundness issues, however, so we further add concreteness polymorphism, which restores soundness without rejecting too many valid programs. To show that our calculus is a useful model for a real language, we implemented Typed Rosette, a typed extension of the solveraided Rosette language. We evaluate Typed Rosette by porting a large code base, demonstrating that our type system accommodates a wide variety of symbolically executed programs. @Article{POPL18p40, author = {Stephen Chang and Alex Knauth and Emina Torlak}, title = {Symbolic Types for Lenient Symbolic Execution}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {40}, numpages = {29}, doi = {10.1145/3158128}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Chatterjee, Krishnendu 
POPL '18: "Optimal Dyck Reachability ..."
Optimal Dyck Reachability for DataDependence and Alias Analysis
Krishnendu Chatterjee , Bhavya Choudhary, and Andreas Pavlogiannis (IST Austria, Austria; IIT Bombay, India) A fundamental algorithmic problem at the heart of static analysis is Dyck reachability. The input is a graph where the edges are labeled with different types of opening and closing parentheses, and the reachability information is computed via paths whose parentheses are properly matched. We present new results for Dyck reachability problems with applications to alias analysis and datadependence analysis. Our main contributions, that include improved upper bounds as well as lower bounds that establish optimality guarantees, are as follows: First, we consider Dyck reachability on bidirected graphs, which is the standard way of performing fieldsensitive pointsto analysis. Given a bidirected graph with n nodes and m edges, we present: (i) an algorithm with worstcase running time O(m + n · α(n)), where α(n) is the inverse Ackermann function, improving the previously known O(n^{2}) time bound; (ii) a matching lower bound that shows that our algorithm is optimal wrt to worstcase complexity; and (iii) an optimal averagecase upper bound of O(m) time, improving the previously known O(m · logn) bound. Second, we consider the problem of contextsensitive datadependence analysis, where the task is to obtain analysis summaries of library code in the presence of callbacks. Our algorithm preprocesses libraries in almost linear time, after which the contribution of the library in the complexity of the client analysis is only linear, and only wrt the number of call sites. Third, we prove that combinatorial algorithms for Dyck reachability on general graphs with truly subcubic bounds cannot be obtained without obtaining subcubic combinatorial algorithms for Boolean Matrix Multiplication, which is a longstanding open problem. Thus we establish that the existing combinatorial algorithms for Dyck reachability are (conditionally) optimal for general graphs. We also show that the same hardness holds for graphs of constant treewidth. Finally, we provide a prototype implementation of our algorithms for both alias analysis and datadependence analysis. Our experimental evaluation demonstrates that the new algorithms significantly outperform all existing methods on the two problems, over realworld benchmarks. @Article{POPL18p30, author = {Krishnendu Chatterjee and Bhavya Choudhary and Andreas Pavlogiannis}, title = {Optimal Dyck Reachability for DataDependence and Alias Analysis}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {30}, numpages = {30}, doi = {10.1145/3158118}, year = {2018}, } Publisher's Version Article Search Artifacts Functional POPL '18: "DataCentric Dynamic Partial ..." DataCentric Dynamic Partial Order Reduction Marek Chalupa, Krishnendu Chatterjee , Andreas Pavlogiannis, Nishant Sinha, and Kapil Vaidya (Masaryk University, Czechia; IST Austria, Austria; Kena Labs, India; IIT Bombay, India) We present a new dynamic partialorder reduction method for stateless model checking of concurrent programs. A common approach for exploring program behaviors relies on enumerating the traces of the program, without storing the visited states (aka stateless exploration). As the number of distinct traces grows exponentially, dynamic partialorder reduction (DPOR) techniques have been successfully used to partition the space of traces into equivalence classes (Mazurkiewicz partitioning), with the goal of exploring only few representative traces from each class. We introduce a new equivalence on traces under sequential consistency semantics, which we call the observation equivalence. Two traces are observationally equivalent if every read event observes the same write event in both traces. While the traditional Mazurkiewicz equivalence is controlcentric, our new definition is datacentric. We show that our observation equivalence is coarser than the Mazurkiewicz equivalence, and in many cases even exponentially coarser. We devise a DPOR exploration of the trace space, called datacentric DPOR, based on the observation equivalence. For acyclic architectures, our algorithm is guaranteed to explore exactly one representative trace from each observation class, while spending polynomial time per class. Hence, our algorithm is optimal wrt the observation equivalence, and in several cases explores exponentially fewer traces than any enumerative method based on the Mazurkiewicz equivalence. For cyclic architectures, we consider an equivalence between traces which is finer than the observation equivalence; but coarser than the Mazurkiewicz equivalence, and in some cases is exponentially coarser. Our datacentric DPOR algorithm remains optimal under this trace equivalence. Finally, we perform a basic experimental comparison between the existing Mazurkiewiczbased DPOR and our datacentric DPOR on a set of academic benchmarks. Our results show a significant reduction in both running time and the number of explored equivalence classes. @Article{POPL18p31, author = {Marek Chalupa and Krishnendu Chatterjee and Andreas Pavlogiannis and Nishant Sinha and Kapil Vaidya}, title = {DataCentric Dynamic Partial Order Reduction}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {31}, numpages = {30}, doi = {10.1145/3158119}, year = {2018}, } Publisher's Version Article Search POPL '18: "Lexicographic Ranking Supermartingales: ..." Lexicographic Ranking Supermartingales: An Efficient Approach to Termination of Probabilistic Programs Sheshansh Agrawal, Krishnendu Chatterjee , and Petr Novotný (IIT Bombay, India; IST Austria, Austria) Probabilistic programs extend classical imperative programs with realvalued random variables and random branching. The most basic liveness property for such programs is the termination property. The qualitative (aka almostsure) termination problem asks whether a given program program terminates with probability 1. While ranking functions provide a sound and complete method for nonprobabilistic programs, the extension of them to probabilistic programs is achieved via ranking supermartingales (RSMs). Although deep theoretical results have been established about RSMs, their application to probabilistic programs with nondeterminism has been limited only to programs of restricted controlflow structure. For nonprobabilistic programs, lexicographic ranking functions provide a compositional and practical approach for termination analysis of realworld programs. In this work we introduce lexicographic RSMs and show that they present a sound method for almostsure termination of probabilistic programs with nondeterminism. We show that lexicographic RSMs provide a tool for compositional reasoning about almostsure termination, and for probabilistic programs with linear arithmetic they can be synthesized efficiently (in polynomial time). We also show that with additional restrictions even asymptotic bounds on expected termination time can be obtained through lexicographic RSMs. Finally, we present experimental results on benchmarks adapted from previous work to demonstrate the effectiveness of our approach. @Article{POPL18p34, author = {Sheshansh Agrawal and Krishnendu Chatterjee and Petr Novotný}, title = {Lexicographic Ranking Supermartingales: An Efficient Approach to Termination of Probabilistic Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {34}, numpages = {32}, doi = {10.1145/3158122}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Chen, Sheng 
POPL '18: "Migrating Gradual Types ..."
Migrating Gradual Types
John Peter Campora, Sheng Chen, Martin Erwig, and Eric Walkingshaw (University of Louisiana at Lafayette, USA; Oregon State University, USA) Gradual typing allows programs to enjoy the benefits of both static typing and dynamic typing. While it is often desirable to migrate a program from more dynamicallytyped to more staticallytyped or vice versa, gradual typing itself does not provide a way to facilitate this migration. This places the burden on programmers who have to manually add or remove type annotations. Besides the general challenge of adding type annotations to dynamically typed code, there are subtle interactions between these annotations in gradually typed code that exacerbate the situation. For example, to migrate a program to be as static as possible, in general, all possible combinations of adding or removing type annotations from parameters must be tried out and compared. In this paper, we address this problem by developing migrational typing, which efficiently types all possible ways of adding or removing type annotations from a gradually typed program. The typing result supports automatically migrating a program to be as static as possible, or introducing the least number of dynamic types necessary to remove a type error. The approach can be extended to support userdefined criteria about which annotations to modify. We have implemented migrational typing and evaluated it on large programs. The results show that migrational typing scales linearly with the size of the program and takes only 2–4 times longer than plain gradual typing. @Article{POPL18p15, author = {John Peter Campora and Sheng Chen and Martin Erwig and Eric Walkingshaw}, title = {Migrating Gradual Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {15}, numpages = {29}, doi = {10.1145/3158103}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Chen, Taolue 
POPL '18: "What Is Decidable about String ..."
What Is Decidable about String Constraints with the ReplaceAll Function
Taolue Chen, Yan Chen, Matthew Hague , Anthony W. Lin, and Zhilin Wu (University of London, UK; Institute of Software at Chinese Academy of Sciences, China; University at Chinese Academy of Sciences, China; Royal Holloway University of London, UK; University of Oxford, UK) The theory of strings with concatenation has been widely argued as the basis of constraint solving for verifying stringmanipulating programs. However, this theory is far from adequate for expressing many string constraints that are also needed in practice; for example, the use of regular constraints (pattern matching against a regular expression), and the stringreplace function (replacing either the first occurrence or all occurrences of a ``pattern'' string constant/variable/regular expression by a ``replacement'' string constant/variable), among many others. Both regular constraints and the stringreplace function are crucial for such applications as analysis of JavaScript (or more generally HTML5 applications) against crosssite scripting (XSS) vulnerabilities, which motivates us to consider a richer class of string constraints. The importance of the stringreplace function (especially the replaceall facility) is increasingly recognised, which can be witnessed by the incorporation of the function in the input languages of several string constraint solvers. Recently, it was shown that any theory of strings containing the stringreplace function (even the most restricted version where pattern/replacement strings are both constant strings) becomes undecidable if we do not impose some kind of straightline (aka acyclicity) restriction on the formulas. Despite this, the straightline restriction is still practically sensible since this condition is typically met by string constraints that are generated by symbolic execution. In this paper, we provide the first systematic study of straightline string constraints with the stringreplace function and the regular constraints as the basic operations. We show that a large class of such constraints (i.e. when only a constant string or a regular expression is permitted in the pattern) is decidable. We note that the stringreplace function, even under this restriction, is sufficiently powerful for expressing the concatenation operator and much more (e.g. extensions of regular expressions with string variables). This gives us the most expressive decidable logic containing concatenation, replace, and regular constraints under the same umbrella. Our decision procedure for the straightline fragment follows an automatatheoretic approach, and is modular in the sense that the stringreplace terms are removed one by one to generate more and more regular constraints, which can then be discharged by the stateoftheart string constraint solvers. We also show that this fragment is, in a way, a maximal decidable subclass of the straightline fragment with stringreplace and regular constraints. To this end, we show undecidability results for the following two extensions: (1) variables are permitted in the pattern parameter of the replace function, (2) length constraints are permitted. @Article{POPL18p3, author = {Taolue Chen and Yan Chen and Matthew Hague and Anthony W. Lin and Zhilin Wu}, title = {What Is Decidable about String Constraints with the ReplaceAll Function}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {3}, numpages = {29}, doi = {10.1145/3158091}, year = {2018}, } Publisher's Version Article Search 

Chen, Yan 
POPL '18: "What Is Decidable about String ..."
What Is Decidable about String Constraints with the ReplaceAll Function
Taolue Chen, Yan Chen, Matthew Hague , Anthony W. Lin, and Zhilin Wu (University of London, UK; Institute of Software at Chinese Academy of Sciences, China; University at Chinese Academy of Sciences, China; Royal Holloway University of London, UK; University of Oxford, UK) The theory of strings with concatenation has been widely argued as the basis of constraint solving for verifying stringmanipulating programs. However, this theory is far from adequate for expressing many string constraints that are also needed in practice; for example, the use of regular constraints (pattern matching against a regular expression), and the stringreplace function (replacing either the first occurrence or all occurrences of a ``pattern'' string constant/variable/regular expression by a ``replacement'' string constant/variable), among many others. Both regular constraints and the stringreplace function are crucial for such applications as analysis of JavaScript (or more generally HTML5 applications) against crosssite scripting (XSS) vulnerabilities, which motivates us to consider a richer class of string constraints. The importance of the stringreplace function (especially the replaceall facility) is increasingly recognised, which can be witnessed by the incorporation of the function in the input languages of several string constraint solvers. Recently, it was shown that any theory of strings containing the stringreplace function (even the most restricted version where pattern/replacement strings are both constant strings) becomes undecidable if we do not impose some kind of straightline (aka acyclicity) restriction on the formulas. Despite this, the straightline restriction is still practically sensible since this condition is typically met by string constraints that are generated by symbolic execution. In this paper, we provide the first systematic study of straightline string constraints with the stringreplace function and the regular constraints as the basic operations. We show that a large class of such constraints (i.e. when only a constant string or a regular expression is permitted in the pattern) is decidable. We note that the stringreplace function, even under this restriction, is sufficiently powerful for expressing the concatenation operator and much more (e.g. extensions of regular expressions with string variables). This gives us the most expressive decidable logic containing concatenation, replace, and regular constraints under the same umbrella. Our decision procedure for the straightline fragment follows an automatatheoretic approach, and is modular in the sense that the stringreplace terms are removed one by one to generate more and more regular constraints, which can then be discharged by the stateoftheart string constraint solvers. We also show that this fragment is, in a way, a maximal decidable subclass of the straightline fragment with stringreplace and regular constraints. To this end, we show undecidability results for the following two extensions: (1) variables are permitted in the pattern parameter of the replace function, (2) length constraints are permitted. @Article{POPL18p3, author = {Taolue Chen and Yan Chen and Matthew Hague and Anthony W. Lin and Zhilin Wu}, title = {What Is Decidable about String Constraints with the ReplaceAll Function}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {3}, numpages = {29}, doi = {10.1145/3158091}, year = {2018}, } Publisher's Version Article Search 

Chin, WeiNgan 
POPL '18: "Automated Lemma Synthesis ..."
Automated Lemma Synthesis in SymbolicHeap Separation Logic
QuangTrung Ta, Ton Chanh Le, SiauCheng Khoo, and WeiNgan Chin (National University of Singapore, Singapore) The symbolicheap fragment of separation logic has been actively developed and advocated for verifying the memorysafety property of computer programs. At present, one of its biggest challenges is to effectively prove entailments containing inductive heap predicates. These entailments are usually proof obligations generated when verifying programs that manipulate complex data structures like linked lists, trees, or graphs. To assist in proving such entailments, this paper introduces a lemma synthesis framework, which automatically discovers lemmas to serve as eureka steps in the proofs. Mathematical induction and templatebased constraint solving are two pillars of our framework. To derive the supporting lemmas for a given entailment, the framework firstly identifies possible lemma templates from the entailment's heap structure. It then sets up unknown relations among each template's variables and conducts structural induction proof to generate constraints about these relations. Finally, it solves the constraints to find out actual definitions of the unknown relations, thus discovers the lemmas. We have integrated this framework into a prototype prover and have experimented it on various entailment benchmarks. The experimental results show that our lemmasynthesisassisted prover can prove many entailments that could not be handled by existing techniques. This new proposal opens up more opportunities to automatically reason with complex inductive heap predicates. @Article{POPL18p9, author = {QuangTrung Ta and Ton Chanh Le and SiauCheng Khoo and WeiNgan Chin}, title = {Automated Lemma Synthesis in SymbolicHeap Separation Logic}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {9}, numpages = {29}, doi = {10.1145/3158097}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Choudhary, Bhavya 
POPL '18: "Optimal Dyck Reachability ..."
Optimal Dyck Reachability for DataDependence and Alias Analysis
Krishnendu Chatterjee , Bhavya Choudhary, and Andreas Pavlogiannis (IST Austria, Austria; IIT Bombay, India) A fundamental algorithmic problem at the heart of static analysis is Dyck reachability. The input is a graph where the edges are labeled with different types of opening and closing parentheses, and the reachability information is computed via paths whose parentheses are properly matched. We present new results for Dyck reachability problems with applications to alias analysis and datadependence analysis. Our main contributions, that include improved upper bounds as well as lower bounds that establish optimality guarantees, are as follows: First, we consider Dyck reachability on bidirected graphs, which is the standard way of performing fieldsensitive pointsto analysis. Given a bidirected graph with n nodes and m edges, we present: (i) an algorithm with worstcase running time O(m + n · α(n)), where α(n) is the inverse Ackermann function, improving the previously known O(n^{2}) time bound; (ii) a matching lower bound that shows that our algorithm is optimal wrt to worstcase complexity; and (iii) an optimal averagecase upper bound of O(m) time, improving the previously known O(m · logn) bound. Second, we consider the problem of contextsensitive datadependence analysis, where the task is to obtain analysis summaries of library code in the presence of callbacks. Our algorithm preprocesses libraries in almost linear time, after which the contribution of the library in the complexity of the client analysis is only linear, and only wrt the number of call sites. Third, we prove that combinatorial algorithms for Dyck reachability on general graphs with truly subcubic bounds cannot be obtained without obtaining subcubic combinatorial algorithms for Boolean Matrix Multiplication, which is a longstanding open problem. Thus we establish that the existing combinatorial algorithms for Dyck reachability are (conditionally) optimal for general graphs. We also show that the same hardness holds for graphs of constant treewidth. Finally, we provide a prototype implementation of our algorithms for both alias analysis and datadependence analysis. Our experimental evaluation demonstrates that the new algorithms significantly outperform all existing methods on the two problems, over realworld benchmarks. @Article{POPL18p30, author = {Krishnendu Chatterjee and Bhavya Choudhary and Andreas Pavlogiannis}, title = {Optimal Dyck Reachability for DataDependence and Alias Analysis}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {30}, numpages = {30}, doi = {10.1145/3158118}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Choudhury, Vikraman 
POPL '18: "Refinement Reflection: Complete ..."
Refinement Reflection: Complete Verification with SMT
Niki Vazou, Anish Tondwalkar, Vikraman Choudhury , Ryan G. Scott, Ryan R. Newton, Philip Wadler , and Ranjit Jhala (University of Maryland, USA; University of California at San Diego, USA; Indiana University, USA; University of Edinburgh, UK; Input Output HK, UK) We introduce Refinement Reflection, a new framework for building SMTbased deductive verifiers. The key idea is to reflect the code implementing a userdefined function into the function’s (output) refinement type. As a consequence, at uses of the function, the function definition is instantiated in the SMT logic in a precise fashion that permits decidable verification. Reflection allows the user to write equational proofs of programs just by writing other programs using patternmatching and recursion to perform casesplitting and induction. Thus, via the propositionsastypes principle, we show that reflection permits the specification of arbitrary functional correctness properties. Finally, we introduce a proofsearch algorithm called Proof by Logical Evaluation that uses techniques from model checking and abstract interpretation, to completely automate equational reasoning. We have implemented reflection in Liquid Haskell and used it to verify that the widely used instances of the Monoid, Applicative, Functor, and Monad typeclasses actually satisfy key algebraic laws required to make the clients safe, and have used reflection to build the first library that actually verifies assumptions about associativity and ordering that are crucial for safe deterministic parallelism. @Article{POPL18p53, author = {Niki Vazou and Anish Tondwalkar and Vikraman Choudhury and Ryan G. Scott and Ryan R. Newton and Philip Wadler and Ranjit Jhala}, title = {Refinement Reflection: Complete Verification with SMT}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {53}, numpages = {31}, doi = {10.1145/3158141}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Clairambault, Pierre 
POPL '18: "Linearity in HigherOrder ..."
Linearity in HigherOrder Recursion Schemes
Pierre Clairambault, Charles Grellois, and Andrzej S. Murawski (University of Lyon, France; CNRS, France; ENS Lyon, France; Claude Bernard University Lyon 1, France; LIP, France; Inria, France; AixMarseille University, France; ENSAM, France; University of Toulon, France; University of Oxford, UK) Higherorder recursion schemes (HORS) have recently emerged as a promising foundation for higherorder program verification. We examine the impact of enriching HORS with linear types. To that end, we introduce two frameworks that blend nonlinear and linear types: a variant of the λY calculus and an extension of HORS, called linear HORS (LHORS). First we prove that the two formalisms are equivalent and there exist polynomialtime translations between them. Then, in order to support modelchecking of (trees generated by) LHORS, we propose a refined version of alternating parity tree automata, called LNAPTA, whose behaviour depends on information about linearity. We show that the complexity of LNAPTA modelchecking for LHORS depends on two typetheoretic parameters: linear order and linear depth. The former is in general smaller than the standard notion of order and ignores linear function spaces. In contrast, the latter measures the depth of linear clusters inside a type. Our main result states that LNAPTA modelchecking of LHORS of linear order n is nEXPTIMEcomplete, when linear depth is fixed. This generalizes and improves upon the classic result of Ong, which relies on the standard notion of order. To illustrate the significance of the result, we consider two applications: the MSO modelchecking problem on variants of HORS with case distinction (RSFD and HORSC) on a finite domain and a callbyvalue resource verification problem. In both cases, decidability can be established by translation into HORS, but the implied complexity bounds will be suboptimal due to increases in type order. In contrast, we show that the complexity bounds derived by translations into LHORS and appealing to our result are optimal in that they match the respective hardness results. @Article{POPL18p39, author = {Pierre Clairambault and Charles Grellois and Andrzej S. Murawski}, title = {Linearity in HigherOrder Recursion Schemes}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {39}, numpages = {29}, doi = {10.1145/3158127}, year = {2018}, } Publisher's Version Article Search 

Cong, Youyou 
POPL '18: "TypePreserving CPS Translation ..."
TypePreserving CPS Translation of Σ and Π Types Is Not Not Possible
William J. Bowman, Youyou Cong, Nick Rioux, and Amal Ahmed (Northeastern University, USA; Ochanomizu University, Japan) Dependently typed languages such as Coq are used to specify and prove functional correctness of source programs, but what we ultimately need are guarantees about correctness of compiled code. By preserving dependent types through each compiler pass, we could preserve sourcelevel specifications and correctness proofs into the generated targetlanguage programs. Unfortunately, typepreserving compilation of dependent types is hard. In 2002, Barthe and Uustalu showed that typepreserving CPS is not possible for languages such as Coq. Specifically, they showed that for strong dependent pairs (Σ types), the standard typed callbyname CPS is not type preserving. They further proved that for dependent case analysis on sums, a class of typed CPS translations—including the standard translation—is not possible. In 2016, Morrisett noticed a similar problem with the standard callbyvalue CPS translation for dependent functions (Π types). In essence, the problem is that the standard typed CPS translation by doublenegation, in which computations are assigned types of the form (A → ⊥) → ⊥, disrupts the term/type equivalence that is used during type checking in a dependently typed language. In this paper, we prove that typepreserving CPS translation for dependently typed languages is not not possible. We develop both callbyname and callbyvalue CPS translations from the Calculus of Constructions with both Π and Σ types (CC) to a dependently typed target language, and prove type preservation and compiler correctness of each translation. Our target language is CC extended with an additional equivalence rule and an additional typing rule, which we prove consistent by giving a model in the extensional Calculus of Constructions. Our key observation is that we can use a CPS translation that employs answertype polymorphism, where CPStranslated computations have type ∀ α. (A → α) → α. This type justifies, by a free theorem, the new equality rule in our target language and allows us to recover the term/type equivalences that CPS translation disrupts. Finally, we conjecture that our translation extends to dependent case analysis on sums, despite the impossibility result, and provide a proof sketch. @Article{POPL18p22, author = {William J. Bowman and Youyou Cong and Nick Rioux and Amal Ahmed}, title = {TypePreserving CPS Translation of Σ and Π Types Is Not Not Possible}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {22}, numpages = {33}, doi = {10.1145/3158110}, year = {2018}, } Publisher's Version Article Search Info 

Cook, William R. 
POPL '18: "Verifying Equivalence of DatabaseDriven ..."
Verifying Equivalence of DatabaseDriven Applications
Yuepeng Wang, Isil Dillig , Shuvendu K. Lahiri, and William R. Cook (University of Texas at Austin, USA; Microsoft Research, USA) This paper addresses the problem of verifying equivalence between a pair of programs that operate over databases with different schemas. This problem is particularly important in the context of web applications, which typically undergo database refactoring either for performance or maintainability reasons. While web applications should have the same externally observable behavior before and after schema migration, there are no existing tools for proving equivalence of such programs. This paper takes a first step towards solving this problem by formalizing the equivalence and refinement checking problems for databasedriven applications. We also propose a proof methodology based on the notion of bisimulation invariants over relational algebra with updates and describe a technique for synthesizing such bisimulation invariants. We have implemented the proposed technique in a tool called Mediator for verifying equivalence between databasedriven applications written in our intermediate language and evaluate our tool on 21 benchmarks extracted from textbooks and realworld web applications. Our results show that the proposed methodology can successfully verify 20 of these benchmarks. @Article{POPL18p56, author = {Yuepeng Wang and Isil Dillig and Shuvendu K. Lahiri and William R. Cook}, title = {Verifying Equivalence of DatabaseDriven Applications}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {56}, numpages = {29}, doi = {10.1145/3158144}, year = {2018}, } Publisher's Version Article Search 

Cyphert, John 
POPL '18: "Nonlinear Reasoning for Invariant ..."
Nonlinear Reasoning for Invariant Synthesis
Zachary Kincaid , John Cyphert, Jason Breck, and Thomas Reps (Princeton University, USA; University of WisconsinMadison, USA; GrammaTech, USA) Automatic generation of nonlinear loop invariants is a longstanding challenge in program analysis, with many applications. For instance, reasoning about exponentials provides a way to find invariants of digitalfilter programs, and reasoning about polynomials and/or logarithms is needed for establishing invariants that describe the time or memory usage of many wellknown algorithms. An appealing approach to this challenge is to exploit the powerful recurrencesolving techniques that have been developed in the field of computer algebra, which can compute exact characterizations of nonlinear repetitive behavior. However, there is a gap between the capabilities of recurrence solvers and the needs of program analysis: (1) loop bodies are not merely systems of recurrence relationsthey may contain conditional branches, nested loops, nondeterministic assignments, etc., and (2) a client program analyzer must be able to reason about the closedform solutions produced by a recurrence solver (e.g., to prove assertions). This paper presents a method for generating nonlinear invariants of general loops based on analyzing recurrence relations. The key components are an abstract domain for reasoning about nonlinear arithmetic, a semanticsbased method for extracting recurrence relations from loop bodies, and a recurrence solver that avoids closed forms that involve complex or irrational numbers. Our technique has been implemented in a program analyzer that can analyze general loops and mutually recursive procedures. Our experiments show that our technique shows promise for nonlinear assertionchecking and resourcebound generation. @Article{POPL18p54, author = {Zachary Kincaid and John Cyphert and Jason Breck and Thomas Reps}, title = {Nonlinear Reasoning for Invariant Synthesis}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {54}, numpages = {33}, doi = {10.1145/3158142}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Danielsson, Nils Anders 
POPL '18: "Upto Techniques using Sized ..."
Upto Techniques using Sized Types
Nils Anders Danielsson (University of Gothenburg, Sweden; Chalmers University of Technology, Sweden) Upto techniques are used to make it easier—or feasible—to construct, for instance, proofs of bisimilarity. This text shows how many upto techniques can be framed as sizepreserving functions, using sized types to keep track of sizes. Through a number of examples it is argued that this approach to upto techniques is often convenient to use in practice. Some examples of functions that cannot be made sizepreserving are also included, in order to illustrate the limits of the approach. On the more theoretical side a class of upto techniques intended to capture a natural mode of use of sizepreserving functions is defined. This class turns out to correspond closely to "functions below the companion", a notion recently introduced by Pous. @Article{POPL18p43, author = {Nils Anders Danielsson}, title = {Upto Techniques using Sized Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {43}, numpages = {28}, doi = {10.1145/3158131}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Deacon, Will 
POPL '18: "Simplifying ARM Concurrency: ..."
Simplifying ARM Concurrency: MulticopyAtomic Axiomatic and Operational Models for ARMv8
Christopher Pulte, Shaked Flur, Will Deacon, Jon French, Susmit Sarkar, and Peter Sewell (University of Cambridge, UK; ARM, UK; University of St. Andrews, UK) ARM has a relaxed memory model, previously specified in informal prose for ARMv7 and ARMv8. Over time, and partly due to work building formal semantics for ARM concurrency, it has become clear that some of the complexity of the model is not justified by the potential benefits. In particular, the model was originally nonmulticopyatomic: writes could become visible to some other threads before becoming visible to all — but this has not been exploited in production implementations, the corresponding potential hardware optimisations are thought to have insufficient benefits in the ARM context, and it gives rise to subtle complications when combined with other ARMv8 features. The ARMv8 architecture has therefore been revised: it now has a multicopyatomic model. It has also been simplified in other respects, including more straightforward notions of dependency, and the architecture now includes a formal concurrency model. In this paper we detail these changes and discuss their motivation. We define two formal concurrency models: an operational one, simplifying the Flowing model of Flur et al., and the axiomatic model of the revised ARMv8 specification. The models were developed by an academic group and by ARM staff, respectively, and this extended collaboration partly motivated the above changes. We prove the equivalence of the two models. The operational model is integrated into an executable exploration tool with new web interface, demonstrated by exhaustively checking the possible behaviours of a loopunrolled version of a Linux kernel lock implementation, a previously known bug due to unprevented speculation, and a fixed version. @Article{POPL18p19, author = {Christopher Pulte and Shaked Flur and Will Deacon and Jon French and Susmit Sarkar and Peter Sewell}, title = {Simplifying ARM Concurrency: MulticopyAtomic Axiomatic and Operational Models for ARMv8}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {19}, numpages = {29}, doi = {10.1145/3158107}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

De Araújo, Marcus R. 
POPL '18: "Inference of Static Semantics ..."
Inference of Static Semantics for Incomplete C Programs
Leandro T. C. Melo, Rodrigo G. Ribeiro, Marcus R. de Araújo, and Fernando Magno Quintão Pereira (Federal University of Minas Gerais, Brazil; Federal University of Ouro Preto, Brazil) Incomplete source code naturally emerges in software development: during the design phase, while evolving, testing and analyzing programs. Therefore, the ability to understand partial programs is a valuable asset. However, this problem is still unsolved in the C programming language. Difficulties stem from the fact that parsing C requires, not only syntax, but also semantic information. Furthermore, inferring types so that they respect C's type system is a challenging task. In this paper we present a technique that lets us solve these problems. We provide a unificationbased type inference capable of dealing with C intricacies. The ideas we present let us reconstruct partial C programs into complete welltyped ones. Such program reconstruction has several applications: enabling static analysis tools in scenarios where software components may be absent; improving static analysis tools that do not rely on buildspecifications; allowing stubgeneration and testing tools to work on snippets; and assisting programmers on the extraction of reusable datastructures out of the program parts that use them. Our evaluation is performed on source code from a variety of C libraries such as GNU's Coreutils, GNULib, GNOME's GLib, and GDSL; on implementations from Sedgewick's books; and on snippets from popular opensource projects like CPython, FreeBSD, and Git. @Article{POPL18p29, author = {Leandro T. C. Melo and Rodrigo G. Ribeiro and Marcus R. de Araújo and Fernando Magno Quintão Pereira}, title = {Inference of Static Semantics for Incomplete C Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {29}, numpages = {28}, doi = {10.1145/3158117}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Devriese, Dominique 
POPL '18: "Parametricity versus the Universal ..."
Parametricity versus the Universal Type
Dominique Devriese, Marco Patrignani, and Frank Piessens (KU Leuven, Belgium; MPISWS, Germany; CISPA, Germany) There has long been speculation in the scientific literature on how to dynamically enforce parametricity such as that yielded by System F. Almost 20 years ago, Sumii and Pierce proposed a formal compiler from System F into the cryptographic lambda calculus: an untyped lambda calculus extended with an idealised model of encryption. They conjectured that this compiler was fully abstract, i.e. that compiled terms are contextually equivalent if and only if the original terms were, a property that can be seen as a form of secure compilation. The conjecture has received attention in several other publications since then, but remains open to this day. More recently, several researchers have been looking at graduallytyped languages that extend System F. In this setting it is natural to wonder whether embedding System F into these graduallytyped languages preserves contextual equivalence and thus parametricity. In this paper, we answer both questions negatively. We provide a concrete counterexample: two System F terms whose contextual equivalence is not preserved by the SumiiPierce compiler, nor the embedding into the polymorphic blame calculus. This counterexample relies on the absence in System F of what we call a universal type, i.e., a type that all other types can be injected into and extracted from. As the languages in which System F is compiled have a universal type, the compilation cannot be fully abstract; this paper explains why. We believe this paper thus sheds light on recent results in the field of gradually typed languages and it provides a perspective for further research into secure compilation of polymorphic languages. @Article{POPL18p38, author = {Dominique Devriese and Marco Patrignani and Frank Piessens}, title = {Parametricity versus the Universal Type}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {38}, numpages = {23}, doi = {10.1145/3158126}, year = {2018}, } Publisher's Version Article Search 

Dillig, Isil 
POPL '18: "Program Synthesis using Abstraction ..."
Program Synthesis using Abstraction Refinement
Xinyu Wang, Isil Dillig , and Rishabh Singh (University of Texas at Austin, USA; Microsoft Research, USA) We present a new approach to exampleguided program synthesis based on counterexampleguided abstraction refinement. Our method uses the abstract semantics of the underlying DSL to find a program P whose abstract behavior satisfies the examples. However, since program P may be spurious with respect to the concrete semantics, our approach iteratively refines the abstraction until we either find a program that satisfies the examples or prove that no such DSL program exists. Because many programs have the same inputoutput behavior in terms of their abstract semantics, this synthesis methodology significantly reduces the search space compared to existing techniques that use purely concrete semantics. While synthesis using abstraction refinement (SYNGAR) could be implemented in different settings, we propose a refinementbased synthesis algorithm that uses abstract finite tree automata (AFTA). Our technique uses a coarse initial program abstraction to construct an initial AFTA, which is iteratively refined by constructing a proof of incorrectness of any spurious program. In addition to ruling out the spurious program accepted by the previous AFTA, proofs of incorrectness are also useful for ruling out many other spurious programs. We implement these ideas in a framework called Blaze, which can be instantiated in different domains by providing a suitable DSL and its corresponding concrete and abstract semantics. We have used the Blaze framework to build synthesizers for string and matrix transformations, and we compare Blaze with existing techniques. Our results for the string domain show that Blaze compares favorably with FlashFill, a domainspecific synthesizer that is now deployed in Microsoft PowerShell. In the context of matrix manipulations, we compare Blaze against Prose, a stateoftheart generalpurpose VSAbased synthesizer, and show that Blaze results in a 90x speedup over Prose. In both application domains, Blaze also consistently improves upon the performance of two other existing techniques by at least an order of magnitude. @Article{POPL18p63, author = {Xinyu Wang and Isil Dillig and Rishabh Singh}, title = {Program Synthesis using Abstraction Refinement}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {63}, numpages = {30}, doi = {10.1145/3158151}, year = {2018}, } Publisher's Version Article Search POPL '18: "Verifying Equivalence of DatabaseDriven ..." Verifying Equivalence of DatabaseDriven Applications Yuepeng Wang, Isil Dillig , Shuvendu K. Lahiri, and William R. Cook (University of Texas at Austin, USA; Microsoft Research, USA) This paper addresses the problem of verifying equivalence between a pair of programs that operate over databases with different schemas. This problem is particularly important in the context of web applications, which typically undergo database refactoring either for performance or maintainability reasons. While web applications should have the same externally observable behavior before and after schema migration, there are no existing tools for proving equivalence of such programs. This paper takes a first step towards solving this problem by formalizing the equivalence and refinement checking problems for databasedriven applications. We also propose a proof methodology based on the notion of bisimulation invariants over relational algebra with updates and describe a technique for synthesizing such bisimulation invariants. We have implemented the proposed technique in a tool called Mediator for verifying equivalence between databasedriven applications written in our intermediate language and evaluate our tool on 21 benchmarks extracted from textbooks and realworld web applications. Our results show that the proposed methodology can successfully verify 20 of these benchmarks. @Article{POPL18p56, author = {Yuepeng Wang and Isil Dillig and Shuvendu K. Lahiri and William R. Cook}, title = {Verifying Equivalence of DatabaseDriven Applications}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {56}, numpages = {29}, doi = {10.1145/3158144}, year = {2018}, } Publisher's Version Article Search 

Dongol, Brijesh 
POPL '18: "Transactions in Relaxed Memory ..."
Transactions in Relaxed Memory Architectures
Brijesh Dongol, Radha Jagadeesan, and James Riely (Brunel University London, UK; DePaul University, USA) The integration of transactions into hardware relaxed memory architectures is a topic of current research both in industry and academia. In this paper, we provide a general architectural framework for the introduction of transactions into models of relaxed memory in hardware, including the SC, TSO, ARMv8 and PPC models. Our framework incorporates flexible and expressive forms of transaction aborts and execution that have hitherto been in the realm of software transactional memory. In contrast to software transactional memory, we account for the characteristics of relaxed memory as a restricted form of distributed system, without a notion of global time. We prove abstraction theorems to demonstrate that the programmer API matches the intuitions and expectations about transactions. @Article{POPL18p18, author = {Brijesh Dongol and Radha Jagadeesan and James Riely}, title = {Transactions in Relaxed Memory Architectures}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {18}, numpages = {29}, doi = {10.1145/3158106}, year = {2018}, } Publisher's Version Article Search 

Dreyer, Derek 
POPL '18: "RustBelt: Securing the Foundations ..."
RustBelt: Securing the Foundations of the Rust Programming Language
Ralf Jung , JacquesHenri Jourdan, Robbert Krebbers , and Derek Dreyer (MPISWS, Germany; Delft University of Technology, Netherlands) Rust is a new systems programming language that promises to overcome the seemingly fundamental tradeoff between highlevel safety guarantees and lowlevel control over resource management. Unfortunately, none of Rust's safety claims have been formally proven, and there is good reason to question whether they actually hold. Specifically, Rust employs a strong, ownershipbased type system, but then extends the expressive power of this core type system through libraries that internally use unsafe features. In this paper, we give the first formal (and machinechecked) safety proof for a language representing a realistic subset of Rust. Our proof is extensible in the sense that, for each new Rust library that uses unsafe features, we can say what verification condition it must satisfy in order for it to be deemed a safe extension to the language. We have carried out this verification for some of the most important libraries that are used throughout the Rust ecosystem. @Article{POPL18p66, author = {Ralf Jung and JacquesHenri Jourdan and Robbert Krebbers and Derek Dreyer}, title = {RustBelt: Securing the Foundations of the Rust Programming Language}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {66}, numpages = {34}, doi = {10.1145/3158154}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Ehrhard, Thomas 
POPL '18: "Measurable Cones and Stable, ..."
Measurable Cones and Stable, Measurable Functions: A Model for Probabilistic HigherOrder Programming
Thomas Ehrhard, Michele Pagani, and Christine Tasson (University of Paris Diderot, France; CNRS, France) We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpoenriched cartesian closed category. This category gives a denotational model of an extension of PCF supporting the main primitives of probabilistic functional programming, like continuous and discrete probabilistic distributions, sampling, conditioning and full recursion. We prove the soundness and adequacy of this model with respect to a callbyname operational semantics and give some examples of its denotations. @Article{POPL18p59, author = {Thomas Ehrhard and Michele Pagani and Christine Tasson}, title = {Measurable Cones and Stable, Measurable Functions: A Model for Probabilistic HigherOrder Programming}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {59}, numpages = {28}, doi = {10.1145/3158147}, year = {2018}, } Publisher's Version Article Search Info 

Emmi, Michael 
POPL '18: "Sound, Complete, and Tractable ..."
Sound, Complete, and Tractable Linearizability Monitoring for Concurrent Collections
Michael Emmi and Constantin Enea (SRI International, USA; University of Paris Diderot, France; CNRS, France) While many program properties like the validity of assertions and inbounds array accesses admit nearlytrivial monitoring algorithms, the standard correctness criterion for concurrent data structures does not. Given an implementation of an arbitrary abstract data type, checking whether the operations invoked in one single concurrent execution are linearizable, i.e., indistinguishable from an execution where the same operations are invoked atomically, requires exponential time in the number of operations. In this work we identify a class of collection abstract data types which admit polynomialtime linearizability monitors. Collections capture the majority of concurrent data structures available in practice, including stacks, queues, sets, and maps. Although monitoring executions of arbitrary abstract data types requires enumerating exponentiallymany possible linearizations, collections enjoy combinatorial properties which avoid the enumeration. We leverage these properties to reduce linearizability to Horn satisfiability. As far as we know, ours is the first sound, complete, and tractable algorithm for monitoring linearizability for types beyond singlevalue registers. @Article{POPL18p25, author = {Michael Emmi and Constantin Enea}, title = {Sound, Complete, and Tractable Linearizability Monitoring for Concurrent Collections}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {25}, numpages = {27}, doi = {10.1145/3158113}, year = {2018}, } Publisher's Version Article Search 

Enea, Constantin 
POPL '18: "Sound, Complete, and Tractable ..."
Sound, Complete, and Tractable Linearizability Monitoring for Concurrent Collections
Michael Emmi and Constantin Enea (SRI International, USA; University of Paris Diderot, France; CNRS, France) While many program properties like the validity of assertions and inbounds array accesses admit nearlytrivial monitoring algorithms, the standard correctness criterion for concurrent data structures does not. Given an implementation of an arbitrary abstract data type, checking whether the operations invoked in one single concurrent execution are linearizable, i.e., indistinguishable from an execution where the same operations are invoked atomically, requires exponential time in the number of operations. In this work we identify a class of collection abstract data types which admit polynomialtime linearizability monitors. Collections capture the majority of concurrent data structures available in practice, including stacks, queues, sets, and maps. Although monitoring executions of arbitrary abstract data types requires enumerating exponentiallymany possible linearizations, collections enjoy combinatorial properties which avoid the enumeration. We leverage these properties to reduce linearizability to Horn satisfiability. As far as we know, ours is the first sound, complete, and tractable algorithm for monitoring linearizability for types beyond singlevalue registers. @Article{POPL18p25, author = {Michael Emmi and Constantin Enea}, title = {Sound, Complete, and Tractable Linearizability Monitoring for Concurrent Collections}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {25}, numpages = {27}, doi = {10.1145/3158113}, year = {2018}, } Publisher's Version Article Search 

