A predicate transformer semantics for effects (functional pearl)

Swierstra, Wouter; Baanen, T.

doi:10.1145/3341707

Cited by 18 publications

(11 citation statements)

References 35 publications

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“…This paper builds upon our previous results [32] by demonstrating their use in non-trivial development.…”

Section: Open Issuessupporting

confidence: 61%

“…In this paper, we explore a novel approach, drawing inspiration from recent work on algebraic effects [3,35,20]. We demonstrate how to reason about all parsers uniformly using predicate transformers [32]. We extend our previous work that uses predicate transformer semantics to reason about a single effect, to handle the combinations of effects used by parsers.…”

Section: Introductionmentioning

confidence: 99%

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Combining predicate transformer semantics for effects: a case study in parsing regular languages

Baanen

Swierstra

2020

Electron. Proc. Theor. Comput. Sci.

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This paper describes how to verify a parser for regular expressions in a functional programming language using predicate transformer semantics for a variety of effects. Where our previous work in this area focused on the semantics for a single effect, parsing requires a combination of effects: non-determinism, general recursion and mutable state. Reasoning about such combinations of effects is notoriously difficult, yet our approach using predicate transformers enables the careful separation of program syntax, correctness proofs and termination proofs.

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“…This paper builds upon our previous results [32] by demonstrating their use in non-trivial development.…”

Section: Open Issuessupporting

confidence: 61%

Section: Introductionmentioning

confidence: 99%

Combining predicate transformer semantics for effects: a case study in parsing regular languages

Baanen

Swierstra

2020

Electron. Proc. Theor. Comput. Sci.

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“…Our optimistic and pessimistic specifications are examples of predicate transformer semantics. They date back to Dijkstra [1975], forming the basis of much work on the verification of effectful programs in type theory [Nanevski et al 2008;Swamy et al 2013;Swierstra 2009;Swierstra and Baanen 2019]. Our predicate transformer semantics are two conventional effect observations [Maillard et al 2019] from the clairvoyance monad-a variant of the powerset monad-to the specification monads respectively for angelic and demonic nondeterminism.…”

Section: Computation Cost and Lazinessmentioning

confidence: 99%

Reasoning about the garden of forking paths

Li,

Xia,

Weirich

2021

Preprint

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Lazy evaluation is a powerful tool for functional programmers. It enables the concise expression of on-demand computation and a form of compositionality not available under other evaluation strategies. However, the stateful nature of lazy evaluation makes it hard to analyze a program's computational cost, either informally or formally. In this work, we present a novel and simple framework for formally reasoning about lazy computation costs based on a recent model of lazy evaluation: clairvoyant call-by-value. The key feature of our framework is its simplicity, as expressed by our definition of the clairvoyance monad. This monad is both simple to define (around 20 lines of Coq) and simple to reason about. We show that this monad can be effectively used to mechanically reason about the computational cost of lazy functional programs written in Coq.

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“…We then define a PRSA on lists of a type that can itself be split-i.e., interleavings with an additional constructor divide for making ends meet. For SCtx, we obtain: Expressions are not interpreted to plain values, but to command trees [18,36] with values at the leaves. Outgoing commands may contain channel endpoint references, and must therefore be separated from their continuation.…”

Section: Stage I: Interpreting the Expression Languagementioning

confidence: 99%

Intrinsically-typed definitional interpreters for linear, session-typed languages

Rouvoet

Poulsen

Krebbers

et al. 2020

Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs

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An intrinsically-typed definitional interpreter is a concise specification of dynamic semantics, that is executable and type safe by construction. Unfortunately, scaling intrinsicallytyped definitional interpreters to more complicated object languages often results in definitions that are cluttered with manual proof work. For linearly-typed languages (including session-typed languages) one has to prove that the interpreter, as well as all the operations on semantic components, treat values linearly. We present new methods and tools that make it possible to implement intrinsically-typed definitional interpreters for linearly-typed languages in a way that hides the majority of the manual proof work. Inspired by separation logic, we develop reusable and composable abstractions for programming with linear operations using dependent types. Using these abstractions, we define interpreters for linear lambda calculi with strong references, concurrency, and session-typed communication in Agda.

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A predicate transformer semantics for effects (functional pearl)

Cited by 18 publications

References 35 publications

Combining predicate transformer semantics for effects: a case study in parsing regular languages

Combining predicate transformer semantics for effects: a case study in parsing regular languages

Reasoning about the garden of forking paths

Intrinsically-typed definitional interpreters for linear, session-typed languages

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