Pattern matching as cut elimination
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–How...
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| Published in | Theoretical computer science Vol. 323; no. 1; pp. 71 - 127 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
14.09.2004
Elsevier |
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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). |
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| AbstractList | 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). |
| Author | Cerrito, Serenella Kesner, Delia |
| Author_xml | – sequence: 1 givenname: Serenella surname: Cerrito fullname: Cerrito, Serenella email: serena@lami.univ-evry.fr organization: LaMI (CNRS UMR 8042) Université d'Evry, Val d'Essonne, 523, place des terrasses de l'agora, 91000 Evry Cedex, France – sequence: 2 givenname: Delia surname: Kesner fullname: Kesner, Delia email: kesner@pps.jussieu.fr organization: PPS (CNRS UMR 7126), Université Paris VII, France |
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| Cites_doi | 10.1016/0304-3975(93)90011-H 10.1007/3-540-61464-8_51 10.1016/S0304-3975(98)00166-2 10.1006/inco.1996.0004 10.1016/S0304-3975(96)00161-2 10.1145/237721.237788 10.1016/0304-3975(82)90026-3 10.1016/0304-3975(93)90181-R 10.1016/B978-0-444-88074-1.50011-1 10.1017/S0956796800001945 10.1017/S0960129500003273 10.1017/S0956796800000186 10.1145/130697.130699 10.1145/800087.802799 |
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| Keywords | Cut elimination Intuitionistic logic Computer theory Substitution Confluence Isomorphism Pattern matching |
| Language | English |
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explicit pattern matching and
explicit substitutions, where both the typing rules and the reduction rules are modeled... |
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| SubjectTerms | Algorithmics. Computability. Computer arithmetics Applied sciences Artificial intelligence Computer Science Computer science; control theory; systems Exact sciences and technology General logic Logic and foundations Mathematical logic, foundations, set theory Mathematics Pattern recognition. Digital image processing. Computational geometry Programming Languages Proof theory and constructive mathematics Sciences and techniques of general use Theoretical computing |
| Title | Pattern matching as cut elimination |
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