ICFP 2022 – Author Index 
Contents 
Abstracts 
Authors

A B C D E G H J K L M N O P Q R S T U V W Y Z
Acar, Umut A. 
ICFP '22: "Entanglement Detection with ..."
Entanglement Detection with NearZero Cost
Sam Westrick , Jatin Arora , and Umut A. Acar (Carnegie Mellon University, USA) Recent research on parallel functional programming has culminated in a provably efficient (in work and space) parallel memory manager, which has been incorporated into the MPL (MaPLe) compiler for Parallel ML and shown to deliver practical efficiency and scalability. The memory manager exploits a property of parallel programs called disentanglement, which restricts computations from accessing concurrently allocated objects. Disentanglement is closely related to racefreedom, but subtly differs from it. Unlike racefreedom, however, no known techniques exists for ensuring disentanglement, leaving the task entirely to the programmer. This is a challenging task, because it requires reasoning about lowlevel memory operations (e.g., allocations and accesses), which is especially difficult in functional languages. In this paper, we present techniques for detecting entanglement dynamically, while the program is running. We first present a dynamic semantics for a functional language with references that checks for entanglement by consulting parallel and sequential dependency relations in the program. Notably, the semantics requires checks for mutable objects only. We prove the soundness of the dynamic semantics and present several techniques for realizing it efficiently, in particular by pruning away a large number of entanglement checks. We also provide bounds on the work and space of our techniques. We show that the entanglement detection techniques are practical by implementing them in the MPL compiler for Parallel ML. Considering a variety of benchmarks, we present an evaluation and measure time and space overheads of less than 5% on average with up to 72 cores. These results show that entanglement detection has negligible cost and can therefore remain deployed with little or no impact on efficiency, scalability, and space. @Article{ICFP22p115, author = {Sam Westrick and Jatin Arora and Umut A. Acar}, title = {Entanglement Detection with NearZero Cost}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {115}, numpages = {32}, doi = {10.1145/3547646}, year = {2022}, } Publisher's Version Archive submitted (490 kB) Artifacts Reusable 

Accattoli, Beniamino 
ICFP '22: "The Theory of CallbyValue ..."
The Theory of CallbyValue Solvability
Beniamino Accattoli and Giulio Guerrieri (Inria, France; École Polytechnique, France; Huawei Edinburgh Research Centre, UK) The semantics of the untyped (callbyname) lambdacalculus is a well developed field built around the concept of solvable terms, which are elegantly characterized in many different ways. In particular, unsolvable terms provide a consistent notion of meaningless term. The semantics of the untyped callbyvalue lambdacalculus (CbV) is instead still in its infancy, because of some inherent difficulties but also because CbV solvable terms are less studied and understood than in callbyname. On the one hand, we show that a carefully crafted presentation of CbV allows us to recover many of the properties that solvability has in callbyname, in particular qualitative and quantitative characterizations via multi types. On the other hand, we stress that, in CbV, solvability plays a different role: identifying unsolvable terms as meaningless induces an inconsistent theory. @Article{ICFP22p121, author = {Beniamino Accattoli and Giulio Guerrieri}, title = {The Theory of CallbyValue Solvability}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {121}, numpages = {31}, doi = {10.1145/3547652}, year = {2022}, } Publisher's Version ICFP '22: "Multi Types and Reasonable ..." Multi Types and Reasonable Space Beniamino Accattoli , Ugo Dal Lago , and Gabriele Vanoni (Inria, France; École Polytechnique, France; University of Bologna, Italy) Accattoli, Dal Lago, and Vanoni have recently proved that the space used by the Space KAM, a variant of the Krivine abstract machine, is a reasonable space cost model for the λcalculus accounting for logarithmic space, solving a longstanding open problem. In this paper, we provide a new system of multi types (a variant of intersection types) and extract from multi type derivations the space used by the Space KAM, capturing into a type system the space complexity of the abstract machine. Additionally, we show how to capture also the time of the Space KAM, which is a reasonable time cost model, via minor changes to the type system. @Article{ICFP22p119, author = {Beniamino Accattoli and Ugo Dal Lago and Gabriele Vanoni}, title = {Multi Types and Reasonable Space}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {119}, numpages = {27}, doi = {10.1145/3547650}, year = {2022}, } Publisher's Version 

Arora, Jatin 
ICFP '22: "Entanglement Detection with ..."
Entanglement Detection with NearZero Cost
Sam Westrick , Jatin Arora , and Umut A. Acar (Carnegie Mellon University, USA) Recent research on parallel functional programming has culminated in a provably efficient (in work and space) parallel memory manager, which has been incorporated into the MPL (MaPLe) compiler for Parallel ML and shown to deliver practical efficiency and scalability. The memory manager exploits a property of parallel programs called disentanglement, which restricts computations from accessing concurrently allocated objects. Disentanglement is closely related to racefreedom, but subtly differs from it. Unlike racefreedom, however, no known techniques exists for ensuring disentanglement, leaving the task entirely to the programmer. This is a challenging task, because it requires reasoning about lowlevel memory operations (e.g., allocations and accesses), which is especially difficult in functional languages. In this paper, we present techniques for detecting entanglement dynamically, while the program is running. We first present a dynamic semantics for a functional language with references that checks for entanglement by consulting parallel and sequential dependency relations in the program. Notably, the semantics requires checks for mutable objects only. We prove the soundness of the dynamic semantics and present several techniques for realizing it efficiently, in particular by pruning away a large number of entanglement checks. We also provide bounds on the work and space of our techniques. We show that the entanglement detection techniques are practical by implementing them in the MPL compiler for Parallel ML. Considering a variety of benchmarks, we present an evaluation and measure time and space overheads of less than 5% on average with up to 72 cores. These results show that entanglement detection has negligible cost and can therefore remain deployed with little or no impact on efficiency, scalability, and space. @Article{ICFP22p115, author = {Sam Westrick and Jatin Arora and Umut A. Acar}, title = {Entanglement Detection with NearZero Cost}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {115}, numpages = {32}, doi = {10.1145/3547646}, year = {2022}, } Publisher's Version Archive submitted (490 kB) Artifacts Reusable 

Bahr, Patrick 
ICFP '22: "Monadic Compiler Calculation ..."
Monadic Compiler Calculation (Functional Pearl)
Patrick Bahr and Graham Hutton (IT University of Copenhagen, Denmark; University of Nottingham, UK) Bahr and Hutton recently developed a new approach to calculating correct compilers directly from specifications of their correctness. However, the methodology only considers converging behaviour of the source language, which means that the compiler could potentially produce arbitrary, erroneous code for source programs that diverge. In this article, we show how the methodology can naturally be extended to support the calculation of compilers that address both convergent and divergent behaviour simultaneously, without the need for separate reasoning for each aspect. Our approach is based on the use of the partiality monad to make divergence explicit, together with the use of strong bisimilarity to support equationalstyle calculations, but also generalises to other forms of effect by changing the underlying monad. @Article{ICFP22p93, author = {Patrick Bahr and Graham Hutton}, title = {Monadic Compiler Calculation (Functional Pearl)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {93}, numpages = {29}, doi = {10.1145/3547624}, year = {2022}, } Publisher's Version Artifacts Reusable 

Balzer, Stephanie 
ICFP '22: "Multiparty GV: Functional ..."
Multiparty GV: Functional Multiparty Session Types with Certified Deadlock Freedom
Jules Jacobs , Stephanie Balzer , and Robbert Krebbers (Radboud University Nijmegen, Netherlands; Carnegie Mellon University, USA) Session types have recently been integrated with functional languages, bringing messagepassing concurrency to functional programming. Channel endpoints then become firstclass and can be stored in data structures, captured in closures, and sent along channels. Representatives of the GV (Wadler's "Good Variation") session type family are of particular appeal because they not only assert session fidelity but also deadlock freedom, inspired by a CurryHoward correspondence to linear logic. A restriction of current versions of GV, however, is the focus on binary sessions, limiting concurrent interactions within a session to two participants. This paper introduces Multiparty GV (MPGV), a functional language with multiparty session types, allowing concurrent interactions among several participants. MPGV upholds the strong guarantees of its ancestor GV, including deadlock freedom, despite session interleaving and delegation. MPGV has a novel redirecting construct for modular programming with firstclass endpoints, thanks to which we give a typepreserving translation from binary session types to MPGV to show that MPGV is strictly more general than binary GV. All results in this paper have been mechanized using the Coq proof assistant. @Article{ICFP22p107, author = {Jules Jacobs and Stephanie Balzer and Robbert Krebbers}, title = {Multiparty GV: Functional Multiparty Session Types with Certified Deadlock Freedom}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {107}, numpages = {30}, doi = {10.1145/3547638}, year = {2022}, } Publisher's Version Artifacts Reusable 

Barthe, Gilles 
ICFP '22: "Safe Couplings: Coupled Refinement ..."
Safe Couplings: Coupled Refinement Types
Elizaveta Vasilenko , Niki Vazou , and Gilles Barthe (IMDEA Software Institute, Spain; HSE University, Russia; MPISP, Germany) We enhance refinement types with mechanisms to reason about relational properties of probabilistic computations. Our mechanisms, which are inspired from probabilistic couplings, are applicable to a rich set of probabilistic properties, including expected sensitivity, which ensures that the distance between outputs of two probabilistic computations can be controlled from the distance between their inputs. We implement our mechanisms in the type system of Liquid Haskell and we use them to formally verify Haskell implementations of two classic machine learning algorithms: Temporal Difference (TD) reinforcement learning and stochastic gradient descent (SGD). We formalize a fragment of our system for discrete distributions and we prove soundness with respect to a settheoretical semantics. @Article{ICFP22p112, author = {Elizaveta Vasilenko and Niki Vazou and Gilles Barthe}, title = {Safe Couplings: Coupled Refinement Types}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {112}, numpages = {29}, doi = {10.1145/3547643}, year = {2022}, } Publisher's Version Artifacts Reusable ICFP '22: "On Feller Continuity and Full ..." On Feller Continuity and Full Abstraction Gilles Barthe , Raphaëlle Crubillé , Ugo Dal Lago , and Francesco Gavazzo (MPISP, Germany; IMDEA Software Institute, Spain; CNRS, France; University of Bologna, Italy; Inria, France) We study the nature of applicative bisimilarity in λcalculi endowed with operators for sampling from contin uous distributions. On the one hand, we show that bisimilarity, logical equivalence, and testing equivalence all coincide with contextual equivalence when real numbers can be manipulated through continuous functions only. The key ingredient towards this result is a notion of Fellercontinuity for labelled Markov processes, which we believe of independent interest, giving rise a broad class of LMPs for which coinductive and logically inspired equivalences coincide. On the other hand, we show that if no constraint is put on the way real numbers are manipulated, characterizing contextual equivalence turns out to be hard, and most of the aforementioned notions of equivalence are even unsound. @Article{ICFP22p120, author = {Gilles Barthe and Raphaëlle Crubillé and Ugo Dal Lago and Francesco Gavazzo}, title = {On Feller Continuity and Full Abstraction}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {120}, numpages = {29}, doi = {10.1145/3547651}, year = {2022}, } Publisher's Version 

Bernardy, JeanPhilippe 
ICFP '22: "Linearly Qualified Types: ..."
Linearly Qualified Types: Generic Inference for Capabilities and Uniqueness
Arnaud Spiwack , Csongor Kiss , JeanPhilippe Bernardy , Nicolas Wu , and Richard A. Eisenberg (Tweag, France; Imperial College London, UK; University of Gothenburg, Sweden) A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used safely. However, writing code with explicit linear arguments requires bureaucracy. This paper presents linear constraints, a frontend feature for linear typing that decreases the bureaucracy of working with linear types. Linear constraints are implicit linear arguments that are filled in automatically by the compiler. We present linear constraints as a qualified type system,together with an inference algorithm which extends GHC's existing constraint solver algorithm. Soundness of linear constraints is ensured by the fact that they desugar into Linear Haskell. @Article{ICFP22p95, author = {Arnaud Spiwack and Csongor Kiss and JeanPhilippe Bernardy and Nicolas Wu and Richard A. Eisenberg}, title = {Linearly Qualified Types: Generic Inference for Capabilities and Uniqueness}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {95}, numpages = {28}, doi = {10.1145/3547626}, year = {2022}, } Publisher's Version 

Biernacka, Małgorzata 
ICFP '22: "A Simple and Efficient Implementation ..."
A Simple and Efficient Implementation of Strong Call by Need by an Abstract Machine
Małgorzata Biernacka , Witold Charatonik , and Tomasz Drab (University of Wrocław, Poland) We present an abstract machine for a strong callbyneed strategy in the lambda calculus. The machine has been derived automatically from a higherorder evaluator that uses the technique of memothunks to implement laziness. The derivation has been done with the use of an offtheshelf transformation tool implementing the "functional correspondence" between higherorder interpreters and abstract machines, and it yields a simple and concise description of the machine. We prove that the resulting machine conservatively extends the lazy version of Krivine machine for the weak callbyneed strategy, and that it simulates the normalorder strategy in bilinear number of steps. @Article{ICFP22p94, author = {Małgorzata Biernacka and Witold Charatonik and Tomasz Drab}, title = {A Simple and Efficient Implementation of Strong Call by Need by an Abstract Machine}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {94}, numpages = {28}, doi = {10.1145/3549822}, year = {2022}, } Publisher's Version Artifacts Reusable 

Binder, David 
ICFP '22: "Introduction and Elimination, ..."
Introduction and Elimination, Left and Right
Klaus Ostermann , David Binder , Ingo Skupin , Tim Süberkrüb , and Paul Downen (University of Tübingen, Germany; University of Massachusetts at Lowell, USA) Functional programming language design has been shaped by the framework of natural deduction, in which language constructs are divided into introduction and elimination rules for producers of values. In sequent calculusbased languages, left introduction rules replace (right) elimination rules and provide a dedicated sublanguage for consumers of values. In this paper, we present and analyze a wider design space of programming languages which encompasses four kinds of rules: Introduction and elimination, both left and right. We analyze the influence of rule choice on program structure and argue that having all kinds of rules enriches a programmer’s modularity arsenal. In particular, we identify four ways of adhering to the principle that ”the structure of the program follows the structure of the data“ and show that they correspond to the four possible choices of rules. We also propose the principle of biexpressibility to guide and validate the design of rules for a connective. Finally, we deepen the wellknown dualities between different connectives by means of the proof/refutation duality. @Article{ICFP22p106, author = {Klaus Ostermann and David Binder and Ingo Skupin and Tim Süberkrüb and Paul Downen}, title = {Introduction and Elimination, Left and Right}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {106}, numpages = {28}, doi = {10.1145/3547637}, year = {2022}, } Publisher's Version Artifacts Reusable 

Birkedal, Lars 
ICFP '22: "Later Credits: Resourceful ..."
Later Credits: Resourceful Reasoning for the Later Modality
Simon Spies , Lennard Gäher , Joseph Tassarotti , Ralf Jung , Robbert Krebbers , Lars Birkedal , and Derek Dreyer (MPISWS, Germany; New York University, USA; Massachusetts Institute of Technology, USA; Radboud University Nijmegen, Netherlands; Aarhus University, Denmark) In the past two decades, stepindexed logical relations and separation logics have both come to play a major role in semantics and verification research. More recently, they have been married together in the form of stepindexed separation logics like VST, iCAP, and Iris, which provide powerful tools for (among other things) building semantic models of richly typed languages like Rust. In these logics, propositions are given semantics using a stepindexed model, and stepindexed reasoning is reflected into the logic through the socalled “later” modality. On the one hand, this modality provides an elegant, highlevel account of stepindexed reasoning; on the other hand, when used in sufficiently sophisticated ways, it can become a nuisance, turning perfectly natural proof strategies into dead ends. In this work, we introduce later credits, a new technique for escaping latermodality quagmires. By leveraging the second ancestor of these logics—separation logic—later credits turn “the right to eliminate a later” into an ownable resource, which is subject to all the traditional modular reasoning principles of separation logic. We develop the theory of later credits in the context of Iris, and present several challenging examples of proofs and proof patterns which were previously not possible in Iris but are now possible due to later credits. @Article{ICFP22p100, author = {Simon Spies and Lennard Gäher and Joseph Tassarotti and Ralf Jung and Robbert Krebbers and Lars Birkedal and Derek Dreyer}, title = {Later Credits: Resourceful Reasoning for the Later Modality}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {100}, numpages = {29}, doi = {10.1145/3547631}, year = {2022}, } Publisher's Version Artifacts Reusable 

Charatonik, Witold 
ICFP '22: "A Simple and Efficient Implementation ..."
A Simple and Efficient Implementation of Strong Call by Need by an Abstract Machine
Małgorzata Biernacka , Witold Charatonik , and Tomasz Drab (University of Wrocław, Poland) We present an abstract machine for a strong callbyneed strategy in the lambda calculus. The machine has been derived automatically from a higherorder evaluator that uses the technique of memothunks to implement laziness. The derivation has been done with the use of an offtheshelf transformation tool implementing the "functional correspondence" between higherorder interpreters and abstract machines, and it yields a simple and concise description of the machine. We prove that the resulting machine conservatively extends the lazy version of Krivine machine for the weak callbyneed strategy, and that it simulates the normalorder strategy in bilinear number of steps. @Article{ICFP22p94, author = {Małgorzata Biernacka and Witold Charatonik and Tomasz Drab}, title = {A Simple and Efficient Implementation of Strong Call by Need by an Abstract Machine}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {94}, numpages = {28}, doi = {10.1145/3549822}, year = {2022}, } Publisher's Version Artifacts Reusable 

Chen, LiangTing 
ICFP '22: "DatatypeGeneric Programming ..."
DatatypeGeneric Programming Meets Elaborator Reflection
HsiangShang Ko , LiangTing Chen , and TzuChi Lin (Academia Sinica, Taiwan) Datatypegeneric programming is natural and useful in dependently typed languages such as Agda. However, datatypegeneric libraries in Agda are not reused as much as they should be, because traditionally they work only on datatypes decoded from a library’s own version of datatype descriptions; this means that different generic libraries cannot be used together, and they do not work on native datatypes, which are preferred by the practical Agda programmer for better language support and access to other libraries. Based on elaborator reflection, we present a framework in Agda featuring a set of general metaprograms for instantiating datatypegeneric programs as, and for, a useful range of native datatypes and functions —including universepolymorphic ones— in programmerfriendly and customisable forms. We expect that datatypegeneric libraries built with our framework will be more attractive to the practical Agda programmer. As the elaborator reflection features used by our framework become more widespread, our design can be ported to other languages too. @Article{ICFP22p98, author = {HsiangShang Ko and LiangTing Chen and TzuChi Lin}, title = {DatatypeGeneric Programming Meets Elaborator Reflection}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {98}, numpages = {29}, doi = {10.1145/3547629}, year = {2022}, } Publisher's Version Artifacts Reusable 