Erwig, Martin 
POPL '18: "Migrating Gradual Types ..."
Migrating Gradual Types
John Peter Campora, Sheng Chen, Martin Erwig, and Eric Walkingshaw (University of Louisiana at Lafayette, USA; Oregon State University, USA) Gradual typing allows programs to enjoy the benefits of both static typing and dynamic typing. While it is often desirable to migrate a program from more dynamicallytyped to more staticallytyped or vice versa, gradual typing itself does not provide a way to facilitate this migration. This places the burden on programmers who have to manually add or remove type annotations. Besides the general challenge of adding type annotations to dynamically typed code, there are subtle interactions between these annotations in gradually typed code that exacerbate the situation. For example, to migrate a program to be as static as possible, in general, all possible combinations of adding or removing type annotations from parameters must be tried out and compared. In this paper, we address this problem by developing migrational typing, which efficiently types all possible ways of adding or removing type annotations from a gradually typed program. The typing result supports automatically migrating a program to be as static as possible, or introducing the least number of dynamic types necessary to remove a type error. The approach can be extended to support userdefined criteria about which annotations to modify. We have implemented migrational typing and evaluated it on large programs. The results show that migrational typing scales linearly with the size of the program and takes only 2–4 times longer than plain gradual typing. @Article{POPL18p15, author = {John Peter Campora and Sheng Chen and Martin Erwig and Eric Walkingshaw}, title = {Migrating Gradual Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {15}, numpages = {29}, doi = {10.1145/3158103}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Espitau, Thomas 
POPL '18: "Proving Expected Sensitivity ..."
Proving Expected Sensitivity of Probabilistic Programs
Gilles Barthe , Thomas Espitau, Benjamin Grégoire, Justin Hsu , and PierreYves Strub (IMDEA Software Institute, Spain; UPMC, France; Inria, France; University College London, UK; École Polytechnique, France) Program sensitivity, also known as Lipschitz continuity, describes how small changes in a program’s input lead to bounded changes in the output. We propose an average notion of program sensitivity for probabilistic programs—expected sensitivity—that averages a distance function over a probabilistic coupling of two output distributions from two similar inputs. By varying the distance, expected sensitivity recovers useful notions of probabilistic function sensitivity, including stability of machine learning algorithms and convergence of Markov chains. Furthermore, expected sensitivity satisfies clean compositional properties and is amenable to formal verification. We develop a relational program logic called EpRHL for proving expected sensitivity properties. Our logic features two key ideas. First, relational preconditions and postconditions are expressed using distances, a realvalued generalization of typical booleanvalued (relational) assertions. Second, judgments are interpreted in terms of expectation coupling, a novel, quantitative generalization of probabilistic couplings which supports compositional reasoning. We demonstrate our logic on examples beyond the reach of prior relational logics. Our main example formalizes uniform stability of the stochastic gradient method. Furthermore, we prove rapid mixing for a probabilistic model of population dynamics. We also extend our logic with a transitivity principle for expectation couplings to capture the path coupling proof technique by Bubley and Dyer, and formalize rapid mixing of the Glauber dynamics from statistical physics. @Article{POPL18p57, author = {Gilles Barthe and Thomas Espitau and Benjamin Grégoire and Justin Hsu and PierreYves Strub}, title = {Proving Expected Sensitivity of Probabilistic Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {57}, numpages = {29}, doi = {10.1145/3158145}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Farzan, Azadeh 
POPL '18: "Strategy Synthesis for Linear ..."
Strategy Synthesis for Linear Arithmetic Games
Azadeh Farzan and Zachary Kincaid (University of Toronto, Canada; Princeton University, USA) Many problems in formal methods can be formalized as twoplayer games. For several applications—program synthesis, for example—in addition to determining which player wins the game, we are interested in computing a winning strategy for that player. This paper studies the strategy synthesis problem for games defined within the theory of linear rational arithmetic. Two types of games are considered. A satisfiability game, described by a quantified formula, is played by two players that take turns instantiating quantifiers. The objective of each player is to prove (or disprove) satisfiability of the formula. A reachability game, described by a pair of formulas defining the legal moves of each player, is played by two players that take turns choosing positions—rational vectors of some fixed dimension. The objective of each player is to reach a position where the opposing player has no legal moves (or to play the game forever). We give a complete algorithm for synthesizing winning strategies for satisfiability games and a sound (but necessarily incomplete) algorithm for synthesizing winning strategies for reachability games. @Article{POPL18p61, author = {Azadeh Farzan and Zachary Kincaid}, title = {Strategy Synthesis for Linear Arithmetic Games}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {61}, numpages = {30}, doi = {10.1145/3158149}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Feng, Xinyu 
POPL '18: "Progress of Concurrent Objects ..."
Progress of Concurrent Objects with Partial Methods
Hongjin Liang and Xinyu Feng (Nanjing University, China; University of Science and Technology of China, China) Various progress properties have been proposed for concurrent objects, such as waitfreedom, lockfreedom, starvationfreedom and deadlockfreedom. However, none of them applies to concurrent objects with partial methods, i.e., methods that are supposed not to return under certain circumstances. A typical example is the lock_acquire method, which must not return when the lock has already been acquired. In this paper we propose two new progress properties, partial starvationfreedom (PSF) and partial deadlockfreedom (PDF), for concurrent objects with partial methods. We also design four patterns to write abstract specifications for PSF or PDF objects under strongly or weakly fair scheduling, so that these objects contextually refine the abstract specifications. Our Abstraction Theorem shows the equivalence between PSF (or PDF) and the progressaware contextual refinement. Finally, we generalize the program logic LiLi to have a new logic to verify the PSF (or PDF) property and linearizability of concurrent objects. @Article{POPL18p20, author = {Hongjin Liang and Xinyu Feng}, title = {Progress of Concurrent Objects with Partial Methods}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {20}, numpages = {31}, doi = {10.1145/3158108}, year = {2018}, } Publisher's Version Article Search 

Fisher, Kathleen 
POPL '18: "Synthesizing Bijective Lenses ..."
Synthesizing Bijective Lenses
Anders Miltner, Kathleen Fisher, Benjamin C. Pierce , David Walker, and Steve Zdancewic (Princeton University, USA; Tufts University, USA; University of Pennsylvania, USA) Bidirectional transformations between different data representations occur frequently in modern software systems. They appear as serializers and deserializers, as parsers and pretty printers, as database views and view updaters, and as a multitude of different kinds of ad hoc data converters. Manually building bidirectional transformationsby writing two separate functions that are intended to be inversesis tedious and error prone. A better approach is to use a domainspecific language in which both directions can be written as a single expression. However, these domainspecific languages can be difficult to program in, requiring programmers to manage fiddly details while working in a complex type system. We present an alternative approach. Instead of coding transformations manually, we synthesize them from declarative format descriptions and examples. Specifically, we present Optician, a tool for typedirected synthesis of bijective string transformers. The inputs to Optician are a pair of ordinary regular expressions representing two data formats and a few concrete examples for disambiguation. The output is a welltyped program in Boomerang (a bidirectional language based on the theory of lenses). The main technical challenge involves navigating the vast program search space efficiently. In particular, and unlike most prior work on typedirected synthesis, our system operates in the context of a language with a rich equivalence relation on types (the theory of regular expressions). Consequently, program synthesis requires search in two dimensions: First, our synthesis algorithm must find a pair of "syntactically compatible types," and second, using the structure of those types, it must find a type and examplecompliant term. Our key insight is that it is possible to reduce the size of this search space without losing any computational power by defining a new language of lenses designed specifically for synthesis. The new language is free from arbitrary function composition and operates only over types and terms in a new disjunctive normal form. We prove (1) our new language is just as powerful as a more natural, compositional, and declarative language and (2) our synthesis algorithm is sound and complete with respect to the new language. We also demonstrate empirically that our new language changes the synthesis problem from one that admits intractable solutions to one that admits highly efficient solutions, able to synthesize intricate lenses between complex file formats in seconds. We evaluate Optician on a benchmark suite of 39 examples that includes both microbenchmarks and realistic examples derived from other data management systems including Flash Fill, a tool for synthesizing string transformations in spreadsheets, and Augeas, a tool for bidirectional processing of Linux system configuration files. @Article{POPL18p1, author = {Anders Miltner and Kathleen Fisher and Benjamin C. Pierce and David Walker and Steve Zdancewic}, title = {Synthesizing Bijective Lenses}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {1}, numpages = {30}, doi = {10.1145/3158089}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Flückiger, Olivier 
POPL '18: "Correctness of Speculative ..."
Correctness of Speculative Optimizations with Dynamic Deoptimization
Olivier Flückiger , Gabriel Scherer , MingHo Yee, Aviral Goel, Amal Ahmed, and Jan Vitek (Northeastern University, USA; Inria, France; Czech Technical University, Czechia) Highperformance dynamic language implementations make heavy use of speculative optimizations to achieve speeds close to statically compiled languages. These optimizations are typically performed by a justintime compiler that generates code under a set of assumptions about the state of the program and its environment. In certain cases, a program may execute code compiled under assumptions that are no longer valid. The implementation must then deoptimize the program onthefly; this entails finding semantically equivalent code that does not rely on invalid assumptions, translating program state to that expected by the target code, and transferring control. This paper looks at the interaction between optimization and deoptimization, and shows that reasoning about speculation is surprisingly easy when assumptions are made explicit in the program representation. This insight is demonstrated on a compiler intermediate representation, named sourir, modeled after the highlevel representation for a dynamic language. Traditional compiler optimizations such as constant folding, unreachable code elimination, and function inlining are shown to be correct in the presence of assumptions. Furthermore, the paper establishes the correctness of compiler transformations specific to deoptimization: namely unrestricted deoptimization, predicate hoisting, and assume composition. @Article{POPL18p49, author = {Olivier Flückiger and Gabriel Scherer and MingHo Yee and Aviral Goel and Amal Ahmed and Jan Vitek}, title = {Correctness of Speculative Optimizations with Dynamic Deoptimization}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {49}, numpages = {28}, doi = {10.1145/3158137}, year = {2018}, } Publisher's Version Article Search 

Flur, Shaked 
POPL '18: "Simplifying ARM Concurrency: ..."
Simplifying ARM Concurrency: MulticopyAtomic Axiomatic and Operational Models for ARMv8
Christopher Pulte, Shaked Flur, Will Deacon, Jon French, Susmit Sarkar, and Peter Sewell (University of Cambridge, UK; ARM, UK; University of St. Andrews, UK) ARM has a relaxed memory model, previously specified in informal prose for ARMv7 and ARMv8. Over time, and partly due to work building formal semantics for ARM concurrency, it has become clear that some of the complexity of the model is not justified by the potential benefits. In particular, the model was originally nonmulticopyatomic: writes could become visible to some other threads before becoming visible to all — but this has not been exploited in production implementations, the corresponding potential hardware optimisations are thought to have insufficient benefits in the ARM context, and it gives rise to subtle complications when combined with other ARMv8 features. The ARMv8 architecture has therefore been revised: it now has a multicopyatomic model. It has also been simplified in other respects, including more straightforward notions of dependency, and the architecture now includes a formal concurrency model. In this paper we detail these changes and discuss their motivation. We define two formal concurrency models: an operational one, simplifying the Flowing model of Flur et al., and the axiomatic model of the revised ARMv8 specification. The models were developed by an academic group and by ARM staff, respectively, and this extended collaboration partly motivated the above changes. We prove the equivalence of the two models. The operational model is integrated into an executable exploration tool with new web interface, demonstrated by exhaustively checking the possible behaviours of a loopunrolled version of a Linux kernel lock implementation, a previously known bug due to unprevented speculation, and a fixed version. @Article{POPL18p19, author = {Christopher Pulte and Shaked Flur and Will Deacon and Jon French and Susmit Sarkar and Peter Sewell}, title = {Simplifying ARM Concurrency: MulticopyAtomic Axiomatic and Operational Models for ARMv8}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {19}, numpages = {29}, doi = {10.1145/3158107}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Fournet, Cédric 
POPL '18: "Recalling a Witness: Foundations ..."
Recalling a Witness: Foundations and Applications of Monotonic State
Danel Ahman, Cédric Fournet, Cătălin Hriţcu, Kenji Maillard , Aseem Rastogi, and Nikhil Swamy (Inria, France; Microsoft Research, UK; ENS Paris, France; Microsoft Research, India; Microsoft Research, USA) We provide a way to ease the verification of programs whose state evolves monotonically. The main idea is that a property witnessed in a prior state can be soundly recalled in the current state, provided (1) state evolves according to a given preorder, and (2) the property is preserved by this preorder. In many scenarios, such monotonic reasoning yields concise modular proofs, saving the need for explicit program invariants. We distill our approach into the monotonicstate monad, a general yet compact interface for Hoarestyle reasoning about monotonic state in a dependently typed language. We prove the soundness of the monotonicstate monad and use it as a unified foundation for reasoning about monotonic state in the F^{⋆} verification system. Based on this foundation, we build libraries for various mutable data structures like monotonic references and apply these libraries at scale to the verification of several distributed applications. @Article{POPL18p65, author = {Danel Ahman and Cédric Fournet and Cătălin Hriţcu and Kenji Maillard and Aseem Rastogi and Nikhil Swamy}, title = {Recalling a Witness: Foundations and Applications of Monotonic State}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {65}, numpages = {30}, doi = {10.1145/3158153}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Fragoso Santos, José 
POPL '18: "JaVerT: JavaScript Verification ..."
JaVerT: JavaScript Verification Toolchain
José Fragoso Santos, Petar Maksimović, Daiva Naudžiūnienė, Thomas Wood, and Philippa Gardner (Imperial College London, UK; Mathematical Institute SASA, Serbia) The dynamic nature of JavaScript and its complex semantics make it a difficult target for logicbased verification. We introduce JaVerT, a semiautomatic JavaScript Verification Toolchain, based on separation logic and aimed at the specialist developer wanting rich, mechanically verified specifications of critical JavaScript code. To specify JavaScript programs, we design abstractions that capture its key heap structures (for example, prototype chains and function closures), allowing the developer to write clear and succinct specifications with minimal knowledge of the JavaScript internals. To verify JavaScript programs, we develop JaVerT, a verification pipeline consisting of: JS2JSIL, a welltested compiler from JavaScript to JSIL, an intermediate goto language capturing the fundamental dynamic features of JavaScript; JSIL Verify, a semiautomatic verification tool based on a sound JSIL separation logic; and verified axiomatic specifications of the JavaScript internal functions. Using JaVerT, we verify functional correctness properties of: datastructure libraries (keyvalue map, priority queue) written in an objectoriented style; operations on data structures such as binary search trees (BSTs) and lists; examples illustrating function closures; and test cases from the official ECMAScript test suite. The verification times suggest that reasoning about larger, more complex code using JaVerT is feasible. @Article{POPL18p50, author = {José Fragoso Santos and Petar Maksimović and Daiva Naudžiūnienė and Thomas Wood and Philippa Gardner}, title = {JaVerT: JavaScript Verification Toolchain}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {50}, numpages = {33}, doi = {10.1145/3158138}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

French, Jon 
POPL '18: "Simplifying ARM Concurrency: ..."
Simplifying ARM Concurrency: MulticopyAtomic Axiomatic and Operational Models for ARMv8
Christopher Pulte, Shaked Flur, Will Deacon, Jon French, Susmit Sarkar, and Peter Sewell (University of Cambridge, UK; ARM, UK; University of St. Andrews, UK) ARM has a relaxed memory model, previously specified in informal prose for ARMv7 and ARMv8. Over time, and partly due to work building formal semantics for ARM concurrency, it has become clear that some of the complexity of the model is not justified by the potential benefits. In particular, the model was originally nonmulticopyatomic: writes could become visible to some other threads before becoming visible to all — but this has not been exploited in production implementations, the corresponding potential hardware optimisations are thought to have insufficient benefits in the ARM context, and it gives rise to subtle complications when combined with other ARMv8 features. The ARMv8 architecture has therefore been revised: it now has a multicopyatomic model. It has also been simplified in other respects, including more straightforward notions of dependency, and the architecture now includes a formal concurrency model. In this paper we detail these changes and discuss their motivation. We define two formal concurrency models: an operational one, simplifying the Flowing model of Flur et al., and the axiomatic model of the revised ARMv8 specification. The models were developed by an academic group and by ARM staff, respectively, and this extended collaboration partly motivated the above changes. We prove the equivalence of the two models. The operational model is integrated into an executable exploration tool with new web interface, demonstrated by exhaustively checking the possible behaviours of a loopunrolled version of a Linux kernel lock implementation, a previously known bug due to unprevented speculation, and a fixed version. @Article{POPL18p19, author = {Christopher Pulte and Shaked Flur and Will Deacon and Jon French and Susmit Sarkar and Peter Sewell}, title = {Simplifying ARM Concurrency: MulticopyAtomic Axiomatic and Operational Models for ARMv8}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {19}, numpages = {29}, doi = {10.1145/3158107}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Gaboardi, Marco 
POPL '18: "Monadic Refinements for Relational ..."
Monadic Refinements for Relational Cost Analysis
Ivan Radiček, Gilles Barthe , Marco Gaboardi, Deepak Garg , and Florian Zuleger (Vienna University of Technology, Austria; IMDEA Software Institute, Spain; SUNY Buffalo, USA; MPISWS, Germany) Formal frameworks for cost analysis of programs have been widely studied in the unary setting and, to a limited extent, in the relational setting. However, many of these frameworks focus only on the cost aspect, largely sidelining functional properties that are often a prerequisite for cost analysis, thus leaving many interesting programs out of their purview. In this paper, we show that elegant, simple, expressive proof systems combining cost analysis and functional properties can be built by combining already known ingredients: higherorder refinements and cost monads. Specifically, we derive two syntaxdirected proof systems, U^{C} and R^{C}, for unary and relational cost analysis, by adding a cost monad to a (syntaxdirected) logic of higherorder programs. We study the metatheory of the systems, show that several nontrivial examples can be verified in them, and prove that existing frameworks for cost analysis (RelCost and RAML) can be embedded in them. @Article{POPL18p36, author = {Ivan Radiček and Gilles Barthe and Marco Gaboardi and Deepak Garg and Florian Zuleger}, title = {Monadic Refinements for Relational Cost Analysis}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {36}, numpages = {32}, doi = {10.1145/3158124}, year = {2018}, } Publisher's Version Article Search 

Gardner, Philippa 
POPL '18: "JaVerT: JavaScript Verification ..."
JaVerT: JavaScript Verification Toolchain
José Fragoso Santos, Petar Maksimović, Daiva Naudžiūnienė, Thomas Wood, and Philippa Gardner (Imperial College London, UK; Mathematical Institute SASA, Serbia) The dynamic nature of JavaScript and its complex semantics make it a difficult target for logicbased verification. We introduce JaVerT, a semiautomatic JavaScript Verification Toolchain, based on separation logic and aimed at the specialist developer wanting rich, mechanically verified specifications of critical JavaScript code. To specify JavaScript programs, we design abstractions that capture its key heap structures (for example, prototype chains and function closures), allowing the developer to write clear and succinct specifications with minimal knowledge of the JavaScript internals. To verify JavaScript programs, we develop JaVerT, a verification pipeline consisting of: JS2JSIL, a welltested compiler from JavaScript to JSIL, an intermediate goto language capturing the fundamental dynamic features of JavaScript; JSIL Verify, a semiautomatic verification tool based on a sound JSIL separation logic; and verified axiomatic specifications of the JavaScript internal functions. Using JaVerT, we verify functional correctness properties of: datastructure libraries (keyvalue map, priority queue) written in an objectoriented style; operations on data structures such as binary search trees (BSTs) and lists; examples illustrating function closures; and test cases from the official ECMAScript test suite. The verification times suggest that reasoning about larger, more complex code using JaVerT is feasible. @Article{POPL18p50, author = {José Fragoso Santos and Petar Maksimović and Daiva Naudžiūnienė and Thomas Wood and Philippa Gardner}, title = {JaVerT: JavaScript Verification Toolchain}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {50}, numpages = {33}, doi = {10.1145/3158138}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Garg, Deepak 
POPL '18: "Monadic Refinements for Relational ..."
Monadic Refinements for Relational Cost Analysis
Ivan Radiček, Gilles Barthe , Marco Gaboardi, Deepak Garg , and Florian Zuleger (Vienna University of Technology, Austria; IMDEA Software Institute, Spain; SUNY Buffalo, USA; MPISWS, Germany) Formal frameworks for cost analysis of programs have been widely studied in the unary setting and, to a limited extent, in the relational setting. However, many of these frameworks focus only on the cost aspect, largely sidelining functional properties that are often a prerequisite for cost analysis, thus leaving many interesting programs out of their purview. In this paper, we show that elegant, simple, expressive proof systems combining cost analysis and functional properties can be built by combining already known ingredients: higherorder refinements and cost monads. Specifically, we derive two syntaxdirected proof systems, U^{C} and R^{C}, for unary and relational cost analysis, by adding a cost monad to a (syntaxdirected) logic of higherorder programs. We study the metatheory of the systems, show that several nontrivial examples can be verified in them, and prove that existing frameworks for cost analysis (RelCost and RAML) can be embedded in them. @Article{POPL18p36, author = {Ivan Radiček and Gilles Barthe and Marco Gaboardi and Deepak Garg and Florian Zuleger}, title = {Monadic Refinements for Relational Cost Analysis}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {36}, numpages = {32}, doi = {10.1145/3158124}, year = {2018}, } Publisher's Version Article Search 

Ghahramani, Zoubin 
POPL '18: "Denotational Validation of ..."
Denotational Validation of HigherOrder Bayesian Inference
Adam Ścibior, Ohad Kammar, Matthijs Vákár, Sam Staton, Hongseok Yang, Yufei Cai, Klaus Ostermann , Sean K. Moss, Chris Heunen , and Zoubin Ghahramani (University of Cambridge, UK; MPI Tübingen, Germany; University of Oxford, UK; KAIST, South Korea; University of Tübingen, Germany; University of Edinburgh, UK; Uber AI Labs, USA) We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higherorder functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higherorder functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasiBorel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasiBorel counterpart to the MetropolisHastingsGreen theorem. @Article{POPL18p60, author = {Adam Ścibior and Ohad Kammar and Matthijs Vákár and Sam Staton and Hongseok Yang and Yufei Cai and Klaus Ostermann and Sean K. Moss and Chris Heunen and Zoubin Ghahramani}, title = {Denotational Validation of HigherOrder Bayesian Inference}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {60}, numpages = {29}, doi = {10.1145/3158148}, year = {2018}, } Publisher's Version Article Search Info 

Gilray, Thomas 
POPL '18: "Soft Contract Verification ..."
Soft Contract Verification for HigherOrder Stateful Programs
Phúc C. Nguyễn, Thomas Gilray, Sam TobinHochstadt, and David Van Horn (University of Maryland, USA; Indiana University, USA) Software contracts allow programmers to state rich program properties using the full expressive power of an object language. However, since they are enforced at runtime, monitoring contracts imposes significant overhead and delays error discovery. So contract veri cation aims to guarantee all or most of these properties ahead of time, enabling valuable optimizations and yielding a more general assurance of correctness. Existing methods for static contract verification satisfy the needs of more restricted target languages, but fail to address the challenges unique to those conjoining untyped, dynamic programming, higherorder functions, modularity, and statefulness. Our approach tackles all these features at once, in the context of the full Racket system—a mature environment for stateful, higherorder, multiparadigm programming with or with out types. Evaluating our method using a set of both pure and stateful benchmarks, we are able to verify 99.94% of checks statically (all but 28 of 49, 861). Stateful, higherorder functions pose significant challenges for static contract verification in particular. In the presence of these features, a modular analysis must permit code from the current module to escape permanently to an opaque context (unspecified code from outside the current module) that may be stateful and therefore store a reference to the escaped closure. Also, contracts themselves, being predicates wri en in unrestricted Racket, may exhibit stateful behavior; a sound approach must be robust to contracts which are arbitrarily expressive and interwoven with the code they monitor. In this paper, we present and evaluate our solution based on higherorder symbolic execution, explain the techniques we used to address such thorny issues, formalize a notion of behavioral approximation, and use it to provide a mechanized proof of soundness. @Article{POPL18p51, author = {Phúc C. Nguyễn and Thomas Gilray and Sam TobinHochstadt and David Van Horn}, title = {Soft Contract Verification for HigherOrder Stateful Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {51}, numpages = {30}, doi = {10.1145/3158139}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Goel, Aviral 
POPL '18: "Correctness of Speculative ..."
Correctness of Speculative Optimizations with Dynamic Deoptimization
Olivier Flückiger , Gabriel Scherer , MingHo Yee, Aviral Goel, Amal Ahmed, and Jan Vitek (Northeastern University, USA; Inria, France; Czech Technical University, Czechia) Highperformance dynamic language implementations make heavy use of speculative optimizations to achieve speeds close to statically compiled languages. These optimizations are typically performed by a justintime compiler that generates code under a set of assumptions about the state of the program and its environment. In certain cases, a program may execute code compiled under assumptions that are no longer valid. The implementation must then deoptimize the program onthefly; this entails finding semantically equivalent code that does not rely on invalid assumptions, translating program state to that expected by the target code, and transferring control. This paper looks at the interaction between optimization and deoptimization, and shows that reasoning about speculation is surprisingly easy when assumptions are made explicit in the program representation. This insight is demonstrated on a compiler intermediate representation, named sourir, modeled after the highlevel representation for a dynamic language. Traditional compiler optimizations such as constant folding, unreachable code elimination, and function inlining are shown to be correct in the presence of assumptions. Furthermore, the paper establishes the correctness of compiler transformations specific to deoptimization: namely unrestricted deoptimization, predicate hoisting, and assume composition. @Article{POPL18p49, author = {Olivier Flückiger and Gabriel Scherer and MingHo Yee and Aviral Goel and Amal Ahmed and Jan Vitek}, title = {Correctness of Speculative Optimizations with Dynamic Deoptimization}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {49}, numpages = {28}, doi = {10.1145/3158137}, year = {2018}, } Publisher's Version Article Search 

GolanGueta, Guy 
POPL '18: "Online Detection of Effectively ..."
Online Detection of Effectively Callback Free Objects with Applications to Smart Contracts
Shelly Grossman, Ittai Abraham, Guy GolanGueta, Yan Michalevsky, Noam Rinetzky, Mooly Sagiv, and Yoni Zohar (Tel Aviv University, Israel; VMware, USA; Stanford University, USA) Callbacks are essential in many programming environments, but drastically complicate program understanding and reasoning because they allow to mutate object's local states by external objects in unexpected fashions, thus breaking modularity. The famous DAO bug in the cryptocurrency framework Ethereum, employed callbacks to steal $150M. We define the notion of Effectively Callback Free (ECF) objects in order to allow callbacks without preventing modular reasoning. An object is ECF in a given execution trace if there exists an equivalent execution trace without callbacks to this object. An object is ECF if it is ECF in every possible execution trace. We study the decidability of dynamically checking ECF in a given execution trace and statically checking if an object is ECF. We also show that dynamically checking ECF in Ethereum is feasible and can be done online. By running the history of all execution traces in Ethereum, we were able to verify that virtually all existing contract executions, excluding these of the DAO or of contracts with similar known vulnerabilities, are ECF. Finally, we show that ECF, whether it is verified dynamically or statically, enables modular reasoning about objects with encapsulated state. @Article{POPL18p48, author = {Shelly Grossman and Ittai Abraham and Guy GolanGueta and Yan Michalevsky and Noam Rinetzky and Mooly Sagiv and Yoni Zohar}, title = {Online Detection of Effectively Callback Free Objects with Applications to Smart Contracts}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {48}, numpages = {28}, doi = {10.1145/3158136}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Grégoire, Benjamin 
POPL '18: "Proving Expected Sensitivity ..."
Proving Expected Sensitivity of Probabilistic Programs
Gilles Barthe , Thomas Espitau, Benjamin Grégoire, Justin Hsu , and PierreYves Strub (IMDEA Software Institute, Spain; UPMC, France; Inria, France; University College London, UK; École Polytechnique, France) Program sensitivity, also known as Lipschitz continuity, describes how small changes in a program’s input lead to bounded changes in the output. We propose an average notion of program sensitivity for probabilistic programs—expected sensitivity—that averages a distance function over a probabilistic coupling of two output distributions from two similar inputs. By varying the distance, expected sensitivity recovers useful notions of probabilistic function sensitivity, including stability of machine learning algorithms and convergence of Markov chains. Furthermore, expected sensitivity satisfies clean compositional properties and is amenable to formal verification. We develop a relational program logic called EpRHL for proving expected sensitivity properties. Our logic features two key ideas. First, relational preconditions and postconditions are expressed using distances, a realvalued generalization of typical booleanvalued (relational) assertions. Second, judgments are interpreted in terms of expectation coupling, a novel, quantitative generalization of probabilistic couplings which supports compositional reasoning. We demonstrate our logic on examples beyond the reach of prior relational logics. Our main example formalizes uniform stability of the stochastic gradient method. Furthermore, we prove rapid mixing for a probabilistic model of population dynamics. We also extend our logic with a transitivity principle for expectation couplings to capture the path coupling proof technique by Bubley and Dyer, and formalize rapid mixing of the Glauber dynamics from statistical physics. @Article{POPL18p57, author = {Gilles Barthe and Thomas Espitau and Benjamin Grégoire and Justin Hsu and PierreYves Strub}, title = {Proving Expected Sensitivity of Probabilistic Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {57}, numpages = {29}, doi = {10.1145/3158145}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Grellois, Charles 
POPL '18: "Linearity in HigherOrder ..."
Linearity in HigherOrder Recursion Schemes
Pierre Clairambault, Charles Grellois, and Andrzej S. Murawski (University of Lyon, France; CNRS, France; ENS Lyon, France; Claude Bernard University Lyon 1, France; LIP, France; Inria, France; AixMarseille University, France; ENSAM, France; University of Toulon, France; University of Oxford, UK) Higherorder recursion schemes (HORS) have recently emerged as a promising foundation for higherorder program verification. We examine the impact of enriching HORS with linear types. To that end, we introduce two frameworks that blend nonlinear and linear types: a variant of the λY calculus and an extension of HORS, called linear HORS (LHORS). First we prove that the two formalisms are equivalent and there exist polynomialtime translations between them. Then, in order to support modelchecking of (trees generated by) LHORS, we propose a refined version of alternating parity tree automata, called LNAPTA, whose behaviour depends on information about linearity. We show that the complexity of LNAPTA modelchecking for LHORS depends on two typetheoretic parameters: linear order and linear depth. The former is in general smaller than the standard notion of order and ignores linear function spaces. In contrast, the latter measures the depth of linear clusters inside a type. Our main result states that LNAPTA modelchecking of LHORS of linear order n is nEXPTIMEcomplete, when linear depth is fixed. This generalizes and improves upon the classic result of Ong, which relies on the standard notion of order. To illustrate the significance of the result, we consider two applications: the MSO modelchecking problem on variants of HORS with case distinction (RSFD and HORSC) on a finite domain and a callbyvalue resource verification problem. In both cases, decidability can be established by translation into HORS, but the implied complexity bounds will be suboptimal due to increases in type order. In contrast, we show that the complexity bounds derived by translations into LHORS and appealing to our result are optimal in that they match the respective hardness results. @Article{POPL18p39, author = {Pierre Clairambault and Charles Grellois and Andrzej S. Murawski}, title = {Linearity in HigherOrder Recursion Schemes}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {39}, numpages = {29}, doi = {10.1145/3158127}, year = {2018}, } Publisher's Version Article Search 

Grossman, Shelly 
POPL '18: "Online Detection of Effectively ..."
Online Detection of Effectively Callback Free Objects with Applications to Smart Contracts
Shelly Grossman, Ittai Abraham, Guy GolanGueta, Yan Michalevsky, Noam Rinetzky, Mooly Sagiv, and Yoni Zohar (Tel Aviv University, Israel; VMware, USA; Stanford University, USA) Callbacks are essential in many programming environments, but drastically complicate program understanding and reasoning because they allow to mutate object's local states by external objects in unexpected fashions, thus breaking modularity. The famous DAO bug in the cryptocurrency framework Ethereum, employed callbacks to steal $150M. We define the notion of Effectively Callback Free (ECF) objects in order to allow callbacks without preventing modular reasoning. An object is ECF in a given execution trace if there exists an equivalent execution trace without callbacks to this object. An object is ECF if it is ECF in every possible execution trace. We study the decidability of dynamically checking ECF in a given execution trace and statically checking if an object is ECF. We also show that dynamically checking ECF in Ethereum is feasible and can be done online. By running the history of all execution traces in Ethereum, we were able to verify that virtually all existing contract executions, excluding these of the DAO or of contracts with similar known vulnerabilities, are ECF. Finally, we show that ECF, whether it is verified dynamically or statically, enables modular reasoning about objects with encapsulated state. @Article{POPL18p48, author = {Shelly Grossman and Ittai Abraham and Guy GolanGueta and Yan Michalevsky and Noam Rinetzky and Mooly Sagiv and Yoni Zohar}, title = {Online Detection of Effectively Callback Free Objects with Applications to Smart Contracts}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {48}, numpages = {28}, doi = {10.1145/3158136}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Hague, Matthew 
POPL '18: "What Is Decidable about String ..."
What Is Decidable about String Constraints with the ReplaceAll Function
Taolue Chen, Yan Chen, Matthew Hague , Anthony W. Lin, and Zhilin Wu (University of London, UK; Institute of Software at Chinese Academy of Sciences, China; University at Chinese Academy of Sciences, China; Royal Holloway University of London, UK; University of Oxford, UK) The theory of strings with concatenation has been widely argued as the basis of constraint solving for verifying stringmanipulating programs. However, this theory is far from adequate for expressing many string constraints that are also needed in practice; for example, the use of regular constraints (pattern matching against a regular expression), and the stringreplace function (replacing either the first occurrence or all occurrences of a ``pattern'' string constant/variable/regular expression by a ``replacement'' string constant/variable), among many others. Both regular constraints and the stringreplace function are crucial for such applications as analysis of JavaScript (or more generally HTML5 applications) against crosssite scripting (XSS) vulnerabilities, which motivates us to consider a richer class of string constraints. The importance of the stringreplace function (especially the replaceall facility) is increasingly recognised, which can be witnessed by the incorporation of the function in the input languages of several string constraint solvers. Recently, it was shown that any theory of strings containing the stringreplace function (even the most restricted version where pattern/replacement strings are both constant strings) becomes undecidable if we do not impose some kind of straightline (aka acyclicity) restriction on the formulas. Despite this, the straightline restriction is still practically sensible since this condition is typically met by string constraints that are generated by symbolic execution. In this paper, we provide the first systematic study of straightline string constraints with the stringreplace function and the regular constraints as the basic operations. We show that a large class of such constraints (i.e. when only a constant string or a regular expression is permitted in the pattern) is decidable. We note that the stringreplace function, even under this restriction, is sufficiently powerful for expressing the concatenation operator and much more (e.g. extensions of regular expressions with string variables). This gives us the most expressive decidable logic containing concatenation, replace, and regular constraints under the same umbrella. Our decision procedure for the straightline fragment follows an automatatheoretic approach, and is modular in the sense that the stringreplace terms are removed one by one to generate more and more regular constraints, which can then be discharged by the stateoftheart string constraint solvers. We also show that this fragment is, in a way, a maximal decidable subclass of the straightline fragment with stringreplace and regular constraints. To this end, we show undecidability results for the following two extensions: (1) variables are permitted in the pattern parameter of the replace function, (2) length constraints are permitted. @Article{POPL18p3, author = {Taolue Chen and Yan Chen and Matthew Hague and Anthony W. Lin and Zhilin Wu}, title = {What Is Decidable about String Constraints with the ReplaceAll Function}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {3}, numpages = {29}, doi = {10.1145/3158091}, year = {2018}, } Publisher's Version Article Search 

Heunen, Chris 
POPL '18: "Denotational Validation of ..."
Denotational Validation of HigherOrder Bayesian Inference
Adam Ścibior, Ohad Kammar, Matthijs Vákár, Sam Staton, Hongseok Yang, Yufei Cai, Klaus Ostermann , Sean K. Moss, Chris Heunen , and Zoubin Ghahramani (University of Cambridge, UK; MPI Tübingen, Germany; University of Oxford, UK; KAIST, South Korea; University of Tübingen, Germany; University of Edinburgh, UK; Uber AI Labs, USA) We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higherorder functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higherorder functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasiBorel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasiBorel counterpart to the MetropolisHastingsGreen theorem. @Article{POPL18p60, author = {Adam Ścibior and Ohad Kammar and Matthijs Vákár and Sam Staton and Hongseok Yang and Yufei Cai and Klaus Ostermann and Sean K. Moss and Chris Heunen and Zoubin Ghahramani}, title = {Denotational Validation of HigherOrder Bayesian Inference}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {60}, numpages = {29}, doi = {10.1145/3158148}, year = {2018}, } Publisher's Version Article Search Info 

