Pure Patterns Type Systems

Gilles Barthe 1 Horatiu Cirstea 2 Claude Kirchner 2 Luigi Liquori 3, 4
1 LEMME - Software and mathematics
CRISAM - Inria Sophia Antipolis - Méditerranée
2 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
4 MIRHO - Objects, types and prototypes : semantics and validation
CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7503
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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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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