Cheney, James 
ICFP '22: "ConstraintBased Type Inference ..."
ConstraintBased Type Inference for FreezeML
Frank Emrich , Jan Stolarek , James Cheney , and Sam Lindley (University of Edinburgh, UK) FreezeML is a new approach to firstclass polymorphic type inference that employs term annotations to control when and how polymorphic types are instantiated and generalised. It conservatively extends HindleyMilner type inference and was first presented as an extension to Algorithm W. More modern type inference techniques such as HM(X) and OutsideIn(X) employ constraints to support features such as type classes, type families, rows, and other extensions. We take the first step towards modernising FreezeML by presenting a constraintbased type inference algorithm. We introduce a new constraint language, inspired by the Pottier/Rémy presentation of HM(X), in order to allow FreezeML type inference problems to be expressed as constraints. We present a deterministic stack machine for solving FreezeML constraints and prove its termination and correctness. @Article{ICFP22p111, author = {Frank Emrich and Jan Stolarek and James Cheney and Sam Lindley}, title = {ConstraintBased Type Inference for FreezeML}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {111}, numpages = {26}, doi = {10.1145/3547642}, year = {2022}, } Publisher's Version 

Cockx, Jesper 
ICFP '22: "Practical Generic Programming ..."
Practical Generic Programming over a Universe of Native Datatypes
Lucas Escot and Jesper Cockx (Delft University of Technology, Netherlands) Datatypegeneric programming makes it possible to define a construction once and apply it to a large class of datatypes. It is often used to avoid code duplication in languages that encourage the definition of custom datatypes, in particular stateoftheart dependently typed languages where one can have many variants of the same datatype with different typelevel invariants. In addition to giving access to familiar programming constructions for free, datatypegeneric programming in the dependently typed setting also allows for the construction of generic proofs. However, the current interfaces available for this purpose are needlessly hard to use or are limited in the range of datatypes they handle. In this paper, we describe the design of a library for safe and userfriendly datatypegeneric programming in the Agda language. Generic constructions in our library are regular Agda functions over a broad universe of datatypes, yet they can be specialized to native Agda datatypes with a simple oneliner. Furthermore, we provide building blocks so that library designers can too define their own datatypegeneric constructions. @Article{ICFP22p113, author = {Lucas Escot and Jesper Cockx}, title = {Practical Generic Programming over a Universe of Native Datatypes}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {113}, numpages = {25}, doi = {10.1145/3547644}, year = {2022}, } Publisher's Version Artifacts Reusable 

Crubillé, Raphaëlle 
ICFP '22: "On Feller Continuity and Full ..."
On Feller Continuity and Full Abstraction
Gilles Barthe , Raphaëlle Crubillé , Ugo Dal Lago , and Francesco Gavazzo (MPISP, Germany; IMDEA Software Institute, Spain; CNRS, France; University of Bologna, Italy; Inria, France) We study the nature of applicative bisimilarity in λcalculi endowed with operators for sampling from contin uous distributions. On the one hand, we show that bisimilarity, logical equivalence, and testing equivalence all coincide with contextual equivalence when real numbers can be manipulated through continuous functions only. The key ingredient towards this result is a notion of Fellercontinuity for labelled Markov processes, which we believe of independent interest, giving rise a broad class of LMPs for which coinductive and logically inspired equivalences coincide. On the other hand, we show that if no constraint is put on the way real numbers are manipulated, characterizing contextual equivalence turns out to be hard, and most of the aforementioned notions of equivalence are even unsound. @Article{ICFP22p120, author = {Gilles Barthe and Raphaëlle Crubillé and Ugo Dal Lago and Francesco Gavazzo}, title = {On Feller Continuity and Full Abstraction}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {120}, numpages = {29}, doi = {10.1145/3547651}, year = {2022}, } Publisher's Version 

Dal Lago, Ugo 
ICFP '22: "Multi Types and Reasonable ..."
Multi Types and Reasonable Space
Beniamino Accattoli , Ugo Dal Lago , and Gabriele Vanoni (Inria, France; École Polytechnique, France; University of Bologna, Italy) Accattoli, Dal Lago, and Vanoni have recently proved that the space used by the Space KAM, a variant of the Krivine abstract machine, is a reasonable space cost model for the λcalculus accounting for logarithmic space, solving a longstanding open problem. In this paper, we provide a new system of multi types (a variant of intersection types) and extract from multi type derivations the space used by the Space KAM, capturing into a type system the space complexity of the abstract machine. Additionally, we show how to capture also the time of the Space KAM, which is a reasonable time cost model, via minor changes to the type system. @Article{ICFP22p119, author = {Beniamino Accattoli and Ugo Dal Lago and Gabriele Vanoni}, title = {Multi Types and Reasonable Space}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {119}, numpages = {27}, doi = {10.1145/3547650}, year = {2022}, } Publisher's Version ICFP '22: "On Feller Continuity and Full ..." On Feller Continuity and Full Abstraction Gilles Barthe , Raphaëlle Crubillé , Ugo Dal Lago , and Francesco Gavazzo (MPISP, Germany; IMDEA Software Institute, Spain; CNRS, France; University of Bologna, Italy; Inria, France) We study the nature of applicative bisimilarity in λcalculi endowed with operators for sampling from contin uous distributions. On the one hand, we show that bisimilarity, logical equivalence, and testing equivalence all coincide with contextual equivalence when real numbers can be manipulated through continuous functions only. The key ingredient towards this result is a notion of Fellercontinuity for labelled Markov processes, which we believe of independent interest, giving rise a broad class of LMPs for which coinductive and logically inspired equivalences coincide. On the other hand, we show that if no constraint is put on the way real numbers are manipulated, characterizing contextual equivalence turns out to be hard, and most of the aforementioned notions of equivalence are even unsound. @Article{ICFP22p120, author = {Gilles Barthe and Raphaëlle Crubillé and Ugo Dal Lago and Francesco Gavazzo}, title = {On Feller Continuity and Full Abstraction}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {120}, numpages = {29}, doi = {10.1145/3547651}, year = {2022}, } Publisher's Version 

De Moura, Leonardo 
ICFP '22: "‘do’ Unchained: Embracing ..."
‘do’ Unchained: Embracing Local Imperativity in a Purely Functional Language (Functional Pearl)
Sebastian Ullrich and Leonardo de Moura (KIT, Germany; Microsoft Research, USA) Purely functional programming languages pride themselves with reifying effects that are implicit in imperative languages into reusable and composable abstractions such as monads. This reification allows for more exact control over effects as well as the introduction of new or derived effects. However, despite libraries of more and more powerful abstractions over effectful operations being developed, syntactically the common 'do' notation still lags behind equivalent imperative code it is supposed to mimic regarding verbosity and code duplication. In this paper, we explore extending 'do' notation with other imperative language features that can be added to simplify monadic code: local mutation, early return, and iteration. We present formal translation rules that compile these features back down to purely functional code, show that the generated code can still be reasoned over using an implementation of the translation in the Lean 4 theorem prover, and formally prove the correctness of the translation rules relative to a simple static and dynamic semantics in Lean. @Article{ICFP22p109, author = {Sebastian Ullrich and Leonardo de Moura}, title = {‘do’ Unchained: Embracing Local Imperativity in a Purely Functional Language (Functional Pearl)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {109}, numpages = {28}, doi = {10.1145/3547640}, year = {2022}, } Publisher's Version Artifacts Reusable 

De Vries, Edsko 
ICFP '22: "Searching Entangled Program ..."
Searching Entangled Program Spaces
James Koppel , Zheng Guo , Edsko de Vries , Armando SolarLezama , and Nadia Polikarpova (Massachusetts Institute of Technology, USA; University of California at San Diego, USA; WellTyped LLP, UK) Many problem domains, including program synthesis and rewritebased optimization, require searching astronomically large spaces of programs. Existing approaches often rely on building specialized data structures—versionspace algebras, finite tree automata, or egraphs—to compactly represent such spaces. At their core, all these data structures exploit independence of subterms; as a result, they cannot efficiently represent more complex program spaces, where the choices of subterms are entangled. We introduce equalityconstrained tree automata (ECTAs), a new data structure, designed to compactly represent large spaces of programs with entangled subterms. We present efficient algorithms for extracting programs from ECTAs, implemented in a performant Haskell library, ecta. Using the ecta library, we construct Hectare, a typedriven program synthesizer for Haskell. Hectare significantly outperforms a stateoftheart synthesizer Hoogle+—providing an average speedup of 8×—despite its implementation being an order of magnitude smaller. @Article{ICFP22p91, author = {James Koppel and Zheng Guo and Edsko de Vries and Armando SolarLezama and Nadia Polikarpova}, title = {Searching Entangled Program Spaces}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {91}, numpages = {29}, doi = {10.1145/3547622}, year = {2022}, } Publisher's Version Artifacts Reusable 

Devriese, Dominique 
ICFP '22: "Verified Symbolic Execution ..."
Verified Symbolic Execution with Kripke Specification Monads (and No Metaprogramming)
Steven Keuchel , Sander Huyghebaert , Georgy Lukyanov , and Dominique Devriese (Vrije Universiteit Brussel, Belgium; Newcastle University, UK; KU Leuven, Belgium) Verifying soundness of symbolic executionbased program verifiers is a significant challenge. This is especially true if the resulting tool needs to be usable outside of the proof assistant, in which case we cannot rely on shallowly embedded assertion logics and metaprogramming. The tool needs to manipulate deeply embedded assertions, and it is crucial for efficiency to eagerly prune unreachable paths and simplify intermediate assertions in a way that can be justified towards the soundness proof. Only a few such tools exist in the literature, and their soundness proofs are intricate and hard to generalize or reuse. We contribute a novel, systematic approach for the construction and soundness proof of such a symbolic executionbased verifier. We first implement a shallow verification condition generator as an object language interpreter in a specification monad, using an abstract interface featuring angelic and demonic nondeterminism. Next, we build a symbolic executor by implementing a similar interpreter, in a symbolic specification monad. This symbolic monad lives in a universe that is Kripkeindexed by variables in scope and a path condition. Finally, we reduce the soundness of the symbolic execution to the soundness of the shallow execution by relating both executors using a Kripke logical relation. We report on the practical application of these techniques in Katamaran, a tool for verifying security guarantees offered by instruction set architectures (ISAs). The tool is fully verified by combining our symbolic execution machinery with a soundness proof of the shallow verification conditions against an axiomatized separation logic, and an Irisbased implementation of the axioms, proven sound against the operational semantics. Based on our experience with Katamaran, we can report good results on practicality and efficiency of the tool, demonstrating practical viability of our symbolic execution approach. @Article{ICFP22p97, author = {Steven Keuchel and Sander Huyghebaert and Georgy Lukyanov and Dominique Devriese}, title = {Verified Symbolic Execution with Kripke Specification Monads (and No Metaprogramming)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {97}, numpages = {31}, doi = {10.1145/3547628}, year = {2022}, } Publisher's Version Artifacts Reusable 

Downen, Paul 
ICFP '22: "Introduction and Elimination, ..."
Introduction and Elimination, Left and Right
Klaus Ostermann , David Binder , Ingo Skupin , Tim Süberkrüb , and Paul Downen (University of Tübingen, Germany; University of Massachusetts at Lowell, USA) Functional programming language design has been shaped by the framework of natural deduction, in which language constructs are divided into introduction and elimination rules for producers of values. In sequent calculusbased languages, left introduction rules replace (right) elimination rules and provide a dedicated sublanguage for consumers of values. In this paper, we present and analyze a wider design space of programming languages which encompasses four kinds of rules: Introduction and elimination, both left and right. We analyze the influence of rule choice on program structure and argue that having all kinds of rules enriches a programmer’s modularity arsenal. In particular, we identify four ways of adhering to the principle that ”the structure of the program follows the structure of the data“ and show that they correspond to the four possible choices of rules. We also propose the principle of biexpressibility to guide and validate the design of rules for a connective. Finally, we deepen the wellknown dualities between different connectives by means of the proof/refutation duality. @Article{ICFP22p106, author = {Klaus Ostermann and David Binder and Ingo Skupin and Tim Süberkrüb and Paul Downen}, title = {Introduction and Elimination, Left and Right}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {106}, numpages = {28}, doi = {10.1145/3547637}, year = {2022}, } Publisher's Version Artifacts Reusable 

Drab, Tomasz 
ICFP '22: "A Simple and Efficient Implementation ..."
A Simple and Efficient Implementation of Strong Call by Need by an Abstract Machine
Małgorzata Biernacka , Witold Charatonik , and Tomasz Drab (University of Wrocław, Poland) We present an abstract machine for a strong callbyneed strategy in the lambda calculus. The machine has been derived automatically from a higherorder evaluator that uses the technique of memothunks to implement laziness. The derivation has been done with the use of an offtheshelf transformation tool implementing the "functional correspondence" between higherorder interpreters and abstract machines, and it yields a simple and concise description of the machine. We prove that the resulting machine conservatively extends the lazy version of Krivine machine for the weak callbyneed strategy, and that it simulates the normalorder strategy in bilinear number of steps. @Article{ICFP22p94, author = {Małgorzata Biernacka and Witold Charatonik and Tomasz Drab}, title = {A Simple and Efficient Implementation of Strong Call by Need by an Abstract Machine}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {94}, numpages = {28}, doi = {10.1145/3549822}, year = {2022}, } Publisher's Version Artifacts Reusable 

Dreyer, Derek 
ICFP '22: "Later Credits: Resourceful ..."
Later Credits: Resourceful Reasoning for the Later Modality
Simon Spies , Lennard Gäher , Joseph Tassarotti , Ralf Jung , Robbert Krebbers , Lars Birkedal , and Derek Dreyer (MPISWS, Germany; New York University, USA; Massachusetts Institute of Technology, USA; Radboud University Nijmegen, Netherlands; Aarhus University, Denmark) In the past two decades, stepindexed logical relations and separation logics have both come to play a major role in semantics and verification research. More recently, they have been married together in the form of stepindexed separation logics like VST, iCAP, and Iris, which provide powerful tools for (among other things) building semantic models of richly typed languages like Rust. In these logics, propositions are given semantics using a stepindexed model, and stepindexed reasoning is reflected into the logic through the socalled “later” modality. On the one hand, this modality provides an elegant, highlevel account of stepindexed reasoning; on the other hand, when used in sufficiently sophisticated ways, it can become a nuisance, turning perfectly natural proof strategies into dead ends. In this work, we introduce later credits, a new technique for escaping latermodality quagmires. By leveraging the second ancestor of these logics—separation logic—later credits turn “the right to eliminate a later” into an ownable resource, which is subject to all the traditional modular reasoning principles of separation logic. We develop the theory of later credits in the context of Iris, and present several challenging examples of proofs and proof patterns which were previously not possible in Iris but are now possible due to later credits. @Article{ICFP22p100, author = {Simon Spies and Lennard Gäher and Joseph Tassarotti and Ralf Jung and Robbert Krebbers and Lars Birkedal and Derek Dreyer}, title = {Later Credits: Resourceful Reasoning for the Later Modality}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {100}, numpages = {29}, doi = {10.1145/3547631}, year = {2022}, } Publisher's Version Artifacts Reusable 

Eisenberg, Richard A. 
ICFP '22: "Linearly Qualified Types: ..."
Linearly Qualified Types: Generic Inference for Capabilities and Uniqueness
Arnaud Spiwack , Csongor Kiss , JeanPhilippe Bernardy , Nicolas Wu , and Richard A. Eisenberg (Tweag, France; Imperial College London, UK; University of Gothenburg, Sweden) A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used safely. However, writing code with explicit linear arguments requires bureaucracy. This paper presents linear constraints, a frontend feature for linear typing that decreases the bureaucracy of working with linear types. Linear constraints are implicit linear arguments that are filled in automatically by the compiler. We present linear constraints as a qualified type system,together with an inference algorithm which extends GHC's existing constraint solver algorithm. Soundness of linear constraints is ensured by the fact that they desugar into Linear Haskell. @Article{ICFP22p95, author = {Arnaud Spiwack and Csongor Kiss and JeanPhilippe Bernardy and Nicolas Wu and Richard A. Eisenberg}, title = {Linearly Qualified Types: Generic Inference for Capabilities and Uniqueness}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {95}, numpages = {28}, doi = {10.1145/3547626}, year = {2022}, } Publisher's Version 

Emrich, Frank 
ICFP '22: "ConstraintBased Type Inference ..."
ConstraintBased Type Inference for FreezeML
Frank Emrich , Jan Stolarek , James Cheney , and Sam Lindley (University of Edinburgh, UK) FreezeML is a new approach to firstclass polymorphic type inference that employs term annotations to control when and how polymorphic types are instantiated and generalised. It conservatively extends HindleyMilner type inference and was first presented as an extension to Algorithm W. More modern type inference techniques such as HM(X) and OutsideIn(X) employ constraints to support features such as type classes, type families, rows, and other extensions. We take the first step towards modernising FreezeML by presenting a constraintbased type inference algorithm. We introduce a new constraint language, inspired by the Pottier/Rémy presentation of HM(X), in order to allow FreezeML type inference problems to be expressed as constraints. We present a deterministic stack machine for solving FreezeML constraints and prove its termination and correctness. @Article{ICFP22p111, author = {Frank Emrich and Jan Stolarek and James Cheney and Sam Lindley}, title = {ConstraintBased Type Inference for FreezeML}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {111}, numpages = {26}, doi = {10.1145/3547642}, year = {2022}, } Publisher's Version 

Eremondi, Joseph 
ICFP '22: "Propositional Equality for ..."
Propositional Equality for Gradual Dependently Typed Programming
Joseph Eremondi , Ronald Garcia , and Éric Tanter (University of British Columbia, Canada; University of Chile, Chile) Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types, though, lack a central feature of type theory: propositional equality. LennonBertrand et al. show that, when the reflexive proof refl is the only closed value of an equality type, a gradual extension of the Calculus of Inductive Constructions (CIC) with propositional equality violates static observational equivalences. Extensionallyequal functions should be indistinguishable at run time, but they can be distinguished using a combination of equality and type imprecision. This work presents a gradual dependently typed language that supports propositional equality. We avoid the above issues by devising an equality type of which refl is not the only closed inhabitant. Instead, each equality proof is accompanied by a term that is at least as precise as the equated terms, acting as a witness of their plausible equality. These witnesses track partial type information as a program runs, raising errors when that information shows that two equated terms are undeniably inconsistent. Composition of type information is internalized as a construct of the language, and is deferred for function bodies whose evaluation is blocked by variables. We thus ensure that extensionallyequal functions compose without error, thereby preventing contexts from distinguishing them. We describe the challenges of designing consistency and precision relations for this system, along with solutions to these challenges. Finally, we prove important metatheory: type safety, conservative embedding of CIC, weak canonicity, and the gradual guarantees of Siek et al., which ensure that reducing a program’s precision introduces no new static or dynamic errors. @Article{ICFP22p96, author = {Joseph Eremondi and Ronald Garcia and Éric Tanter}, title = {Propositional Equality for Gradual Dependently Typed Programming}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {96}, numpages = {29}, doi = {10.1145/3547627}, year = {2022}, } Publisher's Version 