Hoenicke, Jochen 
POPL '18: "Reducing Liveness to Safety ..."
Reducing Liveness to Safety in FirstOrder Logic
Oded Padon, Jochen Hoenicke, Giuliano Losa, Andreas Podelski , Mooly Sagiv, and Sharon Shoham (Tel Aviv University, Israel; University of Freiburg, Germany; University of California at Los Angeles, USA) We develop a new technique for verifying temporal properties of infinitestate (distributed) systems. The main idea is to reduce the temporal verification problem to the problem of verifying the safety of infinitestate systems expressed in firstorder logic. This allows to leverage existing techniques for safety verification to verify temporal properties of interesting distributed protocols, including some that have not been mechanically verified before. We model infinitestate systems using firstorder logic, and use firstorder temporal logic (FOLTL) to specify temporal properties. This general formalism allows to naturally model distributed systems, while supporting both unboundedparallelism (where the system is allowed to dynamically create processes), and infinitestate per process. The traditional approach for verifying temporal properties of infinitestate systems employs wellfounded relations (e.g. using linear arithmetic ranking functions). In contrast, our approach is based the idea of fair cycle detection. In finitestate systems, temporal verification can always be reduced to fair cycle detection (a system contains a fair cycle if it revisits a state after satisfying all fairness constraints). However, with both infinitely many states and infinitely many fairness constraints, a straightforward reduction to fair cycle detection is unsound. To regain soundness, we augment the infinitestate transition system by a dynamically computed finite set, that exploits the locality of transitions. This set lets us define a form of fair cycle detection that is sound in the presence of both infinitely many states, and infinitely many fairness constraints. Our approach allows a new style of temporal verification that does not explicitly involve ranking functions. This fits well with pure firstorder verification which does not explicitly reason about numerical values. In particular, it can be used with effectively propositional firstorder logic (EPR), in which case checking verification conditions is decidable. We applied our technique to verify temporal properties of several interesting protocols. To the best of our knowledge, we have obtained the first mechanized liveness proof for both TLB Shootdown, and Stoppable Paxos. @Article{POPL18p26, author = {Oded Padon and Jochen Hoenicke and Giuliano Losa and Andreas Podelski and Mooly Sagiv and Sharon Shoham}, title = {Reducing Liveness to Safety in FirstOrder Logic}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {26}, numpages = {33}, doi = {10.1145/3158114}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Holík, Lukáš 
POPL '18: "String Constraints with Concatenation ..."
String Constraints with Concatenation and Transducers Solved Efficiently
Lukáš Holík , Petr Janků, Anthony W. Lin, Philipp Rümmer, and Tomáš Vojnar (Brno University of Technology, Czechia; University of Oxford, UK; Uppsala University, Sweden) String analysis is the problem of reasoning about how strings are manipulated by a program. It has numerous applications including automatic detection of crosssite scripting, and automatic testcase generation. A popular string analysis technique includes symbolic executions, which at their core use constraint solvers over the string domain, a.k.a. string solvers. Such solvers typically reason about constraints expressed in theories over strings with the concatenation operator as an atomic constraint. In recent years, researchers started to recognise the importance of incorporating the replaceall operator (i.e. replace all occurrences of a string by another string) and, more generally, finitestate transductions in the theories of strings with concatenation. Such string operations are typically crucial for reasoning about XSS vulnerabilities in web applications, especially for modelling sanitisation functions and implicit browser transductions (e.g. innerHTML). Although this results in an undecidable theory in general, it was recently shown that the straightline fragment of the theory is decidable, and is sufficiently expressive in practice. In this paper, we provide the first string solver that can reason about constraints involving both concatenation and finitestate transductions. Moreover, it has a completeness and termination guarantee for several important fragments (e.g. straightline fragment). The main challenge addressed in the paper is the prohibitive worstcase complexity of the theory (doubleexponential time), which is exponentially harder than the case without finitestate transductions. To this end, we propose a method that exploits succinct alternating finitestate automata as concise symbolic representations of string constraints. In contrast to previous approaches using nondeterministic automata, alternation offers not only exponential savings in space when representing Boolean combinations of transducers, but also a possibility of succinct representation of otherwise costly combinations of transducers and concatenation. Reasoning about the emptiness of the AFA language requires a statespace exploration in an exponentialsized graph, for which we use model checking algorithms (e.g. IC3). We have implemented our algorithm and demonstrated its efficacy on benchmarks that are derived from crosssite scripting analysis and other examples in the literature. @Article{POPL18p4, author = {Lukáš Holík and Petr Janků and Anthony W. Lin and Philipp Rümmer and Tomáš Vojnar}, title = {String Constraints with Concatenation and Transducers Solved Efficiently}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {4}, numpages = {32}, doi = {10.1145/3158092}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Hriţcu, Cătălin 
POPL '18: "Recalling a Witness: Foundations ..."
Recalling a Witness: Foundations and Applications of Monotonic State
Danel Ahman, Cédric Fournet, Cătălin Hriţcu, Kenji Maillard , Aseem Rastogi, and Nikhil Swamy (Inria, France; Microsoft Research, UK; ENS Paris, France; Microsoft Research, India; Microsoft Research, USA) We provide a way to ease the verification of programs whose state evolves monotonically. The main idea is that a property witnessed in a prior state can be soundly recalled in the current state, provided (1) state evolves according to a given preorder, and (2) the property is preserved by this preorder. In many scenarios, such monotonic reasoning yields concise modular proofs, saving the need for explicit program invariants. We distill our approach into the monotonicstate monad, a general yet compact interface for Hoarestyle reasoning about monotonic state in a dependently typed language. We prove the soundness of the monotonicstate monad and use it as a unified foundation for reasoning about monotonic state in the F^{⋆} verification system. Based on this foundation, we build libraries for various mutable data structures like monotonic references and apply these libraries at scale to the verification of several distributed applications. @Article{POPL18p65, author = {Danel Ahman and Cédric Fournet and Cătălin Hriţcu and Kenji Maillard and Aseem Rastogi and Nikhil Swamy}, title = {Recalling a Witness: Foundations and Applications of Monotonic State}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {65}, numpages = {30}, doi = {10.1145/3158153}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Hsu, Justin 
POPL '18: "Synthesizing Coupling Proofs ..."
Synthesizing Coupling Proofs of Differential Privacy
Aws Albarghouthi and Justin Hsu (University of WisconsinMadison, USA; University College London, UK) Differential privacy has emerged as a promising probabilistic formulation of privacy, generating intense interest within academia and industry. We present a pushbutton, automated technique for verifying εdifferential privacy of sophisticated randomized algorithms. We make several conceptual, algorithmic, and practical contributions: (i) Inspired by the recent advances on approximate couplings and randomness alignment, we present a new proof technique called coupling strategies, which casts differential privacy proofs as a winning strategy in a game where we have finite privacy resources to expend. (ii) To discover a winning strategy, we present a constraintbased formulation of the problem as a set of Horn modulo couplings (HMC) constraints, a novel combination of firstorder Horn clauses and probabilistic constraints. (iii) We present a technique for solving HMC constraints by transforming probabilistic constraints into logical constraints with uninterpreted functions. (iv) Finally, we implement our technique in the FairSquare verifier and provide the first automated privacy proofs for a number of challenging algorithms from the differential privacy literature, including Report Noisy Max, the Exponential Mechanism, and the Sparse Vector Mechanism. @Article{POPL18p58, author = {Aws Albarghouthi and Justin Hsu}, title = {Synthesizing Coupling Proofs of Differential Privacy}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {58}, numpages = {30}, doi = {10.1145/3158146}, year = {2018}, } Publisher's Version Article Search POPL '18: "Proving Expected Sensitivity ..." Proving Expected Sensitivity of Probabilistic Programs Gilles Barthe , Thomas Espitau, Benjamin Grégoire, Justin Hsu , and PierreYves Strub (IMDEA Software Institute, Spain; UPMC, France; Inria, France; University College London, UK; École Polytechnique, France) Program sensitivity, also known as Lipschitz continuity, describes how small changes in a program’s input lead to bounded changes in the output. We propose an average notion of program sensitivity for probabilistic programs—expected sensitivity—that averages a distance function over a probabilistic coupling of two output distributions from two similar inputs. By varying the distance, expected sensitivity recovers useful notions of probabilistic function sensitivity, including stability of machine learning algorithms and convergence of Markov chains. Furthermore, expected sensitivity satisfies clean compositional properties and is amenable to formal verification. We develop a relational program logic called EpRHL for proving expected sensitivity properties. Our logic features two key ideas. First, relational preconditions and postconditions are expressed using distances, a realvalued generalization of typical booleanvalued (relational) assertions. Second, judgments are interpreted in terms of expectation coupling, a novel, quantitative generalization of probabilistic couplings which supports compositional reasoning. We demonstrate our logic on examples beyond the reach of prior relational logics. Our main example formalizes uniform stability of the stochastic gradient method. Furthermore, we prove rapid mixing for a probabilistic model of population dynamics. We also extend our logic with a transitivity principle for expectation couplings to capture the path coupling proof technique by Bubley and Dyer, and formalize rapid mixing of the Glauber dynamics from statistical physics. @Article{POPL18p57, author = {Gilles Barthe and Thomas Espitau and Benjamin Grégoire and Justin Hsu and PierreYves Strub}, title = {Proving Expected Sensitivity of Probabilistic Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {57}, numpages = {29}, doi = {10.1145/3158145}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Hu, Zhenjiang 
POPL '18: "An Axiomatic Basis for Bidirectional ..."
An Axiomatic Basis for Bidirectional Programming
HsiangShang Ko and Zhenjiang Hu (National Institute of Informatics, Japan) Among the frameworks of bidirectional transformations proposed for addressing various synchronisation (consistency maintenance) problems, Foster et al.’s [2007] asymmetric lenses have influenced the design of a generation of bidirectional programming languages. Most of these languages are based on a declarative programming model, and only allow the programmer to describe a consistency specification with ad hoc and/or awkward control over the consistency restoration behaviour. However, synchronisation problems are diverse and require vastly different consistency restoration strategies, and to cope with the diversity, the programmer must have the ability to fully control and reason about the consistency restoration behaviour. The putbackbased approach to bidirectional programming aims to provide exactly this ability, and this paper strengthens the putbackbased position by proposing the first fully fledged reasoning framework for a bidirectional language — a Hoarestyle logic for Ko et al.’s [2016] putbackbased language BiGUL. The Hoarestyle logic lets the BiGUL programmer precisely characterise the bidirectional behaviour of their programs by reasoning solely in the putback direction, thereby offering a unidirectional programming abstraction that is reasonably straightforward to work with and yet provides full control not achieved by previous approaches. The theory has been formalised and checked in Agda, but this paper presents the Hoarestyle logic in a semiformal way to make it easily understood and usable by the working BiGUL programmer. @Article{POPL18p41, author = {HsiangShang Ko and Zhenjiang Hu}, title = {An Axiomatic Basis for Bidirectional Programming}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {41}, numpages = {29}, doi = {10.1145/3158129}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Inala, Jeevana Priya 
POPL '18: "WebRelate: Integrating Web ..."
WebRelate: Integrating Web Data with Spreadsheets using Examples
Jeevana Priya Inala and Rishabh Singh (Massachusetts Institute of Technology, USA; Microsoft Research, USA) Data integration between web sources and relational data is a key challenge faced by data scientists and spreadsheet users. There are two main challenges in programmatically joining web data with relational data. First, most websites do not expose a direct interface to obtain tabular data, so the user needs to formulate a logic to get to different webpages for each input row in the relational table. Second, after reaching the desired webpage, the user needs to write complex scripts to extract the relevant data, which is often conditioned on the input data. Since many data scientists and endusers come from diverse backgrounds, writing such complex regularexpression based logical scripts to perform data integration tasks is unfortunately often beyond their programming expertise. We present WebRelate, a system that allows users to join semistructured web data with relational data in spreadsheets using inputoutput examples. WebRelate decomposes the web data integration task into two subtasks of i) URL learning and ii) inputdependent web extraction. We introduce a novel synthesis paradigm called "Outputconstrained Programming By Examples", which allows us to use the finite set of possible outputs for the new inputs to efficiently constrain the search in the synthesis algorithm. We instantiate this paradigm for the two subtasks in WebRelate. The first subtask generates the URLs for the webpages containing the desired data for all rows in the relational table. WebRelate achieves this by learning a string transformation program using a few example URLs. The second subtask uses examples of desired data to be extracted from the corresponding webpages and learns a program to extract the data for the other rows. We design expressive domainspecific languages for URL generation and web data extraction, and present efficient synthesis algorithms for learning programs in these DSLs from few inputoutput examples. We evaluate WebRelate on 88 realworld web data integration tasks taken from online help forums and Excel product team, and show that WebRelate can learn the desired programs within few seconds using only 1 example for the majority of the tasks. @Article{POPL18p2, author = {Jeevana Priya Inala and Rishabh Singh}, title = {WebRelate: Integrating Web Data with Spreadsheets using Examples}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {2}, numpages = {28}, doi = {10.1145/3158090}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Jagadeesan, Radha 
POPL '18: "Transactions in Relaxed Memory ..."
Transactions in Relaxed Memory Architectures
Brijesh Dongol, Radha Jagadeesan, and James Riely (Brunel University London, UK; DePaul University, USA) The integration of transactions into hardware relaxed memory architectures is a topic of current research both in industry and academia. In this paper, we provide a general architectural framework for the introduction of transactions into models of relaxed memory in hardware, including the SC, TSO, ARMv8 and PPC models. Our framework incorporates flexible and expressive forms of transaction aborts and execution that have hitherto been in the realm of software transactional memory. In contrast to software transactional memory, we account for the characteristics of relaxed memory as a restricted form of distributed system, without a notion of global time. We prove abstraction theorems to demonstrate that the programmer API matches the intuitions and expectations about transactions. @Article{POPL18p18, author = {Brijesh Dongol and Radha Jagadeesan and James Riely}, title = {Transactions in Relaxed Memory Architectures}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {18}, numpages = {29}, doi = {10.1145/3158106}, year = {2018}, } Publisher's Version Article Search 

Jagannathan, Suresh 
POPL '18: "Alone Together: Compositional ..."
Alone Together: Compositional Reasoning and Inference for Weak Isolation
Gowtham Kaki, Kartik Nagar, Mahsa Najafzadeh, and Suresh Jagannathan (Purdue University, USA) Serializability is a wellunderstood correctness criterion that simplifies reasoning about the behavior of concurrent transactions by ensuring they are isolated from each other while they execute. However, enforcing serializable isolation comes at a steep cost in performance because it necessarily restricts opportunities to exploit concurrency even when such opportunities would not violate applicationspecific invariants. As a result, database systems in practice support, and often encourage, developers to implement transactions using weaker alternatives. These alternatives break the strong isolation guarantees offered by serializable transactions to permit greater concurrency. Unfortunately, the semantics of weak isolation is poorly understood, and usually explained only informally in terms of lowlevel implementation artifacts. Consequently, verifying highlevel correctness properties in such environments remains a challenging problem. To address this issue, we present a novel program logic that enables compositional reasoning about the behavior of concurrently executing weaklyisolated transactions. Recognizing that the proof burden necessary to use this logic may dissuade application developers, we also describe an inference procedure based on this foundation that ascertains the weakest isolation level that still guarantees the safety of highlevel consistency assertions associated with such transactions. The key to effective inference is the observation that weaklyisolated transactions can be viewed as functional (monadic) computations over an abstract database state, allowing us to treat their operations as state transformers over the database. This interpretation enables automated verification using offtheshelf SMT solvers. Our development is parametric over a transaction’s specific isolation semantics, allowing it to be applicable over a range of concurrency control mechanisms. Case studies and experiments on realworld applications (written in an embedded DSL in OCaml) demonstrate the utility of our approach, and provide strong evidence that automated verification of weaklyisolated transactions can be placed on the same formal footing as their stronglyisolated serializable counterparts. @Article{POPL18p27, author = {Gowtham Kaki and Kartik Nagar and Mahsa Najafzadeh and Suresh Jagannathan}, title = {Alone Together: Compositional Reasoning and Inference for Weak Isolation}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {27}, numpages = {34}, doi = {10.1145/3158115}, year = {2018}, } Publisher's Version Article Search 

Janků, Petr 
POPL '18: "String Constraints with Concatenation ..."
String Constraints with Concatenation and Transducers Solved Efficiently
Lukáš Holík , Petr Janků, Anthony W. Lin, Philipp Rümmer, and Tomáš Vojnar (Brno University of Technology, Czechia; University of Oxford, UK; Uppsala University, Sweden) String analysis is the problem of reasoning about how strings are manipulated by a program. It has numerous applications including automatic detection of crosssite scripting, and automatic testcase generation. A popular string analysis technique includes symbolic executions, which at their core use constraint solvers over the string domain, a.k.a. string solvers. Such solvers typically reason about constraints expressed in theories over strings with the concatenation operator as an atomic constraint. In recent years, researchers started to recognise the importance of incorporating the replaceall operator (i.e. replace all occurrences of a string by another string) and, more generally, finitestate transductions in the theories of strings with concatenation. Such string operations are typically crucial for reasoning about XSS vulnerabilities in web applications, especially for modelling sanitisation functions and implicit browser transductions (e.g. innerHTML). Although this results in an undecidable theory in general, it was recently shown that the straightline fragment of the theory is decidable, and is sufficiently expressive in practice. In this paper, we provide the first string solver that can reason about constraints involving both concatenation and finitestate transductions. Moreover, it has a completeness and termination guarantee for several important fragments (e.g. straightline fragment). The main challenge addressed in the paper is the prohibitive worstcase complexity of the theory (doubleexponential time), which is exponentially harder than the case without finitestate transductions. To this end, we propose a method that exploits succinct alternating finitestate automata as concise symbolic representations of string constraints. In contrast to previous approaches using nondeterministic automata, alternation offers not only exponential savings in space when representing Boolean combinations of transducers, but also a possibility of succinct representation of otherwise costly combinations of transducers and concatenation. Reasoning about the emptiness of the AFA language requires a statespace exploration in an exponentialsized graph, for which we use model checking algorithms (e.g. IC3). We have implemented our algorithm and demonstrated its efficacy on benchmarks that are derived from crosssite scripting analysis and other examples in the literature. @Article{POPL18p4, author = {Lukáš Holík and Petr Janků and Anthony W. Lin and Philipp Rümmer and Tomáš Vojnar}, title = {String Constraints with Concatenation and Transducers Solved Efficiently}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {4}, numpages = {32}, doi = {10.1145/3158092}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Jhala, Ranjit 
POPL '18: "Refinement Reflection: Complete ..."
Refinement Reflection: Complete Verification with SMT
Niki Vazou, Anish Tondwalkar, Vikraman Choudhury , Ryan G. Scott, Ryan R. Newton, Philip Wadler , and Ranjit Jhala (University of Maryland, USA; University of California at San Diego, USA; Indiana University, USA; University of Edinburgh, UK; Input Output HK, UK) We introduce Refinement Reflection, a new framework for building SMTbased deductive verifiers. The key idea is to reflect the code implementing a userdefined function into the function’s (output) refinement type. As a consequence, at uses of the function, the function definition is instantiated in the SMT logic in a precise fashion that permits decidable verification. Reflection allows the user to write equational proofs of programs just by writing other programs using patternmatching and recursion to perform casesplitting and induction. Thus, via the propositionsastypes principle, we show that reflection permits the specification of arbitrary functional correctness properties. Finally, we introduce a proofsearch algorithm called Proof by Logical Evaluation that uses techniques from model checking and abstract interpretation, to completely automate equational reasoning. We have implemented reflection in Liquid Haskell and used it to verify that the widely used instances of the Monoid, Applicative, Functor, and Monad typeclasses actually satisfy key algebraic laws required to make the clients safe, and have used reflection to build the first library that actually verifies assumptions about associativity and ordering that are crucial for safe deterministic parallelism. @Article{POPL18p53, author = {Niki Vazou and Anish Tondwalkar and Vikraman Choudhury and Ryan G. Scott and Ryan R. Newton and Philip Wadler and Ranjit Jhala}, title = {Refinement Reflection: Complete Verification with SMT}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {53}, numpages = {31}, doi = {10.1145/3158141}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Jourdan, JacquesHenri 
POPL '18: "RustBelt: Securing the Foundations ..."
RustBelt: Securing the Foundations of the Rust Programming Language
Ralf Jung , JacquesHenri Jourdan, Robbert Krebbers , and Derek Dreyer (MPISWS, Germany; Delft University of Technology, Netherlands) Rust is a new systems programming language that promises to overcome the seemingly fundamental tradeoff between highlevel safety guarantees and lowlevel control over resource management. Unfortunately, none of Rust's safety claims have been formally proven, and there is good reason to question whether they actually hold. Specifically, Rust employs a strong, ownershipbased type system, but then extends the expressive power of this core type system through libraries that internally use unsafe features. In this paper, we give the first formal (and machinechecked) safety proof for a language representing a realistic subset of Rust. Our proof is extensible in the sense that, for each new Rust library that uses unsafe features, we can say what verification condition it must satisfy in order for it to be deemed a safe extension to the language. We have carried out this verification for some of the most important libraries that are used throughout the Rust ecosystem. @Article{POPL18p66, author = {Ralf Jung and JacquesHenri Jourdan and Robbert Krebbers and Derek Dreyer}, title = {RustBelt: Securing the Foundations of the Rust Programming Language}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {66}, numpages = {34}, doi = {10.1145/3158154}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Jung, Ralf 
POPL '18: "RustBelt: Securing the Foundations ..."
RustBelt: Securing the Foundations of the Rust Programming Language
Ralf Jung , JacquesHenri Jourdan, Robbert Krebbers , and Derek Dreyer (MPISWS, Germany; Delft University of Technology, Netherlands) Rust is a new systems programming language that promises to overcome the seemingly fundamental tradeoff between highlevel safety guarantees and lowlevel control over resource management. Unfortunately, none of Rust's safety claims have been formally proven, and there is good reason to question whether they actually hold. Specifically, Rust employs a strong, ownershipbased type system, but then extends the expressive power of this core type system through libraries that internally use unsafe features. In this paper, we give the first formal (and machinechecked) safety proof for a language representing a realistic subset of Rust. Our proof is extensible in the sense that, for each new Rust library that uses unsafe features, we can say what verification condition it must satisfy in order for it to be deemed a safe extension to the language. We have carried out this verification for some of the most important libraries that are used throughout the Rust ecosystem. @Article{POPL18p66, author = {Ralf Jung and JacquesHenri Jourdan and Robbert Krebbers and Derek Dreyer}, title = {RustBelt: Securing the Foundations of the Rust Programming Language}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {66}, numpages = {34}, doi = {10.1145/3158154}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Kaki, Gowtham 
POPL '18: "Alone Together: Compositional ..."
Alone Together: Compositional Reasoning and Inference for Weak Isolation
Gowtham Kaki, Kartik Nagar, Mahsa Najafzadeh, and Suresh Jagannathan (Purdue University, USA) Serializability is a wellunderstood correctness criterion that simplifies reasoning about the behavior of concurrent transactions by ensuring they are isolated from each other while they execute. However, enforcing serializable isolation comes at a steep cost in performance because it necessarily restricts opportunities to exploit concurrency even when such opportunities would not violate applicationspecific invariants. As a result, database systems in practice support, and often encourage, developers to implement transactions using weaker alternatives. These alternatives break the strong isolation guarantees offered by serializable transactions to permit greater concurrency. Unfortunately, the semantics of weak isolation is poorly understood, and usually explained only informally in terms of lowlevel implementation artifacts. Consequently, verifying highlevel correctness properties in such environments remains a challenging problem. To address this issue, we present a novel program logic that enables compositional reasoning about the behavior of concurrently executing weaklyisolated transactions. Recognizing that the proof burden necessary to use this logic may dissuade application developers, we also describe an inference procedure based on this foundation that ascertains the weakest isolation level that still guarantees the safety of highlevel consistency assertions associated with such transactions. The key to effective inference is the observation that weaklyisolated transactions can be viewed as functional (monadic) computations over an abstract database state, allowing us to treat their operations as state transformers over the database. This interpretation enables automated verification using offtheshelf SMT solvers. Our development is parametric over a transaction’s specific isolation semantics, allowing it to be applicable over a range of concurrency control mechanisms. Case studies and experiments on realworld applications (written in an embedded DSL in OCaml) demonstrate the utility of our approach, and provide strong evidence that automated verification of weaklyisolated transactions can be placed on the same formal footing as their stronglyisolated serializable counterparts. @Article{POPL18p27, author = {Gowtham Kaki and Kartik Nagar and Mahsa Najafzadeh and Suresh Jagannathan}, title = {Alone Together: Compositional Reasoning and Inference for Weak Isolation}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {27}, numpages = {34}, doi = {10.1145/3158115}, year = {2018}, } Publisher's Version Article Search 

Kaminski, Benjamin Lucien 
POPL '18: "A New Proof Rule for AlmostSure ..."
A New Proof Rule for AlmostSure Termination
Annabelle McIver, Carroll Morgan, Benjamin Lucien Kaminski, and JoostPieter Katoen (Macquarie University, Australia; UNSW, Australia; Data61 at CSIRO, Australia; RWTH Aachen University, Germany; University College London, UK; IST Austria, Austria) We present a new proof rule for proving almostsure termination of probabilistic programs, including those that contain demonic nondeterminism. An important question for a probabilistic program is whether the probability mass of all its diverging runs is zero, that is that it terminates "almost surely". Proving that can be hard, and this paper presents a new method for doing so. It applies directly to the program's source code, even if the program contains demonic choice. Like others, we use variant functions (a.k.a. "supermartingales") that are realvalued and decrease randomly on each loop iteration; but our key innovation is that the amount as well as the probability of the decrease are parametric. We prove the soundness of the new rule, indicate where its applicability goes beyond existing rules, and explain its connection to classical results on denumerable (nondemonic) Markov chains. @Article{POPL18p33, author = {Annabelle McIver and Carroll Morgan and Benjamin Lucien Kaminski and JoostPieter Katoen}, title = {A New Proof Rule for AlmostSure Termination}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {33}, numpages = {28}, doi = {10.1145/3158121}, year = {2018}, } Publisher's Version Article Search 

Kammar, Ohad 
POPL '18: "Denotational Validation of ..."
Denotational Validation of HigherOrder Bayesian Inference
Adam Ścibior, Ohad Kammar, Matthijs Vákár, Sam Staton, Hongseok Yang, Yufei Cai, Klaus Ostermann , Sean K. Moss, Chris Heunen , and Zoubin Ghahramani (University of Cambridge, UK; MPI Tübingen, Germany; University of Oxford, UK; KAIST, South Korea; University of Tübingen, Germany; University of Edinburgh, UK; Uber AI Labs, USA) We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higherorder functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higherorder functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasiBorel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasiBorel counterpart to the MetropolisHastingsGreen theorem. @Article{POPL18p60, author = {Adam Ścibior and Ohad Kammar and Matthijs Vákár and Sam Staton and Hongseok Yang and Yufei Cai and Klaus Ostermann and Sean K. Moss and Chris Heunen and Zoubin Ghahramani}, title = {Denotational Validation of HigherOrder Bayesian Inference}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {60}, numpages = {29}, doi = {10.1145/3158148}, year = {2018}, } Publisher's Version Article Search Info 

Katoen, JoostPieter 
POPL '18: "A New Proof Rule for AlmostSure ..."
A New Proof Rule for AlmostSure Termination
Annabelle McIver, Carroll Morgan, Benjamin Lucien Kaminski, and JoostPieter Katoen (Macquarie University, Australia; UNSW, Australia; Data61 at CSIRO, Australia; RWTH Aachen University, Germany; University College London, UK; IST Austria, Austria) We present a new proof rule for proving almostsure termination of probabilistic programs, including those that contain demonic nondeterminism. An important question for a probabilistic program is whether the probability mass of all its diverging runs is zero, that is that it terminates "almost surely". Proving that can be hard, and this paper presents a new method for doing so. It applies directly to the program's source code, even if the program contains demonic choice. Like others, we use variant functions (a.k.a. "supermartingales") that are realvalued and decrease randomly on each loop iteration; but our key innovation is that the amount as well as the probability of the decrease are parametric. We prove the soundness of the new rule, indicate where its applicability goes beyond existing rules, and explain its connection to classical results on denumerable (nondemonic) Markov chains. @Article{POPL18p33, author = {Annabelle McIver and Carroll Morgan and Benjamin Lucien Kaminski and JoostPieter Katoen}, title = {A New Proof Rule for AlmostSure Termination}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {33}, numpages = {28}, doi = {10.1145/3158121}, year = {2018}, } Publisher's Version Article Search 

Khoo, SiauCheng 
POPL '18: "Automated Lemma Synthesis ..."
Automated Lemma Synthesis in SymbolicHeap Separation Logic
QuangTrung Ta, Ton Chanh Le, SiauCheng Khoo, and WeiNgan Chin (National University of Singapore, Singapore) The symbolicheap fragment of separation logic has been actively developed and advocated for verifying the memorysafety property of computer programs. At present, one of its biggest challenges is to effectively prove entailments containing inductive heap predicates. These entailments are usually proof obligations generated when verifying programs that manipulate complex data structures like linked lists, trees, or graphs. To assist in proving such entailments, this paper introduces a lemma synthesis framework, which automatically discovers lemmas to serve as eureka steps in the proofs. Mathematical induction and templatebased constraint solving are two pillars of our framework. To derive the supporting lemmas for a given entailment, the framework firstly identifies possible lemma templates from the entailment's heap structure. It then sets up unknown relations among each template's variables and conducts structural induction proof to generate constraints about these relations. Finally, it solves the constraints to find out actual definitions of the unknown relations, thus discovers the lemmas. We have integrated this framework into a prototype prover and have experimented it on various entailment benchmarks. The experimental results show that our lemmasynthesisassisted prover can prove many entailments that could not be handled by existing techniques. This new proposal opens up more opportunities to automatically reason with complex inductive heap predicates. @Article{POPL18p9, author = {QuangTrung Ta and Ton Chanh Le and SiauCheng Khoo and WeiNgan Chin}, title = {Automated Lemma Synthesis in SymbolicHeap Separation Logic}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {9}, numpages = {29}, doi = {10.1145/3158097}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Kincaid, Zachary 
POPL '18: "Nonlinear Reasoning for Invariant ..."
Nonlinear Reasoning for Invariant Synthesis
Zachary Kincaid , John Cyphert, Jason Breck, and Thomas Reps (Princeton University, USA; University of WisconsinMadison, USA; GrammaTech, USA) Automatic generation of nonlinear loop invariants is a longstanding challenge in program analysis, with many applications. For instance, reasoning about exponentials provides a way to find invariants of digitalfilter programs, and reasoning about polynomials and/or logarithms is needed for establishing invariants that describe the time or memory usage of many wellknown algorithms. An appealing approach to this challenge is to exploit the powerful recurrencesolving techniques that have been developed in the field of computer algebra, which can compute exact characterizations of nonlinear repetitive behavior. However, there is a gap between the capabilities of recurrence solvers and the needs of program analysis: (1) loop bodies are not merely systems of recurrence relationsthey may contain conditional branches, nested loops, nondeterministic assignments, etc., and (2) a client program analyzer must be able to reason about the closedform solutions produced by a recurrence solver (e.g., to prove assertions). This paper presents a method for generating nonlinear invariants of general loops based on analyzing recurrence relations. The key components are an abstract domain for reasoning about nonlinear arithmetic, a semanticsbased method for extracting recurrence relations from loop bodies, and a recurrence solver that avoids closed forms that involve complex or irrational numbers. Our technique has been implemented in a program analyzer that can analyze general loops and mutually recursive procedures. Our experiments show that our technique shows promise for nonlinear assertionchecking and resourcebound generation. @Article{POPL18p54, author = {Zachary Kincaid and John Cyphert and Jason Breck and Thomas Reps}, title = {Nonlinear Reasoning for Invariant Synthesis}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {54}, numpages = {33}, doi = {10.1145/3158142}, year = {2018}, } Publisher's Version Article Search Artifacts Functional POPL '18: "Strategy Synthesis for Linear ..." Strategy Synthesis for Linear Arithmetic Games Azadeh Farzan and Zachary Kincaid (University of Toronto, Canada; Princeton University, USA) Many problems in formal methods can be formalized as twoplayer games. For several applications—program synthesis, for example—in addition to determining which player wins the game, we are interested in computing a winning strategy for that player. This paper studies the strategy synthesis problem for games defined within the theory of linear rational arithmetic. Two types of games are considered. A satisfiability game, described by a quantified formula, is played by two players that take turns instantiating quantifiers. The objective of each player is to prove (or disprove) satisfiability of the formula. A reachability game, described by a pair of formulas defining the legal moves of each player, is played by two players that take turns choosing positions—rational vectors of some fixed dimension. The objective of each player is to reach a position where the opposing player has no legal moves (or to play the game forever). We give a complete algorithm for synthesizing winning strategies for satisfiability games and a sound (but necessarily incomplete) algorithm for synthesizing winning strategies for reachability games. @Article{POPL18p61, author = {Azadeh Farzan and Zachary Kincaid}, title = {Strategy Synthesis for Linear Arithmetic Games}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {61}, numpages = {30}, doi = {10.1145/3158149}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Knauth, Alex 
POPL '18: "Symbolic Types for Lenient ..."
Symbolic Types for Lenient Symbolic Execution
Stephen Chang, Alex Knauth, and Emina Torlak (Northeastern University, USA; University of Washington, USA) We present lambda_sym, a typed λcalculus for lenient symbolic execution, where some language constructs do not recognize symbolic values. Its type system, however, ensures safe behavior of all symbolic values in a program. Our calculus extends a base occurrence typing system with symbolic types and mutable state, making it a suitable model for both functional and imperative symbolically executed languages. Naively allowing mutation in this mixed setting introduces soundness issues, however, so we further add concreteness polymorphism, which restores soundness without rejecting too many valid programs. To show that our calculus is a useful model for a real language, we implemented Typed Rosette, a typed extension of the solveraided Rosette language. We evaluate Typed Rosette by porting a large code base, demonstrating that our type system accommodates a wide variety of symbolically executed programs. @Article{POPL18p40, author = {Stephen Chang and Alex Knauth and Emina Torlak}, title = {Symbolic Types for Lenient Symbolic Execution}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {40}, numpages = {29}, doi = {10.1145/3158128}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Ko, HsiangShang 
POPL '18: "An Axiomatic Basis for Bidirectional ..."
An Axiomatic Basis for Bidirectional Programming
HsiangShang Ko and Zhenjiang Hu (National Institute of Informatics, Japan) Among the frameworks of bidirectional transformations proposed for addressing various synchronisation (consistency maintenance) problems, Foster et al.’s [2007] asymmetric lenses have influenced the design of a generation of bidirectional programming languages. Most of these languages are based on a declarative programming model, and only allow the programmer to describe a consistency specification with ad hoc and/or awkward control over the consistency restoration behaviour. However, synchronisation problems are diverse and require vastly different consistency restoration strategies, and to cope with the diversity, the programmer must have the ability to fully control and reason about the consistency restoration behaviour. The putbackbased approach to bidirectional programming aims to provide exactly this ability, and this paper strengthens the putbackbased position by proposing the first fully fledged reasoning framework for a bidirectional language — a Hoarestyle logic for Ko et al.’s [2016] putbackbased language BiGUL. The Hoarestyle logic lets the BiGUL programmer precisely characterise the bidirectional behaviour of their programs by reasoning solely in the putback direction, thereby offering a unidirectional programming abstraction that is reasonably straightforward to work with and yet provides full control not achieved by previous approaches. The theory has been formalised and checked in Agda, but this paper presents the Hoarestyle logic in a semiformal way to make it easily understood and usable by the working BiGUL programmer. @Article{POPL18p41, author = {HsiangShang Ko and Zhenjiang Hu}, title = {An Axiomatic Basis for Bidirectional Programming}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {41}, numpages = {29}, doi = {10.1145/3158129}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Koch, Christoph E. 
POPL '18: "Unifying Analytic and StaticallyTyped ..."
Unifying Analytic and StaticallyTyped Quasiquotes
Lionel Parreaux , Antoine Voizard, Amir Shaikhha, and Christoph E. Koch (EPFL, Switzerland; University of Pennsylvania, USA) Metaprograms are programs that manipulate (generate, analyze and evaluate) other programs. These tasks are greatly facilitated by quasiquotation, a technique to construct and deconstruct program fragments using quoted code templates expressed in the syntax of the manipulated language. We argue that two main flavors of quasiquotes have existed so far: Lispstyle quasiquotes, which can both construct and deconstruct programs but may produce code that contains type mismatches and unbound variables; and MetaMLstyle quasiquotes, which rely on static typing to prevent these errors, but can only construct programs. In this paper, we show how to combine the advantages of both flavors into a unified framework: we allow the construction, deconstruction and evaluation of program fragments while ensuring that generated programs are welltyped and wellscoped, a combination unseen in previous work. We formalize our approach as λ^{{}}, a multistage calculus with code pattern matching and rewriting, and prove its type safety. We also present its realization in Squid, a metaprogramming framework for Scala, leveraging Scala’s expressive type system. To demonstrate the usefulness of our approach, we introduce speculative rewrite rules, a novel code transformation technique that makes decisive use of these capabilities, and we outline how it simplifies the design of some crucial query compiler optimizations. @Article{POPL18p13, author = {Lionel Parreaux and Antoine Voizard and Amir Shaikhha and Christoph E. Koch}, title = {Unifying Analytic and StaticallyTyped Quasiquotes}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {13}, numpages = {33}, doi = {10.1145/3158101}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Kokologiannakis, Michalis 
POPL '18: "Effective Stateless Model ..."
Effective Stateless Model Checking for C/C++ Concurrency
Michalis Kokologiannakis, Ori Lahav , Konstantinos Sagonas , and Viktor Vafeiadis (National Technical University of Athens, Greece; Tel Aviv University, Israel; Uppsala University, Sweden; MPISWS, Germany) We present a stateless model checking algorithm for verifying concurrent programs running under RC11, a repaired version of the C/C++11 memory model without dependency cycles. Unlike most previous approaches, which enumerate thread interleavings up to some partial order reduction improvements, our approach works directly on execution graphs and (in the absence of RMW instructions and SC atomics) avoids redundant exploration by construction. We have implemented a model checker, called RCMC, based on this approach and applied it to a number of challenging concurrent programs. Our experiments confirm that RCMC is significantly faster, scales better than other model checking tools, and is also more resilient to small changes in the benchmarks. @Article{POPL18p17, author = {Michalis Kokologiannakis and Ori Lahav and Konstantinos Sagonas and Viktor Vafeiadis}, title = {Effective Stateless Model Checking for C/C++ Concurrency}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {17}, numpages = {32}, doi = {10.1145/3158105}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Kraus, Nicolai 
POPL '18: "Univalent Higher Categories ..."
Univalent Higher Categories via Complete SemiSegal Types
Paolo Capriotti and Nicolai Kraus (University of Nottingham, UK) Category theory in homotopy type theory is intricate as categorical laws can only be stated ”up to homotopy”, and thus require coherences. The established notion of a univalent category (as introduced by Ahrens et al.) solves this by considering only truncated types, roughly corresponding to an ordinary category. This fails to capture many naturally occurring structures, stemming from the fact that the naturally occurring structures in homotopy type theory are not ordinary, but rather higher categories. Out of the large variety of approaches to higher category theory that mathematicians have proposed, we believe that, for type theory, the simplicial strategy is best suited. Work by Lurie and Harpaz motivates the following definition. Given the first (n+3) levels of a semisimplicial type S, we can equip S with three properties: first, contractibility of the types of certain horn fillers; second, a completeness property; and third, a truncation condition. We call this a complete semiSegal ntype. This is very similar to an earlier suggestion by Schreiber. The definition of a univalent (1) category by Ahrens et al. can easily be extended or restricted to the definition of a univalent ncategory (more precisely, (n,1)category) for n ∈ {0,1,2}, and we show that the type of complete semiSegal ntypes is equivalent to the type of univalent ncategories in these cases. Thus, we believe that the notion of a complete semiSegal ntype can be taken as the definition of a univalent ncategory. We provide a formalisation in the proof assistant Agda using a completely explicit representation of semisimplicial types for levels up to 4. @Article{POPL18p44, author = {Paolo Capriotti and Nicolai Kraus}, title = {Univalent Higher Categories via Complete SemiSegal Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {44}, numpages = {29}, doi = {10.1145/3158132}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Krebbers, Robbert 
POPL '18: "RustBelt: Securing the Foundations ..."
RustBelt: Securing the Foundations of the Rust Programming Language
Ralf Jung , JacquesHenri Jourdan, Robbert Krebbers , and Derek Dreyer (MPISWS, Germany; Delft University of Technology, Netherlands) Rust is a new systems programming language that promises to overcome the seemingly fundamental tradeoff between highlevel safety guarantees and lowlevel control over resource management. Unfortunately, none of Rust's safety claims have been formally proven, and there is good reason to question whether they actually hold. Specifically, Rust employs a strong, ownershipbased type system, but then extends the expressive power of this core type system through libraries that internally use unsafe features. In this paper, we give the first formal (and machinechecked) safety proof for a language representing a realistic subset of Rust. Our proof is extensible in the sense that, for each new Rust library that uses unsafe features, we can say what verification condition it must satisfy in order for it to be deemed a safe extension to the language. We have carried out this verification for some of the most important libraries that are used throughout the Rust ecosystem. @Article{POPL18p66, author = {Ralf Jung and JacquesHenri Jourdan and Robbert Krebbers and Derek Dreyer}, title = {RustBelt: Securing the Foundations of the Rust Programming Language}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {66}, numpages = {34}, doi = {10.1145/3158154}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional POPL '18: "IntrinsicallyTyped Definitional ..." IntrinsicallyTyped Definitional Interpreters for Imperative Languages Casper Bach Poulsen , Arjen Rouvoet , Andrew Tolmach, Robbert Krebbers , and Eelco Visser (Delft University of Technology, Netherlands; Portland State University, USA) A definitional interpreter defines the semantics of an object language in terms of the (wellknown) semantics of a host language, enabling understanding and validation of the semantics through execution. Combining a definitional interpreter with a separate type system requires a separate type safety proof. An alternative approach, at least for pure object languages, is to use a dependentlytyped language to encode the object language type system in the definition of the abstract syntax. Using such intrinsicallytyped abstract syntax definitions allows the host language type checker to verify automatically that the interpreter satisfies type safety. Does this approach scale to larger and more realistic object languages, and in particular to languages with mutable state and objects? In this paper, we describe and demonstrate techniques and libraries in Agda that successfully scale up intrinsicallytyped definitional interpreters to handle rich object languages with nontrivial binding structures and mutable state. While the resulting interpreters are certainly more complex than the simplytyped λcalculus interpreter we start with, we claim that they still meet the goals of being concise, comprehensible, and executable, while guaranteeing type safety for more elaborate object languages. We make the following contributions: (1) A dependentpassing style technique for hiding the weakening of indexed values as they propagate through monadic code. (2) An Agda library for programming with scope graphs and frames, which provides a uniform approach to dealing with name binding in intrinsicallytyped interpreters. (3) Case studies of intrinsicallytyped definitional interpreters for the simplytyped λcalculus with references (STLC+Ref) and for a large subset of Middleweight Java (MJ). @Article{POPL18p16, author = {Casper Bach Poulsen and Arjen Rouvoet and Andrew Tolmach and Robbert Krebbers and Eelco Visser}, title = {IntrinsicallyTyped Definitional Interpreters for Imperative Languages}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {16}, numpages = {34}, doi = {10.1145/3158104}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Krishna, Siddharth 
POPL '18: "Go with the Flow: Compositional ..."
Go with the Flow: Compositional Abstractions for Concurrent Data Structures
Siddharth Krishna, Dennis Shasha, and Thomas Wies (New York University, USA) Concurrent separation logics have helped to significantly simplify correctness proofs for concurrent data structures. However, a recurring problem in such proofs is that data structure abstractions that work well in the sequential setting are much harder to reason about in a concurrent setting due to complex sharing and overlays. To solve this problem, we propose a novel approach to abstracting regions in the heap by encoding the data structure invariant into a local condition on each individual node. This condition may depend on a quantity associated with the node that is computed as a fixpoint over the entire heap graph. We refer to this quantity as a flow. Flows can encode both structural properties of the heap (e.g. the reachable nodes from the root form a tree) as well as data invariants (e.g. sortedness). We then introduce the notion of a flow interface, which expresses the relies and guarantees that a heap region imposes on its context to maintain the local flow invariant with respect to the global heap. Our main technical result is that this notion leads to a new semantic model of separation logic. In this model, flow interfaces provide a general abstraction mechanism for describing complex data structures. This abstraction mechanism admits proof rules that generalize over a wide variety of data structures. To demonstrate the versatility of our approach, we show how to extend the logic RGSep with flow interfaces. We have used this new logic to prove linearizability and memory safety of nontrivial concurrent data structures. In particular, we obtain parametric linearizability proofs for concurrent dictionary algorithms that abstract from the details of the underlying data structure representation. These proofs cannot be easily expressed using the abstraction mechanisms provided by existing separation logics. @Article{POPL18p37, author = {Siddharth Krishna and Dennis Shasha and Thomas Wies}, title = {Go with the Flow: Compositional Abstractions for Concurrent Data Structures}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {37}, numpages = {31}, doi = {10.1145/3158125}, year = {2018}, } Publisher's Version Article Search 

Krishnamoorthy, Sriram 
POPL '18: "Analytical Modeling of Cache ..."
Analytical Modeling of Cache Behavior for Affine Programs
Wenlei Bao, Sriram Krishnamoorthy, LouisNoel Pouchet, and P. Sadayappan (Ohio State University, USA; Pacific Northwest National Laboratory, USA; Colorado State University, USA) Optimizing compilers implement program transformation strategies aimed at reducing data movement to or from main memory by exploiting the datacache hierarchy. However, instead of attempting to minimize the number of cache misses, very approximate cost models are used, due to the lack of precise compiletime models for misses for hierarchical caches. The current state of practice for cache miss analysis is based on accurate simulation. However, simulation requires time proportional to the dataset/problem size, as well as the number of distinct cache configurations of interest to be evaluated. This paper takes a fundamentally different approach, by focusing on polyhedral programs with static control flow. Instead of relying on costly simulation, a closedform solution for modeling of misses in a set associative cache hierarchy is developed. This solution can enable program transformation choice at compile time to optimize cache misses. A tool implementing the approach has been developed and used for validation of the framework. @Article{POPL18p32, author = {Wenlei Bao and Sriram Krishnamoorthy and LouisNoel Pouchet and P. Sadayappan}, title = {Analytical Modeling of Cache Behavior for Affine Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {32}, numpages = {26}, doi = {10.1145/3158120}, year = {2018}, } Publisher's Version Article Search 

KroghJespersen, Morten 
POPL '18: "A Logical Relation for Monadic ..."
A Logical Relation for Monadic Encapsulation of State: Proving Contextual Equivalences in the Presence of runST
Amin Timany, Léo Stefanesco, Morten KroghJespersen, and Lars Birkedal (KU Leuven, Belgium; IRIF, France; CNRS, France; University of Paris Diderot, France; Aarhus University, Denmark) We present a logical relations model of a higherorder functional programming language with impredicative polymorphism, recursive types, and a Haskellstyle ST monad type with runST. We use our logical relations model to show that runST provides proper encapsulation of state, by showing that effectful computations encapsulated by runST are heap independent. Furthermore, we show that contextual refinements and equivalences that are expected to hold for pure computations do indeed hold in the presence of runST. This is the first time such relational results have been proven for a language with monadic encapsulation of state. We have formalized all the technical development and results in Coq. @Article{POPL18p64, author = {Amin Timany and Léo Stefanesco and Morten KroghJespersen and Lars Birkedal}, title = {A Logical Relation for Monadic Encapsulation of State: Proving Contextual Equivalences in the Presence of runST}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {64}, numpages = {28}, doi = {10.1145/3158152}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Kunčar, Ondřej 
POPL '18: "Safety and Conservativity ..."
Safety and Conservativity of Definitions in HOL and Isabelle/HOL
Ondřej Kunčar and Andrei Popescu (TU Munich, Germany; Middlesex University, UK; Institute of Mathematics at Romanian Academy, Romania) Definitions are traditionally considered to be a safe mechanism for introducing concepts on top of a logic known to be consistent. In contrast to arbitrary axioms, definitions should in principle be treatable as a form of abbreviation, and thus compiled away from the theory without losing provability. In particular, definitions should form a conservative extension of the pure logic. These properties are crucial for modern interactive theorem provers, since they ensure the consistency of the logic, as well as a valid environment for total/certified functional programming. We prove these properties, namely, safety and conservativity, for HigherOrder Logic (HOL), a logic implemented in several mainstream theorem provers and relied upon by thousands of users. Some unique features of HOL, such as the requirement to give nonemptiness proofs when defining new types and the impossibility to unfold type definitions, make the proof of these properties, and also the very formulation of safety, nontrivial. Our study also factors in the essential variation of HOL definitions featured by Isabelle/HOL, a popular member of the HOLbased provers family. The current work improves on recent results which showed a weaker property, consistency of Isabelle/HOL's definitions. @Article{POPL18p24, author = {Ondřej Kunčar and Andrei Popescu}, title = {Safety and Conservativity of Definitions in HOL and Isabelle/HOL}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {24}, numpages = {26}, doi = {10.1145/3158112}, year = {2018}, } Publisher's Version Article Search Info 

