Basic Pattern Matching Calculi: a Fresh View on Matching Failure

Kahl, Wolfram

doi:10.1007/978-3-540-24754-8_20

Cited by 11 publications

(17 citation statements)

References 17 publications

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“…5 (see [Kahl 2004] and Appendix B for more explanation), we prove the following soundness result in Appendix D:…”

Section: Soundness Of the Core Reduction Rulesmentioning

confidence: 75%

“…For deterministic functional programming, [Kahl 2004] proposes a rule that turns expression matchings into left-zeros for alternative, and so essentially prohibits backtracking (and non-deterministic choice):…”

Section: Using Different Monad Instancesmentioning

confidence: 99%

“…The pattern matching calculus (PMC) introduced by Kahl [Kahl 2004] remedies this situation. It separates pattern matching aspects into a separate syntactic category of "matchings", not unlike groups of "case branches p -> e" considered by Harrison et al [Harrison, Sheard + 2002], but with an additional "argument supply" constructor that rationalises and generalises the pattern guards proposed by Erwig and Peyton Jones [Erwig, Jones 2001].…”

Section: Introductionmentioning

confidence: 99%

“…PMC is equipped with a confluent (secondorder) rewriting system, thereby enabling equational reasoning starting from the definitions of a program. The rewriting system directly gives a normalisation strategy [Kahl 2004]. …”

Section: Introductionmentioning

confidence: 99%

“…In Sect. 5 we give the soundness theorem for the core reduction rules from [Kahl 2004] (listed in Appendix B) with respect to our semantics without further constraints on the two monads, and explain the core of its proof steps. We then start an exploration of possible bimonadic constellations for alternative interpretations of PMC in Sect.…”

Section: Introductionmentioning

confidence: 99%

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Bimonadic Semantics for Basic Pattern Matching Calculi

Kahl

Carette

2006

Lecture Notes in Computer Science

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The pattern matching calculi introduced by the first author are a refinement of the λ-calculus that integrates mechanisms appropriate for fine-grained modelling of non-strict pattern matching.While related work in the literature only uses a single monad, typically Maybe, for matchings, we present an axiomatic approach to semantics of these pattern matching calculi using two monads, one for expressions and one for matchings.Although these two monads only need to be relatively lightly coupled, this semantics implies soundness of all core PMC rules, and is a useful tool for exploration of the design space for pattern matching calculi.Using lifting and Maybe monads, we obtain standard Haskell semantics, and by adding another level of Maybe to both, we obtain a denotational semantics of the "matching failure as exceptions" approach of Erwig and Peyton Jones. Using list-like monads opens up interesting extensions in the direction of functional-logic programming.A short version of this report appears as [Kahl, Carette + 2006].

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“…5 (see [Kahl 2004] and Appendix B for more explanation), we prove the following soundness result in Appendix D:…”

Section: Soundness Of the Core Reduction Rulesmentioning

confidence: 75%

Section: Using Different Monad Instancesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bimonadic Semantics for Basic Pattern Matching Calculi

Kahl

Carette

2006

Lecture Notes in Computer Science

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A Lambda-Calculus with Constructors

Arbiser

Miquel

Ríos

2006

Lecture Notes in Computer Science

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We present an extension of the ()-calculus with a case construct that propagates through functions like a head linear substitution, and show that this construction permits to recover the expressiveness of ML-style pattern matching. We then prove that this system enjoys the Church-Rosser property using a semi-automatic`divide and conquer' technique by which we determine all the pairs of commuting subsystems of the formalism (considering all the possible combinations of the nine primitive reduction rules). Finally, we prove a separation theorem similar to B ohm's theorem for the whole formalism.

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ML Pattern-Matching, Recursion, and Rewriting: From FoCaLiZe to Dedukti

Cauderlier

Dubois

2016

Theoretical Aspects of Computing – ICTAC 2016

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Abstract. The programming environment FoCaLiZe allows the user to specify, implement, and prove programs with the help of the theorem prover Zenon. In the actual version, those proofs are verified by Coq. In this paper we propose to extend the FoCaLiZe compiler by a backend to the Dedukti language in order to benefit from Zenon Modulo, an extension of Zenon for Deduction modulo. By doing so, FoCaLiZe can benefit from a technique for finding and verifying proofs more quickly. The paper focuses mainly on the process that overcomes the lack of local pattern-matching and recursive definitions in Dedukti.

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Basic Pattern Matching Calculi: a Fresh View on Matching Failure

Cited by 11 publications

References 17 publications

Bimonadic Semantics for Basic Pattern Matching Calculi

Bimonadic Semantics for Basic Pattern Matching Calculi

A Lambda-Calculus with Constructors

ML Pattern-Matching, Recursion, and Rewriting: From FoCaLiZe to Dedukti

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