Escot, Lucas 
ICFP '22: "Practical Generic Programming ..."
Practical Generic Programming over a Universe of Native Datatypes
Lucas Escot and Jesper Cockx (Delft University of Technology, Netherlands) Datatypegeneric programming makes it possible to define a construction once and apply it to a large class of datatypes. It is often used to avoid code duplication in languages that encourage the definition of custom datatypes, in particular stateoftheart dependently typed languages where one can have many variants of the same datatype with different typelevel invariants. In addition to giving access to familiar programming constructions for free, datatypegeneric programming in the dependently typed setting also allows for the construction of generic proofs. However, the current interfaces available for this purpose are needlessly hard to use or are limited in the range of datatypes they handle. In this paper, we describe the design of a library for safe and userfriendly datatypegeneric programming in the Agda language. Generic constructions in our library are regular Agda functions over a broad universe of datatypes, yet they can be specialized to native Agda datatypes with a simple oneliner. Furthermore, we provide building blocks so that library designers can too define their own datatypegeneric constructions. @Article{ICFP22p113, author = {Lucas Escot and Jesper Cockx}, title = {Practical Generic Programming over a Universe of Native Datatypes}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {113}, numpages = {25}, doi = {10.1145/3547644}, year = {2022}, } Publisher's Version Artifacts Reusable 

Gäher, Lennard 
ICFP '22: "Later Credits: Resourceful ..."
Later Credits: Resourceful Reasoning for the Later Modality
Simon Spies , Lennard Gäher , Joseph Tassarotti , Ralf Jung , Robbert Krebbers , Lars Birkedal , and Derek Dreyer (MPISWS, Germany; New York University, USA; Massachusetts Institute of Technology, USA; Radboud University Nijmegen, Netherlands; Aarhus University, Denmark) In the past two decades, stepindexed logical relations and separation logics have both come to play a major role in semantics and verification research. More recently, they have been married together in the form of stepindexed separation logics like VST, iCAP, and Iris, which provide powerful tools for (among other things) building semantic models of richly typed languages like Rust. In these logics, propositions are given semantics using a stepindexed model, and stepindexed reasoning is reflected into the logic through the socalled “later” modality. On the one hand, this modality provides an elegant, highlevel account of stepindexed reasoning; on the other hand, when used in sufficiently sophisticated ways, it can become a nuisance, turning perfectly natural proof strategies into dead ends. In this work, we introduce later credits, a new technique for escaping latermodality quagmires. By leveraging the second ancestor of these logics—separation logic—later credits turn “the right to eliminate a later” into an ownable resource, which is subject to all the traditional modular reasoning principles of separation logic. We develop the theory of later credits in the context of Iris, and present several challenging examples of proofs and proof patterns which were previously not possible in Iris but are now possible due to later credits. @Article{ICFP22p100, author = {Simon Spies and Lennard Gäher and Joseph Tassarotti and Ralf Jung and Robbert Krebbers and Lars Birkedal and Derek Dreyer}, title = {Later Credits: Resourceful Reasoning for the Later Modality}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {100}, numpages = {29}, doi = {10.1145/3547631}, year = {2022}, } Publisher's Version Artifacts Reusable 

Garcia, Ronald 
ICFP '22: "Propositional Equality for ..."
Propositional Equality for Gradual Dependently Typed Programming
Joseph Eremondi , Ronald Garcia , and Éric Tanter (University of British Columbia, Canada; University of Chile, Chile) Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types, though, lack a central feature of type theory: propositional equality. LennonBertrand et al. show that, when the reflexive proof refl is the only closed value of an equality type, a gradual extension of the Calculus of Inductive Constructions (CIC) with propositional equality violates static observational equivalences. Extensionallyequal functions should be indistinguishable at run time, but they can be distinguished using a combination of equality and type imprecision. This work presents a gradual dependently typed language that supports propositional equality. We avoid the above issues by devising an equality type of which refl is not the only closed inhabitant. Instead, each equality proof is accompanied by a term that is at least as precise as the equated terms, acting as a witness of their plausible equality. These witnesses track partial type information as a program runs, raising errors when that information shows that two equated terms are undeniably inconsistent. Composition of type information is internalized as a construct of the language, and is deferred for function bodies whose evaluation is blocked by variables. We thus ensure that extensionallyequal functions compose without error, thereby preventing contexts from distinguishing them. We describe the challenges of designing consistency and precision relations for this system, along with solutions to these challenges. Finally, we prove important metatheory: type safety, conservative embedding of CIC, weak canonicity, and the gradual guarantees of Siek et al., which ensure that reducing a program’s precision introduces no new static or dynamic errors. @Article{ICFP22p96, author = {Joseph Eremondi and Ronald Garcia and Éric Tanter}, title = {Propositional Equality for Gradual Dependently Typed Programming}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {96}, numpages = {29}, doi = {10.1145/3547627}, year = {2022}, } Publisher's Version 

Gavazzo, Francesco 
ICFP '22: "On Feller Continuity and Full ..."
On Feller Continuity and Full Abstraction
Gilles Barthe , Raphaëlle Crubillé , Ugo Dal Lago , and Francesco Gavazzo (MPISP, Germany; IMDEA Software Institute, Spain; CNRS, France; University of Bologna, Italy; Inria, France) We study the nature of applicative bisimilarity in λcalculi endowed with operators for sampling from contin uous distributions. On the one hand, we show that bisimilarity, logical equivalence, and testing equivalence all coincide with contextual equivalence when real numbers can be manipulated through continuous functions only. The key ingredient towards this result is a notion of Fellercontinuity for labelled Markov processes, which we believe of independent interest, giving rise a broad class of LMPs for which coinductive and logically inspired equivalences coincide. On the other hand, we show that if no constraint is put on the way real numbers are manipulated, characterizing contextual equivalence turns out to be hard, and most of the aforementioned notions of equivalence are even unsound. @Article{ICFP22p120, author = {Gilles Barthe and Raphaëlle Crubillé and Ugo Dal Lago and Francesco Gavazzo}, title = {On Feller Continuity and Full Abstraction}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {120}, numpages = {29}, doi = {10.1145/3547651}, year = {2022}, } Publisher's Version 

Guerrieri, Giulio 
ICFP '22: "The Theory of CallbyValue ..."
The Theory of CallbyValue Solvability
Beniamino Accattoli and Giulio Guerrieri (Inria, France; École Polytechnique, France; Huawei Edinburgh Research Centre, UK) The semantics of the untyped (callbyname) lambdacalculus is a well developed field built around the concept of solvable terms, which are elegantly characterized in many different ways. In particular, unsolvable terms provide a consistent notion of meaningless term. The semantics of the untyped callbyvalue lambdacalculus (CbV) is instead still in its infancy, because of some inherent difficulties but also because CbV solvable terms are less studied and understood than in callbyname. On the one hand, we show that a carefully crafted presentation of CbV allows us to recover many of the properties that solvability has in callbyname, in particular qualitative and quantitative characterizations via multi types. On the other hand, we stress that, in CbV, solvability plays a different role: identifying unsolvable terms as meaningless induces an inconsistent theory. @Article{ICFP22p121, author = {Beniamino Accattoli and Giulio Guerrieri}, title = {The Theory of CallbyValue Solvability}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {121}, numpages = {31}, doi = {10.1145/3547652}, year = {2022}, } Publisher's Version 

Guo, Zheng 
ICFP '22: "Searching Entangled Program ..."
Searching Entangled Program Spaces
James Koppel , Zheng Guo , Edsko de Vries , Armando SolarLezama , and Nadia Polikarpova (Massachusetts Institute of Technology, USA; University of California at San Diego, USA; WellTyped LLP, UK) Many problem domains, including program synthesis and rewritebased optimization, require searching astronomically large spaces of programs. Existing approaches often rely on building specialized data structures—versionspace algebras, finite tree automata, or egraphs—to compactly represent such spaces. At their core, all these data structures exploit independence of subterms; as a result, they cannot efficiently represent more complex program spaces, where the choices of subterms are entangled. We introduce equalityconstrained tree automata (ECTAs), a new data structure, designed to compactly represent large spaces of programs with entangled subterms. We present efficient algorithms for extracting programs from ECTAs, implemented in a performant Haskell library, ecta. Using the ecta library, we construct Hectare, a typedriven program synthesizer for Haskell. Hectare significantly outperforms a stateoftheart synthesizer Hoogle+—providing an average speedup of 8×—despite its implementation being an order of magnitude smaller. @Article{ICFP22p91, author = {James Koppel and Zheng Guo and Edsko de Vries and Armando SolarLezama and Nadia Polikarpova}, title = {Searching Entangled Program Spaces}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {91}, numpages = {29}, doi = {10.1145/3547622}, year = {2022}, } Publisher's Version Artifacts Reusable 

Ho, Son 
ICFP '22: "Aeneas: Rust Verification ..."
Aeneas: Rust Verification by Functional Translation
Son Ho and Jonathan Protzenko (Inria, France; Microsoft Research, USA) We present Aeneas, a new verification toolchain for Rust programs based on a lightweight functional translation. We leverage Rust’s rich regionbased type system to eliminate memory reasoning for a large class of Rust programs, as long as they do not rely on interior mutability or unsafe code. Doing so, we relieve the proof engineer of the burden of memorybased reasoning, allowing them to instead focus on functional properties of their code. The first contribution of Aeneas is a new approach to borrows and controlled aliasing. We propose a pure, functional semantics for LLBC, a LowLevel Borrow Calculus that captures a large subset of Rust programs. Our semantics is valuebased, meaning there is no notion of memory, addresses or pointer arithmetic. Our semantics is also ownershipcentric, meaning that we enforce soundness of borrows via a semantic criterion based on loans rather than through a syntactic typebased lifetime discipline. We claim that our semantics captures the essence of the borrow mechanism rather than its current implementation in the Rust compiler. The second contribution of Aeneas is a translation from LLBC to a pure lambdacalculus. This allows the user to reason about the original Rust program through the theorem prover of their choice, and fulfills our promise of enabling lightweight verification of Rust programs. To deal with the wellknown technical difficulty of terminating a borrow, we rely on a novel approach, in which we approximate the borrow graph in the presence of function calls. This in turn allows us to perform the translation using a new technical device called backward functions. We implement our toolchain in a mixture of Rust and OCaml; our chief case study is a lowlevel, resizing hash table, for which we prove functional correctness, the first such result in Rust. Our evaluation shows significant gains of verification productivity for the programmer. This paper therefore establishes a new point in the design space of Rust verification toolchains, one that aims to verify Rust programs simply, and at scale. Rust goes to great lengths to enforce static control of aliasing; the proof engineer should not waste any time on memory reasoning when so much already comes “for free”! @Article{ICFP22p116, author = {Son Ho and Jonathan Protzenko}, title = {Aeneas: Rust Verification by Functional Translation}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {116}, numpages = {31}, doi = {10.1145/3547647}, year = {2022}, } Publisher's Version Info Artifacts Reusable 

Hoang, Tram 
ICFP '22: "Random Testing of a HigherOrder ..."
Random Testing of a HigherOrder Blockchain Language (Experience Report)
Tram Hoang , Anton Trunov , Leonidas Lampropoulos , and Ilya Sergey (National University of Singapore, Singapore; Zilliqa Research, Russia; University of Maryland at College Park, USA) We describe our experience of using propertybased testingan approach for automatically generating random inputs to check executable program specificationsin a development of a higherorder smart contract language that powers a stateoftheart blockchain with thousands of active daily users. We outline the process of integrating QuickChicka framework for propertybased testing built on top of the Coq proof assistantinto a realworld language implementation in OCaml. We discuss the challenges we have encountered when generating welltyped programs for a realistic higherorder smart contract language, which mixes purely functional and imperative computations and features runtime resource accounting. We describe the set of the language implementation properties that we tested, as well as the semantic harness required to enable their validation. The properties range from the standard type safety to the soundness of a control and typeflow analysis used by the optimizing compiler. Finally, we present the list of bugs discovered and rediscovered with the help of QuickChick and discuss their severity and possible ramifications. @Article{ICFP22p122, author = {Tram Hoang and Anton Trunov and Leonidas Lampropoulos and Ilya Sergey}, title = {Random Testing of a HigherOrder Blockchain Language (Experience Report)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {122}, numpages = {16}, doi = {10.1145/3547653}, year = {2022}, } Publisher's Version Artifacts Reusable 

Hutton, Graham 
ICFP '22: "Monadic Compiler Calculation ..."
Monadic Compiler Calculation (Functional Pearl)
Patrick Bahr and Graham Hutton (IT University of Copenhagen, Denmark; University of Nottingham, UK) Bahr and Hutton recently developed a new approach to calculating correct compilers directly from specifications of their correctness. However, the methodology only considers converging behaviour of the source language, which means that the compiler could potentially produce arbitrary, erroneous code for source programs that diverge. In this article, we show how the methodology can naturally be extended to support the calculation of compilers that address both convergent and divergent behaviour simultaneously, without the need for separate reasoning for each aspect. Our approach is based on the use of the partiality monad to make divergence explicit, together with the use of strong bisimilarity to support equationalstyle calculations, but also generalises to other forms of effect by changing the underlying monad. @Article{ICFP22p93, author = {Patrick Bahr and Graham Hutton}, title = {Monadic Compiler Calculation (Functional Pearl)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {93}, numpages = {29}, doi = {10.1145/3547624}, year = {2022}, } Publisher's Version Artifacts Reusable 

Huyghebaert, Sander 
ICFP '22: "Verified Symbolic Execution ..."
Verified Symbolic Execution with Kripke Specification Monads (and No Metaprogramming)
Steven Keuchel , Sander Huyghebaert , Georgy Lukyanov , and Dominique Devriese (Vrije Universiteit Brussel, Belgium; Newcastle University, UK; KU Leuven, Belgium) Verifying soundness of symbolic executionbased program verifiers is a significant challenge. This is especially true if the resulting tool needs to be usable outside of the proof assistant, in which case we cannot rely on shallowly embedded assertion logics and metaprogramming. The tool needs to manipulate deeply embedded assertions, and it is crucial for efficiency to eagerly prune unreachable paths and simplify intermediate assertions in a way that can be justified towards the soundness proof. Only a few such tools exist in the literature, and their soundness proofs are intricate and hard to generalize or reuse. We contribute a novel, systematic approach for the construction and soundness proof of such a symbolic executionbased verifier. We first implement a shallow verification condition generator as an object language interpreter in a specification monad, using an abstract interface featuring angelic and demonic nondeterminism. Next, we build a symbolic executor by implementing a similar interpreter, in a symbolic specification monad. This symbolic monad lives in a universe that is Kripkeindexed by variables in scope and a path condition. Finally, we reduce the soundness of the symbolic execution to the soundness of the shallow execution by relating both executors using a Kripke logical relation. We report on the practical application of these techniques in Katamaran, a tool for verifying security guarantees offered by instruction set architectures (ISAs). The tool is fully verified by combining our symbolic execution machinery with a soundness proof of the shallow verification conditions against an axiomatized separation logic, and an Irisbased implementation of the axioms, proven sound against the operational semantics. Based on our experience with Katamaran, we can report good results on practicality and efficiency of the tool, demonstrating practical viability of our symbolic execution approach. @Article{ICFP22p97, author = {Steven Keuchel and Sander Huyghebaert and Georgy Lukyanov and Dominique Devriese}, title = {Verified Symbolic Execution with Kripke Specification Monads (and No Metaprogramming)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {97}, numpages = {31}, doi = {10.1145/3547628}, year = {2022}, } Publisher's Version Artifacts Reusable 

Jacobs, Jules 
ICFP '22: "Multiparty GV: Functional ..."
Multiparty GV: Functional Multiparty Session Types with Certified Deadlock Freedom
Jules Jacobs , Stephanie Balzer , and Robbert Krebbers (Radboud University Nijmegen, Netherlands; Carnegie Mellon University, USA) Session types have recently been integrated with functional languages, bringing messagepassing concurrency to functional programming. Channel endpoints then become firstclass and can be stored in data structures, captured in closures, and sent along channels. Representatives of the GV (Wadler's "Good Variation") session type family are of particular appeal because they not only assert session fidelity but also deadlock freedom, inspired by a CurryHoward correspondence to linear logic. A restriction of current versions of GV, however, is the focus on binary sessions, limiting concurrent interactions within a session to two participants. This paper introduces Multiparty GV (MPGV), a functional language with multiparty session types, allowing concurrent interactions among several participants. MPGV upholds the strong guarantees of its ancestor GV, including deadlock freedom, despite session interleaving and delegation. MPGV has a novel redirecting construct for modular programming with firstclass endpoints, thanks to which we give a typepreserving translation from binary session types to MPGV to show that MPGV is strictly more general than binary GV. All results in this paper have been mechanized using the Coq proof assistant. @Article{ICFP22p107, author = {Jules Jacobs and Stephanie Balzer and Robbert Krebbers}, title = {Multiparty GV: Functional Multiparty Session Types with Certified Deadlock Freedom}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {107}, numpages = {30}, doi = {10.1145/3547638}, year = {2022}, } Publisher's Version Artifacts Reusable 

Jung, Ralf 
ICFP '22: "Later Credits: Resourceful ..."
Later Credits: Resourceful Reasoning for the Later Modality
Simon Spies , Lennard Gäher , Joseph Tassarotti , Ralf Jung , Robbert Krebbers , Lars Birkedal , and Derek Dreyer (MPISWS, Germany; New York University, USA; Massachusetts Institute of Technology, USA; Radboud University Nijmegen, Netherlands; Aarhus University, Denmark) In the past two decades, stepindexed logical relations and separation logics have both come to play a major role in semantics and verification research. More recently, they have been married together in the form of stepindexed separation logics like VST, iCAP, and Iris, which provide powerful tools for (among other things) building semantic models of richly typed languages like Rust. In these logics, propositions are given semantics using a stepindexed model, and stepindexed reasoning is reflected into the logic through the socalled “later” modality. On the one hand, this modality provides an elegant, highlevel account of stepindexed reasoning; on the other hand, when used in sufficiently sophisticated ways, it can become a nuisance, turning perfectly natural proof strategies into dead ends. In this work, we introduce later credits, a new technique for escaping latermodality quagmires. By leveraging the second ancestor of these logics—separation logic—later credits turn “the right to eliminate a later” into an ownable resource, which is subject to all the traditional modular reasoning principles of separation logic. We develop the theory of later credits in the context of Iris, and present several challenging examples of proofs and proof patterns which were previously not possible in Iris but are now possible due to later credits. @Article{ICFP22p100, author = {Simon Spies and Lennard Gäher and Joseph Tassarotti and Ralf Jung and Robbert Krebbers and Lars Birkedal and Derek Dreyer}, title = {Later Credits: Resourceful Reasoning for the Later Modality}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {100}, numpages = {29}, doi = {10.1145/3547631}, year = {2022}, } Publisher's Version Artifacts Reusable 

Katsumata, Shinya 
ICFP '22: "Flexible Presentations of ..."
Flexible Presentations of Graded Monads
Shinya Katsumata , Dylan McDermott , Tarmo Uustalu , and Nicolas Wu (National Institute of Informatics, Japan; Reykjavik University, Iceland; Tallinn University of Technology, Estonia; Imperial College London, UK) A large class of monads used to model computational effects have natural presentations by operations and equations, for example, the list monad can be presented by a constant and a binary operation subject to unitality and associativity. Graded monads are a generalization of monads that enable us to track quantitative information about the effects being modelled. Correspondingly, a large class of graded monads can be presented using an existing notion of graded presentation. However, the existing notion has some deficiencies, in particular many effects do not have natural graded presentations. We introduce a notion of flexibly graded presentation that does not suffer from these issues, and develop the associated theory. We show that every flexibly graded presentation induces a graded monad equipped with interpretations of the operations of the presentation, and that all graded monads satisfying a particular condition on colimits have a flexibly graded presentation. As part of this, we show that the usual algebrapreserving correspondence between presentations and a class of monads transfers to an algebrapreserving correspondence between flexibly graded presentations and a class of flexibly graded monads. @Article{ICFP22p123, author = {Shinya Katsumata and Dylan McDermott and Tarmo Uustalu and Nicolas Wu}, title = {Flexible Presentations of Graded Monads}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {123}, numpages = {29}, doi = {10.1145/3547654}, year = {2022}, } Publisher's Version 