Lahav, Ori 
POPL '18: "Effective Stateless Model ..."
Effective Stateless Model Checking for C/C++ Concurrency
Michalis Kokologiannakis, Ori Lahav , Konstantinos Sagonas , and Viktor Vafeiadis (National Technical University of Athens, Greece; Tel Aviv University, Israel; Uppsala University, Sweden; MPISWS, Germany) We present a stateless model checking algorithm for verifying concurrent programs running under RC11, a repaired version of the C/C++11 memory model without dependency cycles. Unlike most previous approaches, which enumerate thread interleavings up to some partial order reduction improvements, our approach works directly on execution graphs and (in the absence of RMW instructions and SC atomics) avoids redundant exploration by construction. We have implemented a model checker, called RCMC, based on this approach and applied it to a number of challenging concurrent programs. Our experiments confirm that RCMC is significantly faster, scales better than other model checking tools, and is also more resilient to small changes in the benchmarks. @Article{POPL18p17, author = {Michalis Kokologiannakis and Ori Lahav and Konstantinos Sagonas and Viktor Vafeiadis}, title = {Effective Stateless Model Checking for C/C++ Concurrency}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {17}, numpages = {32}, doi = {10.1145/3158105}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Lahiri, Shuvendu K. 
POPL '18: "Verifying Equivalence of DatabaseDriven ..."
Verifying Equivalence of DatabaseDriven Applications
Yuepeng Wang, Isil Dillig , Shuvendu K. Lahiri, and William R. Cook (University of Texas at Austin, USA; Microsoft Research, USA) This paper addresses the problem of verifying equivalence between a pair of programs that operate over databases with different schemas. This problem is particularly important in the context of web applications, which typically undergo database refactoring either for performance or maintainability reasons. While web applications should have the same externally observable behavior before and after schema migration, there are no existing tools for proving equivalence of such programs. This paper takes a first step towards solving this problem by formalizing the equivalence and refinement checking problems for databasedriven applications. We also propose a proof methodology based on the notion of bisimulation invariants over relational algebra with updates and describe a technique for synthesizing such bisimulation invariants. We have implemented the proposed technique in a tool called Mediator for verifying equivalence between databasedriven applications written in our intermediate language and evaluate our tool on 21 benchmarks extracted from textbooks and realworld web applications. Our results show that the proposed methodology can successfully verify 20 of these benchmarks. @Article{POPL18p56, author = {Yuepeng Wang and Isil Dillig and Shuvendu K. Lahiri and William R. Cook}, title = {Verifying Equivalence of DatabaseDriven Applications}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {56}, numpages = {29}, doi = {10.1145/3158144}, year = {2018}, } Publisher's Version Article Search 

Lampropoulos, Leonidas 
POPL '18: "Generating Good Generators ..."
Generating Good Generators for Inductive Relations
Leonidas Lampropoulos, Zoe Paraskevopoulou, and Benjamin C. Pierce (University of Pennsylvania, USA; Princeton University, USA) Propertybased random testing (PBRT) is widely used in the functional programming and verification communities. For testing simple properties, PBRT tools such as QuickCheck can automatically generate random inputs of a given type. But for more complex properties, effective testing often demands generators for random inputs that belong to a given type and satisfy some logical condition. QuickCheck provides a library of combinators for building such generators by hand, but this can be tedious for simple conditions and error prone for more complex ones. Fortunately, the process can often be automated. The most prominent method, narrowing, works by traversing the structure of the condition, lazily instantiating parts of the data structure as constraints involving them are met. We show how to use ideas from narrowing to compile a large subclass of Coq's inductive relations into efficient generators, avoiding the interpretive overhead of previous implementations. More importantly, the same compilation technique allows us to produce proof terms certifying that each derived generator is goodi.e., sound and complete with respect to the inductive relation it was derived from. We implement our algorithm as an extension of QuickChick, an existing tool for propertybased testing in Coq. We evaluate our method by automatically deriving good generators for the majority of the specifications in Software Foundations, a formalized textbook on programming language foundations. @Article{POPL18p45, author = {Leonidas Lampropoulos and Zoe Paraskevopoulou and Benjamin C. Pierce}, title = {Generating Good Generators for Inductive Relations}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {45}, numpages = {30}, doi = {10.1145/3158133}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Le, Ton Chanh 
POPL '18: "Automated Lemma Synthesis ..."
Automated Lemma Synthesis in SymbolicHeap Separation Logic
QuangTrung Ta, Ton Chanh Le, SiauCheng Khoo, and WeiNgan Chin (National University of Singapore, Singapore) The symbolicheap fragment of separation logic has been actively developed and advocated for verifying the memorysafety property of computer programs. At present, one of its biggest challenges is to effectively prove entailments containing inductive heap predicates. These entailments are usually proof obligations generated when verifying programs that manipulate complex data structures like linked lists, trees, or graphs. To assist in proving such entailments, this paper introduces a lemma synthesis framework, which automatically discovers lemmas to serve as eureka steps in the proofs. Mathematical induction and templatebased constraint solving are two pillars of our framework. To derive the supporting lemmas for a given entailment, the framework firstly identifies possible lemma templates from the entailment's heap structure. It then sets up unknown relations among each template's variables and conducts structural induction proof to generate constraints about these relations. Finally, it solves the constraints to find out actual definitions of the unknown relations, thus discovers the lemmas. We have integrated this framework into a prototype prover and have experimented it on various entailment benchmarks. The experimental results show that our lemmasynthesisassisted prover can prove many entailments that could not be handled by existing techniques. This new proposal opens up more opportunities to automatically reason with complex inductive heap predicates. @Article{POPL18p9, author = {QuangTrung Ta and Ton Chanh Le and SiauCheng Khoo and WeiNgan Chin}, title = {Automated Lemma Synthesis in SymbolicHeap Separation Logic}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {9}, numpages = {29}, doi = {10.1145/3158097}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Lee, Wonyeol 
POPL '18: "On Automatically Proving the ..."
On Automatically Proving the Correctness of math.h Implementations
Wonyeol Lee, Rahul Sharma, and Alex Aiken (Stanford University, USA; Microsoft Research, India) Industry standard implementations of math.h claim (often without formal proof) tight bounds on floatingpoint errors. We demonstrate a novel static analysis that proves these bounds and verifies the correctness of these implementations. Our key insight is a reduction of this verification task to a set of mathematical optimization problems that can be solved by offtheshelf computer algebra systems. We use this analysis to prove the correctness of implementations in Intel's math library automatically. Prior to this work, these implementations could only be verified with significant manual effort. @Article{POPL18p47, author = {Wonyeol Lee and Rahul Sharma and Alex Aiken}, title = {On Automatically Proving the Correctness of math.h Implementations}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {47}, numpages = {32}, doi = {10.1145/3158135}, year = {2018}, } Publisher's Version Article Search 

Li, Yangjia 
POPL '18: "Algorithmic Analysis of Termination ..."
Algorithmic Analysis of Termination Problems for Quantum Programs
Yangjia Li and Mingsheng Ying (Institute of Software at Chinese Academy of Sciences, China; University of Technology Sydney, Australia; Tsinghua University, China) We introduce the notion of linear ranking supermartingale (LRSM) for quantum programs (with nondeterministic choices, namely angelic and demonic choices). Several termination theorems are established showing that the existence of the LRSMs of a quantum program implies its termination. Thus, the termination problems of quantum programs is reduced to realisability and synthesis of LRSMs. We further show that the realisability and synthesis problem of LRSMs for quantum programs can be reduced to an SDP (SemiDefinite Programming) problem, which can be settled with the existing SDP solvers. The techniques developed in this paper are used to analyse the termination of several example quantum programs, including quantum random walks and quantum Bernoulli factory for random number generation. This work is essentially a generalisation of constraintbased approach to the corresponding problems for probabilistic programs developed in the recent literature by adding two novel ideas: (1) employing the fundamental Gleason's theorem in quantum mechanics to guide the choices of templates; and (2) a generalised Farkas' lemma in terms of observables (Hermitian operators) in quantum physics. @Article{POPL18p35, author = {Yangjia Li and Mingsheng Ying}, title = {Algorithmic Analysis of Termination Problems for Quantum Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {35}, numpages = {29}, doi = {10.1145/3158123}, year = {2018}, } Publisher's Version Article Search 

Liang, Hongjin 
POPL '18: "Progress of Concurrent Objects ..."
Progress of Concurrent Objects with Partial Methods
Hongjin Liang and Xinyu Feng (Nanjing University, China; University of Science and Technology of China, China) Various progress properties have been proposed for concurrent objects, such as waitfreedom, lockfreedom, starvationfreedom and deadlockfreedom. However, none of them applies to concurrent objects with partial methods, i.e., methods that are supposed not to return under certain circumstances. A typical example is the lock_acquire method, which must not return when the lock has already been acquired. In this paper we propose two new progress properties, partial starvationfreedom (PSF) and partial deadlockfreedom (PDF), for concurrent objects with partial methods. We also design four patterns to write abstract specifications for PSF or PDF objects under strongly or weakly fair scheduling, so that these objects contextually refine the abstract specifications. Our Abstraction Theorem shows the equivalence between PSF (or PDF) and the progressaware contextual refinement. Finally, we generalize the program logic LiLi to have a new logic to verify the PSF (or PDF) property and linearizability of concurrent objects. @Article{POPL18p20, author = {Hongjin Liang and Xinyu Feng}, title = {Progress of Concurrent Objects with Partial Methods}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {20}, numpages = {31}, doi = {10.1145/3158108}, year = {2018}, } Publisher's Version Article Search 

Lin, Anthony W. 
POPL '18: "String Constraints with Concatenation ..."
String Constraints with Concatenation and Transducers Solved Efficiently
Lukáš Holík , Petr Janků, Anthony W. Lin, Philipp Rümmer, and Tomáš Vojnar (Brno University of Technology, Czechia; University of Oxford, UK; Uppsala University, Sweden) String analysis is the problem of reasoning about how strings are manipulated by a program. It has numerous applications including automatic detection of crosssite scripting, and automatic testcase generation. A popular string analysis technique includes symbolic executions, which at their core use constraint solvers over the string domain, a.k.a. string solvers. Such solvers typically reason about constraints expressed in theories over strings with the concatenation operator as an atomic constraint. In recent years, researchers started to recognise the importance of incorporating the replaceall operator (i.e. replace all occurrences of a string by another string) and, more generally, finitestate transductions in the theories of strings with concatenation. Such string operations are typically crucial for reasoning about XSS vulnerabilities in web applications, especially for modelling sanitisation functions and implicit browser transductions (e.g. innerHTML). Although this results in an undecidable theory in general, it was recently shown that the straightline fragment of the theory is decidable, and is sufficiently expressive in practice. In this paper, we provide the first string solver that can reason about constraints involving both concatenation and finitestate transductions. Moreover, it has a completeness and termination guarantee for several important fragments (e.g. straightline fragment). The main challenge addressed in the paper is the prohibitive worstcase complexity of the theory (doubleexponential time), which is exponentially harder than the case without finitestate transductions. To this end, we propose a method that exploits succinct alternating finitestate automata as concise symbolic representations of string constraints. In contrast to previous approaches using nondeterministic automata, alternation offers not only exponential savings in space when representing Boolean combinations of transducers, but also a possibility of succinct representation of otherwise costly combinations of transducers and concatenation. Reasoning about the emptiness of the AFA language requires a statespace exploration in an exponentialsized graph, for which we use model checking algorithms (e.g. IC3). We have implemented our algorithm and demonstrated its efficacy on benchmarks that are derived from crosssite scripting analysis and other examples in the literature. @Article{POPL18p4, author = {Lukáš Holík and Petr Janků and Anthony W. Lin and Philipp Rümmer and Tomáš Vojnar}, title = {String Constraints with Concatenation and Transducers Solved Efficiently}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {4}, numpages = {32}, doi = {10.1145/3158092}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional POPL '18: "What Is Decidable about String ..." What Is Decidable about String Constraints with the ReplaceAll Function Taolue Chen, Yan Chen, Matthew Hague , Anthony W. Lin, and Zhilin Wu (University of London, UK; Institute of Software at Chinese Academy of Sciences, China; University at Chinese Academy of Sciences, China; Royal Holloway University of London, UK; University of Oxford, UK) The theory of strings with concatenation has been widely argued as the basis of constraint solving for verifying stringmanipulating programs. However, this theory is far from adequate for expressing many string constraints that are also needed in practice; for example, the use of regular constraints (pattern matching against a regular expression), and the stringreplace function (replacing either the first occurrence or all occurrences of a ``pattern'' string constant/variable/regular expression by a ``replacement'' string constant/variable), among many others. Both regular constraints and the stringreplace function are crucial for such applications as analysis of JavaScript (or more generally HTML5 applications) against crosssite scripting (XSS) vulnerabilities, which motivates us to consider a richer class of string constraints. The importance of the stringreplace function (especially the replaceall facility) is increasingly recognised, which can be witnessed by the incorporation of the function in the input languages of several string constraint solvers. Recently, it was shown that any theory of strings containing the stringreplace function (even the most restricted version where pattern/replacement strings are both constant strings) becomes undecidable if we do not impose some kind of straightline (aka acyclicity) restriction on the formulas. Despite this, the straightline restriction is still practically sensible since this condition is typically met by string constraints that are generated by symbolic execution. In this paper, we provide the first systematic study of straightline string constraints with the stringreplace function and the regular constraints as the basic operations. We show that a large class of such constraints (i.e. when only a constant string or a regular expression is permitted in the pattern) is decidable. We note that the stringreplace function, even under this restriction, is sufficiently powerful for expressing the concatenation operator and much more (e.g. extensions of regular expressions with string variables). This gives us the most expressive decidable logic containing concatenation, replace, and regular constraints under the same umbrella. Our decision procedure for the straightline fragment follows an automatatheoretic approach, and is modular in the sense that the stringreplace terms are removed one by one to generate more and more regular constraints, which can then be discharged by the stateoftheart string constraint solvers. We also show that this fragment is, in a way, a maximal decidable subclass of the straightline fragment with stringreplace and regular constraints. To this end, we show undecidability results for the following two extensions: (1) variables are permitted in the pattern parameter of the replace function, (2) length constraints are permitted. @Article{POPL18p3, author = {Taolue Chen and Yan Chen and Matthew Hague and Anthony W. Lin and Zhilin Wu}, title = {What Is Decidable about String Constraints with the ReplaceAll Function}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {3}, numpages = {29}, doi = {10.1145/3158091}, year = {2018}, } Publisher's Version Article Search 

Liu, Fengyun 
POPL '18: "Simplicitly: Foundations and ..."
Simplicitly: Foundations and Applications of Implicit Function Types
Martin Odersky, Olivier Blanvillain, Fengyun Liu, Aggelos Biboudis, Heather Miller, and Sandro Stucki (EPFL, Switzerland; Northeastern University, USA) Understanding a program entails understanding its context; dependencies, configurations and even implementations are all forms of contexts. Modern programming languages and theorem provers offer an array of constructs to define contexts, implicitly. Scala offers implicit parameters which are used pervasively, but which cannot be abstracted over. This paper describes a generalization of implicit parameters to implicit function types, a powerful way to abstract over the context in which some piece of code is run. We provide a formalization based on bidirectional typechecking that closely follows the semantics implemented by the Scala compiler. To demonstrate their range of abstraction capabilities, we present several applications that make use of implicit function types. We show how to encode the builder pattern, tagless interpreters, reader and free monads and we assess the performance of the monadic structures presented. @Article{POPL18p42, author = {Martin Odersky and Olivier Blanvillain and Fengyun Liu and Aggelos Biboudis and Heather Miller and Sandro Stucki}, title = {Simplicitly: Foundations and Applications of Implicit Function Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {42}, numpages = {29}, doi = {10.1145/3158130}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Löding, Christof 
POPL '18: "Foundations for Natural Proofs ..."
Foundations for Natural Proofs and Quantifier Instantiation
Christof Löding, P. Madhusudan , and Lucas Peña (RWTH Aachen University, Germany; University of Illinois at UrbanaChampaign, USA) We give foundational results that explain the efficacy of heuristics used for dealing with quantified formulas and recursive definitions. We develop a framework for first order logic (FOL) over an uninterpreted combination of background theories. Our central technical result is that systematic term instantiation is complete for a fragment of FOL that we call safe. Coupled with the fact that unfolding recursive definitions is essentially term instantiation and with the observation that heap verification engines generate verification conditions in the safe fragment explains the efficacy of verification engines like natural proofs that resort to such heuristics. Furthermore, we study recursive definitions with least fixpoint semantics and show that though they are not amenable to complete procedures, we can systematically introduce induction principles that in practice bridge the divide between FOL and FOL with recursive definitions. @Article{POPL18p10, author = {Christof Löding and P. Madhusudan and Lucas Peña}, title = {Foundations for Natural Proofs and Quantifier Instantiation}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {10}, numpages = {30}, doi = {10.1145/3158098}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Losa, Giuliano 
POPL '18: "Reducing Liveness to Safety ..."
Reducing Liveness to Safety in FirstOrder Logic
Oded Padon, Jochen Hoenicke, Giuliano Losa, Andreas Podelski , Mooly Sagiv, and Sharon Shoham (Tel Aviv University, Israel; University of Freiburg, Germany; University of California at Los Angeles, USA) We develop a new technique for verifying temporal properties of infinitestate (distributed) systems. The main idea is to reduce the temporal verification problem to the problem of verifying the safety of infinitestate systems expressed in firstorder logic. This allows to leverage existing techniques for safety verification to verify temporal properties of interesting distributed protocols, including some that have not been mechanically verified before. We model infinitestate systems using firstorder logic, and use firstorder temporal logic (FOLTL) to specify temporal properties. This general formalism allows to naturally model distributed systems, while supporting both unboundedparallelism (where the system is allowed to dynamically create processes), and infinitestate per process. The traditional approach for verifying temporal properties of infinitestate systems employs wellfounded relations (e.g. using linear arithmetic ranking functions). In contrast, our approach is based the idea of fair cycle detection. In finitestate systems, temporal verification can always be reduced to fair cycle detection (a system contains a fair cycle if it revisits a state after satisfying all fairness constraints). However, with both infinitely many states and infinitely many fairness constraints, a straightforward reduction to fair cycle detection is unsound. To regain soundness, we augment the infinitestate transition system by a dynamically computed finite set, that exploits the locality of transitions. This set lets us define a form of fair cycle detection that is sound in the presence of both infinitely many states, and infinitely many fairness constraints. Our approach allows a new style of temporal verification that does not explicitly involve ranking functions. This fits well with pure firstorder verification which does not explicitly reason about numerical values. In particular, it can be used with effectively propositional firstorder logic (EPR), in which case checking verification conditions is decidable. We applied our technique to verify temporal properties of several interesting protocols. To the best of our knowledge, we have obtained the first mechanized liveness proof for both TLB Shootdown, and Stoppable Paxos. @Article{POPL18p26, author = {Oded Padon and Jochen Hoenicke and Giuliano Losa and Andreas Podelski and Mooly Sagiv and Sharon Shoham}, title = {Reducing Liveness to Safety in FirstOrder Logic}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {26}, numpages = {33}, doi = {10.1145/3158114}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Madhusudan, P. 
POPL '18: "Foundations for Natural Proofs ..."
Foundations for Natural Proofs and Quantifier Instantiation
Christof Löding, P. Madhusudan , and Lucas Peña (RWTH Aachen University, Germany; University of Illinois at UrbanaChampaign, USA) We give foundational results that explain the efficacy of heuristics used for dealing with quantified formulas and recursive definitions. We develop a framework for first order logic (FOL) over an uninterpreted combination of background theories. Our central technical result is that systematic term instantiation is complete for a fragment of FOL that we call safe. Coupled with the fact that unfolding recursive definitions is essentially term instantiation and with the observation that heap verification engines generate verification conditions in the safe fragment explains the efficacy of verification engines like natural proofs that resort to such heuristics. Furthermore, we study recursive definitions with least fixpoint semantics and show that though they are not amenable to complete procedures, we can systematically introduce induction principles that in practice bridge the divide between FOL and FOL with recursive definitions. @Article{POPL18p10, author = {Christof Löding and P. Madhusudan and Lucas Peña}, title = {Foundations for Natural Proofs and Quantifier Instantiation}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {10}, numpages = {30}, doi = {10.1145/3158098}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Maillard, Kenji 
POPL '18: "Recalling a Witness: Foundations ..."
Recalling a Witness: Foundations and Applications of Monotonic State
Danel Ahman, Cédric Fournet, Cătălin Hriţcu, Kenji Maillard , Aseem Rastogi, and Nikhil Swamy (Inria, France; Microsoft Research, UK; ENS Paris, France; Microsoft Research, India; Microsoft Research, USA) We provide a way to ease the verification of programs whose state evolves monotonically. The main idea is that a property witnessed in a prior state can be soundly recalled in the current state, provided (1) state evolves according to a given preorder, and (2) the property is preserved by this preorder. In many scenarios, such monotonic reasoning yields concise modular proofs, saving the need for explicit program invariants. We distill our approach into the monotonicstate monad, a general yet compact interface for Hoarestyle reasoning about monotonic state in a dependently typed language. We prove the soundness of the monotonicstate monad and use it as a unified foundation for reasoning about monotonic state in the F^{⋆} verification system. Based on this foundation, we build libraries for various mutable data structures like monotonic references and apply these libraries at scale to the verification of several distributed applications. @Article{POPL18p65, author = {Danel Ahman and Cédric Fournet and Cătălin Hriţcu and Kenji Maillard and Aseem Rastogi and Nikhil Swamy}, title = {Recalling a Witness: Foundations and Applications of Monotonic State}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {65}, numpages = {30}, doi = {10.1145/3158153}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Majumdar, Rupak 
POPL '18: "Why Is Random Testing Effective ..."
Why Is Random Testing Effective for Partition Tolerance Bugs?
Rupak Majumdar and Filip Niksic (MPISWS, Germany) Random testing has proven to be an effective way to catch bugs in distributed systems in the presence of network partition faults. This is surprising, as the space of potentially faulty executions is enormous, and the bugs depend on a subtle interplay between sequences of operations and faults. We provide a theoretical justification of the effectiveness of random testing in this context. First, we show a general construction, using the probabilistic method from combinatorics, that shows that whenever a random test covers a fixed coverage goal with sufficiently high probability, a small randomlychosen set of tests achieves full coverage with high probability. In particular, we show that our construction can give test sets exponentially smaller than systematic enumeration. Second, based on an empirical study of many bugs found by random testing in production distributed systems, we introduce notions of test coverage relating to network partition faults which are effective in finding bugs. Finally, we show using combinatorial arguments that for these notions of test coverage we introduce, we can find a lower bound on the probability that a random test covers a given goal. Our general construction then explains why random testing tools achieve good coverageand hence, find bugsquickly. While we formulate our results in terms of network partition faults, our construction provides a step towards rigorous analysis of random testing algorithms, and can be applicable in other scenarios. @Article{POPL18p46, author = {Rupak Majumdar and Filip Niksic}, title = {Why Is Random Testing Effective for Partition Tolerance Bugs?}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {46}, numpages = {24}, doi = {10.1145/3158134}, year = {2018}, } Publisher's Version Article Search 

Maksimović, Petar 
POPL '18: "JaVerT: JavaScript Verification ..."
JaVerT: JavaScript Verification Toolchain
José Fragoso Santos, Petar Maksimović, Daiva Naudžiūnienė, Thomas Wood, and Philippa Gardner (Imperial College London, UK; Mathematical Institute SASA, Serbia) The dynamic nature of JavaScript and its complex semantics make it a difficult target for logicbased verification. We introduce JaVerT, a semiautomatic JavaScript Verification Toolchain, based on separation logic and aimed at the specialist developer wanting rich, mechanically verified specifications of critical JavaScript code. To specify JavaScript programs, we design abstractions that capture its key heap structures (for example, prototype chains and function closures), allowing the developer to write clear and succinct specifications with minimal knowledge of the JavaScript internals. To verify JavaScript programs, we develop JaVerT, a verification pipeline consisting of: JS2JSIL, a welltested compiler from JavaScript to JSIL, an intermediate goto language capturing the fundamental dynamic features of JavaScript; JSIL Verify, a semiautomatic verification tool based on a sound JSIL separation logic; and verified axiomatic specifications of the JavaScript internal functions. Using JaVerT, we verify functional correctness properties of: datastructure libraries (keyvalue map, priority queue) written in an objectoriented style; operations on data structures such as binary search trees (BSTs) and lists; examples illustrating function closures; and test cases from the official ECMAScript test suite. The verification times suggest that reasoning about larger, more complex code using JaVerT is feasible. @Article{POPL18p50, author = {José Fragoso Santos and Petar Maksimović and Daiva Naudžiūnienė and Thomas Wood and Philippa Gardner}, title = {JaVerT: JavaScript Verification Toolchain}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {50}, numpages = {33}, doi = {10.1145/3158138}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Mazza, Damiano 
POPL '18: "Polyadic Approximations, Fibrations ..."
Polyadic Approximations, Fibrations and Intersection Types
Damiano Mazza, Luc Pellissier, and Pierre Vial (CNRS, France; University of Paris 13, France; University of Paris Diderot, France) Starting from an exact correspondence between linear approximations and nonidempotent intersection types, we develop a general framework for building systems of intersection types characterizing normalization properties. We show how this construction, which uses in a fundamental way Melliès and Zeilberger's ``type systems as functors'' viewpoint, allows us to recover equivalent versions of every well known intersection type system (including Coppo and Dezani's original system, as well as its nonidempotent variants independently introduced by Gardner and de Carvalho). We also show how new systems of intersection types may be built almost automatically in this way. @Article{POPL18p6, author = {Damiano Mazza and Luc Pellissier and Pierre Vial}, title = {Polyadic Approximations, Fibrations and Intersection Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {6}, numpages = {28}, doi = {10.1145/3158094}, year = {2018}, } Publisher's Version Article Search 

McIver, Annabelle 
POPL '18: "A New Proof Rule for AlmostSure ..."
A New Proof Rule for AlmostSure Termination
Annabelle McIver, Carroll Morgan, Benjamin Lucien Kaminski, and JoostPieter Katoen (Macquarie University, Australia; UNSW, Australia; Data61 at CSIRO, Australia; RWTH Aachen University, Germany; University College London, UK; IST Austria, Austria) We present a new proof rule for proving almostsure termination of probabilistic programs, including those that contain demonic nondeterminism. An important question for a probabilistic program is whether the probability mass of all its diverging runs is zero, that is that it terminates "almost surely". Proving that can be hard, and this paper presents a new method for doing so. It applies directly to the program's source code, even if the program contains demonic choice. Like others, we use variant functions (a.k.a. "supermartingales") that are realvalued and decrease randomly on each loop iteration; but our key innovation is that the amount as well as the probability of the decrease are parametric. We prove the soundness of the new rule, indicate where its applicability goes beyond existing rules, and explain its connection to classical results on denumerable (nondemonic) Markov chains. @Article{POPL18p33, author = {Annabelle McIver and Carroll Morgan and Benjamin Lucien Kaminski and JoostPieter Katoen}, title = {A New Proof Rule for AlmostSure Termination}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {33}, numpages = {28}, doi = {10.1145/3158121}, year = {2018}, } Publisher's Version Article Search 

Melo, Leandro T. C. 
POPL '18: "Inference of Static Semantics ..."
Inference of Static Semantics for Incomplete C Programs
Leandro T. C. Melo, Rodrigo G. Ribeiro, Marcus R. de Araújo, and Fernando Magno Quintão Pereira (Federal University of Minas Gerais, Brazil; Federal University of Ouro Preto, Brazil) Incomplete source code naturally emerges in software development: during the design phase, while evolving, testing and analyzing programs. Therefore, the ability to understand partial programs is a valuable asset. However, this problem is still unsolved in the C programming language. Difficulties stem from the fact that parsing C requires, not only syntax, but also semantic information. Furthermore, inferring types so that they respect C's type system is a challenging task. In this paper we present a technique that lets us solve these problems. We provide a unificationbased type inference capable of dealing with C intricacies. The ideas we present let us reconstruct partial C programs into complete welltyped ones. Such program reconstruction has several applications: enabling static analysis tools in scenarios where software components may be absent; improving static analysis tools that do not rely on buildspecifications; allowing stubgeneration and testing tools to work on snippets; and assisting programmers on the extraction of reusable datastructures out of the program parts that use them. Our evaluation is performed on source code from a variety of C libraries such as GNU's Coreutils, GNULib, GNOME's GLib, and GDSL; on implementations from Sedgewick's books; and on snippets from popular opensource projects like CPython, FreeBSD, and Git. @Article{POPL18p29, author = {Leandro T. C. Melo and Rodrigo G. Ribeiro and Marcus R. de Araújo and Fernando Magno Quintão Pereira}, title = {Inference of Static Semantics for Incomplete C Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {29}, numpages = {28}, doi = {10.1145/3158117}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Michalevsky, Yan 
POPL '18: "Online Detection of Effectively ..."
Online Detection of Effectively Callback Free Objects with Applications to Smart Contracts
Shelly Grossman, Ittai Abraham, Guy GolanGueta, Yan Michalevsky, Noam Rinetzky, Mooly Sagiv, and Yoni Zohar (Tel Aviv University, Israel; VMware, USA; Stanford University, USA) Callbacks are essential in many programming environments, but drastically complicate program understanding and reasoning because they allow to mutate object's local states by external objects in unexpected fashions, thus breaking modularity. The famous DAO bug in the cryptocurrency framework Ethereum, employed callbacks to steal $150M. We define the notion of Effectively Callback Free (ECF) objects in order to allow callbacks without preventing modular reasoning. An object is ECF in a given execution trace if there exists an equivalent execution trace without callbacks to this object. An object is ECF if it is ECF in every possible execution trace. We study the decidability of dynamically checking ECF in a given execution trace and statically checking if an object is ECF. We also show that dynamically checking ECF in Ethereum is feasible and can be done online. By running the history of all execution traces in Ethereum, we were able to verify that virtually all existing contract executions, excluding these of the DAO or of contracts with similar known vulnerabilities, are ECF. Finally, we show that ECF, whether it is verified dynamically or statically, enables modular reasoning about objects with encapsulated state. @Article{POPL18p48, author = {Shelly Grossman and Ittai Abraham and Guy GolanGueta and Yan Michalevsky and Noam Rinetzky and Mooly Sagiv and Yoni Zohar}, title = {Online Detection of Effectively Callback Free Objects with Applications to Smart Contracts}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {48}, numpages = {28}, doi = {10.1145/3158136}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Miller, Heather 
POPL '18: "Simplicitly: Foundations and ..."
Simplicitly: Foundations and Applications of Implicit Function Types
Martin Odersky, Olivier Blanvillain, Fengyun Liu, Aggelos Biboudis, Heather Miller, and Sandro Stucki (EPFL, Switzerland; Northeastern University, USA) Understanding a program entails understanding its context; dependencies, configurations and even implementations are all forms of contexts. Modern programming languages and theorem provers offer an array of constructs to define contexts, implicitly. Scala offers implicit parameters which are used pervasively, but which cannot be abstracted over. This paper describes a generalization of implicit parameters to implicit function types, a powerful way to abstract over the context in which some piece of code is run. We provide a formalization based on bidirectional typechecking that closely follows the semantics implemented by the Scala compiler. To demonstrate their range of abstraction capabilities, we present several applications that make use of implicit function types. We show how to encode the builder pattern, tagless interpreters, reader and free monads and we assess the performance of the monadic structures presented. @Article{POPL18p42, author = {Martin Odersky and Olivier Blanvillain and Fengyun Liu and Aggelos Biboudis and Heather Miller and Sandro Stucki}, title = {Simplicitly: Foundations and Applications of Implicit Function Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {42}, numpages = {29}, doi = {10.1145/3158130}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Miltner, Anders 
POPL '18: "Synthesizing Bijective Lenses ..."
Synthesizing Bijective Lenses
Anders Miltner, Kathleen Fisher, Benjamin C. Pierce , David Walker, and Steve Zdancewic (Princeton University, USA; Tufts University, USA; University of Pennsylvania, USA) Bidirectional transformations between different data representations occur frequently in modern software systems. They appear as serializers and deserializers, as parsers and pretty printers, as database views and view updaters, and as a multitude of different kinds of ad hoc data converters. Manually building bidirectional transformationsby writing two separate functions that are intended to be inversesis tedious and error prone. A better approach is to use a domainspecific language in which both directions can be written as a single expression. However, these domainspecific languages can be difficult to program in, requiring programmers to manage fiddly details while working in a complex type system. We present an alternative approach. Instead of coding transformations manually, we synthesize them from declarative format descriptions and examples. Specifically, we present Optician, a tool for typedirected synthesis of bijective string transformers. The inputs to Optician are a pair of ordinary regular expressions representing two data formats and a few concrete examples for disambiguation. The output is a welltyped program in Boomerang (a bidirectional language based on the theory of lenses). The main technical challenge involves navigating the vast program search space efficiently. In particular, and unlike most prior work on typedirected synthesis, our system operates in the context of a language with a rich equivalence relation on types (the theory of regular expressions). Consequently, program synthesis requires search in two dimensions: First, our synthesis algorithm must find a pair of "syntactically compatible types," and second, using the structure of those types, it must find a type and examplecompliant term. Our key insight is that it is possible to reduce the size of this search space without losing any computational power by defining a new language of lenses designed specifically for synthesis. The new language is free from arbitrary function composition and operates only over types and terms in a new disjunctive normal form. We prove (1) our new language is just as powerful as a more natural, compositional, and declarative language and (2) our synthesis algorithm is sound and complete with respect to the new language. We also demonstrate empirically that our new language changes the synthesis problem from one that admits intractable solutions to one that admits highly efficient solutions, able to synthesize intricate lenses between complex file formats in seconds. We evaluate Optician on a benchmark suite of 39 examples that includes both microbenchmarks and realistic examples derived from other data management systems including Flash Fill, a tool for synthesizing string transformations in spreadsheets, and Augeas, a tool for bidirectional processing of Linux system configuration files. @Article{POPL18p1, author = {Anders Miltner and Kathleen Fisher and Benjamin C. Pierce and David Walker and Steve Zdancewic}, title = {Synthesizing Bijective Lenses}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {1}, numpages = {30}, doi = {10.1145/3158089}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Morgan, Carroll 
POPL '18: "A New Proof Rule for AlmostSure ..."
A New Proof Rule for AlmostSure Termination
Annabelle McIver, Carroll Morgan, Benjamin Lucien Kaminski, and JoostPieter Katoen (Macquarie University, Australia; UNSW, Australia; Data61 at CSIRO, Australia; RWTH Aachen University, Germany; University College London, UK; IST Austria, Austria) We present a new proof rule for proving almostsure termination of probabilistic programs, including those that contain demonic nondeterminism. An important question for a probabilistic program is whether the probability mass of all its diverging runs is zero, that is that it terminates "almost surely". Proving that can be hard, and this paper presents a new method for doing so. It applies directly to the program's source code, even if the program contains demonic choice. Like others, we use variant functions (a.k.a. "supermartingales") that are realvalued and decrease randomly on each loop iteration; but our key innovation is that the amount as well as the probability of the decrease are parametric. We prove the soundness of the new rule, indicate where its applicability goes beyond existing rules, and explain its connection to classical results on denumerable (nondemonic) Markov chains. @Article{POPL18p33, author = {Annabelle McIver and Carroll Morgan and Benjamin Lucien Kaminski and JoostPieter Katoen}, title = {A New Proof Rule for AlmostSure Termination}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {33}, numpages = {28}, doi = {10.1145/3158121}, year = {2018}, } Publisher's Version Article Search 

Moss, Sean K. 
POPL '18: "Denotational Validation of ..."
Denotational Validation of HigherOrder Bayesian Inference
Adam Ścibior, Ohad Kammar, Matthijs Vákár, Sam Staton, Hongseok Yang, Yufei Cai, Klaus Ostermann , Sean K. Moss, Chris Heunen , and Zoubin Ghahramani (University of Cambridge, UK; MPI Tübingen, Germany; University of Oxford, UK; KAIST, South Korea; University of Tübingen, Germany; University of Edinburgh, UK; Uber AI Labs, USA) We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higherorder functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higherorder functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasiBorel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasiBorel counterpart to the MetropolisHastingsGreen theorem. @Article{POPL18p60, author = {Adam Ścibior and Ohad Kammar and Matthijs Vákár and Sam Staton and Hongseok Yang and Yufei Cai and Klaus Ostermann and Sean K. Moss and Chris Heunen and Zoubin Ghahramani}, title = {Denotational Validation of HigherOrder Bayesian Inference}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {60}, numpages = {29}, doi = {10.1145/3158148}, year = {2018}, } Publisher's Version Article Search Info 

Murawski, Andrzej S. 
POPL '18: "Linearity in HigherOrder ..."
Linearity in HigherOrder Recursion Schemes
Pierre Clairambault, Charles Grellois, and Andrzej S. Murawski (University of Lyon, France; CNRS, France; ENS Lyon, France; Claude Bernard University Lyon 1, France; LIP, France; Inria, France; AixMarseille University, France; ENSAM, France; University of Toulon, France; University of Oxford, UK) Higherorder recursion schemes (HORS) have recently emerged as a promising foundation for higherorder program verification. We examine the impact of enriching HORS with linear types. To that end, we introduce two frameworks that blend nonlinear and linear types: a variant of the λY calculus and an extension of HORS, called linear HORS (LHORS). First we prove that the two formalisms are equivalent and there exist polynomialtime translations between them. Then, in order to support modelchecking of (trees generated by) LHORS, we propose a refined version of alternating parity tree automata, called LNAPTA, whose behaviour depends on information about linearity. We show that the complexity of LNAPTA modelchecking for LHORS depends on two typetheoretic parameters: linear order and linear depth. The former is in general smaller than the standard notion of order and ignores linear function spaces. In contrast, the latter measures the depth of linear clusters inside a type. Our main result states that LNAPTA modelchecking of LHORS of linear order n is nEXPTIMEcomplete, when linear depth is fixed. This generalizes and improves upon the classic result of Ong, which relies on the standard notion of order. To illustrate the significance of the result, we consider two applications: the MSO modelchecking problem on variants of HORS with case distinction (RSFD and HORSC) on a finite domain and a callbyvalue resource verification problem. In both cases, decidability can be established by translation into HORS, but the implied complexity bounds will be suboptimal due to increases in type order. In contrast, we show that the complexity bounds derived by translations into LHORS and appealing to our result are optimal in that they match the respective hardness results. @Article{POPL18p39, author = {Pierre Clairambault and Charles Grellois and Andrzej S. Murawski}, title = {Linearity in HigherOrder Recursion Schemes}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {39}, numpages = {29}, doi = {10.1145/3158127}, year = {2018}, } Publisher's Version Article Search 

Nagar, Kartik 
POPL '18: "Alone Together: Compositional ..."
Alone Together: Compositional Reasoning and Inference for Weak Isolation
Gowtham Kaki, Kartik Nagar, Mahsa Najafzadeh, and Suresh Jagannathan (Purdue University, USA) Serializability is a wellunderstood correctness criterion that simplifies reasoning about the behavior of concurrent transactions by ensuring they are isolated from each other while they execute. However, enforcing serializable isolation comes at a steep cost in performance because it necessarily restricts opportunities to exploit concurrency even when such opportunities would not violate applicationspecific invariants. As a result, database systems in practice support, and often encourage, developers to implement transactions using weaker alternatives. These alternatives break the strong isolation guarantees offered by serializable transactions to permit greater concurrency. Unfortunately, the semantics of weak isolation is poorly understood, and usually explained only informally in terms of lowlevel implementation artifacts. Consequently, verifying highlevel correctness properties in such environments remains a challenging problem. To address this issue, we present a novel program logic that enables compositional reasoning about the behavior of concurrently executing weaklyisolated transactions. Recognizing that the proof burden necessary to use this logic may dissuade application developers, we also describe an inference procedure based on this foundation that ascertains the weakest isolation level that still guarantees the safety of highlevel consistency assertions associated with such transactions. The key to effective inference is the observation that weaklyisolated transactions can be viewed as functional (monadic) computations over an abstract database state, allowing us to treat their operations as state transformers over the database. This interpretation enables automated verification using offtheshelf SMT solvers. Our development is parametric over a transaction’s specific isolation semantics, allowing it to be applicable over a range of concurrency control mechanisms. Case studies and experiments on realworld applications (written in an embedded DSL in OCaml) demonstrate the utility of our approach, and provide strong evidence that automated verification of weaklyisolated transactions can be placed on the same formal footing as their stronglyisolated serializable counterparts. @Article{POPL18p27, author = {Gowtham Kaki and Kartik Nagar and Mahsa Najafzadeh and Suresh Jagannathan}, title = {Alone Together: Compositional Reasoning and Inference for Weak Isolation}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {27}, numpages = {34}, doi = {10.1145/3158115}, year = {2018}, } Publisher's Version Article Search 

