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Conference Papers Year : 2003

Pure Patterns Type Systems

Abstract

We introduce a new framework of algebraic pure type systems in which we consider rewrite rules as lambda terms with patterns and rewrite rule application as abstraction application with built-in matching facilities. This framework, that we call "Pure Pattern Type Systems'', is particularly well-suited for the foundations of programming (meta)languages and proof assistants since it provides in a fully unified setting higher-order capabilities and pattern matching ability together with powerful type systems. We prove some standard properties like confluence and subject reduction for the case of a syntactic theory and under a classical (syntactical) restriction over the shape of patterns. We also conjecture the strong normalization of typable terms. This work should be seen as a contribution to a formal connection between logics and rewriting, and a step towards new proof engines based on the Curry-Howard isomorphism.
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Dates and versions

inria-00099463 , version 1 (26-09-2006)
inria-00099463 , version 2 (13-05-2015)

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Cite

Gilles Barthe, Horatiu Cirstea, Claude Kirchner, Luigi Liquori. Pure Patterns Type Systems. Proceedings of the 30th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL, New Orleans, LA, USA — January 15 - 17, 2003, Jan 2003, New Orleans, United States. pp.250 - 261, ⟨10.1145/604131.604152⟩. ⟨inria-00099463v2⟩
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