Kearl, Jackson 
ICFP '22: "Automatically Deriving ControlFlow ..."
Automatically Deriving ControlFlow Graph Generators from Operational Semantics
James Koppel , Jackson Kearl , and Armando SolarLezama (Massachusetts Institute of Technology, USA) We develop the first theory of controlflow graphs from first principles, and use it to create an algorithm for automatically synthesizing many variants of controlflow graph generators from a language’s operational semantics. Our approach first introduces a new algorithm for converting a large class of smallstep operational semantics to an abstract machine. It next uses a technique called ”abstract rewriting” to automatically abstract the semantics of a language, which is used both to directly generate a CFG from a program (”interpreted mode”) and to generate standalone code, similar to a humanwritten CFG generator, for any program in a language. We show how the choice of two abstraction and projection parameters allow our approach to synthesize several families of CFGgenerators useful for different kinds of tools. We prove the correspondence between the generated graphs and the original semantics. We provide and prove an algorithm for automatically proving the termination of interpretedmode generators. In addition to our theoretical results, we have implemented this algorithm in a tool called Mandate, and show that it produces humanreadable code on two mediumsize languages with 60−80 rules, featuring nearly all intraprocedural control constructs common in modern languages. We then show these CFGgenerators were sufficient to build two static analyses atop them. Our work is a promising step towards the grand vision of being able to synthesize all desired tools from the semantics of a programming language. @Article{ICFP22p117, author = {James Koppel and Jackson Kearl and Armando SolarLezama}, title = {Automatically Deriving ControlFlow Graph Generators from Operational Semantics}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {117}, numpages = {30}, doi = {10.1145/3547648}, year = {2022}, } Publisher's Version Artifacts Reusable 

Keuchel, Steven 
ICFP '22: "Verified Symbolic Execution ..."
Verified Symbolic Execution with Kripke Specification Monads (and No Metaprogramming)
Steven Keuchel , Sander Huyghebaert , Georgy Lukyanov , and Dominique Devriese (Vrije Universiteit Brussel, Belgium; Newcastle University, UK; KU Leuven, Belgium) Verifying soundness of symbolic executionbased program verifiers is a significant challenge. This is especially true if the resulting tool needs to be usable outside of the proof assistant, in which case we cannot rely on shallowly embedded assertion logics and metaprogramming. The tool needs to manipulate deeply embedded assertions, and it is crucial for efficiency to eagerly prune unreachable paths and simplify intermediate assertions in a way that can be justified towards the soundness proof. Only a few such tools exist in the literature, and their soundness proofs are intricate and hard to generalize or reuse. We contribute a novel, systematic approach for the construction and soundness proof of such a symbolic executionbased verifier. We first implement a shallow verification condition generator as an object language interpreter in a specification monad, using an abstract interface featuring angelic and demonic nondeterminism. Next, we build a symbolic executor by implementing a similar interpreter, in a symbolic specification monad. This symbolic monad lives in a universe that is Kripkeindexed by variables in scope and a path condition. Finally, we reduce the soundness of the symbolic execution to the soundness of the shallow execution by relating both executors using a Kripke logical relation. We report on the practical application of these techniques in Katamaran, a tool for verifying security guarantees offered by instruction set architectures (ISAs). The tool is fully verified by combining our symbolic execution machinery with a soundness proof of the shallow verification conditions against an axiomatized separation logic, and an Irisbased implementation of the axioms, proven sound against the operational semantics. Based on our experience with Katamaran, we can report good results on practicality and efficiency of the tool, demonstrating practical viability of our symbolic execution approach. @Article{ICFP22p97, author = {Steven Keuchel and Sander Huyghebaert and Georgy Lukyanov and Dominique Devriese}, title = {Verified Symbolic Execution with Kripke Specification Monads (and No Metaprogramming)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {97}, numpages = {31}, doi = {10.1145/3547628}, year = {2022}, } Publisher's Version Artifacts Reusable 

Kiss, Csongor 
ICFP '22: "Linearly Qualified Types: ..."
Linearly Qualified Types: Generic Inference for Capabilities and Uniqueness
Arnaud Spiwack , Csongor Kiss , JeanPhilippe Bernardy , Nicolas Wu , and Richard A. Eisenberg (Tweag, France; Imperial College London, UK; University of Gothenburg, Sweden) A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used safely. However, writing code with explicit linear arguments requires bureaucracy. This paper presents linear constraints, a frontend feature for linear typing that decreases the bureaucracy of working with linear types. Linear constraints are implicit linear arguments that are filled in automatically by the compiler. We present linear constraints as a qualified type system,together with an inference algorithm which extends GHC's existing constraint solver algorithm. Soundness of linear constraints is ensured by the fact that they desugar into Linear Haskell. @Article{ICFP22p95, author = {Arnaud Spiwack and Csongor Kiss and JeanPhilippe Bernardy and Nicolas Wu and Richard A. Eisenberg}, title = {Linearly Qualified Types: Generic Inference for Capabilities and Uniqueness}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {95}, numpages = {28}, doi = {10.1145/3547626}, year = {2022}, } Publisher's Version 

Ko, HsiangShang 
ICFP '22: "DatatypeGeneric Programming ..."
DatatypeGeneric Programming Meets Elaborator Reflection
HsiangShang Ko , LiangTing Chen , and TzuChi Lin (Academia Sinica, Taiwan) Datatypegeneric programming is natural and useful in dependently typed languages such as Agda. However, datatypegeneric libraries in Agda are not reused as much as they should be, because traditionally they work only on datatypes decoded from a library’s own version of datatype descriptions; this means that different generic libraries cannot be used together, and they do not work on native datatypes, which are preferred by the practical Agda programmer for better language support and access to other libraries. Based on elaborator reflection, we present a framework in Agda featuring a set of general metaprograms for instantiating datatypegeneric programs as, and for, a useful range of native datatypes and functions —including universepolymorphic ones— in programmerfriendly and customisable forms. We expect that datatypegeneric libraries built with our framework will be more attractive to the practical Agda programmer. As the elaborator reflection features used by our framework become more widespread, our design can be ported to other languages too. @Article{ICFP22p98, author = {HsiangShang Ko and LiangTing Chen and TzuChi Lin}, title = {DatatypeGeneric Programming Meets Elaborator Reflection}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {98}, numpages = {29}, doi = {10.1145/3547629}, year = {2022}, } Publisher's Version Artifacts Reusable 

Koppel, James 
ICFP '22: "Automatically Deriving ControlFlow ..."
Automatically Deriving ControlFlow Graph Generators from Operational Semantics
James Koppel , Jackson Kearl , and Armando SolarLezama (Massachusetts Institute of Technology, USA) We develop the first theory of controlflow graphs from first principles, and use it to create an algorithm for automatically synthesizing many variants of controlflow graph generators from a language’s operational semantics. Our approach first introduces a new algorithm for converting a large class of smallstep operational semantics to an abstract machine. It next uses a technique called ”abstract rewriting” to automatically abstract the semantics of a language, which is used both to directly generate a CFG from a program (”interpreted mode”) and to generate standalone code, similar to a humanwritten CFG generator, for any program in a language. We show how the choice of two abstraction and projection parameters allow our approach to synthesize several families of CFGgenerators useful for different kinds of tools. We prove the correspondence between the generated graphs and the original semantics. We provide and prove an algorithm for automatically proving the termination of interpretedmode generators. In addition to our theoretical results, we have implemented this algorithm in a tool called Mandate, and show that it produces humanreadable code on two mediumsize languages with 60−80 rules, featuring nearly all intraprocedural control constructs common in modern languages. We then show these CFGgenerators were sufficient to build two static analyses atop them. Our work is a promising step towards the grand vision of being able to synthesize all desired tools from the semantics of a programming language. @Article{ICFP22p117, author = {James Koppel and Jackson Kearl and Armando SolarLezama}, title = {Automatically Deriving ControlFlow Graph Generators from Operational Semantics}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {117}, numpages = {30}, doi = {10.1145/3547648}, year = {2022}, } Publisher's Version Artifacts Reusable ICFP '22: "Searching Entangled Program ..." Searching Entangled Program Spaces James Koppel , Zheng Guo , Edsko de Vries , Armando SolarLezama , and Nadia Polikarpova (Massachusetts Institute of Technology, USA; University of California at San Diego, USA; WellTyped LLP, UK) Many problem domains, including program synthesis and rewritebased optimization, require searching astronomically large spaces of programs. Existing approaches often rely on building specialized data structures—versionspace algebras, finite tree automata, or egraphs—to compactly represent such spaces. At their core, all these data structures exploit independence of subterms; as a result, they cannot efficiently represent more complex program spaces, where the choices of subterms are entangled. We introduce equalityconstrained tree automata (ECTAs), a new data structure, designed to compactly represent large spaces of programs with entangled subterms. We present efficient algorithms for extracting programs from ECTAs, implemented in a performant Haskell library, ecta. Using the ecta library, we construct Hectare, a typedriven program synthesizer for Haskell. Hectare significantly outperforms a stateoftheart synthesizer Hoogle+—providing an average speedup of 8×—despite its implementation being an order of magnitude smaller. @Article{ICFP22p91, author = {James Koppel and Zheng Guo and Edsko de Vries and Armando SolarLezama and Nadia Polikarpova}, title = {Searching Entangled Program Spaces}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {91}, numpages = {29}, doi = {10.1145/3547622}, year = {2022}, } Publisher's Version Artifacts Reusable 

Kovács, András 
ICFP '22: "Staged Compilation with TwoLevel ..."
Staged Compilation with TwoLevel Type Theory
András Kovács (Eötvös Loránd University, Hungary) The aim of staged compilation is to enable metaprogramming in a way such that we have guarantees about the wellformedness of code output, and we can also mix together objectlevel and metalevel code in a concise and convenient manner. In this work, we observe that twolevel type theory (2LTT), a system originally devised for the purpose of developing synthetic homotopy theory, also serves as a system for staged compilation with dependent types. 2LTT has numerous good properties for this use case: it has a concise specification, wellbehaved model theory, and it supports a wide range of language features both at the object and the meta level. First, we give an overview of 2LTT's features and applications in staging. Then, we present a staging algorithm and prove its correctness. Our algorithm is "stagingbyevaluation", analogously to the technique of normalizationbyevaluation, in that staging is given by the evaluation of 2LTT syntax in a semantic domain. The staging algorithm together with its correctness constitutes a proof of strong conservativity of 2LLT over the object theory. To our knowledge, this is the first description of staged compilation which supports full dependent types and unrestricted staging for types. @Article{ICFP22p110, author = {András Kovács}, title = {Staged Compilation with TwoLevel Type Theory}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {110}, numpages = {30}, doi = {10.1145/3547641}, year = {2022}, } Publisher's Version Info Artifacts Reusable 

Krebbers, Robbert 
ICFP '22: "Multiparty GV: Functional ..."
Multiparty GV: Functional Multiparty Session Types with Certified Deadlock Freedom
Jules Jacobs , Stephanie Balzer , and Robbert Krebbers (Radboud University Nijmegen, Netherlands; Carnegie Mellon University, USA) Session types have recently been integrated with functional languages, bringing messagepassing concurrency to functional programming. Channel endpoints then become firstclass and can be stored in data structures, captured in closures, and sent along channels. Representatives of the GV (Wadler's "Good Variation") session type family are of particular appeal because they not only assert session fidelity but also deadlock freedom, inspired by a CurryHoward correspondence to linear logic. A restriction of current versions of GV, however, is the focus on binary sessions, limiting concurrent interactions within a session to two participants. This paper introduces Multiparty GV (MPGV), a functional language with multiparty session types, allowing concurrent interactions among several participants. MPGV upholds the strong guarantees of its ancestor GV, including deadlock freedom, despite session interleaving and delegation. MPGV has a novel redirecting construct for modular programming with firstclass endpoints, thanks to which we give a typepreserving translation from binary session types to MPGV to show that MPGV is strictly more general than binary GV. All results in this paper have been mechanized using the Coq proof assistant. @Article{ICFP22p107, author = {Jules Jacobs and Stephanie Balzer and Robbert Krebbers}, title = {Multiparty GV: Functional Multiparty Session Types with Certified Deadlock Freedom}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {107}, numpages = {30}, doi = {10.1145/3547638}, year = {2022}, } Publisher's Version Artifacts Reusable ICFP '22: "Later Credits: Resourceful ..." Later Credits: Resourceful Reasoning for the Later Modality Simon Spies , Lennard Gäher , Joseph Tassarotti , Ralf Jung , Robbert Krebbers , Lars Birkedal , and Derek Dreyer (MPISWS, Germany; New York University, USA; Massachusetts Institute of Technology, USA; Radboud University Nijmegen, Netherlands; Aarhus University, Denmark) In the past two decades, stepindexed logical relations and separation logics have both come to play a major role in semantics and verification research. More recently, they have been married together in the form of stepindexed separation logics like VST, iCAP, and Iris, which provide powerful tools for (among other things) building semantic models of richly typed languages like Rust. In these logics, propositions are given semantics using a stepindexed model, and stepindexed reasoning is reflected into the logic through the socalled “later” modality. On the one hand, this modality provides an elegant, highlevel account of stepindexed reasoning; on the other hand, when used in sufficiently sophisticated ways, it can become a nuisance, turning perfectly natural proof strategies into dead ends. In this work, we introduce later credits, a new technique for escaping latermodality quagmires. By leveraging the second ancestor of these logics—separation logic—later credits turn “the right to eliminate a later” into an ownable resource, which is subject to all the traditional modular reasoning principles of separation logic. We develop the theory of later credits in the context of Iris, and present several challenging examples of proofs and proof patterns which were previously not possible in Iris but are now possible due to later credits. @Article{ICFP22p100, author = {Simon Spies and Lennard Gäher and Joseph Tassarotti and Ralf Jung and Robbert Krebbers and Lars Birkedal and Derek Dreyer}, title = {Later Credits: Resourceful Reasoning for the Later Modality}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {100}, numpages = {29}, doi = {10.1145/3547631}, year = {2022}, } Publisher's Version Artifacts Reusable 

Krishnamurthi, Shriram 
ICFP '22: "Structural versus Pipeline ..."
Structural versus Pipeline Composition of HigherOrder Functions (Experience Report)
Elijah Rivera and Shriram Krishnamurthi (Brown University, USA) In teaching students to program with compositions of higherorder functions, we have encountered a sharp distinction in the difficulty of problems as perceived by students. This distinction especially matters as growing numbers of programmers learn about functional programming for data processing. We have made initial progress on identifying this distinction, which appears counterintuitive to some. We describe the phenomenon, provide some preliminary evidence of the difference in difficulty, and suggest consequences for functional programming pedagogy. @Article{ICFP22p102, author = {Elijah Rivera and Shriram Krishnamurthi}, title = {Structural versus Pipeline Composition of HigherOrder Functions (Experience Report)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {102}, numpages = {14}, doi = {10.1145/3547633}, year = {2022}, } Publisher's Version 

Lampropoulos, Leonidas 
ICFP '22: "Random Testing of a HigherOrder ..."
Random Testing of a HigherOrder Blockchain Language (Experience Report)
Tram Hoang , Anton Trunov , Leonidas Lampropoulos , and Ilya Sergey (National University of Singapore, Singapore; Zilliqa Research, Russia; University of Maryland at College Park, USA) We describe our experience of using propertybased testingan approach for automatically generating random inputs to check executable program specificationsin a development of a higherorder smart contract language that powers a stateoftheart blockchain with thousands of active daily users. We outline the process of integrating QuickChicka framework for propertybased testing built on top of the Coq proof assistantinto a realworld language implementation in OCaml. We discuss the challenges we have encountered when generating welltyped programs for a realistic higherorder smart contract language, which mixes purely functional and imperative computations and features runtime resource accounting. We describe the set of the language implementation properties that we tested, as well as the semantic harness required to enable their validation. The properties range from the standard type safety to the soundness of a control and typeflow analysis used by the optimizing compiler. Finally, we present the list of bugs discovered and rediscovered with the help of QuickChick and discuss their severity and possible ramifications. @Article{ICFP22p122, author = {Tram Hoang and Anton Trunov and Leonidas Lampropoulos and Ilya Sergey}, title = {Random Testing of a HigherOrder Blockchain Language (Experience Report)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {122}, numpages = {16}, doi = {10.1145/3547653}, year = {2022}, } Publisher's Version Artifacts Reusable 

Leijen, Daan 
ICFP '22: "Reference Counting with Frame ..."
Reference Counting with Frame Limited Reuse
Anton Lorenzen and Daan Leijen (University of Bonn, Germany; Microsoft Research, USA) The recently introduced _Perceus_ algorithm can automatically insert reference count instructions such that the resulting (cyclefree) program is _garbage free_: objects are freed at the very moment they can no longer be referenced. An important extension is reuse analysis. This optimization pairs objects of known size with fresh allocations of the same size and tries to reuse the object inplace at runtime if it happens to be unique. Unfortunately, current implementations of reuse analysis are fragile with respect to small program transformations, or can cause an arbitrary increase in the peak heap usage. We present a novel _dropguided_ reuse algorithm that is simpler and more robust than previous approaches. Moreover, we generalize the linear resource calculus to precisely characterize garbagefree and framelimited evaluations. On each function call, a framelimited evaluation may hold on to memory longer if the size is bounded by a constant factor. Using this framework we show that our dropguided reuse _is_ framelimited and find that an implementation of our new reuse approach in Koka can provide significant speedups. @Article{ICFP22p103, author = {Anton Lorenzen and Daan Leijen}, title = {Reference Counting with Frame Limited Reuse}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {103}, numpages = {24}, doi = {10.1145/3547634}, year = {2022}, } Publisher's Version Info Artifacts Reusable 

LennonBertrand, Meven 
ICFP '22: "A Reasonably Gradual Type ..."
A Reasonably Gradual Type Theory
Kenji Maillard , Meven LennonBertrand , Nicolas Tabareau , and Éric Tanter (Inria, France; University of Chile, Chile) Gradualizing the Calculus of Inductive Constructions (CIC) involves dealing with subtle tensions between normalization, graduality, and conservativity with respect to CIC. Recently, GCIC has been proposed as a parametrized gradual type theory that admits three variants, each sacrificing one of these properties. For devising a gradual proof assistant based on CIC, normalization and conservativity with respect to CIC are key, but the tension with graduality needs to be addressed. Additionally, several challenges remain: (1) The presence of two wildcard terms at any typethe error and unknown termsenables trivial proofs of any theorem, jeopardizing the use of a gradual type theory in a proof assistant; (2) Supporting general indexed inductive families, most prominently equality, is an open problem; (3) Theoretical accounts of gradual typing and graduality so far do not support handling type mismatches detected during reduction; (4) Precision and graduality are external notions not amenable to reasoning within a gradual type theory. All these issues manifest primally in CastCIC, the cast calculus used to define GCIC. In this work, we present an extension of CastCIC called GRIP. GRIP is a reasonably gradual type theory that addresses the issues above, featuring internal precision and general exception handling. By adopting a novel interpretation of the unknown term that carefully accounts for universe levels, GRIP satisfies graduality for a large and welldefined class of terms, in addition to being normalizing and a conservative extension of CIC. Internal precision supports reasoning about graduality within GRIP itself, for instance to characterize gradual exceptionhandling terms, and supports gradual subset types. We develop the metatheory of GRIP using a model formalized in Coq, and provide a prototype implementation of GRIP in Agda. @Article{ICFP22p124, author = {Kenji Maillard and Meven LennonBertrand and Nicolas Tabareau and Éric Tanter}, title = {A Reasonably Gradual Type Theory}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {124}, numpages = {29}, doi = {10.1145/3547655}, year = {2022}, } Publisher's Version Artifacts Reusable 