Najafzadeh, Mahsa 
POPL '18: "Alone Together: Compositional ..."
Alone Together: Compositional Reasoning and Inference for Weak Isolation
Gowtham Kaki, Kartik Nagar, Mahsa Najafzadeh, and Suresh Jagannathan (Purdue University, USA) Serializability is a wellunderstood correctness criterion that simplifies reasoning about the behavior of concurrent transactions by ensuring they are isolated from each other while they execute. However, enforcing serializable isolation comes at a steep cost in performance because it necessarily restricts opportunities to exploit concurrency even when such opportunities would not violate applicationspecific invariants. As a result, database systems in practice support, and often encourage, developers to implement transactions using weaker alternatives. These alternatives break the strong isolation guarantees offered by serializable transactions to permit greater concurrency. Unfortunately, the semantics of weak isolation is poorly understood, and usually explained only informally in terms of lowlevel implementation artifacts. Consequently, verifying highlevel correctness properties in such environments remains a challenging problem. To address this issue, we present a novel program logic that enables compositional reasoning about the behavior of concurrently executing weaklyisolated transactions. Recognizing that the proof burden necessary to use this logic may dissuade application developers, we also describe an inference procedure based on this foundation that ascertains the weakest isolation level that still guarantees the safety of highlevel consistency assertions associated with such transactions. The key to effective inference is the observation that weaklyisolated transactions can be viewed as functional (monadic) computations over an abstract database state, allowing us to treat their operations as state transformers over the database. This interpretation enables automated verification using offtheshelf SMT solvers. Our development is parametric over a transaction’s specific isolation semantics, allowing it to be applicable over a range of concurrency control mechanisms. Case studies and experiments on realworld applications (written in an embedded DSL in OCaml) demonstrate the utility of our approach, and provide strong evidence that automated verification of weaklyisolated transactions can be placed on the same formal footing as their stronglyisolated serializable counterparts. @Article{POPL18p27, author = {Gowtham Kaki and Kartik Nagar and Mahsa Najafzadeh and Suresh Jagannathan}, title = {Alone Together: Compositional Reasoning and Inference for Weak Isolation}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {27}, numpages = {34}, doi = {10.1145/3158115}, year = {2018}, } Publisher's Version Article Search 

Naudžiūnienė, Daiva 
POPL '18: "JaVerT: JavaScript Verification ..."
JaVerT: JavaScript Verification Toolchain
José Fragoso Santos, Petar Maksimović, Daiva Naudžiūnienė, Thomas Wood, and Philippa Gardner (Imperial College London, UK; Mathematical Institute SASA, Serbia) The dynamic nature of JavaScript and its complex semantics make it a difficult target for logicbased verification. We introduce JaVerT, a semiautomatic JavaScript Verification Toolchain, based on separation logic and aimed at the specialist developer wanting rich, mechanically verified specifications of critical JavaScript code. To specify JavaScript programs, we design abstractions that capture its key heap structures (for example, prototype chains and function closures), allowing the developer to write clear and succinct specifications with minimal knowledge of the JavaScript internals. To verify JavaScript programs, we develop JaVerT, a verification pipeline consisting of: JS2JSIL, a welltested compiler from JavaScript to JSIL, an intermediate goto language capturing the fundamental dynamic features of JavaScript; JSIL Verify, a semiautomatic verification tool based on a sound JSIL separation logic; and verified axiomatic specifications of the JavaScript internal functions. Using JaVerT, we verify functional correctness properties of: datastructure libraries (keyvalue map, priority queue) written in an objectoriented style; operations on data structures such as binary search trees (BSTs) and lists; examples illustrating function closures; and test cases from the official ECMAScript test suite. The verification times suggest that reasoning about larger, more complex code using JaVerT is feasible. @Article{POPL18p50, author = {José Fragoso Santos and Petar Maksimović and Daiva Naudžiūnienė and Thomas Wood and Philippa Gardner}, title = {JaVerT: JavaScript Verification Toolchain}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {50}, numpages = {33}, doi = {10.1145/3158138}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Newton, Ryan R. 
POPL '18: "Linear Haskell: Practical ..."
Linear Haskell: Practical Linearity in a HigherOrder Polymorphic Language
JeanPhilippe Bernardy, Mathieu Boespflug, Ryan R. Newton, Simon Peyton Jones, and Arnaud Spiwack (University of Gothenburg, Sweden; Tweag I/O, France; Indiana University, USA; Microsoft Research, UK) Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind: backwardscompatibility and code reuse across linear and nonlinear users of a library. Only then can the benefits of linear types permeate conventional functional programming. Rather than bifurcate types into linear and nonlinear counterparts, we instead attach linearity to function arrows. Linear functions can receive inputs from linearlybound values, but can also operate over unrestricted, regular values. To demonstrate the efficacy of our linear type system — both how easy it can be integrated in an existing language implementation and how streamlined it makes it to write programs with linear types — we implemented our type system in ghc, the leading Haskell compiler, and demonstrate two kinds of applications of linear types: mutable data with pure interfaces; and enforcing protocols in I/Operforming functions. @Article{POPL18p5, author = {JeanPhilippe Bernardy and Mathieu Boespflug and Ryan R. Newton and Simon Peyton Jones and Arnaud Spiwack}, title = {Linear Haskell: Practical Linearity in a HigherOrder Polymorphic Language}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {5}, numpages = {29}, doi = {10.1145/3158093}, year = {2018}, } Publisher's Version Article Search Artifacts Functional POPL '18: "Refinement Reflection: Complete ..." Refinement Reflection: Complete Verification with SMT Niki Vazou, Anish Tondwalkar, Vikraman Choudhury , Ryan G. Scott, Ryan R. Newton, Philip Wadler , and Ranjit Jhala (University of Maryland, USA; University of California at San Diego, USA; Indiana University, USA; University of Edinburgh, UK; Input Output HK, UK) We introduce Refinement Reflection, a new framework for building SMTbased deductive verifiers. The key idea is to reflect the code implementing a userdefined function into the function’s (output) refinement type. As a consequence, at uses of the function, the function definition is instantiated in the SMT logic in a precise fashion that permits decidable verification. Reflection allows the user to write equational proofs of programs just by writing other programs using patternmatching and recursion to perform casesplitting and induction. Thus, via the propositionsastypes principle, we show that reflection permits the specification of arbitrary functional correctness properties. Finally, we introduce a proofsearch algorithm called Proof by Logical Evaluation that uses techniques from model checking and abstract interpretation, to completely automate equational reasoning. We have implemented reflection in Liquid Haskell and used it to verify that the widely used instances of the Monoid, Applicative, Functor, and Monad typeclasses actually satisfy key algebraic laws required to make the clients safe, and have used reflection to build the first library that actually verifies assumptions about associativity and ordering that are crucial for safe deterministic parallelism. @Article{POPL18p53, author = {Niki Vazou and Anish Tondwalkar and Vikraman Choudhury and Ryan G. Scott and Ryan R. Newton and Philip Wadler and Ranjit Jhala}, title = {Refinement Reflection: Complete Verification with SMT}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {53}, numpages = {31}, doi = {10.1145/3158141}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Nguyễn, Phúc C. 
POPL '18: "Soft Contract Verification ..."
Soft Contract Verification for HigherOrder Stateful Programs
Phúc C. Nguyễn, Thomas Gilray, Sam TobinHochstadt, and David Van Horn (University of Maryland, USA; Indiana University, USA) Software contracts allow programmers to state rich program properties using the full expressive power of an object language. However, since they are enforced at runtime, monitoring contracts imposes significant overhead and delays error discovery. So contract veri cation aims to guarantee all or most of these properties ahead of time, enabling valuable optimizations and yielding a more general assurance of correctness. Existing methods for static contract verification satisfy the needs of more restricted target languages, but fail to address the challenges unique to those conjoining untyped, dynamic programming, higherorder functions, modularity, and statefulness. Our approach tackles all these features at once, in the context of the full Racket system—a mature environment for stateful, higherorder, multiparadigm programming with or with out types. Evaluating our method using a set of both pure and stateful benchmarks, we are able to verify 99.94% of checks statically (all but 28 of 49, 861). Stateful, higherorder functions pose significant challenges for static contract verification in particular. In the presence of these features, a modular analysis must permit code from the current module to escape permanently to an opaque context (unspecified code from outside the current module) that may be stateful and therefore store a reference to the escaped closure. Also, contracts themselves, being predicates wri en in unrestricted Racket, may exhibit stateful behavior; a sound approach must be robust to contracts which are arbitrarily expressive and interwoven with the code they monitor. In this paper, we present and evaluate our solution based on higherorder symbolic execution, explain the techniques we used to address such thorny issues, formalize a notion of behavioral approximation, and use it to provide a mechanized proof of soundness. @Article{POPL18p51, author = {Phúc C. Nguyễn and Thomas Gilray and Sam TobinHochstadt and David Van Horn}, title = {Soft Contract Verification for HigherOrder Stateful Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {51}, numpages = {30}, doi = {10.1145/3158139}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Niksic, Filip 
POPL '18: "Why Is Random Testing Effective ..."
Why Is Random Testing Effective for Partition Tolerance Bugs?
Rupak Majumdar and Filip Niksic (MPISWS, Germany) Random testing has proven to be an effective way to catch bugs in distributed systems in the presence of network partition faults. This is surprising, as the space of potentially faulty executions is enormous, and the bugs depend on a subtle interplay between sequences of operations and faults. We provide a theoretical justification of the effectiveness of random testing in this context. First, we show a general construction, using the probabilistic method from combinatorics, that shows that whenever a random test covers a fixed coverage goal with sufficiently high probability, a small randomlychosen set of tests achieves full coverage with high probability. In particular, we show that our construction can give test sets exponentially smaller than systematic enumeration. Second, based on an empirical study of many bugs found by random testing in production distributed systems, we introduce notions of test coverage relating to network partition faults which are effective in finding bugs. Finally, we show using combinatorial arguments that for these notions of test coverage we introduce, we can find a lower bound on the probability that a random test covers a given goal. Our general construction then explains why random testing tools achieve good coverageand hence, find bugsquickly. While we formulate our results in terms of network partition faults, our construction provides a step towards rigorous analysis of random testing algorithms, and can be applicable in other scenarios. @Article{POPL18p46, author = {Rupak Majumdar and Filip Niksic}, title = {Why Is Random Testing Effective for Partition Tolerance Bugs?}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {46}, numpages = {24}, doi = {10.1145/3158134}, year = {2018}, } Publisher's Version Article Search 

Novotný, Petr 
POPL '18: "Lexicographic Ranking Supermartingales: ..."
Lexicographic Ranking Supermartingales: An Efficient Approach to Termination of Probabilistic Programs
Sheshansh Agrawal, Krishnendu Chatterjee , and Petr Novotný (IIT Bombay, India; IST Austria, Austria) Probabilistic programs extend classical imperative programs with realvalued random variables and random branching. The most basic liveness property for such programs is the termination property. The qualitative (aka almostsure) termination problem asks whether a given program program terminates with probability 1. While ranking functions provide a sound and complete method for nonprobabilistic programs, the extension of them to probabilistic programs is achieved via ranking supermartingales (RSMs). Although deep theoretical results have been established about RSMs, their application to probabilistic programs with nondeterminism has been limited only to programs of restricted controlflow structure. For nonprobabilistic programs, lexicographic ranking functions provide a compositional and practical approach for termination analysis of realworld programs. In this work we introduce lexicographic RSMs and show that they present a sound method for almostsure termination of probabilistic programs with nondeterminism. We show that lexicographic RSMs provide a tool for compositional reasoning about almostsure termination, and for probabilistic programs with linear arithmetic they can be synthesized efficiently (in polynomial time). We also show that with additional restrictions even asymptotic bounds on expected termination time can be obtained through lexicographic RSMs. Finally, we present experimental results on benchmarks adapted from previous work to demonstrate the effectiveness of our approach. @Article{POPL18p34, author = {Sheshansh Agrawal and Krishnendu Chatterjee and Petr Novotný}, title = {Lexicographic Ranking Supermartingales: An Efficient Approach to Termination of Probabilistic Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {34}, numpages = {32}, doi = {10.1145/3158122}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Odersky, Martin 
POPL '18: "Simplicitly: Foundations and ..."
Simplicitly: Foundations and Applications of Implicit Function Types
Martin Odersky, Olivier Blanvillain, Fengyun Liu, Aggelos Biboudis, Heather Miller, and Sandro Stucki (EPFL, Switzerland; Northeastern University, USA) Understanding a program entails understanding its context; dependencies, configurations and even implementations are all forms of contexts. Modern programming languages and theorem provers offer an array of constructs to define contexts, implicitly. Scala offers implicit parameters which are used pervasively, but which cannot be abstracted over. This paper describes a generalization of implicit parameters to implicit function types, a powerful way to abstract over the context in which some piece of code is run. We provide a formalization based on bidirectional typechecking that closely follows the semantics implemented by the Scala compiler. To demonstrate their range of abstraction capabilities, we present several applications that make use of implicit function types. We show how to encode the builder pattern, tagless interpreters, reader and free monads and we assess the performance of the monadic structures presented. @Article{POPL18p42, author = {Martin Odersky and Olivier Blanvillain and Fengyun Liu and Aggelos Biboudis and Heather Miller and Sandro Stucki}, title = {Simplicitly: Foundations and Applications of Implicit Function Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {42}, numpages = {29}, doi = {10.1145/3158130}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Öhman, Joakim 
POPL '18: "Decidability of Conversion ..."
Decidability of Conversion for Type Theory in Type Theory
Andreas Abel, Joakim Öhman , and Andrea Vezzosi (University of Gothenburg, Sweden; IMDEA Software Institute, Spain; Chalmers University of Technology, Sweden) Type theory should be able to handle its own metatheory, both to justify its foundational claims and to obtain a verified implementation. At the core of a type checker for intensional type theory lies an algorithm to check equality of types, or in other words, to check whether two types are convertible. We have formalized in Agda a practical conversion checking algorithm for a dependent type theory with one universe à la Russell, natural numbers, and ηequality for Π types. We prove the algorithm correct via a Kripke logical relation parameterized by a suitable notion of equivalence of terms. We then instantiate the parameterized fundamental lemma twice: once to obtain canonicity and injectivity of type formers, and once again to prove the completeness of the algorithm. Our proof relies on inductiverecursive definitions, but not on the uniqueness of identity proofs. Thus, it is valid in variants of intensional MartinLöf Type Theory as long as they support inductionrecursion, for instance, Extensional, Observational, or Homotopy Type Theory. @Article{POPL18p23, author = {Andreas Abel and Joakim Öhman and Andrea Vezzosi}, title = {Decidability of Conversion for Type Theory in Type Theory}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {23}, numpages = {29}, doi = {10.1145/3158111}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Ong, C.H. Luke 
POPL '18: "HigherOrder Constrained Horn ..."
HigherOrder Constrained Horn Clauses for Verification
Toby Cathcart Burn, C.H. Luke Ong, and Steven J. Ramsay (University of Oxford, UK; University of Bristol, UK) Motivated by applications in automated verification of higherorder functional programs, we develop a notion of constrained Horn clauses in higherorder logic and a decision problem concerning their satisfiability. We show that, although satisfiable systems of higherorder clauses do not generally have least models, there is a notion of canonical model obtained through a reduction to a problem concerning a kind of monotone logic program. Following work in higherorder program verification, we develop a refinement type system in order to reason about and automate the search for models. This provides a sound but incomplete method for solving the decision problem. Finally, we show that there is a sense in which we can use refinement types to express properties of terms whilst staying within the higherorder constrained Horn clause framework. @Article{POPL18p11, author = {Toby Cathcart Burn and C.H. Luke Ong and Steven J. Ramsay}, title = {HigherOrder Constrained Horn Clauses for Verification}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {11}, numpages = {28}, doi = {10.1145/3158099}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Ostermann, Klaus 
POPL '18: "Denotational Validation of ..."
Denotational Validation of HigherOrder Bayesian Inference
Adam Ścibior, Ohad Kammar, Matthijs Vákár, Sam Staton, Hongseok Yang, Yufei Cai, Klaus Ostermann , Sean K. Moss, Chris Heunen , and Zoubin Ghahramani (University of Cambridge, UK; MPI Tübingen, Germany; University of Oxford, UK; KAIST, South Korea; University of Tübingen, Germany; University of Edinburgh, UK; Uber AI Labs, USA) We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higherorder functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higherorder functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasiBorel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasiBorel counterpart to the MetropolisHastingsGreen theorem. @Article{POPL18p60, author = {Adam Ścibior and Ohad Kammar and Matthijs Vákár and Sam Staton and Hongseok Yang and Yufei Cai and Klaus Ostermann and Sean K. Moss and Chris Heunen and Zoubin Ghahramani}, title = {Denotational Validation of HigherOrder Bayesian Inference}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {60}, numpages = {29}, doi = {10.1145/3158148}, year = {2018}, } Publisher's Version Article Search Info 

Padon, Oded 
POPL '18: "Reducing Liveness to Safety ..."
Reducing Liveness to Safety in FirstOrder Logic
Oded Padon, Jochen Hoenicke, Giuliano Losa, Andreas Podelski , Mooly Sagiv, and Sharon Shoham (Tel Aviv University, Israel; University of Freiburg, Germany; University of California at Los Angeles, USA) We develop a new technique for verifying temporal properties of infinitestate (distributed) systems. The main idea is to reduce the temporal verification problem to the problem of verifying the safety of infinitestate systems expressed in firstorder logic. This allows to leverage existing techniques for safety verification to verify temporal properties of interesting distributed protocols, including some that have not been mechanically verified before. We model infinitestate systems using firstorder logic, and use firstorder temporal logic (FOLTL) to specify temporal properties. This general formalism allows to naturally model distributed systems, while supporting both unboundedparallelism (where the system is allowed to dynamically create processes), and infinitestate per process. The traditional approach for verifying temporal properties of infinitestate systems employs wellfounded relations (e.g. using linear arithmetic ranking functions). In contrast, our approach is based the idea of fair cycle detection. In finitestate systems, temporal verification can always be reduced to fair cycle detection (a system contains a fair cycle if it revisits a state after satisfying all fairness constraints). However, with both infinitely many states and infinitely many fairness constraints, a straightforward reduction to fair cycle detection is unsound. To regain soundness, we augment the infinitestate transition system by a dynamically computed finite set, that exploits the locality of transitions. This set lets us define a form of fair cycle detection that is sound in the presence of both infinitely many states, and infinitely many fairness constraints. Our approach allows a new style of temporal verification that does not explicitly involve ranking functions. This fits well with pure firstorder verification which does not explicitly reason about numerical values. In particular, it can be used with effectively propositional firstorder logic (EPR), in which case checking verification conditions is decidable. We applied our technique to verify temporal properties of several interesting protocols. To the best of our knowledge, we have obtained the first mechanized liveness proof for both TLB Shootdown, and Stoppable Paxos. @Article{POPL18p26, author = {Oded Padon and Jochen Hoenicke and Giuliano Losa and Andreas Podelski and Mooly Sagiv and Sharon Shoham}, title = {Reducing Liveness to Safety in FirstOrder Logic}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {26}, numpages = {33}, doi = {10.1145/3158114}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Pagani, Michele 
POPL '18: "Measurable Cones and Stable, ..."
Measurable Cones and Stable, Measurable Functions: A Model for Probabilistic HigherOrder Programming
Thomas Ehrhard, Michele Pagani, and Christine Tasson (University of Paris Diderot, France; CNRS, France) We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpoenriched cartesian closed category. This category gives a denotational model of an extension of PCF supporting the main primitives of probabilistic functional programming, like continuous and discrete probabilistic distributions, sampling, conditioning and full recursion. We prove the soundness and adequacy of this model with respect to a callbyname operational semantics and give some examples of its denotations. @Article{POPL18p59, author = {Thomas Ehrhard and Michele Pagani and Christine Tasson}, title = {Measurable Cones and Stable, Measurable Functions: A Model for Probabilistic HigherOrder Programming}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {59}, numpages = {28}, doi = {10.1145/3158147}, year = {2018}, } Publisher's Version Article Search Info 

Palsberg, Jens 
POPL '18: "JonesOptimal Partial Evaluation ..."
JonesOptimal Partial Evaluation by SpecializationSafe Normalization
Matt Brown and Jens Palsberg (University of California at Los Angeles, USA) We present partial evaluation by specializationsafe normalization, a novel partial evaluation technique that is Jonesoptimal, that can be selfapplied to achieve the Futamura projections and that can be typechecked to ensure it always generates code with the correct type. Jonesoptimality is the goldstandard for nontrivial partial evaluation and guarantees that a specializer can remove an entire layer of interpretation. We achieve Jonesoptimality by using a novel affinevariable static analysis that directs specializationsafe normalization to always decrease a program’s runtime. We demonstrate the robustness of our approach by showing Jonesoptimality in a variety of settings. We have formally proved that our partial evaluator is Jonesoptimal for callbyvalue reduction, and we have experimentally shown that it is Jonesoptimal for callbyvalue, normalorder, and memoized normalorder. Each of our experiments tests Jonesoptimality with three different selfinterpreters. We implemented our partial evaluator in F_{ω}^{µ i}, a recent language for typed selfapplicable metaprogramming. It is the first Jonesoptimal and selfapplicable partial evaluator whose type guarantees that it always generates typecorrect code. @Article{POPL18p14, author = {Matt Brown and Jens Palsberg}, title = {JonesOptimal Partial Evaluation by SpecializationSafe Normalization}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {14}, numpages = {28}, doi = {10.1145/3158102}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Paraskevopoulou, Zoe 
POPL '18: "Generating Good Generators ..."
Generating Good Generators for Inductive Relations
Leonidas Lampropoulos, Zoe Paraskevopoulou, and Benjamin C. Pierce (University of Pennsylvania, USA; Princeton University, USA) Propertybased random testing (PBRT) is widely used in the functional programming and verification communities. For testing simple properties, PBRT tools such as QuickCheck can automatically generate random inputs of a given type. But for more complex properties, effective testing often demands generators for random inputs that belong to a given type and satisfy some logical condition. QuickCheck provides a library of combinators for building such generators by hand, but this can be tedious for simple conditions and error prone for more complex ones. Fortunately, the process can often be automated. The most prominent method, narrowing, works by traversing the structure of the condition, lazily instantiating parts of the data structure as constraints involving them are met. We show how to use ideas from narrowing to compile a large subclass of Coq's inductive relations into efficient generators, avoiding the interpretive overhead of previous implementations. More importantly, the same compilation technique allows us to produce proof terms certifying that each derived generator is goodi.e., sound and complete with respect to the inductive relation it was derived from. We implement our algorithm as an extension of QuickChick, an existing tool for propertybased testing in Coq. We evaluate our method by automatically deriving good generators for the majority of the specifications in Software Foundations, a formalized textbook on programming language foundations. @Article{POPL18p45, author = {Leonidas Lampropoulos and Zoe Paraskevopoulou and Benjamin C. Pierce}, title = {Generating Good Generators for Inductive Relations}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {45}, numpages = {30}, doi = {10.1145/3158133}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Parreaux, Lionel 
POPL '18: "Unifying Analytic and StaticallyTyped ..."
Unifying Analytic and StaticallyTyped Quasiquotes
Lionel Parreaux , Antoine Voizard, Amir Shaikhha, and Christoph E. Koch (EPFL, Switzerland; University of Pennsylvania, USA) Metaprograms are programs that manipulate (generate, analyze and evaluate) other programs. These tasks are greatly facilitated by quasiquotation, a technique to construct and deconstruct program fragments using quoted code templates expressed in the syntax of the manipulated language. We argue that two main flavors of quasiquotes have existed so far: Lispstyle quasiquotes, which can both construct and deconstruct programs but may produce code that contains type mismatches and unbound variables; and MetaMLstyle quasiquotes, which rely on static typing to prevent these errors, but can only construct programs. In this paper, we show how to combine the advantages of both flavors into a unified framework: we allow the construction, deconstruction and evaluation of program fragments while ensuring that generated programs are welltyped and wellscoped, a combination unseen in previous work. We formalize our approach as λ^{{}}, a multistage calculus with code pattern matching and rewriting, and prove its type safety. We also present its realization in Squid, a metaprogramming framework for Scala, leveraging Scala’s expressive type system. To demonstrate the usefulness of our approach, we introduce speculative rewrite rules, a novel code transformation technique that makes decisive use of these capabilities, and we outline how it simplifies the design of some crucial query compiler optimizations. @Article{POPL18p13, author = {Lionel Parreaux and Antoine Voizard and Amir Shaikhha and Christoph E. Koch}, title = {Unifying Analytic and StaticallyTyped Quasiquotes}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {13}, numpages = {33}, doi = {10.1145/3158101}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Patrignani, Marco 
POPL '18: "Parametricity versus the Universal ..."
Parametricity versus the Universal Type
Dominique Devriese, Marco Patrignani, and Frank Piessens (KU Leuven, Belgium; MPISWS, Germany; CISPA, Germany) There has long been speculation in the scientific literature on how to dynamically enforce parametricity such as that yielded by System F. Almost 20 years ago, Sumii and Pierce proposed a formal compiler from System F into the cryptographic lambda calculus: an untyped lambda calculus extended with an idealised model of encryption. They conjectured that this compiler was fully abstract, i.e. that compiled terms are contextually equivalent if and only if the original terms were, a property that can be seen as a form of secure compilation. The conjecture has received attention in several other publications since then, but remains open to this day. More recently, several researchers have been looking at graduallytyped languages that extend System F. In this setting it is natural to wonder whether embedding System F into these graduallytyped languages preserves contextual equivalence and thus parametricity. In this paper, we answer both questions negatively. We provide a concrete counterexample: two System F terms whose contextual equivalence is not preserved by the SumiiPierce compiler, nor the embedding into the polymorphic blame calculus. This counterexample relies on the absence in System F of what we call a universal type, i.e., a type that all other types can be injected into and extracted from. As the languages in which System F is compiled have a universal type, the compilation cannot be fully abstract; this paper explains why. We believe this paper thus sheds light on recent results in the field of gradually typed languages and it provides a perspective for further research into secure compilation of polymorphic languages. @Article{POPL18p38, author = {Dominique Devriese and Marco Patrignani and Frank Piessens}, title = {Parametricity versus the Universal Type}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {38}, numpages = {23}, doi = {10.1145/3158126}, year = {2018}, } Publisher's Version Article Search 

Pavlogiannis, Andreas 
POPL '18: "Optimal Dyck Reachability ..."
Optimal Dyck Reachability for DataDependence and Alias Analysis
Krishnendu Chatterjee , Bhavya Choudhary, and Andreas Pavlogiannis (IST Austria, Austria; IIT Bombay, India) A fundamental algorithmic problem at the heart of static analysis is Dyck reachability. The input is a graph where the edges are labeled with different types of opening and closing parentheses, and the reachability information is computed via paths whose parentheses are properly matched. We present new results for Dyck reachability problems with applications to alias analysis and datadependence analysis. Our main contributions, that include improved upper bounds as well as lower bounds that establish optimality guarantees, are as follows: First, we consider Dyck reachability on bidirected graphs, which is the standard way of performing fieldsensitive pointsto analysis. Given a bidirected graph with n nodes and m edges, we present: (i) an algorithm with worstcase running time O(m + n · α(n)), where α(n) is the inverse Ackermann function, improving the previously known O(n^{2}) time bound; (ii) a matching lower bound that shows that our algorithm is optimal wrt to worstcase complexity; and (iii) an optimal averagecase upper bound of O(m) time, improving the previously known O(m · logn) bound. Second, we consider the problem of contextsensitive datadependence analysis, where the task is to obtain analysis summaries of library code in the presence of callbacks. Our algorithm preprocesses libraries in almost linear time, after which the contribution of the library in the complexity of the client analysis is only linear, and only wrt the number of call sites. Third, we prove that combinatorial algorithms for Dyck reachability on general graphs with truly subcubic bounds cannot be obtained without obtaining subcubic combinatorial algorithms for Boolean Matrix Multiplication, which is a longstanding open problem. Thus we establish that the existing combinatorial algorithms for Dyck reachability are (conditionally) optimal for general graphs. We also show that the same hardness holds for graphs of constant treewidth. Finally, we provide a prototype implementation of our algorithms for both alias analysis and datadependence analysis. Our experimental evaluation demonstrates that the new algorithms significantly outperform all existing methods on the two problems, over realworld benchmarks. @Article{POPL18p30, author = {Krishnendu Chatterjee and Bhavya Choudhary and Andreas Pavlogiannis}, title = {Optimal Dyck Reachability for DataDependence and Alias Analysis}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {30}, numpages = {30}, doi = {10.1145/3158118}, year = {2018}, } Publisher's Version Article Search Artifacts Functional POPL '18: "DataCentric Dynamic Partial ..." DataCentric Dynamic Partial Order Reduction Marek Chalupa, Krishnendu Chatterjee , Andreas Pavlogiannis, Nishant Sinha, and Kapil Vaidya (Masaryk University, Czechia; IST Austria, Austria; Kena Labs, India; IIT Bombay, India) We present a new dynamic partialorder reduction method for stateless model checking of concurrent programs. A common approach for exploring program behaviors relies on enumerating the traces of the program, without storing the visited states (aka stateless exploration). As the number of distinct traces grows exponentially, dynamic partialorder reduction (DPOR) techniques have been successfully used to partition the space of traces into equivalence classes (Mazurkiewicz partitioning), with the goal of exploring only few representative traces from each class. We introduce a new equivalence on traces under sequential consistency semantics, which we call the observation equivalence. Two traces are observationally equivalent if every read event observes the same write event in both traces. While the traditional Mazurkiewicz equivalence is controlcentric, our new definition is datacentric. We show that our observation equivalence is coarser than the Mazurkiewicz equivalence, and in many cases even exponentially coarser. We devise a DPOR exploration of the trace space, called datacentric DPOR, based on the observation equivalence. For acyclic architectures, our algorithm is guaranteed to explore exactly one representative trace from each observation class, while spending polynomial time per class. Hence, our algorithm is optimal wrt the observation equivalence, and in several cases explores exponentially fewer traces than any enumerative method based on the Mazurkiewicz equivalence. For cyclic architectures, we consider an equivalence between traces which is finer than the observation equivalence; but coarser than the Mazurkiewicz equivalence, and in some cases is exponentially coarser. Our datacentric DPOR algorithm remains optimal under this trace equivalence. Finally, we perform a basic experimental comparison between the existing Mazurkiewiczbased DPOR and our datacentric DPOR on a set of academic benchmarks. Our results show a significant reduction in both running time and the number of explored equivalence classes. @Article{POPL18p31, author = {Marek Chalupa and Krishnendu Chatterjee and Andreas Pavlogiannis and Nishant Sinha and Kapil Vaidya}, title = {DataCentric Dynamic Partial Order Reduction}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {31}, numpages = {30}, doi = {10.1145/3158119}, year = {2018}, } Publisher's Version Article Search 

Pellissier, Luc 
POPL '18: "Polyadic Approximations, Fibrations ..."
Polyadic Approximations, Fibrations and Intersection Types
Damiano Mazza, Luc Pellissier, and Pierre Vial (CNRS, France; University of Paris 13, France; University of Paris Diderot, France) Starting from an exact correspondence between linear approximations and nonidempotent intersection types, we develop a general framework for building systems of intersection types characterizing normalization properties. We show how this construction, which uses in a fundamental way Melliès and Zeilberger's ``type systems as functors'' viewpoint, allows us to recover equivalent versions of every well known intersection type system (including Coppo and Dezani's original system, as well as its nonidempotent variants independently introduced by Gardner and de Carvalho). We also show how new systems of intersection types may be built almost automatically in this way. @Article{POPL18p6, author = {Damiano Mazza and Luc Pellissier and Pierre Vial}, title = {Polyadic Approximations, Fibrations and Intersection Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {6}, numpages = {28}, doi = {10.1145/3158094}, year = {2018}, } Publisher's Version Article Search 

Peña, Lucas 
POPL '18: "Foundations for Natural Proofs ..."
Foundations for Natural Proofs and Quantifier Instantiation
Christof Löding, P. Madhusudan , and Lucas Peña (RWTH Aachen University, Germany; University of Illinois at UrbanaChampaign, USA) We give foundational results that explain the efficacy of heuristics used for dealing with quantified formulas and recursive definitions. We develop a framework for first order logic (FOL) over an uninterpreted combination of background theories. Our central technical result is that systematic term instantiation is complete for a fragment of FOL that we call safe. Coupled with the fact that unfolding recursive definitions is essentially term instantiation and with the observation that heap verification engines generate verification conditions in the safe fragment explains the efficacy of verification engines like natural proofs that resort to such heuristics. Furthermore, we study recursive definitions with least fixpoint semantics and show that though they are not amenable to complete procedures, we can systematically introduce induction principles that in practice bridge the divide between FOL and FOL with recursive definitions. @Article{POPL18p10, author = {Christof Löding and P. Madhusudan and Lucas Peña}, title = {Foundations for Natural Proofs and Quantifier Instantiation}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {10}, numpages = {30}, doi = {10.1145/3158098}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Pereira, Fernando Magno Quintão 
POPL '18: "Inference of Static Semantics ..."
Inference of Static Semantics for Incomplete C Programs
Leandro T. C. Melo, Rodrigo G. Ribeiro, Marcus R. de Araújo, and Fernando Magno Quintão Pereira (Federal University of Minas Gerais, Brazil; Federal University of Ouro Preto, Brazil) Incomplete source code naturally emerges in software development: during the design phase, while evolving, testing and analyzing programs. Therefore, the ability to understand partial programs is a valuable asset. However, this problem is still unsolved in the C programming language. Difficulties stem from the fact that parsing C requires, not only syntax, but also semantic information. Furthermore, inferring types so that they respect C's type system is a challenging task. In this paper we present a technique that lets us solve these problems. We provide a unificationbased type inference capable of dealing with C intricacies. The ideas we present let us reconstruct partial C programs into complete welltyped ones. Such program reconstruction has several applications: enabling static analysis tools in scenarios where software components may be absent; improving static analysis tools that do not rely on buildspecifications; allowing stubgeneration and testing tools to work on snippets; and assisting programmers on the extraction of reusable datastructures out of the program parts that use them. Our evaluation is performed on source code from a variety of C libraries such as GNU's Coreutils, GNULib, GNOME's GLib, and GDSL; on implementations from Sedgewick's books; and on snippets from popular opensource projects like CPython, FreeBSD, and Git. @Article{POPL18p29, author = {Leandro T. C. Melo and Rodrigo G. Ribeiro and Marcus R. de Araújo and Fernando Magno Quintão Pereira}, title = {Inference of Static Semantics for Incomplete C Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {29}, numpages = {28}, doi = {10.1145/3158117}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Peyton Jones, Simon 
POPL '18: "Linear Haskell: Practical ..."
Linear Haskell: Practical Linearity in a HigherOrder Polymorphic Language
JeanPhilippe Bernardy, Mathieu Boespflug, Ryan R. Newton, Simon Peyton Jones, and Arnaud Spiwack (University of Gothenburg, Sweden; Tweag I/O, France; Indiana University, USA; Microsoft Research, UK) Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind: backwardscompatibility and code reuse across linear and nonlinear users of a library. Only then can the benefits of linear types permeate conventional functional programming. Rather than bifurcate types into linear and nonlinear counterparts, we instead attach linearity to function arrows. Linear functions can receive inputs from linearlybound values, but can also operate over unrestricted, regular values. To demonstrate the efficacy of our linear type system — both how easy it can be integrated in an existing language implementation and how streamlined it makes it to write programs with linear types — we implemented our type system in ghc, the leading Haskell compiler, and demonstrate two kinds of applications of linear types: mutable data with pure interfaces; and enforcing protocols in I/Operforming functions. @Article{POPL18p5, author = {JeanPhilippe Bernardy and Mathieu Boespflug and Ryan R. Newton and Simon Peyton Jones and Arnaud Spiwack}, title = {Linear Haskell: Practical Linearity in a HigherOrder Polymorphic Language}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {5}, numpages = {29}, doi = {10.1145/3158093}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Pierce, Benjamin C. 
POPL '18: "Generating Good Generators ..."
Generating Good Generators for Inductive Relations
Leonidas Lampropoulos, Zoe Paraskevopoulou, and Benjamin C. Pierce (University of Pennsylvania, USA; Princeton University, USA) Propertybased random testing (PBRT) is widely used in the functional programming and verification communities. For testing simple properties, PBRT tools such as QuickCheck can automatically generate random inputs of a given type. But for more complex properties, effective testing often demands generators for random inputs that belong to a given type and satisfy some logical condition. QuickCheck provides a library of combinators for building such generators by hand, but this can be tedious for simple conditions and error prone for more complex ones. Fortunately, the process can often be automated. The most prominent method, narrowing, works by traversing the structure of the condition, lazily instantiating parts of the data structure as constraints involving them are met. We show how to use ideas from narrowing to compile a large subclass of Coq's inductive relations into efficient generators, avoiding the interpretive overhead of previous implementations. More importantly, the same compilation technique allows us to produce proof terms certifying that each derived generator is goodi.e., sound and complete with respect to the inductive relation it was derived from. We implement our algorithm as an extension of QuickChick, an existing tool for propertybased testing in Coq. We evaluate our method by automatically deriving good generators for the majority of the specifications in Software Foundations, a formalized textbook on programming language foundations. @Article{POPL18p45, author = {Leonidas Lampropoulos and Zoe Paraskevopoulou and Benjamin C. Pierce}, title = {Generating Good Generators for Inductive Relations}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {45}, numpages = {30}, doi = {10.1145/3158133}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional POPL '18: "Synthesizing Bijective Lenses ..." Synthesizing Bijective Lenses Anders Miltner, Kathleen Fisher, Benjamin C. Pierce , David Walker, and Steve Zdancewic (Princeton University, USA; Tufts University, USA; University of Pennsylvania, USA) Bidirectional transformations between different data representations occur frequently in modern software systems. They appear as serializers and deserializers, as parsers and pretty printers, as database views and view updaters, and as a multitude of different kinds of ad hoc data converters. Manually building bidirectional transformationsby writing two separate functions that are intended to be inversesis tedious and error prone. A better approach is to use a domainspecific language in which both directions can be written as a single expression. However, these domainspecific languages can be difficult to program in, requiring programmers to manage fiddly details while working in a complex type system. We present an alternative approach. Instead of coding transformations manually, we synthesize them from declarative format descriptions and examples. Specifically, we present Optician, a tool for typedirected synthesis of bijective string transformers. The inputs to Optician are a pair of ordinary regular expressions representing two data formats and a few concrete examples for disambiguation. The output is a welltyped program in Boomerang (a bidirectional language based on the theory of lenses). The main technical challenge involves navigating the vast program search space efficiently. In particular, and unlike most prior work on typedirected synthesis, our system operates in the context of a language with a rich equivalence relation on types (the theory of regular expressions). Consequently, program synthesis requires search in two dimensions: First, our synthesis algorithm must find a pair of "syntactically compatible types," and second, using the structure of those types, it must find a type and examplecompliant term. Our key insight is that it is possible to reduce the size of this search space without losing any computational power by defining a new language of lenses designed specifically for synthesis. The new language is free from arbitrary function composition and operates only over types and terms in a new disjunctive normal form. We prove (1) our new language is just as powerful as a more natural, compositional, and declarative language and (2) our synthesis algorithm is sound and complete with respect to the new language. We also demonstrate empirically that our new language changes the synthesis problem from one that admits intractable solutions to one that admits highly efficient solutions, able to synthesize intricate lenses between complex file formats in seconds. We evaluate Optician on a benchmark suite of 39 examples that includes both microbenchmarks and realistic examples derived from other data management systems including Flash Fill, a tool for synthesizing string transformations in spreadsheets, and Augeas, a tool for bidirectional processing of Linux system configuration files. @Article{POPL18p1, author = {Anders Miltner and Kathleen Fisher and Benjamin C. Pierce and David Walker and Steve Zdancewic}, title = {Synthesizing Bijective Lenses}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {1}, numpages = {30}, doi = {10.1145/3158089}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Piessens, Frank 
POPL '18: "Parametricity versus the Universal ..."
Parametricity versus the Universal Type
Dominique Devriese, Marco Patrignani, and Frank Piessens (KU Leuven, Belgium; MPISWS, Germany; CISPA, Germany) There has long been speculation in the scientific literature on how to dynamically enforce parametricity such as that yielded by System F. Almost 20 years ago, Sumii and Pierce proposed a formal compiler from System F into the cryptographic lambda calculus: an untyped lambda calculus extended with an idealised model of encryption. They conjectured that this compiler was fully abstract, i.e. that compiled terms are contextually equivalent if and only if the original terms were, a property that can be seen as a form of secure compilation. The conjecture has received attention in several other publications since then, but remains open to this day. More recently, several researchers have been looking at graduallytyped languages that extend System F. In this setting it is natural to wonder whether embedding System F into these graduallytyped languages preserves contextual equivalence and thus parametricity. In this paper, we answer both questions negatively. We provide a concrete counterexample: two System F terms whose contextual equivalence is not preserved by the SumiiPierce compiler, nor the embedding into the polymorphic blame calculus. This counterexample relies on the absence in System F of what we call a universal type, i.e., a type that all other types can be injected into and extracted from. As the languages in which System F is compiled have a universal type, the compilation cannot be fully abstract; this paper explains why. We believe this paper thus sheds light on recent results in the field of gradually typed languages and it provides a perspective for further research into secure compilation of polymorphic languages. @Article{POPL18p38, author = {Dominique Devriese and Marco Patrignani and Frank Piessens}, title = {Parametricity versus the Universal Type}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {38}, numpages = {23}, doi = {10.1145/3158126}, year = {2018}, } Publisher's Version Article Search 

