A Typed Pattern Calculus

The theory of programming with pattern-matching function definitions has been studied mainly in the framework of first-order rewrite systems. We present a typed functional calculus that emphasizes the strong connection between the structures of whole pattern definitions and their types. In this calc...

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Vydané v:Information and computation Ročník 124; číslo 1; s. 32 - 61
Hlavní autori: Kesner, Delia, Puel, Laurence, Tannen, Val
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: San Diego, CA Elsevier Inc 10.01.1996
Elsevier
Predmet:
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Programming theory
Theoretical computing
Functional language
Proof system
Reduction
Intuitionistic logic
Typing
Lambda calculus
Definition
Pattern matching
Programming theory
Sequent calculus
ISSN:0890-5401, 1090-2651
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Shrnutí:The theory of programming with pattern-matching function definitions has been studied mainly in the framework of first-order rewrite systems. We present a typed functional calculus that emphasizes the strong connection between the structures of whole pattern definitions and their types. In this calculus, type-checking guarantees the absence of runtime errors caused by non-exhaustive pattern-matching definitions. Its operational semantics is deterministic in a natural way, without the imposition of ad hoc solutions such as clause order or “best fit”. In the spirit of the Curry–Howard isomorphism, we design the calculus as a computational interpretation of the Gentzen sequent proofs for the intuitionistic propositional logic. We prove the basic properties connecting typing and evaluation: subject reduction and strong normalization. We believe that this calculus offers a rational reconstruction of the pattern-matching features found in successful functional languages.
ISSN:0890-5401
1090-2651
DOI:10.1006/inco.1996.0004