Li, Yao 
ICFP '22: "Program Adverbs and Tlön ..."
Program Adverbs and Tlön Embeddings
Yao Li and Stephanie Weirich (Portland State University, USA; University of Pennsylvania, USA) Free monads (and their variants) have become a popular generalpurpose tool for representing the semantics of effectful programs in proof assistants. These data structures support the compositional definition of semantics parameterized by uninterpreted events, while admitting a rich equational theory of equivalence. But monads are not the only way to structure effectful computation, why should we limit ourselves? In this paper, inspired by applicative functors, selective functors, and other structures, we define a collection of data structures and theories, which we call program adverbs, that capture a variety of computational patterns. Program adverbs are themselves composable, allowing them to be used to specify the semantics of languages with multiple computation patterns. We use program adverbs as the basis for a new class of semantic embeddings called Tlön embeddings. Compared with embeddings based on free monads, Tlön embeddings allow more flexibility in computational modeling of effects, while retaining more information about the program's syntactic structure. @Article{ICFP22p101, author = {Yao Li and Stephanie Weirich}, title = {Program Adverbs and Tlön Embeddings}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {101}, numpages = {31}, doi = {10.1145/3547632}, year = {2022}, } Publisher's Version Artifacts Reusable 

Lin, TzuChi 
ICFP '22: "DatatypeGeneric Programming ..."
DatatypeGeneric Programming Meets Elaborator Reflection
HsiangShang Ko , LiangTing Chen , and TzuChi Lin (Academia Sinica, Taiwan) Datatypegeneric programming is natural and useful in dependently typed languages such as Agda. However, datatypegeneric libraries in Agda are not reused as much as they should be, because traditionally they work only on datatypes decoded from a library’s own version of datatype descriptions; this means that different generic libraries cannot be used together, and they do not work on native datatypes, which are preferred by the practical Agda programmer for better language support and access to other libraries. Based on elaborator reflection, we present a framework in Agda featuring a set of general metaprograms for instantiating datatypegeneric programs as, and for, a useful range of native datatypes and functions —including universepolymorphic ones— in programmerfriendly and customisable forms. We expect that datatypegeneric libraries built with our framework will be more attractive to the practical Agda programmer. As the elaborator reflection features used by our framework become more widespread, our design can be ported to other languages too. @Article{ICFP22p98, author = {HsiangShang Ko and LiangTing Chen and TzuChi Lin}, title = {DatatypeGeneric Programming Meets Elaborator Reflection}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {98}, numpages = {29}, doi = {10.1145/3547629}, year = {2022}, } Publisher's Version Artifacts Reusable 

Lindley, Sam 
ICFP '22: "ConstraintBased Type Inference ..."
ConstraintBased Type Inference for FreezeML
Frank Emrich , Jan Stolarek , James Cheney , and Sam Lindley (University of Edinburgh, UK) FreezeML is a new approach to firstclass polymorphic type inference that employs term annotations to control when and how polymorphic types are instantiated and generalised. It conservatively extends HindleyMilner type inference and was first presented as an extension to Algorithm W. More modern type inference techniques such as HM(X) and OutsideIn(X) employ constraints to support features such as type classes, type families, rows, and other extensions. We take the first step towards modernising FreezeML by presenting a constraintbased type inference algorithm. We introduce a new constraint language, inspired by the Pottier/Rémy presentation of HM(X), in order to allow FreezeML type inference problems to be expressed as constraints. We present a deterministic stack machine for solving FreezeML constraints and prove its termination and correctness. @Article{ICFP22p111, author = {Frank Emrich and Jan Stolarek and James Cheney and Sam Lindley}, title = {ConstraintBased Type Inference for FreezeML}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {111}, numpages = {26}, doi = {10.1145/3547642}, year = {2022}, } Publisher's Version 

Lorenzen, Anton 
ICFP '22: "Reference Counting with Frame ..."
Reference Counting with Frame Limited Reuse
Anton Lorenzen and Daan Leijen (University of Bonn, Germany; Microsoft Research, USA) The recently introduced _Perceus_ algorithm can automatically insert reference count instructions such that the resulting (cyclefree) program is _garbage free_: objects are freed at the very moment they can no longer be referenced. An important extension is reuse analysis. This optimization pairs objects of known size with fresh allocations of the same size and tries to reuse the object inplace at runtime if it happens to be unique. Unfortunately, current implementations of reuse analysis are fragile with respect to small program transformations, or can cause an arbitrary increase in the peak heap usage. We present a novel _dropguided_ reuse algorithm that is simpler and more robust than previous approaches. Moreover, we generalize the linear resource calculus to precisely characterize garbagefree and framelimited evaluations. On each function call, a framelimited evaluation may hold on to memory longer if the size is bounded by a constant factor. Using this framework we show that our dropguided reuse _is_ framelimited and find that an implementation of our new reuse approach in Koka can provide significant speedups. @Article{ICFP22p103, author = {Anton Lorenzen and Daan Leijen}, title = {Reference Counting with Frame Limited Reuse}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {103}, numpages = {24}, doi = {10.1145/3547634}, year = {2022}, } Publisher's Version Info Artifacts Reusable 

Lukyanov, Georgy 
ICFP '22: "Verified Symbolic Execution ..."
Verified Symbolic Execution with Kripke Specification Monads (and No Metaprogramming)
Steven Keuchel , Sander Huyghebaert , Georgy Lukyanov , and Dominique Devriese (Vrije Universiteit Brussel, Belgium; Newcastle University, UK; KU Leuven, Belgium) Verifying soundness of symbolic executionbased program verifiers is a significant challenge. This is especially true if the resulting tool needs to be usable outside of the proof assistant, in which case we cannot rely on shallowly embedded assertion logics and metaprogramming. The tool needs to manipulate deeply embedded assertions, and it is crucial for efficiency to eagerly prune unreachable paths and simplify intermediate assertions in a way that can be justified towards the soundness proof. Only a few such tools exist in the literature, and their soundness proofs are intricate and hard to generalize or reuse. We contribute a novel, systematic approach for the construction and soundness proof of such a symbolic executionbased verifier. We first implement a shallow verification condition generator as an object language interpreter in a specification monad, using an abstract interface featuring angelic and demonic nondeterminism. Next, we build a symbolic executor by implementing a similar interpreter, in a symbolic specification monad. This symbolic monad lives in a universe that is Kripkeindexed by variables in scope and a path condition. Finally, we reduce the soundness of the symbolic execution to the soundness of the shallow execution by relating both executors using a Kripke logical relation. We report on the practical application of these techniques in Katamaran, a tool for verifying security guarantees offered by instruction set architectures (ISAs). The tool is fully verified by combining our symbolic execution machinery with a soundness proof of the shallow verification conditions against an axiomatized separation logic, and an Irisbased implementation of the axioms, proven sound against the operational semantics. Based on our experience with Katamaran, we can report good results on practicality and efficiency of the tool, demonstrating practical viability of our symbolic execution approach. @Article{ICFP22p97, author = {Steven Keuchel and Sander Huyghebaert and Georgy Lukyanov and Dominique Devriese}, title = {Verified Symbolic Execution with Kripke Specification Monads (and No Metaprogramming)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {97}, numpages = {31}, doi = {10.1145/3547628}, year = {2022}, } Publisher's Version Artifacts Reusable 

Maillard, Kenji 
ICFP '22: "A Reasonably Gradual Type ..."
A Reasonably Gradual Type Theory
Kenji Maillard , Meven LennonBertrand , Nicolas Tabareau , and Éric Tanter (Inria, France; University of Chile, Chile) Gradualizing the Calculus of Inductive Constructions (CIC) involves dealing with subtle tensions between normalization, graduality, and conservativity with respect to CIC. Recently, GCIC has been proposed as a parametrized gradual type theory that admits three variants, each sacrificing one of these properties. For devising a gradual proof assistant based on CIC, normalization and conservativity with respect to CIC are key, but the tension with graduality needs to be addressed. Additionally, several challenges remain: (1) The presence of two wildcard terms at any typethe error and unknown termsenables trivial proofs of any theorem, jeopardizing the use of a gradual type theory in a proof assistant; (2) Supporting general indexed inductive families, most prominently equality, is an open problem; (3) Theoretical accounts of gradual typing and graduality so far do not support handling type mismatches detected during reduction; (4) Precision and graduality are external notions not amenable to reasoning within a gradual type theory. All these issues manifest primally in CastCIC, the cast calculus used to define GCIC. In this work, we present an extension of CastCIC called GRIP. GRIP is a reasonably gradual type theory that addresses the issues above, featuring internal precision and general exception handling. By adopting a novel interpretation of the unknown term that carefully accounts for universe levels, GRIP satisfies graduality for a large and welldefined class of terms, in addition to being normalizing and a conservative extension of CIC. Internal precision supports reasoning about graduality within GRIP itself, for instance to characterize gradual exceptionhandling terms, and supports gradual subset types. We develop the metatheory of GRIP using a model formalized in Coq, and provide a prototype implementation of GRIP in Agda. @Article{ICFP22p124, author = {Kenji Maillard and Meven LennonBertrand and Nicolas Tabareau and Éric Tanter}, title = {A Reasonably Gradual Type Theory}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {124}, numpages = {29}, doi = {10.1145/3547655}, year = {2022}, } Publisher's Version Artifacts Reusable 

Materzok, Marek 
ICFP '22: "Generating Circuits with Generators ..."
Generating Circuits with Generators
Marek Materzok (University of Wrocław, Poland) The most widely used languages and methods used for designing digital hardware fall into two rough categories. One of them, register transfer level (RTL), requires specifying each and every component in the designed circuit. This gives the designer full control, but burdens the designer with many trivial details. The other, the highlevel synthesis (HLS) method, allows the designer to abstract the details of hardware away and focus on the problem being solved. This method however cannot be used for a class of hardware design problems because the circuit's clock is also abstracted away. We present YieldFSM, a hardware description language that uses the generator abstraction to represent clocklevel timing in a digital circuit. It represents a middle ground between the RTL and HLS approaches: the abstraction level is higher than in RTL, but thanks to explicit information about clocklevel timing, it can be used in applications where RTL is traditionally used. We also present the YieldFSM compiler, which uses methods developed by the functional programming community  including continuationpasssing style translation and defunctionalization  to translate YieldFSM programs to Mealy machines. It is implemented using Template Haskell and the Clash functional hardware description language. We show that this approach leads to short and conceptually simple hardware descriptions. @Article{ICFP22p92, author = {Marek Materzok}, title = {Generating Circuits with Generators}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {92}, numpages = {28}, doi = {10.1145/3549821}, year = {2022}, } Publisher's Version Artifacts Reusable 

McDermott, Dylan 
ICFP '22: "Flexible Presentations of ..."
Flexible Presentations of Graded Monads
Shinya Katsumata , Dylan McDermott , Tarmo Uustalu , and Nicolas Wu (National Institute of Informatics, Japan; Reykjavik University, Iceland; Tallinn University of Technology, Estonia; Imperial College London, UK) A large class of monads used to model computational effects have natural presentations by operations and equations, for example, the list monad can be presented by a constant and a binary operation subject to unitality and associativity. Graded monads are a generalization of monads that enable us to track quantitative information about the effects being modelled. Correspondingly, a large class of graded monads can be presented using an existing notion of graded presentation. However, the existing notion has some deficiencies, in particular many effects do not have natural graded presentations. We introduce a notion of flexibly graded presentation that does not suffer from these issues, and develop the associated theory. We show that every flexibly graded presentation induces a graded monad equipped with interpretations of the operations of the presentation, and that all graded monads satisfying a particular condition on colimits have a flexibly graded presentation. As part of this, we show that the usual algebrapreserving correspondence between presentations and a class of monads transfers to an algebrapreserving correspondence between flexibly graded presentations and a class of flexibly graded monads. @Article{ICFP22p123, author = {Shinya Katsumata and Dylan McDermott and Tarmo Uustalu and Nicolas Wu}, title = {Flexible Presentations of Graded Monads}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {123}, numpages = {29}, doi = {10.1145/3547654}, year = {2022}, } Publisher's Version 

Nguyen, Minh 
ICFP '22: "Modular Probabilistic Models ..."
Modular Probabilistic Models via Algebraic Effects
Minh Nguyen , Roly Perera , Meng Wang , and Nicolas Wu (University of Bristol, UK; Alan Turing Institute, UK; Imperial College London, UK) Probabilistic programming languages (PPLs) allow programmers to construct statistical models and then simulate data or perform inference over them. Many PPLs restrict models to a particular instance of simulation or inference, limiting their reusability. In other PPLs, models are not readily composable. Using Haskell as the host language, we present an embedded domain specific language based on algebraic effects, where probabilistic models are modular, firstclass, and reusable for both simulation and inference. We also demonstrate how simulation and inference can be expressed naturally as composable program transformations using algebraic effect handlers. @Article{ICFP22p104, author = {Minh Nguyen and Roly Perera and Meng Wang and Nicolas Wu}, title = {Modular Probabilistic Models via Algebraic Effects}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {104}, numpages = {30}, doi = {10.1145/3547635}, year = {2022}, } Publisher's Version Artifacts Reusable 

Ostermann, Klaus 
ICFP '22: "Introduction and Elimination, ..."
Introduction and Elimination, Left and Right
Klaus Ostermann , David Binder , Ingo Skupin , Tim Süberkrüb , and Paul Downen (University of Tübingen, Germany; University of Massachusetts at Lowell, USA) Functional programming language design has been shaped by the framework of natural deduction, in which language constructs are divided into introduction and elimination rules for producers of values. In sequent calculusbased languages, left introduction rules replace (right) elimination rules and provide a dedicated sublanguage for consumers of values. In this paper, we present and analyze a wider design space of programming languages which encompasses four kinds of rules: Introduction and elimination, both left and right. We analyze the influence of rule choice on program structure and argue that having all kinds of rules enriches a programmer’s modularity arsenal. In particular, we identify four ways of adhering to the principle that ”the structure of the program follows the structure of the data“ and show that they correspond to the four possible choices of rules. We also propose the principle of biexpressibility to guide and validate the design of rules for a connective. Finally, we deepen the wellknown dualities between different connectives by means of the proof/refutation duality. @Article{ICFP22p106, author = {Klaus Ostermann and David Binder and Ingo Skupin and Tim Süberkrüb and Paul Downen}, title = {Introduction and Elimination, Left and Right}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {106}, numpages = {28}, doi = {10.1145/3547637}, year = {2022}, } Publisher's Version Artifacts Reusable 

Perera, Roly 
ICFP '22: "Modular Probabilistic Models ..."
Modular Probabilistic Models via Algebraic Effects
Minh Nguyen , Roly Perera , Meng Wang , and Nicolas Wu (University of Bristol, UK; Alan Turing Institute, UK; Imperial College London, UK) Probabilistic programming languages (PPLs) allow programmers to construct statistical models and then simulate data or perform inference over them. Many PPLs restrict models to a particular instance of simulation or inference, limiting their reusability. In other PPLs, models are not readily composable. Using Haskell as the host language, we present an embedded domain specific language based on algebraic effects, where probabilistic models are modular, firstclass, and reusable for both simulation and inference. We also demonstrate how simulation and inference can be expressed naturally as composable program transformations using algebraic effect handlers. @Article{ICFP22p104, author = {Minh Nguyen and Roly Perera and Meng Wang and Nicolas Wu}, title = {Modular Probabilistic Models via Algebraic Effects}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {104}, numpages = {30}, doi = {10.1145/3547635}, year = {2022}, } Publisher's Version Artifacts Reusable 

Polikarpova, Nadia 
ICFP '22: "Searching Entangled Program ..."
Searching Entangled Program Spaces
James Koppel , Zheng Guo , Edsko de Vries , Armando SolarLezama , and Nadia Polikarpova (Massachusetts Institute of Technology, USA; University of California at San Diego, USA; WellTyped LLP, UK) Many problem domains, including program synthesis and rewritebased optimization, require searching astronomically large spaces of programs. Existing approaches often rely on building specialized data structures—versionspace algebras, finite tree automata, or egraphs—to compactly represent such spaces. At their core, all these data structures exploit independence of subterms; as a result, they cannot efficiently represent more complex program spaces, where the choices of subterms are entangled. We introduce equalityconstrained tree automata (ECTAs), a new data structure, designed to compactly represent large spaces of programs with entangled subterms. We present efficient algorithms for extracting programs from ECTAs, implemented in a performant Haskell library, ecta. Using the ecta library, we construct Hectare, a typedriven program synthesizer for Haskell. Hectare significantly outperforms a stateoftheart synthesizer Hoogle+—providing an average speedup of 8×—despite its implementation being an order of magnitude smaller. @Article{ICFP22p91, author = {James Koppel and Zheng Guo and Edsko de Vries and Armando SolarLezama and Nadia Polikarpova}, title = {Searching Entangled Program Spaces}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {91}, numpages = {29}, doi = {10.1145/3547622}, year = {2022}, } Publisher's Version Artifacts Reusable 

Protzenko, Jonathan 
ICFP '22: "Aeneas: Rust Verification ..."
Aeneas: Rust Verification by Functional Translation
Son Ho and Jonathan Protzenko (Inria, France; Microsoft Research, USA) We present Aeneas, a new verification toolchain for Rust programs based on a lightweight functional translation. We leverage Rust’s rich regionbased type system to eliminate memory reasoning for a large class of Rust programs, as long as they do not rely on interior mutability or unsafe code. Doing so, we relieve the proof engineer of the burden of memorybased reasoning, allowing them to instead focus on functional properties of their code. The first contribution of Aeneas is a new approach to borrows and controlled aliasing. We propose a pure, functional semantics for LLBC, a LowLevel Borrow Calculus that captures a large subset of Rust programs. Our semantics is valuebased, meaning there is no notion of memory, addresses or pointer arithmetic. Our semantics is also ownershipcentric, meaning that we enforce soundness of borrows via a semantic criterion based on loans rather than through a syntactic typebased lifetime discipline. We claim that our semantics captures the essence of the borrow mechanism rather than its current implementation in the Rust compiler. The second contribution of Aeneas is a translation from LLBC to a pure lambdacalculus. This allows the user to reason about the original Rust program through the theorem prover of their choice, and fulfills our promise of enabling lightweight verification of Rust programs. To deal with the wellknown technical difficulty of terminating a borrow, we rely on a novel approach, in which we approximate the borrow graph in the presence of function calls. This in turn allows us to perform the translation using a new technical device called backward functions. We implement our toolchain in a mixture of Rust and OCaml; our chief case study is a lowlevel, resizing hash table, for which we prove functional correctness, the first such result in Rust. Our evaluation shows significant gains of verification productivity for the programmer. This paper therefore establishes a new point in the design space of Rust verification toolchains, one that aims to verify Rust programs simply, and at scale. Rust goes to great lengths to enforce static control of aliasing; the proof engineer should not waste any time on memory reasoning when so much already comes “for free”! @Article{ICFP22p116, author = {Son Ho and Jonathan Protzenko}, title = {Aeneas: Rust Verification by Functional Translation}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {116}, numpages = {31}, doi = {10.1145/3547647}, year = {2022}, } Publisher's Version Info Artifacts Reusable 