Piróg, Maciej 
POPL '18: "Handle with Care: Relational ..."
Handle with Care: Relational Interpretation of Algebraic Effects and Handlers
Dariusz Biernacki, Maciej Piróg, Piotr Polesiuk, and Filip Sieczkowski (University of Wrocław, Poland) Algebraic effects and handlers have received a lot of attention recently, both from the theoretical point of view and in practical language design. This stems from the fact that algebraic effects give the programmer unprecedented freedom to define, combine, and interpret computational effects. This plentyofrope, however, demands not only a deep understanding of the underlying semantics, but also access to practical means of reasoning about effectful code, including correctness and program equivalence. In this paper we tackle this problem by constructing a stepindexed relational interpretation of a callbyvalue calculus with algebraic effect handlers and a rowbased polymorphic typeandeffect system. Our calculus, while striving for simplicity, enjoys desirable theoretical properties, and is close to the cores of programming languages with algebraic effects used in the wild, while the logical relation we build for it can be used to reason about nontrivial properties, such as contextual equivalence and contextual approximation of programs. Our development has been fully formalised in the Coq proof assistant. @Article{POPL18p8, author = {Dariusz Biernacki and Maciej Piróg and Piotr Polesiuk and Filip Sieczkowski}, title = {Handle with Care: Relational Interpretation of Algebraic Effects and Handlers}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {8}, numpages = {30}, doi = {10.1145/3158096}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Podelski, Andreas 
POPL '18: "Reducing Liveness to Safety ..."
Reducing Liveness to Safety in FirstOrder Logic
Oded Padon, Jochen Hoenicke, Giuliano Losa, Andreas Podelski , Mooly Sagiv, and Sharon Shoham (Tel Aviv University, Israel; University of Freiburg, Germany; University of California at Los Angeles, USA) We develop a new technique for verifying temporal properties of infinitestate (distributed) systems. The main idea is to reduce the temporal verification problem to the problem of verifying the safety of infinitestate systems expressed in firstorder logic. This allows to leverage existing techniques for safety verification to verify temporal properties of interesting distributed protocols, including some that have not been mechanically verified before. We model infinitestate systems using firstorder logic, and use firstorder temporal logic (FOLTL) to specify temporal properties. This general formalism allows to naturally model distributed systems, while supporting both unboundedparallelism (where the system is allowed to dynamically create processes), and infinitestate per process. The traditional approach for verifying temporal properties of infinitestate systems employs wellfounded relations (e.g. using linear arithmetic ranking functions). In contrast, our approach is based the idea of fair cycle detection. In finitestate systems, temporal verification can always be reduced to fair cycle detection (a system contains a fair cycle if it revisits a state after satisfying all fairness constraints). However, with both infinitely many states and infinitely many fairness constraints, a straightforward reduction to fair cycle detection is unsound. To regain soundness, we augment the infinitestate transition system by a dynamically computed finite set, that exploits the locality of transitions. This set lets us define a form of fair cycle detection that is sound in the presence of both infinitely many states, and infinitely many fairness constraints. Our approach allows a new style of temporal verification that does not explicitly involve ranking functions. This fits well with pure firstorder verification which does not explicitly reason about numerical values. In particular, it can be used with effectively propositional firstorder logic (EPR), in which case checking verification conditions is decidable. We applied our technique to verify temporal properties of several interesting protocols. To the best of our knowledge, we have obtained the first mechanized liveness proof for both TLB Shootdown, and Stoppable Paxos. @Article{POPL18p26, author = {Oded Padon and Jochen Hoenicke and Giuliano Losa and Andreas Podelski and Mooly Sagiv and Sharon Shoham}, title = {Reducing Liveness to Safety in FirstOrder Logic}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {26}, numpages = {33}, doi = {10.1145/3158114}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Polesiuk, Piotr 
POPL '18: "Handle with Care: Relational ..."
Handle with Care: Relational Interpretation of Algebraic Effects and Handlers
Dariusz Biernacki, Maciej Piróg, Piotr Polesiuk, and Filip Sieczkowski (University of Wrocław, Poland) Algebraic effects and handlers have received a lot of attention recently, both from the theoretical point of view and in practical language design. This stems from the fact that algebraic effects give the programmer unprecedented freedom to define, combine, and interpret computational effects. This plentyofrope, however, demands not only a deep understanding of the underlying semantics, but also access to practical means of reasoning about effectful code, including correctness and program equivalence. In this paper we tackle this problem by constructing a stepindexed relational interpretation of a callbyvalue calculus with algebraic effect handlers and a rowbased polymorphic typeandeffect system. Our calculus, while striving for simplicity, enjoys desirable theoretical properties, and is close to the cores of programming languages with algebraic effects used in the wild, while the logical relation we build for it can be used to reason about nontrivial properties, such as contextual equivalence and contextual approximation of programs. Our development has been fully formalised in the Coq proof assistant. @Article{POPL18p8, author = {Dariusz Biernacki and Maciej Piróg and Piotr Polesiuk and Filip Sieczkowski}, title = {Handle with Care: Relational Interpretation of Algebraic Effects and Handlers}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {8}, numpages = {30}, doi = {10.1145/3158096}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Popescu, Andrei 
POPL '18: "Safety and Conservativity ..."
Safety and Conservativity of Definitions in HOL and Isabelle/HOL
Ondřej Kunčar and Andrei Popescu (TU Munich, Germany; Middlesex University, UK; Institute of Mathematics at Romanian Academy, Romania) Definitions are traditionally considered to be a safe mechanism for introducing concepts on top of a logic known to be consistent. In contrast to arbitrary axioms, definitions should in principle be treatable as a form of abbreviation, and thus compiled away from the theory without losing provability. In particular, definitions should form a conservative extension of the pure logic. These properties are crucial for modern interactive theorem provers, since they ensure the consistency of the logic, as well as a valid environment for total/certified functional programming. We prove these properties, namely, safety and conservativity, for HigherOrder Logic (HOL), a logic implemented in several mainstream theorem provers and relied upon by thousands of users. Some unique features of HOL, such as the requirement to give nonemptiness proofs when defining new types and the impossibility to unfold type definitions, make the proof of these properties, and also the very formulation of safety, nontrivial. Our study also factors in the essential variation of HOL definitions featured by Isabelle/HOL, a popular member of the HOLbased provers family. The current work improves on recent results which showed a weaker property, consistency of Isabelle/HOL's definitions. @Article{POPL18p24, author = {Ondřej Kunčar and Andrei Popescu}, title = {Safety and Conservativity of Definitions in HOL and Isabelle/HOL}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {24}, numpages = {26}, doi = {10.1145/3158112}, year = {2018}, } Publisher's Version Article Search Info 

Pouchet, LouisNoel 
POPL '18: "Analytical Modeling of Cache ..."
Analytical Modeling of Cache Behavior for Affine Programs
Wenlei Bao, Sriram Krishnamoorthy, LouisNoel Pouchet, and P. Sadayappan (Ohio State University, USA; Pacific Northwest National Laboratory, USA; Colorado State University, USA) Optimizing compilers implement program transformation strategies aimed at reducing data movement to or from main memory by exploiting the datacache hierarchy. However, instead of attempting to minimize the number of cache misses, very approximate cost models are used, due to the lack of precise compiletime models for misses for hierarchical caches. The current state of practice for cache miss analysis is based on accurate simulation. However, simulation requires time proportional to the dataset/problem size, as well as the number of distinct cache configurations of interest to be evaluated. This paper takes a fundamentally different approach, by focusing on polyhedral programs with static control flow. Instead of relying on costly simulation, a closedform solution for modeling of misses in a set associative cache hierarchy is developed. This solution can enable program transformation choice at compile time to optimize cache misses. A tool implementing the approach has been developed and used for validation of the framework. @Article{POPL18p32, author = {Wenlei Bao and Sriram Krishnamoorthy and LouisNoel Pouchet and P. Sadayappan}, title = {Analytical Modeling of Cache Behavior for Affine Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {32}, numpages = {26}, doi = {10.1145/3158120}, year = {2018}, } Publisher's Version Article Search 

Pulte, Christopher 
POPL '18: "Simplifying ARM Concurrency: ..."
Simplifying ARM Concurrency: MulticopyAtomic Axiomatic and Operational Models for ARMv8
Christopher Pulte, Shaked Flur, Will Deacon, Jon French, Susmit Sarkar, and Peter Sewell (University of Cambridge, UK; ARM, UK; University of St. Andrews, UK) ARM has a relaxed memory model, previously specified in informal prose for ARMv7 and ARMv8. Over time, and partly due to work building formal semantics for ARM concurrency, it has become clear that some of the complexity of the model is not justified by the potential benefits. In particular, the model was originally nonmulticopyatomic: writes could become visible to some other threads before becoming visible to all — but this has not been exploited in production implementations, the corresponding potential hardware optimisations are thought to have insufficient benefits in the ARM context, and it gives rise to subtle complications when combined with other ARMv8 features. The ARMv8 architecture has therefore been revised: it now has a multicopyatomic model. It has also been simplified in other respects, including more straightforward notions of dependency, and the architecture now includes a formal concurrency model. In this paper we detail these changes and discuss their motivation. We define two formal concurrency models: an operational one, simplifying the Flowing model of Flur et al., and the axiomatic model of the revised ARMv8 specification. The models were developed by an academic group and by ARM staff, respectively, and this extended collaboration partly motivated the above changes. We prove the equivalence of the two models. The operational model is integrated into an executable exploration tool with new web interface, demonstrated by exhaustively checking the possible behaviours of a loopunrolled version of a Linux kernel lock implementation, a previously known bug due to unprevented speculation, and a fixed version. @Article{POPL18p19, author = {Christopher Pulte and Shaked Flur and Will Deacon and Jon French and Susmit Sarkar and Peter Sewell}, title = {Simplifying ARM Concurrency: MulticopyAtomic Axiomatic and Operational Models for ARMv8}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {19}, numpages = {29}, doi = {10.1145/3158107}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Püschel, Markus 
POPL '18: "A Practical Construction for ..."
A Practical Construction for Decomposing Numerical Abstract Domains
Gagandeep Singh, Markus Püschel, and Martin Vechev (ETH Zurich, Switzerland) Numerical abstract domains such as Polyhedra, Octahedron, Octagon, Interval, and others are an essential component of static program analysis. The choice of domain offers a performance/precision tradeoff ranging from cheap and imprecise (Interval) to expensive and precise (Polyhedra). Recently, significant speedups were achieved for Octagon and Polyhedra by manually decomposing their transformers to work with the Cartesian product of projections associated with partitions of the variable set. While practically useful, this manual process is time consuming, errorprone, and has to be applied from scratch for every domain. In this paper, we present a generic approach for decomposing the transformers of subpolyhedra domains along with conditions for checking whether the decomposed transformers lose precision with respect to the original transformers. These conditions are satisfied by most practical transformers, thus our approach is suitable for increasing the performance of these transformers without compromising their precision. Furthermore, our approach is ``black box:'' it does not require changes to the internals of the original nondecomposed transformers or additional manual effort per domain. We implemented our approach and applied it to the domains of Zones, Octagon, and Polyhedra. We then compared the performance of the decomposed transformers obtained with our generic method versus the state of the art: the (nondecomposed) PPL for Polyhedra and the much faster ELINA (which uses manual decomposition) for Polyhedra and Octagon. Against ELINA we demonstrate finer partitions and an associated speedup of about 2x on average. Our results indicate that the general construction presented in this work is a viable method for improving the performance of subpolyhedra domains. It enables designers of abstract domains to benefit from decomposition without rewriting all of their transformers from scratch as required by prior work. @Article{POPL18p55, author = {Gagandeep Singh and Markus Püschel and Martin Vechev}, title = {A Practical Construction for Decomposing Numerical Abstract Domains}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {55}, numpages = {28}, doi = {10.1145/3158143}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Radiček, Ivan 
POPL '18: "Monadic Refinements for Relational ..."
Monadic Refinements for Relational Cost Analysis
Ivan Radiček, Gilles Barthe , Marco Gaboardi, Deepak Garg , and Florian Zuleger (Vienna University of Technology, Austria; IMDEA Software Institute, Spain; SUNY Buffalo, USA; MPISWS, Germany) Formal frameworks for cost analysis of programs have been widely studied in the unary setting and, to a limited extent, in the relational setting. However, many of these frameworks focus only on the cost aspect, largely sidelining functional properties that are often a prerequisite for cost analysis, thus leaving many interesting programs out of their purview. In this paper, we show that elegant, simple, expressive proof systems combining cost analysis and functional properties can be built by combining already known ingredients: higherorder refinements and cost monads. Specifically, we derive two syntaxdirected proof systems, U^{C} and R^{C}, for unary and relational cost analysis, by adding a cost monad to a (syntaxdirected) logic of higherorder programs. We study the metatheory of the systems, show that several nontrivial examples can be verified in them, and prove that existing frameworks for cost analysis (RelCost and RAML) can be embedded in them. @Article{POPL18p36, author = {Ivan Radiček and Gilles Barthe and Marco Gaboardi and Deepak Garg and Florian Zuleger}, title = {Monadic Refinements for Relational Cost Analysis}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {36}, numpages = {32}, doi = {10.1145/3158124}, year = {2018}, } Publisher's Version Article Search 

Ramsay, Steven J. 
POPL '18: "HigherOrder Constrained Horn ..."
HigherOrder Constrained Horn Clauses for Verification
Toby Cathcart Burn, C.H. Luke Ong, and Steven J. Ramsay (University of Oxford, UK; University of Bristol, UK) Motivated by applications in automated verification of higherorder functional programs, we develop a notion of constrained Horn clauses in higherorder logic and a decision problem concerning their satisfiability. We show that, although satisfiable systems of higherorder clauses do not generally have least models, there is a notion of canonical model obtained through a reduction to a problem concerning a kind of monotone logic program. Following work in higherorder program verification, we develop a refinement type system in order to reason about and automate the search for models. This provides a sound but incomplete method for solving the decision problem. Finally, we show that there is a sense in which we can use refinement types to express properties of terms whilst staying within the higherorder constrained Horn clause framework. @Article{POPL18p11, author = {Toby Cathcart Burn and C.H. Luke Ong and Steven J. Ramsay}, title = {HigherOrder Constrained Horn Clauses for Verification}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {11}, numpages = {28}, doi = {10.1145/3158099}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Rastogi, Aseem 
POPL '18: "Recalling a Witness: Foundations ..."
Recalling a Witness: Foundations and Applications of Monotonic State
Danel Ahman, Cédric Fournet, Cătălin Hriţcu, Kenji Maillard , Aseem Rastogi, and Nikhil Swamy (Inria, France; Microsoft Research, UK; ENS Paris, France; Microsoft Research, India; Microsoft Research, USA) We provide a way to ease the verification of programs whose state evolves monotonically. The main idea is that a property witnessed in a prior state can be soundly recalled in the current state, provided (1) state evolves according to a given preorder, and (2) the property is preserved by this preorder. In many scenarios, such monotonic reasoning yields concise modular proofs, saving the need for explicit program invariants. We distill our approach into the monotonicstate monad, a general yet compact interface for Hoarestyle reasoning about monotonic state in a dependently typed language. We prove the soundness of the monotonicstate monad and use it as a unified foundation for reasoning about monotonic state in the F^{⋆} verification system. Based on this foundation, we build libraries for various mutable data structures like monotonic references and apply these libraries at scale to the verification of several distributed applications. @Article{POPL18p65, author = {Danel Ahman and Cédric Fournet and Cătălin Hriţcu and Kenji Maillard and Aseem Rastogi and Nikhil Swamy}, title = {Recalling a Witness: Foundations and Applications of Monotonic State}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {65}, numpages = {30}, doi = {10.1145/3158153}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Rémy, Didier 
POPL '18: "A Principled Approach to Ornamentation ..."
A Principled Approach to Ornamentation in ML
Thomas Williams and Didier Rémy (Inria, France) Ornaments are a way to describe changes in datatype definitions reorganizing, adding, or dropping some pieces of data so that functions operating on the bare definition can be partially and sometimes totally lifted into functions operating on the ornamented structure. We propose an extension of ML with higherorder ornaments, demonstrate its expressiveness with a few typical examples, including code refactoring, study the metatheoretical properties of ornaments, and describe their elaboration process. We formalize ornamentation via an a posteriori abstraction of the bare code, returning a generic term, which lives in a metalanguage above ML. The lifted code is obtained by application of the generic term to wellchosen arguments, followed by staged reduction, and some remaining simplifications. We use logical relations to closely relate the lifted code to the bare code. @Article{POPL18p21, author = {Thomas Williams and Didier Rémy}, title = {A Principled Approach to Ornamentation in ML}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {21}, numpages = {30}, doi = {10.1145/3158109}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Reps, Thomas 
POPL '18: "Nonlinear Reasoning for Invariant ..."
Nonlinear Reasoning for Invariant Synthesis
Zachary Kincaid , John Cyphert, Jason Breck, and Thomas Reps (Princeton University, USA; University of WisconsinMadison, USA; GrammaTech, USA) Automatic generation of nonlinear loop invariants is a longstanding challenge in program analysis, with many applications. For instance, reasoning about exponentials provides a way to find invariants of digitalfilter programs, and reasoning about polynomials and/or logarithms is needed for establishing invariants that describe the time or memory usage of many wellknown algorithms. An appealing approach to this challenge is to exploit the powerful recurrencesolving techniques that have been developed in the field of computer algebra, which can compute exact characterizations of nonlinear repetitive behavior. However, there is a gap between the capabilities of recurrence solvers and the needs of program analysis: (1) loop bodies are not merely systems of recurrence relationsthey may contain conditional branches, nested loops, nondeterministic assignments, etc., and (2) a client program analyzer must be able to reason about the closedform solutions produced by a recurrence solver (e.g., to prove assertions). This paper presents a method for generating nonlinear invariants of general loops based on analyzing recurrence relations. The key components are an abstract domain for reasoning about nonlinear arithmetic, a semanticsbased method for extracting recurrence relations from loop bodies, and a recurrence solver that avoids closed forms that involve complex or irrational numbers. Our technique has been implemented in a program analyzer that can analyze general loops and mutually recursive procedures. Our experiments show that our technique shows promise for nonlinear assertionchecking and resourcebound generation. @Article{POPL18p54, author = {Zachary Kincaid and John Cyphert and Jason Breck and Thomas Reps}, title = {Nonlinear Reasoning for Invariant Synthesis}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {54}, numpages = {33}, doi = {10.1145/3158142}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Ribeiro, Rodrigo G. 
POPL '18: "Inference of Static Semantics ..."
Inference of Static Semantics for Incomplete C Programs
Leandro T. C. Melo, Rodrigo G. Ribeiro, Marcus R. de Araújo, and Fernando Magno Quintão Pereira (Federal University of Minas Gerais, Brazil; Federal University of Ouro Preto, Brazil) Incomplete source code naturally emerges in software development: during the design phase, while evolving, testing and analyzing programs. Therefore, the ability to understand partial programs is a valuable asset. However, this problem is still unsolved in the C programming language. Difficulties stem from the fact that parsing C requires, not only syntax, but also semantic information. Furthermore, inferring types so that they respect C's type system is a challenging task. In this paper we present a technique that lets us solve these problems. We provide a unificationbased type inference capable of dealing with C intricacies. The ideas we present let us reconstruct partial C programs into complete welltyped ones. Such program reconstruction has several applications: enabling static analysis tools in scenarios where software components may be absent; improving static analysis tools that do not rely on buildspecifications; allowing stubgeneration and testing tools to work on snippets; and assisting programmers on the extraction of reusable datastructures out of the program parts that use them. Our evaluation is performed on source code from a variety of C libraries such as GNU's Coreutils, GNULib, GNOME's GLib, and GDSL; on implementations from Sedgewick's books; and on snippets from popular opensource projects like CPython, FreeBSD, and Git. @Article{POPL18p29, author = {Leandro T. C. Melo and Rodrigo G. Ribeiro and Marcus R. de Araújo and Fernando Magno Quintão Pereira}, title = {Inference of Static Semantics for Incomplete C Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {29}, numpages = {28}, doi = {10.1145/3158117}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Riely, James 
POPL '18: "Transactions in Relaxed Memory ..."
Transactions in Relaxed Memory Architectures
Brijesh Dongol, Radha Jagadeesan, and James Riely (Brunel University London, UK; DePaul University, USA) The integration of transactions into hardware relaxed memory architectures is a topic of current research both in industry and academia. In this paper, we provide a general architectural framework for the introduction of transactions into models of relaxed memory in hardware, including the SC, TSO, ARMv8 and PPC models. Our framework incorporates flexible and expressive forms of transaction aborts and execution that have hitherto been in the realm of software transactional memory. In contrast to software transactional memory, we account for the characteristics of relaxed memory as a restricted form of distributed system, without a notion of global time. We prove abstraction theorems to demonstrate that the programmer API matches the intuitions and expectations about transactions. @Article{POPL18p18, author = {Brijesh Dongol and Radha Jagadeesan and James Riely}, title = {Transactions in Relaxed Memory Architectures}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {18}, numpages = {29}, doi = {10.1145/3158106}, year = {2018}, } Publisher's Version Article Search 

Rinetzky, Noam 
POPL '18: "Online Detection of Effectively ..."
Online Detection of Effectively Callback Free Objects with Applications to Smart Contracts
Shelly Grossman, Ittai Abraham, Guy GolanGueta, Yan Michalevsky, Noam Rinetzky, Mooly Sagiv, and Yoni Zohar (Tel Aviv University, Israel; VMware, USA; Stanford University, USA) Callbacks are essential in many programming environments, but drastically complicate program understanding and reasoning because they allow to mutate object's local states by external objects in unexpected fashions, thus breaking modularity. The famous DAO bug in the cryptocurrency framework Ethereum, employed callbacks to steal $150M. We define the notion of Effectively Callback Free (ECF) objects in order to allow callbacks without preventing modular reasoning. An object is ECF in a given execution trace if there exists an equivalent execution trace without callbacks to this object. An object is ECF if it is ECF in every possible execution trace. We study the decidability of dynamically checking ECF in a given execution trace and statically checking if an object is ECF. We also show that dynamically checking ECF in Ethereum is feasible and can be done online. By running the history of all execution traces in Ethereum, we were able to verify that virtually all existing contract executions, excluding these of the DAO or of contracts with similar known vulnerabilities, are ECF. Finally, we show that ECF, whether it is verified dynamically or statically, enables modular reasoning about objects with encapsulated state. @Article{POPL18p48, author = {Shelly Grossman and Ittai Abraham and Guy GolanGueta and Yan Michalevsky and Noam Rinetzky and Mooly Sagiv and Yoni Zohar}, title = {Online Detection of Effectively Callback Free Objects with Applications to Smart Contracts}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {48}, numpages = {28}, doi = {10.1145/3158136}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Rioux, Nick 
POPL '18: "TypePreserving CPS Translation ..."
TypePreserving CPS Translation of Σ and Π Types Is Not Not Possible
William J. Bowman, Youyou Cong, Nick Rioux, and Amal Ahmed (Northeastern University, USA; Ochanomizu University, Japan) Dependently typed languages such as Coq are used to specify and prove functional correctness of source programs, but what we ultimately need are guarantees about correctness of compiled code. By preserving dependent types through each compiler pass, we could preserve sourcelevel specifications and correctness proofs into the generated targetlanguage programs. Unfortunately, typepreserving compilation of dependent types is hard. In 2002, Barthe and Uustalu showed that typepreserving CPS is not possible for languages such as Coq. Specifically, they showed that for strong dependent pairs (Σ types), the standard typed callbyname CPS is not type preserving. They further proved that for dependent case analysis on sums, a class of typed CPS translations—including the standard translation—is not possible. In 2016, Morrisett noticed a similar problem with the standard callbyvalue CPS translation for dependent functions (Π types). In essence, the problem is that the standard typed CPS translation by doublenegation, in which computations are assigned types of the form (A → ⊥) → ⊥, disrupts the term/type equivalence that is used during type checking in a dependently typed language. In this paper, we prove that typepreserving CPS translation for dependently typed languages is not not possible. We develop both callbyname and callbyvalue CPS translations from the Calculus of Constructions with both Π and Σ types (CC) to a dependently typed target language, and prove type preservation and compiler correctness of each translation. Our target language is CC extended with an additional equivalence rule and an additional typing rule, which we prove consistent by giving a model in the extensional Calculus of Constructions. Our key observation is that we can use a CPS translation that employs answertype polymorphism, where CPStranslated computations have type ∀ α. (A → α) → α. This type justifies, by a free theorem, the new equality rule in our target language and allows us to recover the term/type equivalences that CPS translation disrupts. Finally, we conjecture that our translation extends to dependent case analysis on sums, despite the impossibility result, and provide a proof sketch. @Article{POPL18p22, author = {William J. Bowman and Youyou Cong and Nick Rioux and Amal Ahmed}, title = {TypePreserving CPS Translation of Σ and Π Types Is Not Not Possible}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {22}, numpages = {33}, doi = {10.1145/3158110}, year = {2018}, } Publisher's Version Article Search Info 

Rompf, Tiark 
POPL '18: "Collapsing Towers of Interpreters ..."
Collapsing Towers of Interpreters
Nada Amin and Tiark Rompf (University of Cambridge, UK; Purdue University, USA) Given a tower of interpreters, i.e., a sequence of multiple interpreters interpreting one another as input programs, we aim to collapse this tower into a compiler that removes all interpretive overhead and runs in a single pass. In the real world, a use case might be Python code executed by an x86 runtime, on a CPU emulated in a JavaScript VM, running on an ARM CPU. Collapsing such a tower can not only exponentially improve runtime performance, but also enable the use of baselanguage tools for interpreted programs, e.g., for analysis and verification. In this paper, we lay the foundations in an idealized but realistic setting. We present a multilevel lambda calculus that features staging constructs and stage polymorphism: based on runtime parameters, an evaluator either executes source code (thereby acting as an interpreter) or generates code (thereby acting as a compiler). We identify stage polymorphism, a programming model from the domain of highperformance program generators, as the key mechanism to make such interpreters compose in a collapsible way. We present Pink, a metacircular Lisplike evaluator on top of this calculus, and demonstrate that we can collapse arbitrarily many levels of selfinterpretation, including levels with semantic modifications. We discuss several examples: compiling regular expressions through an interpreter to base code, building program transformers from modi ed interpreters, and others. We develop these ideas further to include reflection and reification, culminating in Purple, a reflective language inspired by Brown, Blond, and Black, which realizes a conceptually infinite tower, where every aspect of the semantics can change dynamically. Addressing an open challenge, we show how user programs can be compiled and recompiled under usermodified semantics. @Article{POPL18p52, author = {Nada Amin and Tiark Rompf}, title = {Collapsing Towers of Interpreters}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {52}, numpages = {33}, doi = {10.1145/3158140}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Rouvoet, Arjen 
POPL '18: "IntrinsicallyTyped Definitional ..."
IntrinsicallyTyped Definitional Interpreters for Imperative Languages
Casper Bach Poulsen , Arjen Rouvoet , Andrew Tolmach, Robbert Krebbers , and Eelco Visser (Delft University of Technology, Netherlands; Portland State University, USA) A definitional interpreter defines the semantics of an object language in terms of the (wellknown) semantics of a host language, enabling understanding and validation of the semantics through execution. Combining a definitional interpreter with a separate type system requires a separate type safety proof. An alternative approach, at least for pure object languages, is to use a dependentlytyped language to encode the object language type system in the definition of the abstract syntax. Using such intrinsicallytyped abstract syntax definitions allows the host language type checker to verify automatically that the interpreter satisfies type safety. Does this approach scale to larger and more realistic object languages, and in particular to languages with mutable state and objects? In this paper, we describe and demonstrate techniques and libraries in Agda that successfully scale up intrinsicallytyped definitional interpreters to handle rich object languages with nontrivial binding structures and mutable state. While the resulting interpreters are certainly more complex than the simplytyped λcalculus interpreter we start with, we claim that they still meet the goals of being concise, comprehensible, and executable, while guaranteeing type safety for more elaborate object languages. We make the following contributions: (1) A dependentpassing style technique for hiding the weakening of indexed values as they propagate through monadic code. (2) An Agda library for programming with scope graphs and frames, which provides a uniform approach to dealing with name binding in intrinsicallytyped interpreters. (3) Case studies of intrinsicallytyped definitional interpreters for the simplytyped λcalculus with references (STLC+Ref) and for a large subset of Middleweight Java (MJ). @Article{POPL18p16, author = {Casper Bach Poulsen and Arjen Rouvoet and Andrew Tolmach and Robbert Krebbers and Eelco Visser}, title = {IntrinsicallyTyped Definitional Interpreters for Imperative Languages}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {16}, numpages = {34}, doi = {10.1145/3158104}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Rümmer, Philipp 
POPL '18: "String Constraints with Concatenation ..."
String Constraints with Concatenation and Transducers Solved Efficiently
Lukáš Holík , Petr Janků, Anthony W. Lin, Philipp Rümmer, and Tomáš Vojnar (Brno University of Technology, Czechia; University of Oxford, UK; Uppsala University, Sweden) String analysis is the problem of reasoning about how strings are manipulated by a program. It has numerous applications including automatic detection of crosssite scripting, and automatic testcase generation. A popular string analysis technique includes symbolic executions, which at their core use constraint solvers over the string domain, a.k.a. string solvers. Such solvers typically reason about constraints expressed in theories over strings with the concatenation operator as an atomic constraint. In recent years, researchers started to recognise the importance of incorporating the replaceall operator (i.e. replace all occurrences of a string by another string) and, more generally, finitestate transductions in the theories of strings with concatenation. Such string operations are typically crucial for reasoning about XSS vulnerabilities in web applications, especially for modelling sanitisation functions and implicit browser transductions (e.g. innerHTML). Although this results in an undecidable theory in general, it was recently shown that the straightline fragment of the theory is decidable, and is sufficiently expressive in practice. In this paper, we provide the first string solver that can reason about constraints involving both concatenation and finitestate transductions. Moreover, it has a completeness and termination guarantee for several important fragments (e.g. straightline fragment). The main challenge addressed in the paper is the prohibitive worstcase complexity of the theory (doubleexponential time), which is exponentially harder than the case without finitestate transductions. To this end, we propose a method that exploits succinct alternating finitestate automata as concise symbolic representations of string constraints. In contrast to previous approaches using nondeterministic automata, alternation offers not only exponential savings in space when representing Boolean combinations of transducers, but also a possibility of succinct representation of otherwise costly combinations of transducers and concatenation. Reasoning about the emptiness of the AFA language requires a statespace exploration in an exponentialsized graph, for which we use model checking algorithms (e.g. IC3). We have implemented our algorithm and demonstrated its efficacy on benchmarks that are derived from crosssite scripting analysis and other examples in the literature. @Article{POPL18p4, author = {Lukáš Holík and Petr Janků and Anthony W. Lin and Philipp Rümmer and Tomáš Vojnar}, title = {String Constraints with Concatenation and Transducers Solved Efficiently}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {4}, numpages = {32}, doi = {10.1145/3158092}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Sadayappan, P. 
POPL '18: "Analytical Modeling of Cache ..."
Analytical Modeling of Cache Behavior for Affine Programs
Wenlei Bao, Sriram Krishnamoorthy, LouisNoel Pouchet, and P. Sadayappan (Ohio State University, USA; Pacific Northwest National Laboratory, USA; Colorado State University, USA) Optimizing compilers implement program transformation strategies aimed at reducing data movement to or from main memory by exploiting the datacache hierarchy. However, instead of attempting to minimize the number of cache misses, very approximate cost models are used, due to the lack of precise compiletime models for misses for hierarchical caches. The current state of practice for cache miss analysis is based on accurate simulation. However, simulation requires time proportional to the dataset/problem size, as well as the number of distinct cache configurations of interest to be evaluated. This paper takes a fundamentally different approach, by focusing on polyhedral programs with static control flow. Instead of relying on costly simulation, a closedform solution for modeling of misses in a set associative cache hierarchy is developed. This solution can enable program transformation choice at compile time to optimize cache misses. A tool implementing the approach has been developed and used for validation of the framework. @Article{POPL18p32, author = {Wenlei Bao and Sriram Krishnamoorthy and LouisNoel Pouchet and P. Sadayappan}, title = {Analytical Modeling of Cache Behavior for Affine Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {32}, numpages = {26}, doi = {10.1145/3158120}, year = {2018}, } Publisher's Version Article Search 

Sagiv, Mooly 
POPL '18: "Reducing Liveness to Safety ..."
Reducing Liveness to Safety in FirstOrder Logic
Oded Padon, Jochen Hoenicke, Giuliano Losa, Andreas Podelski , Mooly Sagiv, and Sharon Shoham (Tel Aviv University, Israel; University of Freiburg, Germany; University of California at Los Angeles, USA) We develop a new technique for verifying temporal properties of infinitestate (distributed) systems. The main idea is to reduce the temporal verification problem to the problem of verifying the safety of infinitestate systems expressed in firstorder logic. This allows to leverage existing techniques for safety verification to verify temporal properties of interesting distributed protocols, including some that have not been mechanically verified before. We model infinitestate systems using firstorder logic, and use firstorder temporal logic (FOLTL) to specify temporal properties. This general formalism allows to naturally model distributed systems, while supporting both unboundedparallelism (where the system is allowed to dynamically create processes), and infinitestate per process. The traditional approach for verifying temporal properties of infinitestate systems employs wellfounded relations (e.g. using linear arithmetic ranking functions). In contrast, our approach is based the idea of fair cycle detection. In finitestate systems, temporal verification can always be reduced to fair cycle detection (a system contains a fair cycle if it revisits a state after satisfying all fairness constraints). However, with both infinitely many states and infinitely many fairness constraints, a straightforward reduction to fair cycle detection is unsound. To regain soundness, we augment the infinitestate transition system by a dynamically computed finite set, that exploits the locality of transitions. This set lets us define a form of fair cycle detection that is sound in the presence of both infinitely many states, and infinitely many fairness constraints. Our approach allows a new style of temporal verification that does not explicitly involve ranking functions. This fits well with pure firstorder verification which does not explicitly reason about numerical values. In particular, it can be used with effectively propositional firstorder logic (EPR), in which case checking verification conditions is decidable. We applied our technique to verify temporal properties of several interesting protocols. To the best of our knowledge, we have obtained the first mechanized liveness proof for both TLB Shootdown, and Stoppable Paxos. @Article{POPL18p26, author = {Oded Padon and Jochen Hoenicke and Giuliano Losa and Andreas Podelski and Mooly Sagiv and Sharon Shoham}, title = {Reducing Liveness to Safety in FirstOrder Logic}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {26}, numpages = {33}, doi = {10.1145/3158114}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional POPL '18: "Online Detection of Effectively ..." Online Detection of Effectively Callback Free Objects with Applications to Smart Contracts Shelly Grossman, Ittai Abraham, Guy GolanGueta, Yan Michalevsky, Noam Rinetzky, Mooly Sagiv, and Yoni Zohar (Tel Aviv University, Israel; VMware, USA; Stanford University, USA) Callbacks are essential in many programming environments, but drastically complicate program understanding and reasoning because they allow to mutate object's local states by external objects in unexpected fashions, thus breaking modularity. The famous DAO bug in the cryptocurrency framework Ethereum, employed callbacks to steal $150M. We define the notion of Effectively Callback Free (ECF) objects in order to allow callbacks without preventing modular reasoning. An object is ECF in a given execution trace if there exists an equivalent execution trace without callbacks to this object. An object is ECF if it is ECF in every possible execution trace. We study the decidability of dynamically checking ECF in a given execution trace and statically checking if an object is ECF. We also show that dynamically checking ECF in Ethereum is feasible and can be done online. By running the history of all execution traces in Ethereum, we were able to verify that virtually all existing contract executions, excluding these of the DAO or of contracts with similar known vulnerabilities, are ECF. Finally, we show that ECF, whether it is verified dynamically or statically, enables modular reasoning about objects with encapsulated state. @Article{POPL18p48, author = {Shelly Grossman and Ittai Abraham and Guy GolanGueta and Yan Michalevsky and Noam Rinetzky and Mooly Sagiv and Yoni Zohar}, title = {Online Detection of Effectively Callback Free Objects with Applications to Smart Contracts}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {48}, numpages = {28}, doi = {10.1145/3158136}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Sagonas, Konstantinos 
POPL '18: "Effective Stateless Model ..."
Effective Stateless Model Checking for C/C++ Concurrency
Michalis Kokologiannakis, Ori Lahav , Konstantinos Sagonas , and Viktor Vafeiadis (National Technical University of Athens, Greece; Tel Aviv University, Israel; Uppsala University, Sweden; MPISWS, Germany) We present a stateless model checking algorithm for verifying concurrent programs running under RC11, a repaired version of the C/C++11 memory model without dependency cycles. Unlike most previous approaches, which enumerate thread interleavings up to some partial order reduction improvements, our approach works directly on execution graphs and (in the absence of RMW instructions and SC atomics) avoids redundant exploration by construction. We have implemented a model checker, called RCMC, based on this approach and applied it to a number of challenging concurrent programs. Our experiments confirm that RCMC is significantly faster, scales better than other model checking tools, and is also more resilient to small changes in the benchmarks. @Article{POPL18p17, author = {Michalis Kokologiannakis and Ori Lahav and Konstantinos Sagonas and Viktor Vafeiadis}, title = {Effective Stateless Model Checking for C/C++ Concurrency}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {17}, numpages = {32}, doi = {10.1145/3158105}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Sarkar, Susmit 
POPL '18: "Simplifying ARM Concurrency: ..."
Simplifying ARM Concurrency: MulticopyAtomic Axiomatic and Operational Models for ARMv8
Christopher Pulte, Shaked Flur, Will Deacon, Jon French, Susmit Sarkar, and Peter Sewell (University of Cambridge, UK; ARM, UK; University of St. Andrews, UK) ARM has a relaxed memory model, previously specified in informal prose for ARMv7 and ARMv8. Over time, and partly due to work building formal semantics for ARM concurrency, it has become clear that some of the complexity of the model is not justified by the potential benefits. In particular, the model was originally nonmulticopyatomic: writes could become visible to some other threads before becoming visible to all — but this has not been exploited in production implementations, the corresponding potential hardware optimisations are thought to have insufficient benefits in the ARM context, and it gives rise to subtle complications when combined with other ARMv8 features. The ARMv8 architecture has therefore been revised: it now has a multicopyatomic model. It has also been simplified in other respects, including more straightforward notions of dependency, and the architecture now includes a formal concurrency model. In this paper we detail these changes and discuss their motivation. We define two formal concurrency models: an operational one, simplifying the Flowing model of Flur et al., and the axiomatic model of the revised ARMv8 specification. The models were developed by an academic group and by ARM staff, respectively, and this extended collaboration partly motivated the above changes. We prove the equivalence of the two models. The operational model is integrated into an executable exploration tool with new web interface, demonstrated by exhaustively checking the possible behaviours of a loopunrolled version of a Linux kernel lock implementation, a previously known bug due to unprevented speculation, and a fixed version. @Article{POPL18p19, author = {Christopher Pulte and Shaked Flur and Will Deacon and Jon French and Susmit Sarkar and Peter Sewell}, title = {Simplifying ARM Concurrency: MulticopyAtomic Axiomatic and Operational Models for ARMv8}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {19}, numpages = {29}, doi = {10.1145/3158107}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Satake, Yuki 
POPL '18: "Relatively Complete Refinement ..."
Relatively Complete Refinement Type System for Verification of HigherOrder Nondeterministic Programs
Hiroshi Unno , Yuki Satake, and Tachio Terauchi (University of Tsukuba, Japan; Waseda University, Japan) This paper considers verification of nondeterministic higherorder functional programs. Our contribution is a novel type system in which the types are used to express and verify (conditional) safety, termination, nonsafety, and nontermination properties in the presence of ∀∃ branching behavior due to nondeterminism. For instance, the judgement ⊢ e:{u: int  φ(u) }^{∀∀} says that every evaluation of e either diverges or reduces to some integer u satisfying φ(u), whereas ⊢ e:{u: int  ψ(u) }^{∃∀} says that there exists an evaluation of e that either diverges or reduces to some integer u satisfying ψ(u). Note that the former is a safety property whereas the latter is a counterexample to a (conditional) termination property. Following the recent work on typebased verification methods for deterministic higherorder functional programs, we formalize the idea on the foundation of dependent refinement types, thereby allowing the type system to express and verify rich properties involving program values, branching behaviors, and the combination thereof. Our type system is able to seamlessly combine deductions of both universal and existential facts within a unified framework, paving the way for an exciting opportunity for new typebased verification methods that combine both universal and existential reasoning. For example, our system can prove the existence of a path violating some safety property from a proof of termination that uses a wellfoundedness termination argument. We prove that our type system is sound and relatively complete, and further, thanks to having both modes of nondeterminism, we show that our types are closed under complement. @Article{POPL18p12, author = {Hiroshi Unno and Yuki Satake and Tachio Terauchi}, title = {Relatively Complete Refinement Type System for Verification of HigherOrder Nondeterministic Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {12}, numpages = {29}, doi = {10.1145/3158100}, year = {2018}, } Publisher's Version Article Search 

Scherer, Gabriel 
POPL '18: "Correctness of Speculative ..."
Correctness of Speculative Optimizations with Dynamic Deoptimization
Olivier Flückiger , Gabriel Scherer , MingHo Yee, Aviral Goel, Amal Ahmed, and Jan Vitek (Northeastern University, USA; Inria, France; Czech Technical University, Czechia) Highperformance dynamic language implementations make heavy use of speculative optimizations to achieve speeds close to statically compiled languages. These optimizations are typically performed by a justintime compiler that generates code under a set of assumptions about the state of the program and its environment. In certain cases, a program may execute code compiled under assumptions that are no longer valid. The implementation must then deoptimize the program onthefly; this entails finding semantically equivalent code that does not rely on invalid assumptions, translating program state to that expected by the target code, and transferring control. This paper looks at the interaction between optimization and deoptimization, and shows that reasoning about speculation is surprisingly easy when assumptions are made explicit in the program representation. This insight is demonstrated on a compiler intermediate representation, named sourir, modeled after the highlevel representation for a dynamic language. Traditional compiler optimizations such as constant folding, unreachable code elimination, and function inlining are shown to be correct in the presence of assumptions. Furthermore, the paper establishes the correctness of compiler transformations specific to deoptimization: namely unrestricted deoptimization, predicate hoisting, and assume composition. @Article{POPL18p49, author = {Olivier Flückiger and Gabriel Scherer and MingHo Yee and Aviral Goel and Amal Ahmed and Jan Vitek}, title = {Correctness of Speculative Optimizations with Dynamic Deoptimization}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {49}, numpages = {28}, doi = {10.1145/3158137}, year = {2018}, } Publisher's Version Article Search 

Ścibior, Adam 
POPL '18: "Denotational Validation of ..."
Denotational Validation of HigherOrder Bayesian Inference
Adam Ścibior, Ohad Kammar, Matthijs Vákár, Sam Staton, Hongseok Yang, Yufei Cai, Klaus Ostermann , Sean K. Moss, Chris Heunen , and Zoubin Ghahramani (University of Cambridge, UK; MPI Tübingen, Germany; University of Oxford, UK; KAIST, South Korea; University of Tübingen, Germany; University of Edinburgh, UK; Uber AI Labs, USA) We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higherorder functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higherorder functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasiBorel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasiBorel counterpart to the MetropolisHastingsGreen theorem. @Article{POPL18p60, author = {Adam Ścibior and Ohad Kammar and Matthijs Vákár and Sam Staton and Hongseok Yang and Yufei Cai and Klaus Ostermann and Sean K. Moss and Chris Heunen and Zoubin Ghahramani}, title = {Denotational Validation of HigherOrder Bayesian Inference}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {60}, numpages = {29}, doi = {10.1145/3158148}, year = {2018}, } Publisher's Version Article Search Info 

