Pattern matching as cut elimination

  • Authors:

  • Serenella Cerrito;Delia Kesner

  • Affiliations:

  • LaMI (CNRS UMR 8042) Université d'Evry, Val d'Essonne, 523, place des terrasses de l'agora, 91000 Evry Cedex, France;PPS (CNRS UMR 7126), Université Paris VII, France

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2004

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Abstract

We present a typed pattern calculus with explicit pattern matching and explicit substitutions, where both the typing rules and the reduction rules are modeled on the same logical proof system, namely Gentzen sequent calculus for intuitionistic minimal logic. Our calculus is inspired by the Curry-Howard Isomorphism, in the sense that types, both for patterns and terms, correspond to propositions, terms correspond to proofs, and term reduction corresponds to sequences of sequent proof normalization steps performed by cut elimination. The calculus enjoys subject reduction, confluence, preservation of strong normalization w.r.t a system with meta-level substitutions and strong normalization for well-typed terms. As a consequence, it can be seen as an implementation calculus for functional formalisms defined with meta-level operations for pattern matching and substitutions. This work is a revised and extended version of Cerrito and Kesner (14th Annual IEEE Symposium on Logic in Computer Science (LICS), IEEE Computer Society Press, Silver Spring, MD, 1999, pp. 98-108).