Quiring, Benjamin 
ICFP '22: "Analyzing Binding Extent in ..."
Analyzing Binding Extent in 3CPS
Benjamin Quiring , John Reppy , and Olin Shivers (University of Maryland, USA; University of Chicago, USA; Northeastern University, USA) To date, the most effective approach to compiling strict, higherorder functional languages (such as OCaml, Scheme, and SML) has been to use wholeprogram techniques to convert the program to a firstorder monomorphic representation that can be optimized using traditional compilation techniques. This approach, popularized by MLton, has limitations, however. We are interested in exploring a different approach to compiling such languages, one that preserves the higherorder and polymorphic character of the program throughout optimization. To enable such an approach, we must have effective analyses that both provide precise information about higherorder programs and that scale to larger units of compilation. This paper describes one such analysis for determining the extent of variable bindings. We classify the extent of variables as either register (only one binding instance can be live at any time), stack (the lifetimes of binding instances obey a LIFO order), or heap (binding lifetimes are arbitrary). These extents naturally connect variables to the machine resources required to represent them. We believe that precise information about binding extents will enable efficient management of environments, which is a key problem in the efficient compilation of higherorder programs. At the core of the paper is the 3CPS intermediate representation, which is a factored CPSbased intermediate representation (IR) that statically marks variables to indicate their binding extent. We formally specify the management of this binding structure by means of a smallstep operational semantics and define a static analysis that determines the extents of the variables in a program. We evaluate our analysis using a standard suite of SML benchmark programs. Our implementation gets surprisingly high yield and exhibits scalable performance. While this paper uses a CPSbased IR, the algorithm and results are easily transferable to other λcalculus IRs, such as ANF. @Article{ICFP22p114, author = {Benjamin Quiring and John Reppy and Olin Shivers}, title = {Analyzing Binding Extent in 3CPS}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {114}, numpages = {29}, doi = {10.1145/3547645}, year = {2022}, } Publisher's Version Artifacts Reusable 

Ramsey, Norman 
ICFP '22: "Beyond Relooper: Recursive ..."
Beyond Relooper: Recursive Translation of Unstructured Control Flow to Structured Control Flow (Functional Pearl)
Norman Ramsey (Tweag, France; Tufts University, USA) In many compilers, control flow is represented using an arbitrary directed graph. But in some interesting target languages, including JavaScript and WebAssembly, intraprocedural control flow can be expressed only in structured ways, using loops, conditionals, and multilevel breaks or exits. As was shown by Peterson, Kasami, and Tokura in 1973, such structured control flow can be obtained by translating arbitrary control flow. The translation uses two standard analyses, but as published, it takes three passes—which may explain why it was overlooked by Emscripten, a popular compiler from C to JavaScript. By tweaking the analyses and by applying fundamental ideas from functional programming (recursive functions and immutable abstractsyntax trees), the translation, along with a couple of code improvements, can be implemented in a single pass. This new implementation is slated to be added to the Glasgow Haskell Compiler. Its singlepass translation, its immutable representation, and its use of dominator trees make it much easier to reason about than the original translation. @Article{ICFP22p90, author = {Norman Ramsey}, title = {Beyond Relooper: Recursive Translation of Unstructured Control Flow to Structured Control Flow (Functional Pearl)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {90}, numpages = {22}, doi = {10.1145/3547621}, year = {2022}, } Publisher's Version Artifacts Reusable 

Reppy, John 
ICFP '22: "Analyzing Binding Extent in ..."
Analyzing Binding Extent in 3CPS
Benjamin Quiring , John Reppy , and Olin Shivers (University of Maryland, USA; University of Chicago, USA; Northeastern University, USA) To date, the most effective approach to compiling strict, higherorder functional languages (such as OCaml, Scheme, and SML) has been to use wholeprogram techniques to convert the program to a firstorder monomorphic representation that can be optimized using traditional compilation techniques. This approach, popularized by MLton, has limitations, however. We are interested in exploring a different approach to compiling such languages, one that preserves the higherorder and polymorphic character of the program throughout optimization. To enable such an approach, we must have effective analyses that both provide precise information about higherorder programs and that scale to larger units of compilation. This paper describes one such analysis for determining the extent of variable bindings. We classify the extent of variables as either register (only one binding instance can be live at any time), stack (the lifetimes of binding instances obey a LIFO order), or heap (binding lifetimes are arbitrary). These extents naturally connect variables to the machine resources required to represent them. We believe that precise information about binding extents will enable efficient management of environments, which is a key problem in the efficient compilation of higherorder programs. At the core of the paper is the 3CPS intermediate representation, which is a factored CPSbased intermediate representation (IR) that statically marks variables to indicate their binding extent. We formally specify the management of this binding structure by means of a smallstep operational semantics and define a static analysis that determines the extents of the variables in a program. We evaluate our analysis using a standard suite of SML benchmark programs. Our implementation gets surprisingly high yield and exhibits scalable performance. While this paper uses a CPSbased IR, the algorithm and results are easily transferable to other λcalculus IRs, such as ANF. @Article{ICFP22p114, author = {Benjamin Quiring and John Reppy and Olin Shivers}, title = {Analyzing Binding Extent in 3CPS}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {114}, numpages = {29}, doi = {10.1145/3547645}, year = {2022}, } Publisher's Version Artifacts Reusable 

Rivera, Elijah 
ICFP '22: "Structural versus Pipeline ..."
Structural versus Pipeline Composition of HigherOrder Functions (Experience Report)
Elijah Rivera and Shriram Krishnamurthi (Brown University, USA) In teaching students to program with compositions of higherorder functions, we have encountered a sharp distinction in the difficulty of problems as perceived by students. This distinction especially matters as growing numbers of programmers learn about functional programming for data processing. We have made initial progress on identifying this distinction, which appears counterintuitive to some. We describe the phenomenon, provide some preliminary evidence of the difference in difficulty, and suggest consequences for functional programming pedagogy. @Article{ICFP22p102, author = {Elijah Rivera and Shriram Krishnamurthi}, title = {Structural versus Pipeline Composition of HigherOrder Functions (Experience Report)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {102}, numpages = {14}, doi = {10.1145/3547633}, year = {2022}, } Publisher's Version 

Rix, Rob 
ICFP '22: "Fusing Industry and Academia ..."
Fusing Industry and Academia at GitHub (Experience Report)
Patrick Thomson , Rob Rix , Nicolas Wu , and Tom Schrijvers (GitHub, USA; GitHub, Canada; Imperial College London, UK; KU Leuven, Belgium) GitHub hosts hundreds of millions of code repositories written in hundreds of different programming languages. In addition to its hosting services, GitHub provides data and insights into code, such as vulnerability analysis and code navigation, with which users can improve and understand their software development process. GitHub has built Semantic, a program analysis tool capable of parsing and extracting detailed information from source code. The development of Semantic has relied extensively on the functional programming literature; this paper describes how connections to academic research inspired and informed the development of an industrialscale program analysis toolkit. @Article{ICFP22p108, author = {Patrick Thomson and Rob Rix and Nicolas Wu and Tom Schrijvers}, title = {Fusing Industry and Academia at GitHub (Experience Report)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {108}, numpages = {16}, doi = {10.1145/3547639}, year = {2022}, } Publisher's Version 

Ruch, Fabian 
ICFP '22: "Normalization for FitchStyle ..."
Normalization for FitchStyle Modal Calculi
Nachiappan Valliappan , Fabian Ruch , and Carlos Tomé Cortiñas (Chalmers University of Technology, Sweden) Fitchstyle modal lambda calculi enable programming with necessity modalities in a typed lambda calculus by extending the typing context with a delimiting operator that is denoted by a lock. The addition of locks simplifies the formulation of typing rules for calculi that incorporate different modal axioms, but each variant demands different, tedious and seemingly ad hoc syntactic lemmas to prove normalization. In this work, we take a semantic approach to normalization, called normalization by evaluation (NbE), by leveraging the possibleworld semantics of Fitchstyle calculi to yield a more modular approach to normalization. We show that NbE models can be constructed for calculi that incorporate the K, T and 4 axioms of modal logic, as suitable instantiations of the possibleworld semantics. In addition to existing results that handle 𝛽equivalence, our normalization result also considers 𝜂equivalence for these calculi. Our key results have been mechanized in the proof assistant Agda. Finally, we showcase several consequences of normalization for proving metatheoretic properties of Fitchstyle calculi as well as programminglanguage applications based on different interpretations of the necessity modality. @Article{ICFP22p118, author = {Nachiappan Valliappan and Fabian Ruch and Carlos Tomé Cortiñas}, title = {Normalization for FitchStyle Modal Calculi}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {118}, numpages = {27}, doi = {10.1145/3547649}, year = {2022}, } Publisher's Version Info Artifacts Reusable 

Schrijvers, Tom 
ICFP '22: "Fusing Industry and Academia ..."
Fusing Industry and Academia at GitHub (Experience Report)
Patrick Thomson , Rob Rix , Nicolas Wu , and Tom Schrijvers (GitHub, USA; GitHub, Canada; Imperial College London, UK; KU Leuven, Belgium) GitHub hosts hundreds of millions of code repositories written in hundreds of different programming languages. In addition to its hosting services, GitHub provides data and insights into code, such as vulnerability analysis and code navigation, with which users can improve and understand their software development process. GitHub has built Semantic, a program analysis tool capable of parsing and extracting detailed information from source code. The development of Semantic has relied extensively on the functional programming literature; this paper describes how connections to academic research inspired and informed the development of an industrialscale program analysis toolkit. @Article{ICFP22p108, author = {Patrick Thomson and Rob Rix and Nicolas Wu and Tom Schrijvers}, title = {Fusing Industry and Academia at GitHub (Experience Report)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {108}, numpages = {16}, doi = {10.1145/3547639}, year = {2022}, } Publisher's Version 

Sergey, Ilya 
ICFP '22: "Random Testing of a HigherOrder ..."
Random Testing of a HigherOrder Blockchain Language (Experience Report)
Tram Hoang , Anton Trunov , Leonidas Lampropoulos , and Ilya Sergey (National University of Singapore, Singapore; Zilliqa Research, Russia; University of Maryland at College Park, USA) We describe our experience of using propertybased testingan approach for automatically generating random inputs to check executable program specificationsin a development of a higherorder smart contract language that powers a stateoftheart blockchain with thousands of active daily users. We outline the process of integrating QuickChicka framework for propertybased testing built on top of the Coq proof assistantinto a realworld language implementation in OCaml. We discuss the challenges we have encountered when generating welltyped programs for a realistic higherorder smart contract language, which mixes purely functional and imperative computations and features runtime resource accounting. We describe the set of the language implementation properties that we tested, as well as the semantic harness required to enable their validation. The properties range from the standard type safety to the soundness of a control and typeflow analysis used by the optimizing compiler. Finally, we present the list of bugs discovered and rediscovered with the help of QuickChick and discuss their severity and possible ramifications. @Article{ICFP22p122, author = {Tram Hoang and Anton Trunov and Leonidas Lampropoulos and Ilya Sergey}, title = {Random Testing of a HigherOrder Blockchain Language (Experience Report)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {122}, numpages = {16}, doi = {10.1145/3547653}, year = {2022}, } Publisher's Version Artifacts Reusable 

Shivers, Olin 
ICFP '22: "Analyzing Binding Extent in ..."
Analyzing Binding Extent in 3CPS
Benjamin Quiring , John Reppy , and Olin Shivers (University of Maryland, USA; University of Chicago, USA; Northeastern University, USA) To date, the most effective approach to compiling strict, higherorder functional languages (such as OCaml, Scheme, and SML) has been to use wholeprogram techniques to convert the program to a firstorder monomorphic representation that can be optimized using traditional compilation techniques. This approach, popularized by MLton, has limitations, however. We are interested in exploring a different approach to compiling such languages, one that preserves the higherorder and polymorphic character of the program throughout optimization. To enable such an approach, we must have effective analyses that both provide precise information about higherorder programs and that scale to larger units of compilation. This paper describes one such analysis for determining the extent of variable bindings. We classify the extent of variables as either register (only one binding instance can be live at any time), stack (the lifetimes of binding instances obey a LIFO order), or heap (binding lifetimes are arbitrary). These extents naturally connect variables to the machine resources required to represent them. We believe that precise information about binding extents will enable efficient management of environments, which is a key problem in the efficient compilation of higherorder programs. At the core of the paper is the 3CPS intermediate representation, which is a factored CPSbased intermediate representation (IR) that statically marks variables to indicate their binding extent. We formally specify the management of this binding structure by means of a smallstep operational semantics and define a static analysis that determines the extents of the variables in a program. We evaluate our analysis using a standard suite of SML benchmark programs. Our implementation gets surprisingly high yield and exhibits scalable performance. While this paper uses a CPSbased IR, the algorithm and results are easily transferable to other λcalculus IRs, such as ANF. @Article{ICFP22p114, author = {Benjamin Quiring and John Reppy and Olin Shivers}, title = {Analyzing Binding Extent in 3CPS}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {114}, numpages = {29}, doi = {10.1145/3547645}, year = {2022}, } Publisher's Version Artifacts Reusable 

Skupin, Ingo 
ICFP '22: "Introduction and Elimination, ..."
Introduction and Elimination, Left and Right
Klaus Ostermann , David Binder , Ingo Skupin , Tim Süberkrüb , and Paul Downen (University of Tübingen, Germany; University of Massachusetts at Lowell, USA) Functional programming language design has been shaped by the framework of natural deduction, in which language constructs are divided into introduction and elimination rules for producers of values. In sequent calculusbased languages, left introduction rules replace (right) elimination rules and provide a dedicated sublanguage for consumers of values. In this paper, we present and analyze a wider design space of programming languages which encompasses four kinds of rules: Introduction and elimination, both left and right. We analyze the influence of rule choice on program structure and argue that having all kinds of rules enriches a programmer’s modularity arsenal. In particular, we identify four ways of adhering to the principle that ”the structure of the program follows the structure of the data“ and show that they correspond to the four possible choices of rules. We also propose the principle of biexpressibility to guide and validate the design of rules for a connective. Finally, we deepen the wellknown dualities between different connectives by means of the proof/refutation duality. @Article{ICFP22p106, author = {Klaus Ostermann and David Binder and Ingo Skupin and Tim Süberkrüb and Paul Downen}, title = {Introduction and Elimination, Left and Right}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {106}, numpages = {28}, doi = {10.1145/3547637}, year = {2022}, } Publisher's Version Artifacts Reusable 

SolarLezama, Armando 
ICFP '22: "Automatically Deriving ControlFlow ..."
Automatically Deriving ControlFlow Graph Generators from Operational Semantics
James Koppel , Jackson Kearl , and Armando SolarLezama (Massachusetts Institute of Technology, USA) We develop the first theory of controlflow graphs from first principles, and use it to create an algorithm for automatically synthesizing many variants of controlflow graph generators from a language’s operational semantics. Our approach first introduces a new algorithm for converting a large class of smallstep operational semantics to an abstract machine. It next uses a technique called ”abstract rewriting” to automatically abstract the semantics of a language, which is used both to directly generate a CFG from a program (”interpreted mode”) and to generate standalone code, similar to a humanwritten CFG generator, for any program in a language. We show how the choice of two abstraction and projection parameters allow our approach to synthesize several families of CFGgenerators useful for different kinds of tools. We prove the correspondence between the generated graphs and the original semantics. We provide and prove an algorithm for automatically proving the termination of interpretedmode generators. In addition to our theoretical results, we have implemented this algorithm in a tool called Mandate, and show that it produces humanreadable code on two mediumsize languages with 60−80 rules, featuring nearly all intraprocedural control constructs common in modern languages. We then show these CFGgenerators were sufficient to build two static analyses atop them. Our work is a promising step towards the grand vision of being able to synthesize all desired tools from the semantics of a programming language. @Article{ICFP22p117, author = {James Koppel and Jackson Kearl and Armando SolarLezama}, title = {Automatically Deriving ControlFlow Graph Generators from Operational Semantics}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {117}, numpages = {30}, doi = {10.1145/3547648}, year = {2022}, } Publisher's Version Artifacts Reusable ICFP '22: "Searching Entangled Program ..." Searching Entangled Program Spaces James Koppel , Zheng Guo , Edsko de Vries , Armando SolarLezama , and Nadia Polikarpova (Massachusetts Institute of Technology, USA; University of California at San Diego, USA; WellTyped LLP, UK) Many problem domains, including program synthesis and rewritebased optimization, require searching astronomically large spaces of programs. Existing approaches often rely on building specialized data structures—versionspace algebras, finite tree automata, or egraphs—to compactly represent such spaces. At their core, all these data structures exploit independence of subterms; as a result, they cannot efficiently represent more complex program spaces, where the choices of subterms are entangled. We introduce equalityconstrained tree automata (ECTAs), a new data structure, designed to compactly represent large spaces of programs with entangled subterms. We present efficient algorithms for extracting programs from ECTAs, implemented in a performant Haskell library, ecta. Using the ecta library, we construct Hectare, a typedriven program synthesizer for Haskell. Hectare significantly outperforms a stateoftheart synthesizer Hoogle+—providing an average speedup of 8×—despite its implementation being an order of magnitude smaller. @Article{ICFP22p91, author = {James Koppel and Zheng Guo and Edsko de Vries and Armando SolarLezama and Nadia Polikarpova}, title = {Searching Entangled Program Spaces}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {91}, numpages = {29}, doi = {10.1145/3547622}, year = {2022}, } Publisher's Version Artifacts Reusable 

Spies, Simon 
ICFP '22: "Later Credits: Resourceful ..."
Later Credits: Resourceful Reasoning for the Later Modality
Simon Spies , Lennard Gäher , Joseph Tassarotti , Ralf Jung , Robbert Krebbers , Lars Birkedal , and Derek Dreyer (MPISWS, Germany; New York University, USA; Massachusetts Institute of Technology, USA; Radboud University Nijmegen, Netherlands; Aarhus University, Denmark) In the past two decades, stepindexed logical relations and separation logics have both come to play a major role in semantics and verification research. More recently, they have been married together in the form of stepindexed separation logics like VST, iCAP, and Iris, which provide powerful tools for (among other things) building semantic models of richly typed languages like Rust. In these logics, propositions are given semantics using a stepindexed model, and stepindexed reasoning is reflected into the logic through the socalled “later” modality. On the one hand, this modality provides an elegant, highlevel account of stepindexed reasoning; on the other hand, when used in sufficiently sophisticated ways, it can become a nuisance, turning perfectly natural proof strategies into dead ends. In this work, we introduce later credits, a new technique for escaping latermodality quagmires. By leveraging the second ancestor of these logics—separation logic—later credits turn “the right to eliminate a later” into an ownable resource, which is subject to all the traditional modular reasoning principles of separation logic. We develop the theory of later credits in the context of Iris, and present several challenging examples of proofs and proof patterns which were previously not possible in Iris but are now possible due to later credits. @Article{ICFP22p100, author = {Simon Spies and Lennard Gäher and Joseph Tassarotti and Ralf Jung and Robbert Krebbers and Lars Birkedal and Derek Dreyer}, title = {Later Credits: Resourceful Reasoning for the Later Modality}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {100}, numpages = {29}, doi = {10.1145/3547631}, year = {2022}, } Publisher's Version Artifacts Reusable 