Scott, Ryan G. 
POPL '18: "Refinement Reflection: Complete ..."
Refinement Reflection: Complete Verification with SMT
Niki Vazou, Anish Tondwalkar, Vikraman Choudhury , Ryan G. Scott, Ryan R. Newton, Philip Wadler , and Ranjit Jhala (University of Maryland, USA; University of California at San Diego, USA; Indiana University, USA; University of Edinburgh, UK; Input Output HK, UK) We introduce Refinement Reflection, a new framework for building SMTbased deductive verifiers. The key idea is to reflect the code implementing a userdefined function into the function’s (output) refinement type. As a consequence, at uses of the function, the function definition is instantiated in the SMT logic in a precise fashion that permits decidable verification. Reflection allows the user to write equational proofs of programs just by writing other programs using patternmatching and recursion to perform casesplitting and induction. Thus, via the propositionsastypes principle, we show that reflection permits the specification of arbitrary functional correctness properties. Finally, we introduce a proofsearch algorithm called Proof by Logical Evaluation that uses techniques from model checking and abstract interpretation, to completely automate equational reasoning. We have implemented reflection in Liquid Haskell and used it to verify that the widely used instances of the Monoid, Applicative, Functor, and Monad typeclasses actually satisfy key algebraic laws required to make the clients safe, and have used reflection to build the first library that actually verifies assumptions about associativity and ordering that are crucial for safe deterministic parallelism. @Article{POPL18p53, author = {Niki Vazou and Anish Tondwalkar and Vikraman Choudhury and Ryan G. Scott and Ryan R. Newton and Philip Wadler and Ranjit Jhala}, title = {Refinement Reflection: Complete Verification with SMT}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {53}, numpages = {31}, doi = {10.1145/3158141}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Sergey, Ilya 
POPL '18: "Programming and Proving with ..."
Programming and Proving with Distributed Protocols
Ilya Sergey, James R. Wilcox, and Zachary Tatlock (University College London, UK; University of Washington, USA) Distributed systems play a crucial role in modern infrastructure, but are notoriously difficult to implement correctly. This difficulty arises from two main challenges: (a) correctly implementing core system components (e.g., twophase commit), so all their internal invariants hold, and (b) correctly composing standalone system components into functioning trustworthy applications (e.g., persistent storage built on top of a twophase commit instance). Recent work has developed several approaches for addressing (a) by means of mechanically verifying implementations of core distributed components, but no methodology exists to address (b) by composing such verified components into larger verified applications. As a result, expensive verification efforts for key system components are not easily reusable, which hinders further verification efforts. In this paper, we present Disel, the first framework for implementation and compositional verification of distributed systems and their clients, all within the mechanized, foundational context of the Coq proof assistant. In Disel, users implement distributed systems using a domain specific language shallowly embedded in Coq and providing both highlevel programming constructs as well as lowlevel communication primitives. Components of composite systems are specified in Disel as protocols, which capture systemspecific logic and disentangle system definitions from implementation details. By virtue of Disel's dependent type system, welltyped implementations always satisfy their protocols' invariants and never go wrong, allowing users to verify system implementations interactively using Disel's Hoarestyle program logic, which extends stateoftheart techniques for concurrency verification to the distributed setting. By virtue of the substitution principle and frame rule provided by Disel's logic, system components can be composed leading to modular, reusable verified distributed systems. We describe Disel, illustrate its use with a series of examples, outline its logic and metatheory, and report on our experience using it as a framework for implementing, specifying, and verifying distributed systems. @Article{POPL18p28, author = {Ilya Sergey and James R. Wilcox and Zachary Tatlock}, title = {Programming and Proving with Distributed Protocols}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {28}, numpages = {30}, doi = {10.1145/3158116}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Sewell, Peter 
POPL '18: "Simplifying ARM Concurrency: ..."
Simplifying ARM Concurrency: MulticopyAtomic Axiomatic and Operational Models for ARMv8
Christopher Pulte, Shaked Flur, Will Deacon, Jon French, Susmit Sarkar, and Peter Sewell (University of Cambridge, UK; ARM, UK; University of St. Andrews, UK) ARM has a relaxed memory model, previously specified in informal prose for ARMv7 and ARMv8. Over time, and partly due to work building formal semantics for ARM concurrency, it has become clear that some of the complexity of the model is not justified by the potential benefits. In particular, the model was originally nonmulticopyatomic: writes could become visible to some other threads before becoming visible to all — but this has not been exploited in production implementations, the corresponding potential hardware optimisations are thought to have insufficient benefits in the ARM context, and it gives rise to subtle complications when combined with other ARMv8 features. The ARMv8 architecture has therefore been revised: it now has a multicopyatomic model. It has also been simplified in other respects, including more straightforward notions of dependency, and the architecture now includes a formal concurrency model. In this paper we detail these changes and discuss their motivation. We define two formal concurrency models: an operational one, simplifying the Flowing model of Flur et al., and the axiomatic model of the revised ARMv8 specification. The models were developed by an academic group and by ARM staff, respectively, and this extended collaboration partly motivated the above changes. We prove the equivalence of the two models. The operational model is integrated into an executable exploration tool with new web interface, demonstrated by exhaustively checking the possible behaviours of a loopunrolled version of a Linux kernel lock implementation, a previously known bug due to unprevented speculation, and a fixed version. @Article{POPL18p19, author = {Christopher Pulte and Shaked Flur and Will Deacon and Jon French and Susmit Sarkar and Peter Sewell}, title = {Simplifying ARM Concurrency: MulticopyAtomic Axiomatic and Operational Models for ARMv8}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {19}, numpages = {29}, doi = {10.1145/3158107}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Shaikhha, Amir 
POPL '18: "Unifying Analytic and StaticallyTyped ..."
Unifying Analytic and StaticallyTyped Quasiquotes
Lionel Parreaux , Antoine Voizard, Amir Shaikhha, and Christoph E. Koch (EPFL, Switzerland; University of Pennsylvania, USA) Metaprograms are programs that manipulate (generate, analyze and evaluate) other programs. These tasks are greatly facilitated by quasiquotation, a technique to construct and deconstruct program fragments using quoted code templates expressed in the syntax of the manipulated language. We argue that two main flavors of quasiquotes have existed so far: Lispstyle quasiquotes, which can both construct and deconstruct programs but may produce code that contains type mismatches and unbound variables; and MetaMLstyle quasiquotes, which rely on static typing to prevent these errors, but can only construct programs. In this paper, we show how to combine the advantages of both flavors into a unified framework: we allow the construction, deconstruction and evaluation of program fragments while ensuring that generated programs are welltyped and wellscoped, a combination unseen in previous work. We formalize our approach as λ^{{}}, a multistage calculus with code pattern matching and rewriting, and prove its type safety. We also present its realization in Squid, a metaprogramming framework for Scala, leveraging Scala’s expressive type system. To demonstrate the usefulness of our approach, we introduce speculative rewrite rules, a novel code transformation technique that makes decisive use of these capabilities, and we outline how it simplifies the design of some crucial query compiler optimizations. @Article{POPL18p13, author = {Lionel Parreaux and Antoine Voizard and Amir Shaikhha and Christoph E. Koch}, title = {Unifying Analytic and StaticallyTyped Quasiquotes}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {13}, numpages = {33}, doi = {10.1145/3158101}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Sharma, Rahul 
POPL '18: "On Automatically Proving the ..."
On Automatically Proving the Correctness of math.h Implementations
Wonyeol Lee, Rahul Sharma, and Alex Aiken (Stanford University, USA; Microsoft Research, India) Industry standard implementations of math.h claim (often without formal proof) tight bounds on floatingpoint errors. We demonstrate a novel static analysis that proves these bounds and verifies the correctness of these implementations. Our key insight is a reduction of this verification task to a set of mathematical optimization problems that can be solved by offtheshelf computer algebra systems. We use this analysis to prove the correctness of implementations in Intel's math library automatically. Prior to this work, these implementations could only be verified with significant manual effort. @Article{POPL18p47, author = {Wonyeol Lee and Rahul Sharma and Alex Aiken}, title = {On Automatically Proving the Correctness of math.h Implementations}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {47}, numpages = {32}, doi = {10.1145/3158135}, year = {2018}, } Publisher's Version Article Search 

Shasha, Dennis 
POPL '18: "Go with the Flow: Compositional ..."
Go with the Flow: Compositional Abstractions for Concurrent Data Structures
Siddharth Krishna, Dennis Shasha, and Thomas Wies (New York University, USA) Concurrent separation logics have helped to significantly simplify correctness proofs for concurrent data structures. However, a recurring problem in such proofs is that data structure abstractions that work well in the sequential setting are much harder to reason about in a concurrent setting due to complex sharing and overlays. To solve this problem, we propose a novel approach to abstracting regions in the heap by encoding the data structure invariant into a local condition on each individual node. This condition may depend on a quantity associated with the node that is computed as a fixpoint over the entire heap graph. We refer to this quantity as a flow. Flows can encode both structural properties of the heap (e.g. the reachable nodes from the root form a tree) as well as data invariants (e.g. sortedness). We then introduce the notion of a flow interface, which expresses the relies and guarantees that a heap region imposes on its context to maintain the local flow invariant with respect to the global heap. Our main technical result is that this notion leads to a new semantic model of separation logic. In this model, flow interfaces provide a general abstraction mechanism for describing complex data structures. This abstraction mechanism admits proof rules that generalize over a wide variety of data structures. To demonstrate the versatility of our approach, we show how to extend the logic RGSep with flow interfaces. We have used this new logic to prove linearizability and memory safety of nontrivial concurrent data structures. In particular, we obtain parametric linearizability proofs for concurrent dictionary algorithms that abstract from the details of the underlying data structure representation. These proofs cannot be easily expressed using the abstraction mechanisms provided by existing separation logics. @Article{POPL18p37, author = {Siddharth Krishna and Dennis Shasha and Thomas Wies}, title = {Go with the Flow: Compositional Abstractions for Concurrent Data Structures}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {37}, numpages = {31}, doi = {10.1145/3158125}, year = {2018}, } Publisher's Version Article Search 

Shoham, Sharon 
POPL '18: "Reducing Liveness to Safety ..."
Reducing Liveness to Safety in FirstOrder Logic
Oded Padon, Jochen Hoenicke, Giuliano Losa, Andreas Podelski , Mooly Sagiv, and Sharon Shoham (Tel Aviv University, Israel; University of Freiburg, Germany; University of California at Los Angeles, USA) We develop a new technique for verifying temporal properties of infinitestate (distributed) systems. The main idea is to reduce the temporal verification problem to the problem of verifying the safety of infinitestate systems expressed in firstorder logic. This allows to leverage existing techniques for safety verification to verify temporal properties of interesting distributed protocols, including some that have not been mechanically verified before. We model infinitestate systems using firstorder logic, and use firstorder temporal logic (FOLTL) to specify temporal properties. This general formalism allows to naturally model distributed systems, while supporting both unboundedparallelism (where the system is allowed to dynamically create processes), and infinitestate per process. The traditional approach for verifying temporal properties of infinitestate systems employs wellfounded relations (e.g. using linear arithmetic ranking functions). In contrast, our approach is based the idea of fair cycle detection. In finitestate systems, temporal verification can always be reduced to fair cycle detection (a system contains a fair cycle if it revisits a state after satisfying all fairness constraints). However, with both infinitely many states and infinitely many fairness constraints, a straightforward reduction to fair cycle detection is unsound. To regain soundness, we augment the infinitestate transition system by a dynamically computed finite set, that exploits the locality of transitions. This set lets us define a form of fair cycle detection that is sound in the presence of both infinitely many states, and infinitely many fairness constraints. Our approach allows a new style of temporal verification that does not explicitly involve ranking functions. This fits well with pure firstorder verification which does not explicitly reason about numerical values. In particular, it can be used with effectively propositional firstorder logic (EPR), in which case checking verification conditions is decidable. We applied our technique to verify temporal properties of several interesting protocols. To the best of our knowledge, we have obtained the first mechanized liveness proof for both TLB Shootdown, and Stoppable Paxos. @Article{POPL18p26, author = {Oded Padon and Jochen Hoenicke and Giuliano Losa and Andreas Podelski and Mooly Sagiv and Sharon Shoham}, title = {Reducing Liveness to Safety in FirstOrder Logic}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {26}, numpages = {33}, doi = {10.1145/3158114}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Sieczkowski, Filip 
POPL '18: "Handle with Care: Relational ..."
Handle with Care: Relational Interpretation of Algebraic Effects and Handlers
Dariusz Biernacki, Maciej Piróg, Piotr Polesiuk, and Filip Sieczkowski (University of Wrocław, Poland) Algebraic effects and handlers have received a lot of attention recently, both from the theoretical point of view and in practical language design. This stems from the fact that algebraic effects give the programmer unprecedented freedom to define, combine, and interpret computational effects. This plentyofrope, however, demands not only a deep understanding of the underlying semantics, but also access to practical means of reasoning about effectful code, including correctness and program equivalence. In this paper we tackle this problem by constructing a stepindexed relational interpretation of a callbyvalue calculus with algebraic effect handlers and a rowbased polymorphic typeandeffect system. Our calculus, while striving for simplicity, enjoys desirable theoretical properties, and is close to the cores of programming languages with algebraic effects used in the wild, while the logical relation we build for it can be used to reason about nontrivial properties, such as contextual equivalence and contextual approximation of programs. Our development has been fully formalised in the Coq proof assistant. @Article{POPL18p8, author = {Dariusz Biernacki and Maciej Piróg and Piotr Polesiuk and Filip Sieczkowski}, title = {Handle with Care: Relational Interpretation of Algebraic Effects and Handlers}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {8}, numpages = {30}, doi = {10.1145/3158096}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Singh, Gagandeep 
POPL '18: "A Practical Construction for ..."
A Practical Construction for Decomposing Numerical Abstract Domains
Gagandeep Singh, Markus Püschel, and Martin Vechev (ETH Zurich, Switzerland) Numerical abstract domains such as Polyhedra, Octahedron, Octagon, Interval, and others are an essential component of static program analysis. The choice of domain offers a performance/precision tradeoff ranging from cheap and imprecise (Interval) to expensive and precise (Polyhedra). Recently, significant speedups were achieved for Octagon and Polyhedra by manually decomposing their transformers to work with the Cartesian product of projections associated with partitions of the variable set. While practically useful, this manual process is time consuming, errorprone, and has to be applied from scratch for every domain. In this paper, we present a generic approach for decomposing the transformers of subpolyhedra domains along with conditions for checking whether the decomposed transformers lose precision with respect to the original transformers. These conditions are satisfied by most practical transformers, thus our approach is suitable for increasing the performance of these transformers without compromising their precision. Furthermore, our approach is ``black box:'' it does not require changes to the internals of the original nondecomposed transformers or additional manual effort per domain. We implemented our approach and applied it to the domains of Zones, Octagon, and Polyhedra. We then compared the performance of the decomposed transformers obtained with our generic method versus the state of the art: the (nondecomposed) PPL for Polyhedra and the much faster ELINA (which uses manual decomposition) for Polyhedra and Octagon. Against ELINA we demonstrate finer partitions and an associated speedup of about 2x on average. Our results indicate that the general construction presented in this work is a viable method for improving the performance of subpolyhedra domains. It enables designers of abstract domains to benefit from decomposition without rewriting all of their transformers from scratch as required by prior work. @Article{POPL18p55, author = {Gagandeep Singh and Markus Püschel and Martin Vechev}, title = {A Practical Construction for Decomposing Numerical Abstract Domains}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {55}, numpages = {28}, doi = {10.1145/3158143}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Singh, Rishabh 
POPL '18: "Program Synthesis using Abstraction ..."
Program Synthesis using Abstraction Refinement
Xinyu Wang, Isil Dillig , and Rishabh Singh (University of Texas at Austin, USA; Microsoft Research, USA) We present a new approach to exampleguided program synthesis based on counterexampleguided abstraction refinement. Our method uses the abstract semantics of the underlying DSL to find a program P whose abstract behavior satisfies the examples. However, since program P may be spurious with respect to the concrete semantics, our approach iteratively refines the abstraction until we either find a program that satisfies the examples or prove that no such DSL program exists. Because many programs have the same inputoutput behavior in terms of their abstract semantics, this synthesis methodology significantly reduces the search space compared to existing techniques that use purely concrete semantics. While synthesis using abstraction refinement (SYNGAR) could be implemented in different settings, we propose a refinementbased synthesis algorithm that uses abstract finite tree automata (AFTA). Our technique uses a coarse initial program abstraction to construct an initial AFTA, which is iteratively refined by constructing a proof of incorrectness of any spurious program. In addition to ruling out the spurious program accepted by the previous AFTA, proofs of incorrectness are also useful for ruling out many other spurious programs. We implement these ideas in a framework called Blaze, which can be instantiated in different domains by providing a suitable DSL and its corresponding concrete and abstract semantics. We have used the Blaze framework to build synthesizers for string and matrix transformations, and we compare Blaze with existing techniques. Our results for the string domain show that Blaze compares favorably with FlashFill, a domainspecific synthesizer that is now deployed in Microsoft PowerShell. In the context of matrix manipulations, we compare Blaze against Prose, a stateoftheart generalpurpose VSAbased synthesizer, and show that Blaze results in a 90x speedup over Prose. In both application domains, Blaze also consistently improves upon the performance of two other existing techniques by at least an order of magnitude. @Article{POPL18p63, author = {Xinyu Wang and Isil Dillig and Rishabh Singh}, title = {Program Synthesis using Abstraction Refinement}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {63}, numpages = {30}, doi = {10.1145/3158151}, year = {2018}, } Publisher's Version Article Search POPL '18: "WebRelate: Integrating Web ..." WebRelate: Integrating Web Data with Spreadsheets using Examples Jeevana Priya Inala and Rishabh Singh (Massachusetts Institute of Technology, USA; Microsoft Research, USA) Data integration between web sources and relational data is a key challenge faced by data scientists and spreadsheet users. There are two main challenges in programmatically joining web data with relational data. First, most websites do not expose a direct interface to obtain tabular data, so the user needs to formulate a logic to get to different webpages for each input row in the relational table. Second, after reaching the desired webpage, the user needs to write complex scripts to extract the relevant data, which is often conditioned on the input data. Since many data scientists and endusers come from diverse backgrounds, writing such complex regularexpression based logical scripts to perform data integration tasks is unfortunately often beyond their programming expertise. We present WebRelate, a system that allows users to join semistructured web data with relational data in spreadsheets using inputoutput examples. WebRelate decomposes the web data integration task into two subtasks of i) URL learning and ii) inputdependent web extraction. We introduce a novel synthesis paradigm called "Outputconstrained Programming By Examples", which allows us to use the finite set of possible outputs for the new inputs to efficiently constrain the search in the synthesis algorithm. We instantiate this paradigm for the two subtasks in WebRelate. The first subtask generates the URLs for the webpages containing the desired data for all rows in the relational table. WebRelate achieves this by learning a string transformation program using a few example URLs. The second subtask uses examples of desired data to be extracted from the corresponding webpages and learns a program to extract the data for the other rows. We design expressive domainspecific languages for URL generation and web data extraction, and present efficient synthesis algorithms for learning programs in these DSLs from few inputoutput examples. We evaluate WebRelate on 88 realworld web data integration tasks taken from online help forums and Excel product team, and show that WebRelate can learn the desired programs within few seconds using only 1 example for the majority of the tasks. @Article{POPL18p2, author = {Jeevana Priya Inala and Rishabh Singh}, title = {WebRelate: Integrating Web Data with Spreadsheets using Examples}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {2}, numpages = {28}, doi = {10.1145/3158090}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Sinha, Nishant 
POPL '18: "DataCentric Dynamic Partial ..."
DataCentric Dynamic Partial Order Reduction
Marek Chalupa, Krishnendu Chatterjee , Andreas Pavlogiannis, Nishant Sinha, and Kapil Vaidya (Masaryk University, Czechia; IST Austria, Austria; Kena Labs, India; IIT Bombay, India) We present a new dynamic partialorder reduction method for stateless model checking of concurrent programs. A common approach for exploring program behaviors relies on enumerating the traces of the program, without storing the visited states (aka stateless exploration). As the number of distinct traces grows exponentially, dynamic partialorder reduction (DPOR) techniques have been successfully used to partition the space of traces into equivalence classes (Mazurkiewicz partitioning), with the goal of exploring only few representative traces from each class. We introduce a new equivalence on traces under sequential consistency semantics, which we call the observation equivalence. Two traces are observationally equivalent if every read event observes the same write event in both traces. While the traditional Mazurkiewicz equivalence is controlcentric, our new definition is datacentric. We show that our observation equivalence is coarser than the Mazurkiewicz equivalence, and in many cases even exponentially coarser. We devise a DPOR exploration of the trace space, called datacentric DPOR, based on the observation equivalence. For acyclic architectures, our algorithm is guaranteed to explore exactly one representative trace from each observation class, while spending polynomial time per class. Hence, our algorithm is optimal wrt the observation equivalence, and in several cases explores exponentially fewer traces than any enumerative method based on the Mazurkiewicz equivalence. For cyclic architectures, we consider an equivalence between traces which is finer than the observation equivalence; but coarser than the Mazurkiewicz equivalence, and in some cases is exponentially coarser. Our datacentric DPOR algorithm remains optimal under this trace equivalence. Finally, we perform a basic experimental comparison between the existing Mazurkiewiczbased DPOR and our datacentric DPOR on a set of academic benchmarks. Our results show a significant reduction in both running time and the number of explored equivalence classes. @Article{POPL18p31, author = {Marek Chalupa and Krishnendu Chatterjee and Andreas Pavlogiannis and Nishant Sinha and Kapil Vaidya}, title = {DataCentric Dynamic Partial Order Reduction}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {31}, numpages = {30}, doi = {10.1145/3158119}, year = {2018}, } Publisher's Version Article Search 

Spiwack, Arnaud 
POPL '18: "Linear Haskell: Practical ..."
Linear Haskell: Practical Linearity in a HigherOrder Polymorphic Language
JeanPhilippe Bernardy, Mathieu Boespflug, Ryan R. Newton, Simon Peyton Jones, and Arnaud Spiwack (University of Gothenburg, Sweden; Tweag I/O, France; Indiana University, USA; Microsoft Research, UK) Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind: backwardscompatibility and code reuse across linear and nonlinear users of a library. Only then can the benefits of linear types permeate conventional functional programming. Rather than bifurcate types into linear and nonlinear counterparts, we instead attach linearity to function arrows. Linear functions can receive inputs from linearlybound values, but can also operate over unrestricted, regular values. To demonstrate the efficacy of our linear type system — both how easy it can be integrated in an existing language implementation and how streamlined it makes it to write programs with linear types — we implemented our type system in ghc, the leading Haskell compiler, and demonstrate two kinds of applications of linear types: mutable data with pure interfaces; and enforcing protocols in I/Operforming functions. @Article{POPL18p5, author = {JeanPhilippe Bernardy and Mathieu Boespflug and Ryan R. Newton and Simon Peyton Jones and Arnaud Spiwack}, title = {Linear Haskell: Practical Linearity in a HigherOrder Polymorphic Language}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {5}, numpages = {29}, doi = {10.1145/3158093}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Staton, Sam 
POPL '18: "Denotational Validation of ..."
Denotational Validation of HigherOrder Bayesian Inference
Adam Ścibior, Ohad Kammar, Matthijs Vákár, Sam Staton, Hongseok Yang, Yufei Cai, Klaus Ostermann , Sean K. Moss, Chris Heunen , and Zoubin Ghahramani (University of Cambridge, UK; MPI Tübingen, Germany; University of Oxford, UK; KAIST, South Korea; University of Tübingen, Germany; University of Edinburgh, UK; Uber AI Labs, USA) We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higherorder functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higherorder functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasiBorel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasiBorel counterpart to the MetropolisHastingsGreen theorem. @Article{POPL18p60, author = {Adam Ścibior and Ohad Kammar and Matthijs Vákár and Sam Staton and Hongseok Yang and Yufei Cai and Klaus Ostermann and Sean K. Moss and Chris Heunen and Zoubin Ghahramani}, title = {Denotational Validation of HigherOrder Bayesian Inference}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {60}, numpages = {29}, doi = {10.1145/3158148}, year = {2018}, } Publisher's Version Article Search Info 

Stefanesco, Léo 
POPL '18: "A Logical Relation for Monadic ..."
A Logical Relation for Monadic Encapsulation of State: Proving Contextual Equivalences in the Presence of runST
Amin Timany, Léo Stefanesco, Morten KroghJespersen, and Lars Birkedal (KU Leuven, Belgium; IRIF, France; CNRS, France; University of Paris Diderot, France; Aarhus University, Denmark) We present a logical relations model of a higherorder functional programming language with impredicative polymorphism, recursive types, and a Haskellstyle ST monad type with runST. We use our logical relations model to show that runST provides proper encapsulation of state, by showing that effectful computations encapsulated by runST are heap independent. Furthermore, we show that contextual refinements and equivalences that are expected to hold for pure computations do indeed hold in the presence of runST. This is the first time such relational results have been proven for a language with monadic encapsulation of state. We have formalized all the technical development and results in Coq. @Article{POPL18p64, author = {Amin Timany and Léo Stefanesco and Morten KroghJespersen and Lars Birkedal}, title = {A Logical Relation for Monadic Encapsulation of State: Proving Contextual Equivalences in the Presence of runST}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {64}, numpages = {28}, doi = {10.1145/3158152}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Strub, PierreYves 
POPL '18: "Proving Expected Sensitivity ..."
Proving Expected Sensitivity of Probabilistic Programs
Gilles Barthe , Thomas Espitau, Benjamin Grégoire, Justin Hsu , and PierreYves Strub (IMDEA Software Institute, Spain; UPMC, France; Inria, France; University College London, UK; École Polytechnique, France) Program sensitivity, also known as Lipschitz continuity, describes how small changes in a program’s input lead to bounded changes in the output. We propose an average notion of program sensitivity for probabilistic programs—expected sensitivity—that averages a distance function over a probabilistic coupling of two output distributions from two similar inputs. By varying the distance, expected sensitivity recovers useful notions of probabilistic function sensitivity, including stability of machine learning algorithms and convergence of Markov chains. Furthermore, expected sensitivity satisfies clean compositional properties and is amenable to formal verification. We develop a relational program logic called EpRHL for proving expected sensitivity properties. Our logic features two key ideas. First, relational preconditions and postconditions are expressed using distances, a realvalued generalization of typical booleanvalued (relational) assertions. Second, judgments are interpreted in terms of expectation coupling, a novel, quantitative generalization of probabilistic couplings which supports compositional reasoning. We demonstrate our logic on examples beyond the reach of prior relational logics. Our main example formalizes uniform stability of the stochastic gradient method. Furthermore, we prove rapid mixing for a probabilistic model of population dynamics. We also extend our logic with a transitivity principle for expectation couplings to capture the path coupling proof technique by Bubley and Dyer, and formalize rapid mixing of the Glauber dynamics from statistical physics. @Article{POPL18p57, author = {Gilles Barthe and Thomas Espitau and Benjamin Grégoire and Justin Hsu and PierreYves Strub}, title = {Proving Expected Sensitivity of Probabilistic Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {57}, numpages = {29}, doi = {10.1145/3158145}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Stucki, Sandro 
POPL '18: "Simplicitly: Foundations and ..."
Simplicitly: Foundations and Applications of Implicit Function Types
Martin Odersky, Olivier Blanvillain, Fengyun Liu, Aggelos Biboudis, Heather Miller, and Sandro Stucki (EPFL, Switzerland; Northeastern University, USA) Understanding a program entails understanding its context; dependencies, configurations and even implementations are all forms of contexts. Modern programming languages and theorem provers offer an array of constructs to define contexts, implicitly. Scala offers implicit parameters which are used pervasively, but which cannot be abstracted over. This paper describes a generalization of implicit parameters to implicit function types, a powerful way to abstract over the context in which some piece of code is run. We provide a formalization based on bidirectional typechecking that closely follows the semantics implemented by the Scala compiler. To demonstrate their range of abstraction capabilities, we present several applications that make use of implicit function types. We show how to encode the builder pattern, tagless interpreters, reader and free monads and we assess the performance of the monadic structures presented. @Article{POPL18p42, author = {Martin Odersky and Olivier Blanvillain and Fengyun Liu and Aggelos Biboudis and Heather Miller and Sandro Stucki}, title = {Simplicitly: Foundations and Applications of Implicit Function Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {42}, numpages = {29}, doi = {10.1145/3158130}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Swamy, Nikhil 
POPL '18: "Recalling a Witness: Foundations ..."
Recalling a Witness: Foundations and Applications of Monotonic State
Danel Ahman, Cédric Fournet, Cătălin Hriţcu, Kenji Maillard , Aseem Rastogi, and Nikhil Swamy (Inria, France; Microsoft Research, UK; ENS Paris, France; Microsoft Research, India; Microsoft Research, USA) We provide a way to ease the verification of programs whose state evolves monotonically. The main idea is that a property witnessed in a prior state can be soundly recalled in the current state, provided (1) state evolves according to a given preorder, and (2) the property is preserved by this preorder. In many scenarios, such monotonic reasoning yields concise modular proofs, saving the need for explicit program invariants. We distill our approach into the monotonicstate monad, a general yet compact interface for Hoarestyle reasoning about monotonic state in a dependently typed language. We prove the soundness of the monotonicstate monad and use it as a unified foundation for reasoning about monotonic state in the F^{⋆} verification system. Based on this foundation, we build libraries for various mutable data structures like monotonic references and apply these libraries at scale to the verification of several distributed applications. @Article{POPL18p65, author = {Danel Ahman and Cédric Fournet and Cătălin Hriţcu and Kenji Maillard and Aseem Rastogi and Nikhil Swamy}, title = {Recalling a Witness: Foundations and Applications of Monotonic State}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {65}, numpages = {30}, doi = {10.1145/3158153}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Ta, QuangTrung 
POPL '18: "Automated Lemma Synthesis ..."
Automated Lemma Synthesis in SymbolicHeap Separation Logic
QuangTrung Ta, Ton Chanh Le, SiauCheng Khoo, and WeiNgan Chin (National University of Singapore, Singapore) The symbolicheap fragment of separation logic has been actively developed and advocated for verifying the memorysafety property of computer programs. At present, one of its biggest challenges is to effectively prove entailments containing inductive heap predicates. These entailments are usually proof obligations generated when verifying programs that manipulate complex data structures like linked lists, trees, or graphs. To assist in proving such entailments, this paper introduces a lemma synthesis framework, which automatically discovers lemmas to serve as eureka steps in the proofs. Mathematical induction and templatebased constraint solving are two pillars of our framework. To derive the supporting lemmas for a given entailment, the framework firstly identifies possible lemma templates from the entailment's heap structure. It then sets up unknown relations among each template's variables and conducts structural induction proof to generate constraints about these relations. Finally, it solves the constraints to find out actual definitions of the unknown relations, thus discovers the lemmas. We have integrated this framework into a prototype prover and have experimented it on various entailment benchmarks. The experimental results show that our lemmasynthesisassisted prover can prove many entailments that could not be handled by existing techniques. This new proposal opens up more opportunities to automatically reason with complex inductive heap predicates. @Article{POPL18p9, author = {QuangTrung Ta and Ton Chanh Le and SiauCheng Khoo and WeiNgan Chin}, title = {Automated Lemma Synthesis in SymbolicHeap Separation Logic}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {9}, numpages = {29}, doi = {10.1145/3158097}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Tasson, Christine 
POPL '18: "Measurable Cones and Stable, ..."
Measurable Cones and Stable, Measurable Functions: A Model for Probabilistic HigherOrder Programming
Thomas Ehrhard, Michele Pagani, and Christine Tasson (University of Paris Diderot, France; CNRS, France) We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpoenriched cartesian closed category. This category gives a denotational model of an extension of PCF supporting the main primitives of probabilistic functional programming, like continuous and discrete probabilistic distributions, sampling, conditioning and full recursion. We prove the soundness and adequacy of this model with respect to a callbyname operational semantics and give some examples of its denotations. @Article{POPL18p59, author = {Thomas Ehrhard and Michele Pagani and Christine Tasson}, title = {Measurable Cones and Stable, Measurable Functions: A Model for Probabilistic HigherOrder Programming}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {59}, numpages = {28}, doi = {10.1145/3158147}, year = {2018}, } Publisher's Version Article Search Info 

Tatlock, Zachary 
POPL '18: "Programming and Proving with ..."
Programming and Proving with Distributed Protocols
Ilya Sergey, James R. Wilcox, and Zachary Tatlock (University College London, UK; University of Washington, USA) Distributed systems play a crucial role in modern infrastructure, but are notoriously difficult to implement correctly. This difficulty arises from two main challenges: (a) correctly implementing core system components (e.g., twophase commit), so all their internal invariants hold, and (b) correctly composing standalone system components into functioning trustworthy applications (e.g., persistent storage built on top of a twophase commit instance). Recent work has developed several approaches for addressing (a) by means of mechanically verifying implementations of core distributed components, but no methodology exists to address (b) by composing such verified components into larger verified applications. As a result, expensive verification efforts for key system components are not easily reusable, which hinders further verification efforts. In this paper, we present Disel, the first framework for implementation and compositional verification of distributed systems and their clients, all within the mechanized, foundational context of the Coq proof assistant. In Disel, users implement distributed systems using a domain specific language shallowly embedded in Coq and providing both highlevel programming constructs as well as lowlevel communication primitives. Components of composite systems are specified in Disel as protocols, which capture systemspecific logic and disentangle system definitions from implementation details. By virtue of Disel's dependent type system, welltyped implementations always satisfy their protocols' invariants and never go wrong, allowing users to verify system implementations interactively using Disel's Hoarestyle program logic, which extends stateoftheart techniques for concurrency verification to the distributed setting. By virtue of the substitution principle and frame rule provided by Disel's logic, system components can be composed leading to modular, reusable verified distributed systems. We describe Disel, illustrate its use with a series of examples, outline its logic and metatheory, and report on our experience using it as a framework for implementing, specifying, and verifying distributed systems. @Article{POPL18p28, author = {Ilya Sergey and James R. Wilcox and Zachary Tatlock}, title = {Programming and Proving with Distributed Protocols}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {28}, numpages = {30}, doi = {10.1145/3158116}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Terauchi, Tachio 
POPL '18: "Relatively Complete Refinement ..."
Relatively Complete Refinement Type System for Verification of HigherOrder Nondeterministic Programs
Hiroshi Unno , Yuki Satake, and Tachio Terauchi (University of Tsukuba, Japan; Waseda University, Japan) This paper considers verification of nondeterministic higherorder functional programs. Our contribution is a novel type system in which the types are used to express and verify (conditional) safety, termination, nonsafety, and nontermination properties in the presence of ∀∃ branching behavior due to nondeterminism. For instance, the judgement ⊢ e:{u: int  φ(u) }^{∀∀} says that every evaluation of e either diverges or reduces to some integer u satisfying φ(u), whereas ⊢ e:{u: int  ψ(u) }^{∃∀} says that there exists an evaluation of e that either diverges or reduces to some integer u satisfying ψ(u). Note that the former is a safety property whereas the latter is a counterexample to a (conditional) termination property. Following the recent work on typebased verification methods for deterministic higherorder functional programs, we formalize the idea on the foundation of dependent refinement types, thereby allowing the type system to express and verify rich properties involving program values, branching behaviors, and the combination thereof. Our type system is able to seamlessly combine deductions of both universal and existential facts within a unified framework, paving the way for an exciting opportunity for new typebased verification methods that combine both universal and existential reasoning. For example, our system can prove the existence of a path violating some safety property from a proof of termination that uses a wellfoundedness termination argument. We prove that our type system is sound and relatively complete, and further, thanks to having both modes of nondeterminism, we show that our types are closed under complement. @Article{POPL18p12, author = {Hiroshi Unno and Yuki Satake and Tachio Terauchi}, title = {Relatively Complete Refinement Type System for Verification of HigherOrder Nondeterministic Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {12}, numpages = {29}, doi = {10.1145/3158100}, year = {2018}, } Publisher's Version Article Search 

Timany, Amin 
POPL '18: "A Logical Relation for Monadic ..."
A Logical Relation for Monadic Encapsulation of State: Proving Contextual Equivalences in the Presence of runST
Amin Timany, Léo Stefanesco, Morten KroghJespersen, and Lars Birkedal (KU Leuven, Belgium; IRIF, France; CNRS, France; University of Paris Diderot, France; Aarhus University, Denmark) We present a logical relations model of a higherorder functional programming language with impredicative polymorphism, recursive types, and a Haskellstyle ST monad type with runST. We use our logical relations model to show that runST provides proper encapsulation of state, by showing that effectful computations encapsulated by runST are heap independent. Furthermore, we show that contextual refinements and equivalences that are expected to hold for pure computations do indeed hold in the presence of runST. This is the first time such relational results have been proven for a language with monadic encapsulation of state. We have formalized all the technical development and results in Coq. @Article{POPL18p64, author = {Amin Timany and Léo Stefanesco and Morten KroghJespersen and Lars Birkedal}, title = {A Logical Relation for Monadic Encapsulation of State: Proving Contextual Equivalences in the Presence of runST}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {64}, numpages = {28}, doi = {10.1145/3158152}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

TobinHochstadt, Sam 
POPL '18: "Soft Contract Verification ..."
Soft Contract Verification for HigherOrder Stateful Programs
Phúc C. Nguyễn, Thomas Gilray, Sam TobinHochstadt, and David Van Horn (University of Maryland, USA; Indiana University, USA) Software contracts allow programmers to state rich program properties using the full expressive power of an object language. However, since they are enforced at runtime, monitoring contracts imposes significant overhead and delays error discovery. So contract veri cation aims to guarantee all or most of these properties ahead of time, enabling valuable optimizations and yielding a more general assurance of correctness. Existing methods for static contract verification satisfy the needs of more restricted target languages, but fail to address the challenges unique to those conjoining untyped, dynamic programming, higherorder functions, modularity, and statefulness. Our approach tackles all these features at once, in the context of the full Racket system—a mature environment for stateful, higherorder, multiparadigm programming with or with out types. Evaluating our method using a set of both pure and stateful benchmarks, we are able to verify 99.94% of checks statically (all but 28 of 49, 861). Stateful, higherorder functions pose significant challenges for static contract verification in particular. In the presence of these features, a modular analysis must permit code from the current module to escape permanently to an opaque context (unspecified code from outside the current module) that may be stateful and therefore store a reference to the escaped closure. Also, contracts themselves, being predicates wri en in unrestricted Racket, may exhibit stateful behavior; a sound approach must be robust to contracts which are arbitrarily expressive and interwoven with the code they monitor. In this paper, we present and evaluate our solution based on higherorder symbolic execution, explain the techniques we used to address such thorny issues, formalize a notion of behavioral approximation, and use it to provide a mechanized proof of soundness. @Article{POPL18p51, author = {Phúc C. Nguyễn and Thomas Gilray and Sam TobinHochstadt and David Van Horn}, title = {Soft Contract Verification for HigherOrder Stateful Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {51}, numpages = {30}, doi = {10.1145/3158139}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Tolmach, Andrew 
POPL '18: "IntrinsicallyTyped Definitional ..."
IntrinsicallyTyped Definitional Interpreters for Imperative Languages
Casper Bach Poulsen , Arjen Rouvoet , Andrew Tolmach, Robbert Krebbers , and Eelco Visser (Delft University of Technology, Netherlands; Portland State University, USA) A definitional interpreter defines the semantics of an object language in terms of the (wellknown) semantics of a host language, enabling understanding and validation of the semantics through execution. Combining a definitional interpreter with a separate type system requires a separate type safety proof. An alternative approach, at least for pure object languages, is to use a dependentlytyped language to encode the object language type system in the definition of the abstract syntax. Using such intrinsicallytyped abstract syntax definitions allows the host language type checker to verify automatically that the interpreter satisfies type safety. Does this approach scale to larger and more realistic object languages, and in particular to languages with mutable state and objects? In this paper, we describe and demonstrate techniques and libraries in Agda that successfully scale up intrinsicallytyped definitional interpreters to handle rich object languages with nontrivial binding structures and mutable state. While the resulting interpreters are certainly more complex than the simplytyped λcalculus interpreter we start with, we claim that they still meet the goals of being concise, comprehensible, and executable, while guaranteeing type safety for more elaborate object languages. We make the following contributions: (1) A dependentpassing style technique for hiding the weakening of indexed values as they propagate through monadic code. (2) An Agda library for programming with scope graphs and frames, which provides a uniform approach to dealing with name binding in intrinsicallytyped interpreters. (3) Case studies of intrinsicallytyped definitional interpreters for the simplytyped λcalculus with references (STLC+Ref) and for a large subset of Middleweight Java (MJ). @Article{POPL18p16, author = {Casper Bach Poulsen and Arjen Rouvoet and Andrew Tolmach and Robbert Krebbers and Eelco Visser}, title = {IntrinsicallyTyped Definitional Interpreters for Imperative Languages}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {16}, numpages = {34}, doi = {10.1145/3158104}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Tondwalkar, Anish 
POPL '18: "Refinement Reflection: Complete ..."
Refinement Reflection: Complete Verification with SMT
Niki Vazou, Anish Tondwalkar, Vikraman Choudhury , Ryan G. Scott, Ryan R. Newton, Philip Wadler , and Ranjit Jhala (University of Maryland, USA; University of California at San Diego, USA; Indiana University, USA; University of Edinburgh, UK; Input Output HK, UK) We introduce Refinement Reflection, a new framework for building SMTbased deductive verifiers. The key idea is to reflect the code implementing a userdefined function into the function’s (output) refinement type. As a consequence, at uses of the function, the function definition is instantiated in the SMT logic in a precise fashion that permits decidable verification. Reflection allows the user to write equational proofs of programs just by writing other programs using patternmatching and recursion to perform casesplitting and induction. Thus, via the propositionsastypes principle, we show that reflection permits the specification of arbitrary functional correctness properties. Finally, we introduce a proofsearch algorithm called Proof by Logical Evaluation that uses techniques from model checking and abstract interpretation, to completely automate equational reasoning. We have implemented reflection in Liquid Haskell and used it to verify that the widely used instances of the Monoid, Applicative, Functor, and Monad typeclasses actually satisfy key algebraic laws required to make the clients safe, and have used reflection to build the first library that actually verifies assumptions about associativity and ordering that are crucial for safe deterministic parallelism. @Article{POPL18p53, author = {Niki Vazou and Anish Tondwalkar and Vikraman Choudhury and Ryan G. Scott and Ryan R. Newton and Philip Wadler and Ranjit Jhala}, title = {Refinement Reflection: Complete Verification with SMT}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {53}, numpages = {31}, doi = {10.1145/3158141}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Torlak, Emina 
POPL '18: "Symbolic Types for Lenient ..."
Symbolic Types for Lenient Symbolic Execution
Stephen Chang, Alex Knauth, and Emina Torlak (Northeastern University, USA; University of Washington, USA) We present lambda_sym, a typed λcalculus for lenient symbolic execution, where some language constructs do not recognize symbolic values. Its type system, however, ensures safe behavior of all symbolic values in a program. Our calculus extends a base occurrence typing system with symbolic types and mutable state, making it a suitable model for both functional and imperative symbolically executed languages. Naively allowing mutation in this mixed setting introduces soundness issues, however, so we further add concreteness polymorphism, which restores soundness without rejecting too many valid programs. To show that our calculus is a useful model for a real language, we implemented Typed Rosette, a typed extension of the solveraided Rosette language. We evaluate Typed Rosette by porting a large code base, demonstrating that our type system accommodates a wide variety of symbolically executed programs. @Article{POPL18p40, author = {Stephen Chang and Alex Knauth and Emina Torlak}, title = {Symbolic Types for Lenient Symbolic Execution}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {40}, numpages = {29}, doi = {10.1145/3158128}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Unno, Hiroshi 
POPL '18: "Relatively Complete Refinement ..."
Relatively Complete Refinement Type System for Verification of HigherOrder Nondeterministic Programs
Hiroshi Unno , Yuki Satake, and Tachio Terauchi (University of Tsukuba, Japan; Waseda University, Japan) This paper considers verification of nondeterministic higherorder functional programs. Our contribution is a novel type system in which the types are used to express and verify (conditional) safety, termination, nonsafety, and nontermination properties in the presence of ∀∃ branching behavior due to nondeterminism. For instance, the judgement ⊢ e:{u: int  φ(u) }^{∀∀} says that every evaluation of e either diverges or reduces to some integer u satisfying φ(u), whereas ⊢ e:{u: int  ψ(u) }^{∃∀} says that there exists an evaluation of e that either diverges or reduces to some integer u satisfying ψ(u). Note that the former is a safety property whereas the latter is a counterexample to a (conditional) termination property. Following the recent work on typebased verification methods for deterministic higherorder functional programs, we formalize the idea on the foundation of dependent refinement types, thereby allowing the type system to express and verify rich properties involving program values, branching behaviors, and the combination thereof. Our type system is able to seamlessly combine deductions of both universal and existential facts within a unified framework, paving the way for an exciting opportunity for new typebased verification methods that combine both universal and existential reasoning. For example, our system can prove the existence of a path violating some safety property from a proof of termination that uses a wellfoundedness termination argument. We prove that our type system is sound and relatively complete, and further, thanks to having both modes of nondeterminism, we show that our types are closed under complement. @Article{POPL18p12, author = {Hiroshi Unno and Yuki Satake and Tachio Terauchi}, title = {Relatively Complete Refinement Type System for Verification of HigherOrder Nondeterministic Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {12}, numpages = {29}, doi = {10.1145/3158100}, year = {2018}, } Publisher's Version Article Search 

Vafeiadis, Viktor 
POPL '18: "Effective Stateless Model ..."
Effective Stateless Model Checking for C/C++ Concurrency
Michalis Kokologiannakis, Ori Lahav , Konstantinos Sagonas , and Viktor Vafeiadis (National Technical University of Athens, Greece; Tel Aviv University, Israel; Uppsala University, Sweden; MPISWS, Germany) We present a stateless model checking algorithm for verifying concurrent programs running under RC11, a repaired version of the C/C++11 memory model without dependency cycles. Unlike most previous approaches, which enumerate thread interleavings up to some partial order reduction improvements, our approach works directly on execution graphs and (in the absence of RMW instructions and SC atomics) avoids redundant exploration by construction. We have implemented a model checker, called RCMC, based on this approach and applied it to a number of challenging concurrent programs. Our experiments confirm that RCMC is significantly faster, scales better than other model checking tools, and is also more resilient to small changes in the benchmarks. @Article{POPL18p17, author = {Michalis Kokologiannakis and Ori Lahav and Konstantinos Sagonas and Viktor Vafeiadis}, title = {Effective Stateless Model Checking for C/C++ Concurrency}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {17}, numpages = {32}, doi = {10.1145/3158105}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Vaidya, Kapil 
POPL '18: "DataCentric Dynamic Partial ..."
DataCentric Dynamic Partial Order Reduction
Marek Chalupa, Krishnendu Chatterjee , Andreas Pavlogiannis, Nishant Sinha, and Kapil Vaidya (Masaryk University, Czechia; IST Austria, Austria; Kena Labs, India; IIT Bombay, India) We present a new dynamic partialorder reduction method for stateless model checking of concurrent programs. A common approach for exploring program behaviors relies on enumerating the traces of the program, without storing the visited states (aka stateless exploration). As the number of distinct traces grows exponentially, dynamic partialorder reduction (DPOR) techniques have been successfully used to partition the space of traces into equivalence classes (Mazurkiewicz partitioning), with the goal of exploring only few representative traces from each class. We introduce a new equivalence on traces under sequential consistency semantics, which we call the observation equivalence. Two traces are observationally equivalent if every read event observes the same write event in both traces. While the traditional Mazurkiewicz equivalence is controlcentric, our new definition is datacentric. We show that our observation equivalence is coarser than the Mazurkiewicz equivalence, and in many cases even exponentially coarser. We devise a DPOR exploration of the trace space, called datacentric DPOR, based on the observation equivalence. For acyclic architectures, our algorithm is guaranteed to explore exactly one representative trace from each observation class, while spending polynomial time per class. Hence, our algorithm is optimal wrt the observation equivalence, and in several cases explores exponentially fewer traces than any enumerative method based on the Mazurkiewicz equivalence. For cyclic architectures, we consider an equivalence between traces which is finer than the observation equivalence; but coarser than the Mazurkiewicz equivalence, and in some cases is exponentially coarser. Our datacentric DPOR algorithm remains optimal under this trace equivalence. Finally, we perform a basic experimental comparison between the existing Mazurkiewiczbased DPOR and our datacentric DPOR on a set of academic benchmarks. Our results show a significant reduction in both running time and the number of explored equivalence classes. @Article{POPL18p31, author = {Marek Chalupa and Krishnendu Chatterjee and Andreas Pavlogiannis and Nishant Sinha and Kapil Vaidya}, title = {DataCentric Dynamic Partial Order Reduction}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {31}, numpages = {30}, doi = {10.1145/3158119}, year = {2018}, } Publisher's Version Article Search 

Vákár, Matthijs 
POPL '18: "Denotational Validation of ..."
Denotational Validation of HigherOrder Bayesian Inference
Adam Ścibior, Ohad Kammar, Matthijs Vákár, Sam Staton, Hongseok Yang, Yufei Cai, Klaus Ostermann , Sean K. Moss, Chris Heunen , and Zoubin Ghahramani (University of Cambridge, UK; MPI Tübingen, Germany; University of Oxford, UK; KAIST, South Korea; University of Tübingen, Germany; University of Edinburgh, UK; Uber AI Labs, USA) We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higherorder functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higherorder functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasiBorel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasiBorel counterpart to the MetropolisHastingsGreen theorem. @Article{POPL18p60, author = {Adam Ścibior and Ohad Kammar and Matthijs Vákár and Sam Staton and Hongseok Yang and Yufei Cai and Klaus Ostermann and Sean K. Moss and Chris Heunen and Zoubin Ghahramani}, title = {Denotational Validation of HigherOrder Bayesian Inference}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {60}, numpages = {29}, doi = {10.1145/3158148}, year = {2018}, } Publisher's Version Article Search Info 

Van Horn, David 
POPL '18: "Soft Contract Verification ..."
Soft Contract Verification for HigherOrder Stateful Programs
Phúc C. Nguyễn, Thomas Gilray, Sam TobinHochstadt, and David Van Horn (University of Maryland, USA; Indiana University, USA) Software contracts allow programmers to state rich program properties using the full expressive power of an object language. However, since they are enforced at runtime, monitoring contracts imposes significant overhead and delays error discovery. So contract veri cation aims to guarantee all or most of these properties ahead of time, enabling valuable optimizations and yielding a more general assurance of correctness. Existing methods for static contract verification satisfy the needs of more restricted target languages, but fail to address the challenges unique to those conjoining untyped, dynamic programming, higherorder functions, modularity, and statefulness. Our approach tackles all these features at once, in the context of the full Racket system—a mature environment for stateful, higherorder, multiparadigm programming with or with out types. Evaluating our method using a set of both pure and stateful benchmarks, we are able to verify 99.94% of checks statically (all but 28 of 49, 861). Stateful, higherorder functions pose significant challenges for static contract verification in particular. In the presence of these features, a modular analysis must permit code from the current module to escape permanently to an opaque context (unspecified code from outside the current module) that may be stateful and therefore store a reference to the escaped closure. Also, contracts themselves, being predicates wri en in unrestricted Racket, may exhibit stateful behavior; a sound approach must be robust to contracts which are arbitrarily expressive and interwoven with the code they monitor. In this paper, we present and evaluate our solution based on higherorder symbolic execution, explain the techniques we used to address such thorny issues, formalize a notion of behavioral approximation, and use it to provide a mechanized proof of soundness. @Article{POPL18p51, author = {Phúc C. Nguyễn and Thomas Gilray and Sam TobinHochstadt and David Van Horn}, title = {Soft Contract Verification for HigherOrder Stateful Programs}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {51}, numpages = {30}, doi = {10.1145/3158139}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Vazou, Niki 
POPL '18: "Refinement Reflection: Complete ..."
Refinement Reflection: Complete Verification with SMT
Niki Vazou, Anish Tondwalkar, Vikraman Choudhury , Ryan G. Scott, Ryan R. Newton, Philip Wadler , and Ranjit Jhala (University of Maryland, USA; University of California at San Diego, USA; Indiana University, USA; University of Edinburgh, UK; Input Output HK, UK) We introduce Refinement Reflection, a new framework for building SMTbased deductive verifiers. The key idea is to reflect the code implementing a userdefined function into the function’s (output) refinement type. As a consequence, at uses of the function, the function definition is instantiated in the SMT logic in a precise fashion that permits decidable verification. Reflection allows the user to write equational proofs of programs just by writing other programs using patternmatching and recursion to perform casesplitting and induction. Thus, via the propositionsastypes principle, we show that reflection permits the specification of arbitrary functional correctness properties. Finally, we introduce a proofsearch algorithm called Proof by Logical Evaluation that uses techniques from model checking and abstract interpretation, to completely automate equational reasoning. We have implemented reflection in Liquid Haskell and used it to verify that the widely used instances of the Monoid, Applicative, Functor, and Monad typeclasses actually satisfy key algebraic laws required to make the clients safe, and have used reflection to build the first library that actually verifies assumptions about associativity and ordering that are crucial for safe deterministic parallelism. @Article{POPL18p53, author = {Niki Vazou and Anish Tondwalkar and Vikraman Choudhury and Ryan G. Scott and Ryan R. Newton and Philip Wadler and Ranjit Jhala}, title = {Refinement Reflection: Complete Verification with SMT}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {53}, numpages = {31}, doi = {10.1145/3158141}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Vechev, Martin 
POPL '18: "A Practical Construction for ..."
A Practical Construction for Decomposing Numerical Abstract Domains
Gagandeep Singh, Markus Püschel, and Martin Vechev (ETH Zurich, Switzerland) Numerical abstract domains such as Polyhedra, Octahedron, Octagon, Interval, and others are an essential component of static program analysis. The choice of domain offers a performance/precision tradeoff ranging from cheap and imprecise (Interval) to expensive and precise (Polyhedra). Recently, significant speedups were achieved for Octagon and Polyhedra by manually decomposing their transformers to work with the Cartesian product of projections associated with partitions of the variable set. While practically useful, this manual process is time consuming, errorprone, and has to be applied from scratch for every domain. In this paper, we present a generic approach for decomposing the transformers of subpolyhedra domains along with conditions for checking whether the decomposed transformers lose precision with respect to the original transformers. These conditions are satisfied by most practical transformers, thus our approach is suitable for increasing the performance of these transformers without compromising their precision. Furthermore, our approach is ``black box:'' it does not require changes to the internals of the original nondecomposed transformers or additional manual effort per domain. We implemented our approach and applied it to the domains of Zones, Octagon, and Polyhedra. We then compared the performance of the decomposed transformers obtained with our generic method versus the state of the art: the (nondecomposed) PPL for Polyhedra and the much faster ELINA (which uses manual decomposition) for Polyhedra and Octagon. Against ELINA we demonstrate finer partitions and an associated speedup of about 2x on average. Our results indicate that the general construction presented in this work is a viable method for improving the performance of subpolyhedra domains. It enables designers of abstract domains to benefit from decomposition without rewriting all of their transformers from scratch as required by prior work. @Article{POPL18p55, author = {Gagandeep Singh and Markus Püschel and Martin Vechev}, title = {A Practical Construction for Decomposing Numerical Abstract Domains}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {55}, numpages = {28}, doi = {10.1145/3158143}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Vezzosi, Andrea 
POPL '18: "Decidability of Conversion ..."
Decidability of Conversion for Type Theory in Type Theory
Andreas Abel, Joakim Öhman , and Andrea Vezzosi (University of Gothenburg, Sweden; IMDEA Software Institute, Spain; Chalmers University of Technology, Sweden) Type theory should be able to handle its own metatheory, both to justify its foundational claims and to obtain a verified implementation. At the core of a type checker for intensional type theory lies an algorithm to check equality of types, or in other words, to check whether two types are convertible. We have formalized in Agda a practical conversion checking algorithm for a dependent type theory with one universe à la Russell, natural numbers, and ηequality for Π types. We prove the algorithm correct via a Kripke logical relation parameterized by a suitable notion of equivalence of terms. We then instantiate the parameterized fundamental lemma twice: once to obtain canonicity and injectivity of type formers, and once again to prove the completeness of the algorithm. Our proof relies on inductiverecursive definitions, but not on the uniqueness of identity proofs. Thus, it is valid in variants of intensional MartinLöf Type Theory as long as they support inductionrecursion, for instance, Extensional, Observational, or Homotopy Type Theory. @Article{POPL18p23, author = {Andreas Abel and Joakim Öhman and Andrea Vezzosi}, title = {Decidability of Conversion for Type Theory in Type Theory}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {23}, numpages = {29}, doi = {10.1145/3158111}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Vial, Pierre 
POPL '18: "Polyadic Approximations, Fibrations ..."
Polyadic Approximations, Fibrations and Intersection Types
Damiano Mazza, Luc Pellissier, and Pierre Vial (CNRS, France; University of Paris 13, France; University of Paris Diderot, France) Starting from an exact correspondence between linear approximations and nonidempotent intersection types, we develop a general framework for building systems of intersection types characterizing normalization properties. We show how this construction, which uses in a fundamental way Melliès and Zeilberger's ``type systems as functors'' viewpoint, allows us to recover equivalent versions of every well known intersection type system (including Coppo and Dezani's original system, as well as its nonidempotent variants independently introduced by Gardner and de Carvalho). We also show how new systems of intersection types may be built almost automatically in this way. @Article{POPL18p6, author = {Damiano Mazza and Luc Pellissier and Pierre Vial}, title = {Polyadic Approximations, Fibrations and Intersection Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {6}, numpages = {28}, doi = {10.1145/3158094}, year = {2018}, } Publisher's Version Article Search 

Visser, Eelco 
POPL '18: "IntrinsicallyTyped Definitional ..."
IntrinsicallyTyped Definitional Interpreters for Imperative Languages
Casper Bach Poulsen , Arjen Rouvoet , Andrew Tolmach, Robbert Krebbers , and Eelco Visser (Delft University of Technology, Netherlands; Portland State University, USA) A definitional interpreter defines the semantics of an object language in terms of the (wellknown) semantics of a host language, enabling understanding and validation of the semantics through execution. Combining a definitional interpreter with a separate type system requires a separate type safety proof. An alternative approach, at least for pure object languages, is to use a dependentlytyped language to encode the object language type system in the definition of the abstract syntax. Using such intrinsicallytyped abstract syntax definitions allows the host language type checker to verify automatically that the interpreter satisfies type safety. Does this approach scale to larger and more realistic object languages, and in particular to languages with mutable state and objects? In this paper, we describe and demonstrate techniques and libraries in Agda that successfully scale up intrinsicallytyped definitional interpreters to handle rich object languages with nontrivial binding structures and mutable state. While the resulting interpreters are certainly more complex than the simplytyped λcalculus interpreter we start with, we claim that they still meet the goals of being concise, comprehensible, and executable, while guaranteeing type safety for more elaborate object languages. We make the following contributions: (1) A dependentpassing style technique for hiding the weakening of indexed values as they propagate through monadic code. (2) An Agda library for programming with scope graphs and frames, which provides a uniform approach to dealing with name binding in intrinsicallytyped interpreters. (3) Case studies of intrinsicallytyped definitional interpreters for the simplytyped λcalculus with references (STLC+Ref) and for a large subset of Middleweight Java (MJ). @Article{POPL18p16, author = {Casper Bach Poulsen and Arjen Rouvoet and Andrew Tolmach and Robbert Krebbers and Eelco Visser}, title = {IntrinsicallyTyped Definitional Interpreters for Imperative Languages}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {16}, numpages = {34}, doi = {10.1145/3158104}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Vitek, Jan 
POPL '18: "Correctness of Speculative ..."
Correctness of Speculative Optimizations with Dynamic Deoptimization
Olivier Flückiger , Gabriel Scherer , MingHo Yee, Aviral Goel, Amal Ahmed, and Jan Vitek (Northeastern University, USA; Inria, France; Czech Technical University, Czechia) Highperformance dynamic language implementations make heavy use of speculative optimizations to achieve speeds close to statically compiled languages. These optimizations are typically performed by a justintime compiler that generates code under a set of assumptions about the state of the program and its environment. In certain cases, a program may execute code compiled under assumptions that are no longer valid. The implementation must then deoptimize the program onthefly; this entails finding semantically equivalent code that does not rely on invalid assumptions, translating program state to that expected by the target code, and transferring control. This paper looks at the interaction between optimization and deoptimization, and shows that reasoning about speculation is surprisingly easy when assumptions are made explicit in the program representation. This insight is demonstrated on a compiler intermediate representation, named sourir, modeled after the highlevel representation for a dynamic language. Traditional compiler optimizations such as constant folding, unreachable code elimination, and function inlining are shown to be correct in the presence of assumptions. Furthermore, the paper establishes the correctness of compiler transformations specific to deoptimization: namely unrestricted deoptimization, predicate hoisting, and assume composition. @Article{POPL18p49, author = {Olivier Flückiger and Gabriel Scherer and MingHo Yee and Aviral Goel and Amal Ahmed and Jan Vitek}, title = {Correctness of Speculative Optimizations with Dynamic Deoptimization}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {49}, numpages = {28}, doi = {10.1145/3158137}, year = {2018}, } Publisher's Version Article Search 

Voizard, Antoine 
POPL '18: "Unifying Analytic and StaticallyTyped ..."
Unifying Analytic and StaticallyTyped Quasiquotes
Lionel Parreaux , Antoine Voizard, Amir Shaikhha, and Christoph E. Koch (EPFL, Switzerland; University of Pennsylvania, USA) Metaprograms are programs that manipulate (generate, analyze and evaluate) other programs. These tasks are greatly facilitated by quasiquotation, a technique to construct and deconstruct program fragments using quoted code templates expressed in the syntax of the manipulated language. We argue that two main flavors of quasiquotes have existed so far: Lispstyle quasiquotes, which can both construct and deconstruct programs but may produce code that contains type mismatches and unbound variables; and MetaMLstyle quasiquotes, which rely on static typing to prevent these errors, but can only construct programs. In this paper, we show how to combine the advantages of both flavors into a unified framework: we allow the construction, deconstruction and evaluation of program fragments while ensuring that generated programs are welltyped and wellscoped, a combination unseen in previous work. We formalize our approach as λ^{{}}, a multistage calculus with code pattern matching and rewriting, and prove its type safety. We also present its realization in Squid, a metaprogramming framework for Scala, leveraging Scala’s expressive type system. To demonstrate the usefulness of our approach, we introduce speculative rewrite rules, a novel code transformation technique that makes decisive use of these capabilities, and we outline how it simplifies the design of some crucial query compiler optimizations. @Article{POPL18p13, author = {Lionel Parreaux and Antoine Voizard and Amir Shaikhha and Christoph E. Koch}, title = {Unifying Analytic and StaticallyTyped Quasiquotes}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {13}, numpages = {33}, doi = {10.1145/3158101}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Vojnar, Tomáš 
POPL '18: "String Constraints with Concatenation ..."
String Constraints with Concatenation and Transducers Solved Efficiently
Lukáš Holík , Petr Janků, Anthony W. Lin, Philipp Rümmer, and Tomáš Vojnar (Brno University of Technology, Czechia; University of Oxford, UK; Uppsala University, Sweden) String analysis is the problem of reasoning about how strings are manipulated by a program. It has numerous applications including automatic detection of crosssite scripting, and automatic testcase generation. A popular string analysis technique includes symbolic executions, which at their core use constraint solvers over the string domain, a.k.a. string solvers. Such solvers typically reason about constraints expressed in theories over strings with the concatenation operator as an atomic constraint. In recent years, researchers started to recognise the importance of incorporating the replaceall operator (i.e. replace all occurrences of a string by another string) and, more generally, finitestate transductions in the theories of strings with concatenation. Such string operations are typically crucial for reasoning about XSS vulnerabilities in web applications, especially for modelling sanitisation functions and implicit browser transductions (e.g. innerHTML). Although this results in an undecidable theory in general, it was recently shown that the straightline fragment of the theory is decidable, and is sufficiently expressive in practice. In this paper, we provide the first string solver that can reason about constraints involving both concatenation and finitestate transductions. Moreover, it has a completeness and termination guarantee for several important fragments (e.g. straightline fragment). The main challenge addressed in the paper is the prohibitive worstcase complexity of the theory (doubleexponential time), which is exponentially harder than the case without finitestate transductions. To this end, we propose a method that exploits succinct alternating finitestate automata as concise symbolic representations of string constraints. In contrast to previous approaches using nondeterministic automata, alternation offers not only exponential savings in space when representing Boolean combinations of transducers, but also a possibility of succinct representation of otherwise costly combinations of transducers and concatenation. Reasoning about the emptiness of the AFA language requires a statespace exploration in an exponentialsized graph, for which we use model checking algorithms (e.g. IC3). We have implemented our algorithm and demonstrated its efficacy on benchmarks that are derived from crosssite scripting analysis and other examples in the literature. @Article{POPL18p4, author = {Lukáš Holík and Petr Janků and Anthony W. Lin and Philipp Rümmer and Tomáš Vojnar}, title = {String Constraints with Concatenation and Transducers Solved Efficiently}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {4}, numpages = {32}, doi = {10.1145/3158092}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Wadler, Philip 
POPL '18: "Refinement Reflection: Complete ..."
Refinement Reflection: Complete Verification with SMT
Niki Vazou, Anish Tondwalkar, Vikraman Choudhury , Ryan G. Scott, Ryan R. Newton, Philip Wadler , and Ranjit Jhala (University of Maryland, USA; University of California at San Diego, USA; Indiana University, USA; University of Edinburgh, UK; Input Output HK, UK) We introduce Refinement Reflection, a new framework for building SMTbased deductive verifiers. The key idea is to reflect the code implementing a userdefined function into the function’s (output) refinement type. As a consequence, at uses of the function, the function definition is instantiated in the SMT logic in a precise fashion that permits decidable verification. Reflection allows the user to write equational proofs of programs just by writing other programs using patternmatching and recursion to perform casesplitting and induction. Thus, via the propositionsastypes principle, we show that reflection permits the specification of arbitrary functional correctness properties. Finally, we introduce a proofsearch algorithm called Proof by Logical Evaluation that uses techniques from model checking and abstract interpretation, to completely automate equational reasoning. We have implemented reflection in Liquid Haskell and used it to verify that the widely used instances of the Monoid, Applicative, Functor, and Monad typeclasses actually satisfy key algebraic laws required to make the clients safe, and have used reflection to build the first library that actually verifies assumptions about associativity and ordering that are crucial for safe deterministic parallelism. @Article{POPL18p53, author = {Niki Vazou and Anish Tondwalkar and Vikraman Choudhury and Ryan G. Scott and Ryan R. Newton and Philip Wadler and Ranjit Jhala}, title = {Refinement Reflection: Complete Verification with SMT}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {53}, numpages = {31}, doi = {10.1145/3158141}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Walker, David 
POPL '18: "Synthesizing Bijective Lenses ..."
Synthesizing Bijective Lenses
Anders Miltner, Kathleen Fisher, Benjamin C. Pierce , David Walker, and Steve Zdancewic (Princeton University, USA; Tufts University, USA; University of Pennsylvania, USA) Bidirectional transformations between different data representations occur frequently in modern software systems. They appear as serializers and deserializers, as parsers and pretty printers, as database views and view updaters, and as a multitude of different kinds of ad hoc data converters. Manually building bidirectional transformationsby writing two separate functions that are intended to be inversesis tedious and error prone. A better approach is to use a domainspecific language in which both directions can be written as a single expression. However, these domainspecific languages can be difficult to program in, requiring programmers to manage fiddly details while working in a complex type system. We present an alternative approach. Instead of coding transformations manually, we synthesize them from declarative format descriptions and examples. Specifically, we present Optician, a tool for typedirected synthesis of bijective string transformers. The inputs to Optician are a pair of ordinary regular expressions representing two data formats and a few concrete examples for disambiguation. The output is a welltyped program in Boomerang (a bidirectional language based on the theory of lenses). The main technical challenge involves navigating the vast program search space efficiently. In particular, and unlike most prior work on typedirected synthesis, our system operates in the context of a language with a rich equivalence relation on types (the theory of regular expressions). Consequently, program synthesis requires search in two dimensions: First, our synthesis algorithm must find a pair of "syntactically compatible types," and second, using the structure of those types, it must find a type and examplecompliant term. Our key insight is that it is possible to reduce the size of this search space without losing any computational power by defining a new language of lenses designed specifically for synthesis. The new language is free from arbitrary function composition and operates only over types and terms in a new disjunctive normal form. We prove (1) our new language is just as powerful as a more natural, compositional, and declarative language and (2) our synthesis algorithm is sound and complete with respect to the new language. We also demonstrate empirically that our new language changes the synthesis problem from one that admits intractable solutions to one that admits highly efficient solutions, able to synthesize intricate lenses between complex file formats in seconds. We evaluate Optician on a benchmark suite of 39 examples that includes both microbenchmarks and realistic examples derived from other data management systems including Flash Fill, a tool for synthesizing string transformations in spreadsheets, and Augeas, a tool for bidirectional processing of Linux system configuration files. @Article{POPL18p1, author = {Anders Miltner and Kathleen Fisher and Benjamin C. Pierce and David Walker and Steve Zdancewic}, title = {Synthesizing Bijective Lenses}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {1}, numpages = {30}, doi = {10.1145/3158089}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Walkingshaw, Eric 
POPL '18: "Migrating Gradual Types ..."
Migrating Gradual Types
John Peter Campora, Sheng Chen, Martin Erwig, and Eric Walkingshaw (University of Louisiana at Lafayette, USA; Oregon State University, USA) Gradual typing allows programs to enjoy the benefits of both static typing and dynamic typing. While it is often desirable to migrate a program from more dynamicallytyped to more staticallytyped or vice versa, gradual typing itself does not provide a way to facilitate this migration. This places the burden on programmers who have to manually add or remove type annotations. Besides the general challenge of adding type annotations to dynamically typed code, there are subtle interactions between these annotations in gradually typed code that exacerbate the situation. For example, to migrate a program to be as static as possible, in general, all possible combinations of adding or removing type annotations from parameters must be tried out and compared. In this paper, we address this problem by developing migrational typing, which efficiently types all possible ways of adding or removing type annotations from a gradually typed program. The typing result supports automatically migrating a program to be as static as possible, or introducing the least number of dynamic types necessary to remove a type error. The approach can be extended to support userdefined criteria about which annotations to modify. We have implemented migrational typing and evaluated it on large programs. The results show that migrational typing scales linearly with the size of the program and takes only 2–4 times longer than plain gradual typing. @Article{POPL18p15, author = {John Peter Campora and Sheng Chen and Martin Erwig and Eric Walkingshaw}, title = {Migrating Gradual Types}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {15}, numpages = {29}, doi = {10.1145/3158103}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Wang, Xinyu 
POPL '18: "Program Synthesis using Abstraction ..."
Program Synthesis using Abstraction Refinement
Xinyu Wang, Isil Dillig , and Rishabh Singh (University of Texas at Austin, USA; Microsoft Research, USA) We present a new approach to exampleguided program synthesis based on counterexampleguided abstraction refinement. Our method uses the abstract semantics of the underlying DSL to find a program P whose abstract behavior satisfies the examples. However, since program P may be spurious with respect to the concrete semantics, our approach iteratively refines the abstraction until we either find a program that satisfies the examples or prove that no such DSL program exists. Because many programs have the same inputoutput behavior in terms of their abstract semantics, this synthesis methodology significantly reduces the search space compared to existing techniques that use purely concrete semantics. While synthesis using abstraction refinement (SYNGAR) could be implemented in different settings, we propose a refinementbased synthesis algorithm that uses abstract finite tree automata (AFTA). Our technique uses a coarse initial program abstraction to construct an initial AFTA, which is iteratively refined by constructing a proof of incorrectness of any spurious program. In addition to ruling out the spurious program accepted by the previous AFTA, proofs of incorrectness are also useful for ruling out many other spurious programs. We implement these ideas in a framework called Blaze, which can be instantiated in different domains by providing a suitable DSL and its corresponding concrete and abstract semantics. We have used the Blaze framework to build synthesizers for string and matrix transformations, and we compare Blaze with existing techniques. Our results for the string domain show that Blaze compares favorably with FlashFill, a domainspecific synthesizer that is now deployed in Microsoft PowerShell. In the context of matrix manipulations, we compare Blaze against Prose, a stateoftheart generalpurpose VSAbased synthesizer, and show that Blaze results in a 90x speedup over Prose. In both application domains, Blaze also consistently improves upon the performance of two other existing techniques by at least an order of magnitude. @Article{POPL18p63, author = {Xinyu Wang and Isil Dillig and Rishabh Singh}, title = {Program Synthesis using Abstraction Refinement}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {63}, numpages = {30}, doi = {10.1145/3158151}, year = {2018}, } Publisher's Version Article Search 

Wang, Yuepeng 
POPL '18: "Verifying Equivalence of DatabaseDriven ..."
Verifying Equivalence of DatabaseDriven Applications
Yuepeng Wang, Isil Dillig , Shuvendu K. Lahiri, and William R. Cook (University of Texas at Austin, USA; Microsoft Research, USA) This paper addresses the problem of verifying equivalence between a pair of programs that operate over databases with different schemas. This problem is particularly important in the context of web applications, which typically undergo database refactoring either for performance or maintainability reasons. While web applications should have the same externally observable behavior before and after schema migration, there are no existing tools for proving equivalence of such programs. This paper takes a first step towards solving this problem by formalizing the equivalence and refinement checking problems for databasedriven applications. We also propose a proof methodology based on the notion of bisimulation invariants over relational algebra with updates and describe a technique for synthesizing such bisimulation invariants. We have implemented the proposed technique in a tool called Mediator for verifying equivalence between databasedriven applications written in our intermediate language and evaluate our tool on 21 benchmarks extracted from textbooks and realworld web applications. Our results show that the proposed methodology can successfully verify 20 of these benchmarks. @Article{POPL18p56, author = {Yuepeng Wang and Isil Dillig and Shuvendu K. Lahiri and William R. Cook}, title = {Verifying Equivalence of DatabaseDriven Applications}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {56}, numpages = {29}, doi = {10.1145/3158144}, year = {2018}, } Publisher's Version Article Search 

Wies, Thomas 
POPL '18: "Go with the Flow: Compositional ..."
Go with the Flow: Compositional Abstractions for Concurrent Data Structures
Siddharth Krishna, Dennis Shasha, and Thomas Wies (New York University, USA) Concurrent separation logics have helped to significantly simplify correctness proofs for concurrent data structures. However, a recurring problem in such proofs is that data structure abstractions that work well in the sequential setting are much harder to reason about in a concurrent setting due to complex sharing and overlays. To solve this problem, we propose a novel approach to abstracting regions in the heap by encoding the data structure invariant into a local condition on each individual node. This condition may depend on a quantity associated with the node that is computed as a fixpoint over the entire heap graph. We refer to this quantity as a flow. Flows can encode both structural properties of the heap (e.g. the reachable nodes from the root form a tree) as well as data invariants (e.g. sortedness). We then introduce the notion of a flow interface, which expresses the relies and guarantees that a heap region imposes on its context to maintain the local flow invariant with respect to the global heap. Our main technical result is that this notion leads to a new semantic model of separation logic. In this model, flow interfaces provide a general abstraction mechanism for describing complex data structures. This abstraction mechanism admits proof rules that generalize over a wide variety of data structures. To demonstrate the versatility of our approach, we show how to extend the logic RGSep with flow interfaces. We have used this new logic to prove linearizability and memory safety of nontrivial concurrent data structures. In particular, we obtain parametric linearizability proofs for concurrent dictionary algorithms that abstract from the details of the underlying data structure representation. These proofs cannot be easily expressed using the abstraction mechanisms provided by existing separation logics. @Article{POPL18p37, author = {Siddharth Krishna and Dennis Shasha and Thomas Wies}, title = {Go with the Flow: Compositional Abstractions for Concurrent Data Structures}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {37}, numpages = {31}, doi = {10.1145/3158125}, year = {2018}, } Publisher's Version Article Search 

Wilcox, James R. 
POPL '18: "Programming and Proving with ..."
Programming and Proving with Distributed Protocols
Ilya Sergey, James R. Wilcox, and Zachary Tatlock (University College London, UK; University of Washington, USA) Distributed systems play a crucial role in modern infrastructure, but are notoriously difficult to implement correctly. This difficulty arises from two main challenges: (a) correctly implementing core system components (e.g., twophase commit), so all their internal invariants hold, and (b) correctly composing standalone system components into functioning trustworthy applications (e.g., persistent storage built on top of a twophase commit instance). Recent work has developed several approaches for addressing (a) by means of mechanically verifying implementations of core distributed components, but no methodology exists to address (b) by composing such verified components into larger verified applications. As a result, expensive verification efforts for key system components are not easily reusable, which hinders further verification efforts. In this paper, we present Disel, the first framework for implementation and compositional verification of distributed systems and their clients, all within the mechanized, foundational context of the Coq proof assistant. In Disel, users implement distributed systems using a domain specific language shallowly embedded in Coq and providing both highlevel programming constructs as well as lowlevel communication primitives. Components of composite systems are specified in Disel as protocols, which capture systemspecific logic and disentangle system definitions from implementation details. By virtue of Disel's dependent type system, welltyped implementations always satisfy their protocols' invariants and never go wrong, allowing users to verify system implementations interactively using Disel's Hoarestyle program logic, which extends stateoftheart techniques for concurrency verification to the distributed setting. By virtue of the substitution principle and frame rule provided by Disel's logic, system components can be composed leading to modular, reusable verified distributed systems. We describe Disel, illustrate its use with a series of examples, outline its logic and metatheory, and report on our experience using it as a framework for implementing, specifying, and verifying distributed systems. @Article{POPL18p28, author = {Ilya Sergey and James R. Wilcox and Zachary Tatlock}, title = {Programming and Proving with Distributed Protocols}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {28}, numpages = {30}, doi = {10.1145/3158116}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Williams, Thomas 
POPL '18: "A Principled Approach to Ornamentation ..."
A Principled Approach to Ornamentation in ML
Thomas Williams and Didier Rémy (Inria, France) Ornaments are a way to describe changes in datatype definitions reorganizing, adding, or dropping some pieces of data so that functions operating on the bare definition can be partially and sometimes totally lifted into functions operating on the ornamented structure. We propose an extension of ML with higherorder ornaments, demonstrate its expressiveness with a few typical examples, including code refactoring, study the metatheoretical properties of ornaments, and describe their elaboration process. We formalize ornamentation via an a posteriori abstraction of the bare code, returning a generic term, which lives in a metalanguage above ML. The lifted code is obtained by application of the generic term to wellchosen arguments, followed by staged reduction, and some remaining simplifications. We use logical relations to closely relate the lifted code to the bare code. @Article{POPL18p21, author = {Thomas Williams and Didier Rémy}, title = {A Principled Approach to Ornamentation in ML}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {21}, numpages = {30}, doi = {10.1145/3158109}, year = {2018}, } Publisher's Version Article Search Info Artifacts Functional 

Wood, Thomas 
POPL '18: "JaVerT: JavaScript Verification ..."
JaVerT: JavaScript Verification Toolchain
José Fragoso Santos, Petar Maksimović, Daiva Naudžiūnienė, Thomas Wood, and Philippa Gardner (Imperial College London, UK; Mathematical Institute SASA, Serbia) The dynamic nature of JavaScript and its complex semantics make it a difficult target for logicbased verification. We introduce JaVerT, a semiautomatic JavaScript Verification Toolchain, based on separation logic and aimed at the specialist developer wanting rich, mechanically verified specifications of critical JavaScript code. To specify JavaScript programs, we design abstractions that capture its key heap structures (for example, prototype chains and function closures), allowing the developer to write clear and succinct specifications with minimal knowledge of the JavaScript internals. To verify JavaScript programs, we develop JaVerT, a verification pipeline consisting of: JS2JSIL, a welltested compiler from JavaScript to JSIL, an intermediate goto language capturing the fundamental dynamic features of JavaScript; JSIL Verify, a semiautomatic verification tool based on a sound JSIL separation logic; and verified axiomatic specifications of the JavaScript internal functions. Using JaVerT, we verify functional correctness properties of: datastructure libraries (keyvalue map, priority queue) written in an objectoriented style; operations on data structures such as binary search trees (BSTs) and lists; examples illustrating function closures; and test cases from the official ECMAScript test suite. The verification times suggest that reasoning about larger, more complex code using JaVerT is feasible. @Article{POPL18p50, author = {José Fragoso Santos and Petar Maksimović and Daiva Naudžiūnienė and Thomas Wood and Philippa Gardner}, title = {JaVerT: JavaScript Verification Toolchain}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {50}, numpages = {33}, doi = {10.1145/3158138}, year = {2018}, } Publisher's Version Article Search Artifacts Functional 

Wu, Zhilin 
POPL '18: "What Is Decidable about String ..."
What Is Decidable about String Constraints with the ReplaceAll Function
Taolue Chen, Yan Chen, Matthew Hague , Anthony W. Lin, and Zhilin Wu (University of London, UK; Institute of Software at Chinese Academy of Sciences, China; University at Chinese Academy of Sciences, China; Royal Holloway University of London, UK; University of Oxford, UK) The theory of strings with concatenation has been widely argued as the basis of constraint solving for verifying stringmanipulating programs. However, this theory is far from adequate for expressing many string constraints that are also needed in practice; for example, the use of regular constraints (pattern matching against a regular expression), and the stringreplace function (replacing either the first occurrence or all occurrences of a ``pattern'' string constant/variable/regular expression by a ``replacement'' string constant/variable), among many others. Both regular constraints and the stringreplace function are crucial for such applications as analysis of JavaScript (or more generally HTML5 applications) against crosssite scripting (XSS) vulnerabilities, which motivates us to consider a richer class of string constraints. The importance of the stringreplace function (especially the replaceall facility) is increasingly recognised, which can be witnessed by the incorporation of the function in the input languages of several string constraint solvers. Recently, it was shown that any theory of strings containing the stringreplace function (even the most restricted version where pattern/replacement strings are both constant strings) becomes undecidable if we do not impose some kind of straightline (aka acyclicity) restriction on the formulas. Despite this, the straightline restriction is still practically sensible since this condition is typically met by string constraints that are generated by symbolic execution. In this paper, we provide the first systematic study of straightline string constraints with the stringreplace function and the regular constraints as the basic operations. We show that a large class of such constraints (i.e. when only a constant string or a regular expression is permitted in the pattern) is decidable. We note that the stringreplace function, even under this restriction, is sufficiently powerful for expressing the concatenation operator and much more (e.g. extensions of regular expressions with string variables). This gives us the most expressive decidable logic containing concatenation, replace, and regular constraints under the same umbrella. Our decision procedure for the straightline fragment follows an automatatheoretic approach, and is modular in the sense that the stringreplace terms are removed one by one to generate more and more regular constraints, which can then be discharged by the stateoftheart string constraint solvers. We also show that this fragment is, in a way, a maximal decidable subclass of the straightline fragment with stringreplace and regular constraints. To this end, we show undecidability results for the following two extensions: (1) variables are permitted in the pattern parameter of the replace function, (2) length constraints are permitted. @Article{POPL18p3, author = {Taolue Chen and Yan Chen and Matthew Hague and Anthony W. Lin and Zhilin Wu}, title = {What Is Decidable about String Constraints with the ReplaceAll Function}, journal = {Proc. ACM Program. Lang.}, volume = {2}, number = {POPL}, articleno = {3}, numpages = {29}, doi = {10.1145/3158091}, year = {2018}, } Publisher's Version Article Search 

Yang, Hongseok 
POPL '18: "Denotational Validation of ..."
Denotational Validation of HigherOrder Bayesian Inference
Adam Ścibior, Ohad Kammar, Matthijs Vákár, Sam Staton, Hongseok Yang, Yufei Cai, Klaus Ostermann , Sean K. Moss, Chris Heunen , and Zoubin Ghahramani (University of Cambridge, UK; MPI Tübingen, Germany; University of Oxford, UK; KAIST, South Korea; University of Tübingen, Germany; University of Edinburgh, UK; Uber AI Labs, USA) We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higherorder functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higherorder functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasiBorel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasiBorel counterpart to the MetropolisHastingsGreen theorem. 