Spiwack, Arnaud 
ICFP '22: "Linearly Qualified Types: ..."
Linearly Qualified Types: Generic Inference for Capabilities and Uniqueness
Arnaud Spiwack , Csongor Kiss , JeanPhilippe Bernardy , Nicolas Wu , and Richard A. Eisenberg (Tweag, France; Imperial College London, UK; University of Gothenburg, Sweden) A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used safely. However, writing code with explicit linear arguments requires bureaucracy. This paper presents linear constraints, a frontend feature for linear typing that decreases the bureaucracy of working with linear types. Linear constraints are implicit linear arguments that are filled in automatically by the compiler. We present linear constraints as a qualified type system,together with an inference algorithm which extends GHC's existing constraint solver algorithm. Soundness of linear constraints is ensured by the fact that they desugar into Linear Haskell. @Article{ICFP22p95, author = {Arnaud Spiwack and Csongor Kiss and JeanPhilippe Bernardy and Nicolas Wu and Richard A. Eisenberg}, title = {Linearly Qualified Types: Generic Inference for Capabilities and Uniqueness}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {95}, numpages = {28}, doi = {10.1145/3547626}, year = {2022}, } Publisher's Version 

Stolarek, Jan 
ICFP '22: "ConstraintBased Type Inference ..."
ConstraintBased Type Inference for FreezeML
Frank Emrich , Jan Stolarek , James Cheney , and Sam Lindley (University of Edinburgh, UK) FreezeML is a new approach to firstclass polymorphic type inference that employs term annotations to control when and how polymorphic types are instantiated and generalised. It conservatively extends HindleyMilner type inference and was first presented as an extension to Algorithm W. More modern type inference techniques such as HM(X) and OutsideIn(X) employ constraints to support features such as type classes, type families, rows, and other extensions. We take the first step towards modernising FreezeML by presenting a constraintbased type inference algorithm. We introduce a new constraint language, inspired by the Pottier/Rémy presentation of HM(X), in order to allow FreezeML type inference problems to be expressed as constraints. We present a deterministic stack machine for solving FreezeML constraints and prove its termination and correctness. @Article{ICFP22p111, author = {Frank Emrich and Jan Stolarek and James Cheney and Sam Lindley}, title = {ConstraintBased Type Inference for FreezeML}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {111}, numpages = {26}, doi = {10.1145/3547642}, year = {2022}, } Publisher's Version 

Süberkrüb, Tim 
ICFP '22: "Introduction and Elimination, ..."
Introduction and Elimination, Left and Right
Klaus Ostermann , David Binder , Ingo Skupin , Tim Süberkrüb , and Paul Downen (University of Tübingen, Germany; University of Massachusetts at Lowell, USA) Functional programming language design has been shaped by the framework of natural deduction, in which language constructs are divided into introduction and elimination rules for producers of values. In sequent calculusbased languages, left introduction rules replace (right) elimination rules and provide a dedicated sublanguage for consumers of values. In this paper, we present and analyze a wider design space of programming languages which encompasses four kinds of rules: Introduction and elimination, both left and right. We analyze the influence of rule choice on program structure and argue that having all kinds of rules enriches a programmer’s modularity arsenal. In particular, we identify four ways of adhering to the principle that ”the structure of the program follows the structure of the data“ and show that they correspond to the four possible choices of rules. We also propose the principle of biexpressibility to guide and validate the design of rules for a connective. Finally, we deepen the wellknown dualities between different connectives by means of the proof/refutation duality. @Article{ICFP22p106, author = {Klaus Ostermann and David Binder and Ingo Skupin and Tim Süberkrüb and Paul Downen}, title = {Introduction and Elimination, Left and Right}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {106}, numpages = {28}, doi = {10.1145/3547637}, year = {2022}, } Publisher's Version Artifacts Reusable 

Swierstra, Wouter 
ICFP '22: "A Completely Unique Account ..."
A Completely Unique Account of Enumeration
Cas van der Rest and Wouter Swierstra (Delft University of Technology, Netherlands; Utrecht University, Netherlands) How can we enumerate the inhabitants of an algebraic datatype? This paper explores a datatype generic solution that works for all regular types and indexed families. The enumerators presented here are provably both complete and unique—they will eventually produce every value exactly once—and fair—they avoid bias when composing enumerators. Finally, these enumerators memoise previously enumerated values whenever possible, thereby avoiding repeatedly recomputing recursive results. @Article{ICFP22p105, author = {Cas van der Rest and Wouter Swierstra}, title = {A Completely Unique Account of Enumeration}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {105}, numpages = {27}, doi = {10.1145/3547636}, year = {2022}, } Publisher's Version 

Tabareau, Nicolas 
ICFP '22: "A Reasonably Gradual Type ..."
A Reasonably Gradual Type Theory
Kenji Maillard , Meven LennonBertrand , Nicolas Tabareau , and Éric Tanter (Inria, France; University of Chile, Chile) Gradualizing the Calculus of Inductive Constructions (CIC) involves dealing with subtle tensions between normalization, graduality, and conservativity with respect to CIC. Recently, GCIC has been proposed as a parametrized gradual type theory that admits three variants, each sacrificing one of these properties. For devising a gradual proof assistant based on CIC, normalization and conservativity with respect to CIC are key, but the tension with graduality needs to be addressed. Additionally, several challenges remain: (1) The presence of two wildcard terms at any typethe error and unknown termsenables trivial proofs of any theorem, jeopardizing the use of a gradual type theory in a proof assistant; (2) Supporting general indexed inductive families, most prominently equality, is an open problem; (3) Theoretical accounts of gradual typing and graduality so far do not support handling type mismatches detected during reduction; (4) Precision and graduality are external notions not amenable to reasoning within a gradual type theory. All these issues manifest primally in CastCIC, the cast calculus used to define GCIC. In this work, we present an extension of CastCIC called GRIP. GRIP is a reasonably gradual type theory that addresses the issues above, featuring internal precision and general exception handling. By adopting a novel interpretation of the unknown term that carefully accounts for universe levels, GRIP satisfies graduality for a large and welldefined class of terms, in addition to being normalizing and a conservative extension of CIC. Internal precision supports reasoning about graduality within GRIP itself, for instance to characterize gradual exceptionhandling terms, and supports gradual subset types. We develop the metatheory of GRIP using a model formalized in Coq, and provide a prototype implementation of GRIP in Agda. @Article{ICFP22p124, author = {Kenji Maillard and Meven LennonBertrand and Nicolas Tabareau and Éric Tanter}, title = {A Reasonably Gradual Type Theory}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {124}, numpages = {29}, doi = {10.1145/3547655}, year = {2022}, } Publisher's Version Artifacts Reusable 

Tanter, Éric 
ICFP '22: "A Reasonably Gradual Type ..."
A Reasonably Gradual Type Theory
Kenji Maillard , Meven LennonBertrand , Nicolas Tabareau , and Éric Tanter (Inria, France; University of Chile, Chile) Gradualizing the Calculus of Inductive Constructions (CIC) involves dealing with subtle tensions between normalization, graduality, and conservativity with respect to CIC. Recently, GCIC has been proposed as a parametrized gradual type theory that admits three variants, each sacrificing one of these properties. For devising a gradual proof assistant based on CIC, normalization and conservativity with respect to CIC are key, but the tension with graduality needs to be addressed. Additionally, several challenges remain: (1) The presence of two wildcard terms at any typethe error and unknown termsenables trivial proofs of any theorem, jeopardizing the use of a gradual type theory in a proof assistant; (2) Supporting general indexed inductive families, most prominently equality, is an open problem; (3) Theoretical accounts of gradual typing and graduality so far do not support handling type mismatches detected during reduction; (4) Precision and graduality are external notions not amenable to reasoning within a gradual type theory. All these issues manifest primally in CastCIC, the cast calculus used to define GCIC. In this work, we present an extension of CastCIC called GRIP. GRIP is a reasonably gradual type theory that addresses the issues above, featuring internal precision and general exception handling. By adopting a novel interpretation of the unknown term that carefully accounts for universe levels, GRIP satisfies graduality for a large and welldefined class of terms, in addition to being normalizing and a conservative extension of CIC. Internal precision supports reasoning about graduality within GRIP itself, for instance to characterize gradual exceptionhandling terms, and supports gradual subset types. We develop the metatheory of GRIP using a model formalized in Coq, and provide a prototype implementation of GRIP in Agda. @Article{ICFP22p124, author = {Kenji Maillard and Meven LennonBertrand and Nicolas Tabareau and Éric Tanter}, title = {A Reasonably Gradual Type Theory}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {124}, numpages = {29}, doi = {10.1145/3547655}, year = {2022}, } Publisher's Version Artifacts Reusable ICFP '22: "Propositional Equality for ..." Propositional Equality for Gradual Dependently Typed Programming Joseph Eremondi , Ronald Garcia , and Éric Tanter (University of British Columbia, Canada; University of Chile, Chile) Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types, though, lack a central feature of type theory: propositional equality. LennonBertrand et al. show that, when the reflexive proof refl is the only closed value of an equality type, a gradual extension of the Calculus of Inductive Constructions (CIC) with propositional equality violates static observational equivalences. Extensionallyequal functions should be indistinguishable at run time, but they can be distinguished using a combination of equality and type imprecision. This work presents a gradual dependently typed language that supports propositional equality. We avoid the above issues by devising an equality type of which refl is not the only closed inhabitant. Instead, each equality proof is accompanied by a term that is at least as precise as the equated terms, acting as a witness of their plausible equality. These witnesses track partial type information as a program runs, raising errors when that information shows that two equated terms are undeniably inconsistent. Composition of type information is internalized as a construct of the language, and is deferred for function bodies whose evaluation is blocked by variables. We thus ensure that extensionallyequal functions compose without error, thereby preventing contexts from distinguishing them. We describe the challenges of designing consistency and precision relations for this system, along with solutions to these challenges. Finally, we prove important metatheory: type safety, conservative embedding of CIC, weak canonicity, and the gradual guarantees of Siek et al., which ensure that reducing a program’s precision introduces no new static or dynamic errors. @Article{ICFP22p96, author = {Joseph Eremondi and Ronald Garcia and Éric Tanter}, title = {Propositional Equality for Gradual Dependently Typed Programming}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {96}, numpages = {29}, doi = {10.1145/3547627}, year = {2022}, } Publisher's Version 

Tassarotti, Joseph 
ICFP '22: "Later Credits: Resourceful ..."
Later Credits: Resourceful Reasoning for the Later Modality
Simon Spies , Lennard Gäher , Joseph Tassarotti , Ralf Jung , Robbert Krebbers , Lars Birkedal , and Derek Dreyer (MPISWS, Germany; New York University, USA; Massachusetts Institute of Technology, USA; Radboud University Nijmegen, Netherlands; Aarhus University, Denmark) In the past two decades, stepindexed logical relations and separation logics have both come to play a major role in semantics and verification research. More recently, they have been married together in the form of stepindexed separation logics like VST, iCAP, and Iris, which provide powerful tools for (among other things) building semantic models of richly typed languages like Rust. In these logics, propositions are given semantics using a stepindexed model, and stepindexed reasoning is reflected into the logic through the socalled “later” modality. On the one hand, this modality provides an elegant, highlevel account of stepindexed reasoning; on the other hand, when used in sufficiently sophisticated ways, it can become a nuisance, turning perfectly natural proof strategies into dead ends. In this work, we introduce later credits, a new technique for escaping latermodality quagmires. By leveraging the second ancestor of these logics—separation logic—later credits turn “the right to eliminate a later” into an ownable resource, which is subject to all the traditional modular reasoning principles of separation logic. We develop the theory of later credits in the context of Iris, and present several challenging examples of proofs and proof patterns which were previously not possible in Iris but are now possible due to later credits. @Article{ICFP22p100, author = {Simon Spies and Lennard Gäher and Joseph Tassarotti and Ralf Jung and Robbert Krebbers and Lars Birkedal and Derek Dreyer}, title = {Later Credits: Resourceful Reasoning for the Later Modality}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {100}, numpages = {29}, doi = {10.1145/3547631}, year = {2022}, } Publisher's Version Artifacts Reusable 

Thomson, Patrick 
ICFP '22: "Fusing Industry and Academia ..."
Fusing Industry and Academia at GitHub (Experience Report)
Patrick Thomson , Rob Rix , Nicolas Wu , and Tom Schrijvers (GitHub, USA; GitHub, Canada; Imperial College London, UK; KU Leuven, Belgium) GitHub hosts hundreds of millions of code repositories written in hundreds of different programming languages. In addition to its hosting services, GitHub provides data and insights into code, such as vulnerability analysis and code navigation, with which users can improve and understand their software development process. GitHub has built Semantic, a program analysis tool capable of parsing and extracting detailed information from source code. The development of Semantic has relied extensively on the functional programming literature; this paper describes how connections to academic research inspired and informed the development of an industrialscale program analysis toolkit. @Article{ICFP22p108, author = {Patrick Thomson and Rob Rix and Nicolas Wu and Tom Schrijvers}, title = {Fusing Industry and Academia at GitHub (Experience Report)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {108}, numpages = {16}, doi = {10.1145/3547639}, year = {2022}, } Publisher's Version 

Tomé Cortiñas, Carlos 
ICFP '22: "Normalization for FitchStyle ..."
Normalization for FitchStyle Modal Calculi
Nachiappan Valliappan , Fabian Ruch , and Carlos Tomé Cortiñas (Chalmers University of Technology, Sweden) Fitchstyle modal lambda calculi enable programming with necessity modalities in a typed lambda calculus by extending the typing context with a delimiting operator that is denoted by a lock. The addition of locks simplifies the formulation of typing rules for calculi that incorporate different modal axioms, but each variant demands different, tedious and seemingly ad hoc syntactic lemmas to prove normalization. In this work, we take a semantic approach to normalization, called normalization by evaluation (NbE), by leveraging the possibleworld semantics of Fitchstyle calculi to yield a more modular approach to normalization. We show that NbE models can be constructed for calculi that incorporate the K, T and 4 axioms of modal logic, as suitable instantiations of the possibleworld semantics. In addition to existing results that handle 𝛽equivalence, our normalization result also considers 𝜂equivalence for these calculi. Our key results have been mechanized in the proof assistant Agda. Finally, we showcase several consequences of normalization for proving metatheoretic properties of Fitchstyle calculi as well as programminglanguage applications based on different interpretations of the necessity modality. @Article{ICFP22p118, author = {Nachiappan Valliappan and Fabian Ruch and Carlos Tomé Cortiñas}, title = {Normalization for FitchStyle Modal Calculi}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {118}, numpages = {27}, doi = {10.1145/3547649}, year = {2022}, } Publisher's Version Info Artifacts Reusable 

Trunov, Anton 
ICFP '22: "Random Testing of a HigherOrder ..."
Random Testing of a HigherOrder Blockchain Language (Experience Report)
Tram Hoang , Anton Trunov , Leonidas Lampropoulos , and Ilya Sergey (National University of Singapore, Singapore; Zilliqa Research, Russia; University of Maryland at College Park, USA) We describe our experience of using propertybased testingan approach for automatically generating random inputs to check executable program specificationsin a development of a higherorder smart contract language that powers a stateoftheart blockchain with thousands of active daily users. We outline the process of integrating QuickChicka framework for propertybased testing built on top of the Coq proof assistantinto a realworld language implementation in OCaml. We discuss the challenges we have encountered when generating welltyped programs for a realistic higherorder smart contract language, which mixes purely functional and imperative computations and features runtime resource accounting. We describe the set of the language implementation properties that we tested, as well as the semantic harness required to enable their validation. The properties range from the standard type safety to the soundness of a control and typeflow analysis used by the optimizing compiler. Finally, we present the list of bugs discovered and rediscovered with the help of QuickChick and discuss their severity and possible ramifications. @Article{ICFP22p122, author = {Tram Hoang and Anton Trunov and Leonidas Lampropoulos and Ilya Sergey}, title = {Random Testing of a HigherOrder Blockchain Language (Experience Report)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {122}, numpages = {16}, doi = {10.1145/3547653}, year = {2022}, } Publisher's Version Artifacts Reusable 

Ullrich, Sebastian 
ICFP '22: "‘do’ Unchained: Embracing ..."
‘do’ Unchained: Embracing Local Imperativity in a Purely Functional Language (Functional Pearl)
Sebastian Ullrich and Leonardo de Moura (KIT, Germany; Microsoft Research, USA) Purely functional programming languages pride themselves with reifying effects that are implicit in imperative languages into reusable and composable abstractions such as monads. This reification allows for more exact control over effects as well as the introduction of new or derived effects. However, despite libraries of more and more powerful abstractions over effectful operations being developed, syntactically the common 'do' notation still lags behind equivalent imperative code it is supposed to mimic regarding verbosity and code duplication. In this paper, we explore extending 'do' notation with other imperative language features that can be added to simplify monadic code: local mutation, early return, and iteration. We present formal translation rules that compile these features back down to purely functional code, show that the generated code can still be reasoned over using an implementation of the translation in the Lean 4 theorem prover, and formally prove the correctness of the translation rules relative to a simple static and dynamic semantics in Lean. @Article{ICFP22p109, author = {Sebastian Ullrich and Leonardo de Moura}, title = {‘do’ Unchained: Embracing Local Imperativity in a Purely Functional Language (Functional Pearl)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {109}, numpages = {28}, doi = {10.1145/3547640}, year = {2022}, } Publisher's Version Artifacts Reusable 

Uustalu, Tarmo 
ICFP '22: "Flexible Presentations of ..."
Flexible Presentations of Graded Monads
Shinya Katsumata , Dylan McDermott , Tarmo Uustalu , and Nicolas Wu (National Institute of Informatics, Japan; Reykjavik University, Iceland; Tallinn University of Technology, Estonia; Imperial College London, UK) A large class of monads used to model computational effects have natural presentations by operations and equations, for example, the list monad can be presented by a constant and a binary operation subject to unitality and associativity. Graded monads are a generalization of monads that enable us to track quantitative information about the effects being modelled. Correspondingly, a large class of graded monads can be presented using an existing notion of graded presentation. However, the existing notion has some deficiencies, in particular many effects do not have natural graded presentations. We introduce a notion of flexibly graded presentation that does not suffer from these issues, and develop the associated theory. We show that every flexibly graded presentation induces a graded monad equipped with interpretations of the operations of the presentation, and that all graded monads satisfying a particular condition on colimits have a flexibly graded presentation. As part of this, we show that the usual algebrapreserving correspondence between presentations and a class of monads transfers to an algebrapreserving correspondence between flexibly graded presentations and a class of flexibly graded monads. @Article{ICFP22p123, author = {Shinya Katsumata and Dylan McDermott and Tarmo Uustalu and Nicolas Wu}, title = {Flexible Presentations of Graded Monads}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {123}, numpages = {29}, doi = {10.1145/3547654}, year = {2022}, } Publisher's Version 

Valliappan, Nachiappan 
ICFP '22: "Normalization for FitchStyle ..."
Normalization for FitchStyle Modal Calculi
Nachiappan Valliappan , Fabian Ruch , and Carlos Tomé Cortiñas (Chalmers University of Technology, Sweden) Fitchstyle modal lambda calculi enable programming with necessity modalities in a typed lambda calculus by extending the typing context with a delimiting operator that is denoted by a lock. The addition of locks simplifies the formulation of typing rules for calculi that incorporate different modal axioms, but each variant demands different, tedious and seemingly ad hoc syntactic lemmas to prove normalization. In this work, we take a semantic approach to normalization, called normalization by evaluation (NbE), by leveraging the possibleworld semantics of Fitchstyle calculi to yield a more modular approach to normalization. We show that NbE models can be constructed for calculi that incorporate the K, T and 4 axioms of modal logic, as suitable instantiations of the possibleworld semantics. In addition to existing results that handle 𝛽equivalence, our normalization result also considers 𝜂equivalence for these calculi. Our key results have been mechanized in the proof assistant Agda. Finally, we showcase several consequences of normalization for proving metatheoretic properties of Fitchstyle calculi as well as programminglanguage applications based on different interpretations of the necessity modality. @Article{ICFP22p118, author = {Nachiappan Valliappan and Fabian Ruch and Carlos Tomé Cortiñas}, title = {Normalization for FitchStyle Modal Calculi}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {118}, numpages = {27}, doi = {10.1145/3547649}, year = {2022}, } Publisher's Version Info Artifacts Reusable 

Van der Rest, Cas 
ICFP '22: "A Completely Unique Account ..."
A Completely Unique Account of Enumeration
Cas van der Rest and Wouter Swierstra (Delft University of Technology, Netherlands; Utrecht University, Netherlands) How can we enumerate the inhabitants of an algebraic datatype? This paper explores a datatype generic solution that works for all regular types and indexed families. The enumerators presented here are provably both complete and unique—they will eventually produce every value exactly once—and fair—they avoid bias when composing enumerators. Finally, these enumerators memoise previously enumerated values whenever possible, thereby avoiding repeatedly recomputing recursive results. @Article{ICFP22p105, author = {Cas van der Rest and Wouter Swierstra}, title = {A Completely Unique Account of Enumeration}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {105}, numpages = {27}, doi = {10.1145/3547636}, year = {2022}, } Publisher's Version 

Vanoni, Gabriele 
ICFP '22: "Multi Types and Reasonable ..."
Multi Types and Reasonable Space
Beniamino Accattoli , Ugo Dal Lago , and Gabriele Vanoni (Inria, France; École Polytechnique, France; University of Bologna, Italy) Accattoli, Dal Lago, and Vanoni have recently proved that the space used by the Space KAM, a variant of the Krivine abstract machine, is a reasonable space cost model for the λcalculus accounting for logarithmic space, solving a longstanding open problem. In this paper, we provide a new system of multi types (a variant of intersection types) and extract from multi type derivations the space used by the Space KAM, capturing into a type system the space complexity of the abstract machine. Additionally, we show how to capture also the time of the Space KAM, which is a reasonable time cost model, via minor changes to the type system. @Article{ICFP22p119, author = {Beniamino Accattoli and Ugo Dal Lago and Gabriele Vanoni}, title = {Multi Types and Reasonable Space}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {119}, numpages = {27}, doi = {10.1145/3547650}, year = {2022}, } Publisher's Version 

Vasilenko, Elizaveta 
ICFP '22: "Safe Couplings: Coupled Refinement ..."
Safe Couplings: Coupled Refinement Types
Elizaveta Vasilenko , Niki Vazou , and Gilles Barthe (IMDEA Software Institute, Spain; HSE University, Russia; MPISP, Germany) We enhance refinement types with mechanisms to reason about relational properties of probabilistic computations. Our mechanisms, which are inspired from probabilistic couplings, are applicable to a rich set of probabilistic properties, including expected sensitivity, which ensures that the distance between outputs of two probabilistic computations can be controlled from the distance between their inputs. We implement our mechanisms in the type system of Liquid Haskell and we use them to formally verify Haskell implementations of two classic machine learning algorithms: Temporal Difference (TD) reinforcement learning and stochastic gradient descent (SGD). We formalize a fragment of our system for discrete distributions and we prove soundness with respect to a settheoretical semantics. @Article{ICFP22p112, author = {Elizaveta Vasilenko and Niki Vazou and Gilles Barthe}, title = {Safe Couplings: Coupled Refinement Types}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {112}, numpages = {29}, doi = {10.1145/3547643}, year = {2022}, } Publisher's Version Artifacts Reusable 

Vazou, Niki 
ICFP '22: "Safe Couplings: Coupled Refinement ..."
Safe Couplings: Coupled Refinement Types
Elizaveta Vasilenko , Niki Vazou , and Gilles Barthe (IMDEA Software Institute, Spain; HSE University, Russia; MPISP, Germany) We enhance refinement types with mechanisms to reason about relational properties of probabilistic computations. Our mechanisms, which are inspired from probabilistic couplings, are applicable to a rich set of probabilistic properties, including expected sensitivity, which ensures that the distance between outputs of two probabilistic computations can be controlled from the distance between their inputs. We implement our mechanisms in the type system of Liquid Haskell and we use them to formally verify Haskell implementations of two classic machine learning algorithms: Temporal Difference (TD) reinforcement learning and stochastic gradient descent (SGD). We formalize a fragment of our system for discrete distributions and we prove soundness with respect to a settheoretical semantics. @Article{ICFP22p112, author = {Elizaveta Vasilenko and Niki Vazou and Gilles Barthe}, title = {Safe Couplings: Coupled Refinement Types}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {112}, numpages = {29}, doi = {10.1145/3547643}, year = {2022}, } Publisher's Version Artifacts Reusable 

Wang, Meng 
ICFP '22: "Modular Probabilistic Models ..."
Modular Probabilistic Models via Algebraic Effects
Minh Nguyen , Roly Perera , Meng Wang , and Nicolas Wu (University of Bristol, UK; Alan Turing Institute, UK; Imperial College London, UK) Probabilistic programming languages (PPLs) allow programmers to construct statistical models and then simulate data or perform inference over them. Many PPLs restrict models to a particular instance of simulation or inference, limiting their reusability. In other PPLs, models are not readily composable. Using Haskell as the host language, we present an embedded domain specific language based on algebraic effects, where probabilistic models are modular, firstclass, and reusable for both simulation and inference. We also demonstrate how simulation and inference can be expressed naturally as composable program transformations using algebraic effect handlers. @Article{ICFP22p104, author = {Minh Nguyen and Roly Perera and Meng Wang and Nicolas Wu}, title = {Modular Probabilistic Models via Algebraic Effects}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {104}, numpages = {30}, doi = {10.1145/3547635}, year = {2022}, } Publisher's Version Artifacts Reusable 

Weirich, Stephanie 
ICFP '22: "Program Adverbs and Tlön ..."
Program Adverbs and Tlön Embeddings
Yao Li and Stephanie Weirich (Portland State University, USA; University of Pennsylvania, USA) Free monads (and their variants) have become a popular generalpurpose tool for representing the semantics of effectful programs in proof assistants. These data structures support the compositional definition of semantics parameterized by uninterpreted events, while admitting a rich equational theory of equivalence. But monads are not the only way to structure effectful computation, why should we limit ourselves? In this paper, inspired by applicative functors, selective functors, and other structures, we define a collection of data structures and theories, which we call program adverbs, that capture a variety of computational patterns. Program adverbs are themselves composable, allowing them to be used to specify the semantics of languages with multiple computation patterns. We use program adverbs as the basis for a new class of semantic embeddings called Tlön embeddings. Compared with embeddings based on free monads, Tlön embeddings allow more flexibility in computational modeling of effects, while retaining more information about the program's syntactic structure. @Article{ICFP22p101, author = {Yao Li and Stephanie Weirich}, title = {Program Adverbs and Tlön Embeddings}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {101}, numpages = {31}, doi = {10.1145/3547632}, year = {2022}, } Publisher's Version Artifacts Reusable 

Westrick, Sam 
ICFP '22: "Entanglement Detection with ..."
Entanglement Detection with NearZero Cost
Sam Westrick , Jatin Arora , and Umut A. Acar (Carnegie Mellon University, USA) Recent research on parallel functional programming has culminated in a provably efficient (in work and space) parallel memory manager, which has been incorporated into the MPL (MaPLe) compiler for Parallel ML and shown to deliver practical efficiency and scalability. The memory manager exploits a property of parallel programs called disentanglement, which restricts computations from accessing concurrently allocated objects. Disentanglement is closely related to racefreedom, but subtly differs from it. Unlike racefreedom, however, no known techniques exists for ensuring disentanglement, leaving the task entirely to the programmer. This is a challenging task, because it requires reasoning about lowlevel memory operations (e.g., allocations and accesses), which is especially difficult in functional languages. In this paper, we present techniques for detecting entanglement dynamically, while the program is running. We first present a dynamic semantics for a functional language with references that checks for entanglement by consulting parallel and sequential dependency relations in the program. Notably, the semantics requires checks for mutable objects only. We prove the soundness of the dynamic semantics and present several techniques for realizing it efficiently, in particular by pruning away a large number of entanglement checks. We also provide bounds on the work and space of our techniques. We show that the entanglement detection techniques are practical by implementing them in the MPL compiler for Parallel ML. Considering a variety of benchmarks, we present an evaluation and measure time and space overheads of less than 5% on average with up to 72 cores. These results show that entanglement detection has negligible cost and can therefore remain deployed with little or no impact on efficiency, scalability, and space. @Article{ICFP22p115, author = {Sam Westrick and Jatin Arora and Umut A. Acar}, title = {Entanglement Detection with NearZero Cost}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {115}, numpages = {32}, doi = {10.1145/3547646}, year = {2022}, } Publisher's Version Archive submitted (490 kB) Artifacts Reusable 

Wu, Nicolas 
ICFP '22: "Fusing Industry and Academia ..."
Fusing Industry and Academia at GitHub (Experience Report)
Patrick Thomson , Rob Rix , Nicolas Wu , and Tom Schrijvers (GitHub, USA; GitHub, Canada; Imperial College London, UK; KU Leuven, Belgium) GitHub hosts hundreds of millions of code repositories written in hundreds of different programming languages. In addition to its hosting services, GitHub provides data and insights into code, such as vulnerability analysis and code navigation, with which users can improve and understand their software development process. GitHub has built Semantic, a program analysis tool capable of parsing and extracting detailed information from source code. The development of Semantic has relied extensively on the functional programming literature; this paper describes how connections to academic research inspired and informed the development of an industrialscale program analysis toolkit. @Article{ICFP22p108, author = {Patrick Thomson and Rob Rix and Nicolas Wu and Tom Schrijvers}, title = {Fusing Industry and Academia at GitHub (Experience Report)}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {108}, numpages = {16}, doi = {10.1145/3547639}, year = {2022}, } Publisher's Version ICFP '22: "Linearly Qualified Types: ..." Linearly Qualified Types: Generic Inference for Capabilities and Uniqueness Arnaud Spiwack , Csongor Kiss , JeanPhilippe Bernardy , Nicolas Wu , and Richard A. Eisenberg (Tweag, France; Imperial College London, UK; University of Gothenburg, Sweden) A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used safely. However, writing code with explicit linear arguments requires bureaucracy. This paper presents linear constraints, a frontend feature for linear typing that decreases the bureaucracy of working with linear types. Linear constraints are implicit linear arguments that are filled in automatically by the compiler. We present linear constraints as a qualified type system,together with an inference algorithm which extends GHC's existing constraint solver algorithm. Soundness of linear constraints is ensured by the fact that they desugar into Linear Haskell. @Article{ICFP22p95, author = {Arnaud Spiwack and Csongor Kiss and JeanPhilippe Bernardy and Nicolas Wu and Richard A. Eisenberg}, title = {Linearly Qualified Types: Generic Inference for Capabilities and Uniqueness}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {95}, numpages = {28}, doi = {10.1145/3547626}, year = {2022}, } Publisher's Version ICFP '22: "Modular Probabilistic Models ..." Modular Probabilistic Models via Algebraic Effects Minh Nguyen , Roly Perera , Meng Wang , and Nicolas Wu (University of Bristol, UK; Alan Turing Institute, UK; Imperial College London, UK) Probabilistic programming languages (PPLs) allow programmers to construct statistical models and then simulate data or perform inference over them. Many PPLs restrict models to a particular instance of simulation or inference, limiting their reusability. In other PPLs, models are not readily composable. Using Haskell as the host language, we present an embedded domain specific language based on algebraic effects, where probabilistic models are modular, firstclass, and reusable for both simulation and inference. We also demonstrate how simulation and inference can be expressed naturally as composable program transformations using algebraic effect handlers. @Article{ICFP22p104, author = {Minh Nguyen and Roly Perera and Meng Wang and Nicolas Wu}, title = {Modular Probabilistic Models via Algebraic Effects}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {104}, numpages = {30}, doi = {10.1145/3547635}, year = {2022}, } Publisher's Version Artifacts Reusable ICFP '22: "Flexible Presentations of ..." Flexible Presentations of Graded Monads Shinya Katsumata , Dylan McDermott , Tarmo Uustalu , and Nicolas Wu (National Institute of Informatics, Japan; Reykjavik University, Iceland; Tallinn University of Technology, Estonia; Imperial College London, UK) A large class of monads used to model computational effects have natural presentations by operations and equations, for example, the list monad can be presented by a constant and a binary operation subject to unitality and associativity. Graded monads are a generalization of monads that enable us to track quantitative information about the effects being modelled. Correspondingly, a large class of graded monads can be presented using an existing notion of graded presentation. However, the existing notion has some deficiencies, in particular many effects do not have natural graded presentations. We introduce a notion of flexibly graded presentation that does not suffer from these issues, and develop the associated theory. We show that every flexibly graded presentation induces a graded monad equipped with interpretations of the operations of the presentation, and that all graded monads satisfying a particular condition on colimits have a flexibly graded presentation. As part of this, we show that the usual algebrapreserving correspondence between presentations and a class of monads transfers to an algebrapreserving correspondence between flexibly graded presentations and a class of flexibly graded monads. @Article{ICFP22p123, author = {Shinya Katsumata and Dylan McDermott and Tarmo Uustalu and Nicolas Wu}, title = {Flexible Presentations of Graded Monads}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {123}, numpages = {29}, doi = {10.1145/3547654}, year = {2022}, } Publisher's Version 

Yoon, Irene 
ICFP '22: "Formal Reasoning about Layered ..."
Formal Reasoning about Layered Monadic Interpreters
Irene Yoon , Yannick Zakowski , and Steve Zdancewic (University of Pennsylvania, USA; Inria, France) Monadic computations built by interpreting, or handling, operations of a free monad are a compelling formalism for modeling language semantics and defining the behaviors of effectful systems. The resulting layered semantics offer the promise of modular reasoning principles based on the equational theory of the underlying monads. However, there are a number of obstacles to using such layered interpreters in practice. With more layers comes more boilerplate and glue code needed to define the monads and interpreters involved. That overhead is compounded by the need to define and justify the relational reasoning principles that characterize the equivalences at each layer. This paper addresses these problems by significantly extending the capabilities of the Coq interaction trees (ITrees) library, which supports layered monadic interpreters. We characterize a rich class of interpretable monadsobtained by applying monad transformers to ITreesand show how to generically lift interpreters through them. We also introduce a corresponding framework for relational reasoning about "equivalence of monads up to a relation R". This collection of typeclasses, instances, new reasoning principles, and tactics greatly generalizes the existing theory of the ITree library, eliminating large amounts of unwieldy boilerplate code and dramatically simplifying proofs. @Article{ICFP22p99, author = {Irene Yoon and Yannick Zakowski and Steve Zdancewic}, title = {Formal Reasoning about Layered Monadic Interpreters}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {99}, numpages = {29}, doi = {10.1145/3547630}, year = {2022}, } Publisher's Version Artifacts Reusable 

Zakowski, Yannick 
ICFP '22: "Formal Reasoning about Layered ..."
Formal Reasoning about Layered Monadic Interpreters
Irene Yoon , Yannick Zakowski , and Steve Zdancewic (University of Pennsylvania, USA; Inria, France) Monadic computations built by interpreting, or handling, operations of a free monad are a compelling formalism for modeling language semantics and defining the behaviors of effectful systems. The resulting layered semantics offer the promise of modular reasoning principles based on the equational theory of the underlying monads. However, there are a number of obstacles to using such layered interpreters in practice. With more layers comes more boilerplate and glue code needed to define the monads and interpreters involved. That overhead is compounded by the need to define and justify the relational reasoning principles that characterize the equivalences at each layer. This paper addresses these problems by significantly extending the capabilities of the Coq interaction trees (ITrees) library, which supports layered monadic interpreters. We characterize a rich class of interpretable monadsobtained by applying monad transformers to ITreesand show how to generically lift interpreters through them. We also introduce a corresponding framework for relational reasoning about "equivalence of monads up to a relation R". This collection of typeclasses, instances, new reasoning principles, and tactics greatly generalizes the existing theory of the ITree library, eliminating large amounts of unwieldy boilerplate code and dramatically simplifying proofs. @Article{ICFP22p99, author = {Irene Yoon and Yannick Zakowski and Steve Zdancewic}, title = {Formal Reasoning about Layered Monadic Interpreters}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {99}, numpages = {29}, doi = {10.1145/3547630}, year = {2022}, } Publisher's Version Artifacts Reusable 

Zdancewic, Steve 
ICFP '22: "Formal Reasoning about Layered ..."
Formal Reasoning about Layered Monadic Interpreters
Irene Yoon , Yannick Zakowski , and Steve Zdancewic (University of Pennsylvania, USA; Inria, France) Monadic computations built by interpreting, or handling, operations of a free monad are a compelling formalism for modeling language semantics and defining the behaviors of effectful systems. The resulting layered semantics offer the promise of modular reasoning principles based on the equational theory of the underlying monads. However, there are a number of obstacles to using such layered interpreters in practice. With more layers comes more boilerplate and glue code needed to define the monads and interpreters involved. That overhead is compounded by the need to define and justify the relational reasoning principles that characterize the equivalences at each layer. This paper addresses these problems by significantly extending the capabilities of the Coq interaction trees (ITrees) library, which supports layered monadic interpreters. We characterize a rich class of interpretable monadsobtained by applying monad transformers to ITreesand show how to generically lift interpreters through them. We also introduce a corresponding framework for relational reasoning about "equivalence of monads up to a relation R". This collection of typeclasses, instances, new reasoning principles, and tactics greatly generalizes the existing theory of the ITree library, eliminating large amounts of unwieldy boilerplate code and dramatically simplifying proofs. @Article{ICFP22p99, author = {Irene Yoon and Yannick Zakowski and Steve Zdancewic}, title = {Formal Reasoning about Layered Monadic Interpreters}, journal = {Proc. ACM Program. Lang.}, volume = {6}, number = {ICFP}, articleno = {99}, numpages = {29}, doi = {10.1145/3547630}, year = {2022}, } Publisher's Version Artifacts Reusable 
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