Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system

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Abstract

We give a proof of strong normalizability of the typed λ-calculas extended by an arbitrary convergent term rewriting system, which provides the affirmative answer to the open problem proposed in Breazu-Tannen [1]. Klop [6] showed that a combined system of the untyped λ-calculus and convergent term rewriting system is not Church-Rosser in general, though both are Church-Rosser. It is well-known that the typed λ-calculus is convergent (Church-Rosser and terminating). Breazu-Tannen [1] showed that a combined system of the typed λ-calculus and an arbitrary Church-Rosser term rewriting system is again Church-Rosser. Our strong normalization result in this paper shows that the combined system of the typed λ-calculus and an arbitrary convergent term rewriting system is again convergent. Our strong normalizability proof is easily extended to the case of the second order (polymorphically) typed lambda calculus and the case in which μ-reduction rule is added.

Original languageEnglish
Title of host publicationProceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, ISSAC 1989
PublisherAssociation for Computing Machinery
Pages357-363
Number of pages7
VolumePart F130182
ISBN (Electronic)0897913256
DOIs
Publication statusPublished - 1989 Jul 17
Externally publishedYes
Event1989 ACM-SIGSAM International Symposium on Symbolic and Algebraic Computation, ISSAC 1989 - Portland, United States
Duration: 1989 Jul 171989 Jul 19

Other

Other1989 ACM-SIGSAM International Symposium on Symbolic and Algebraic Computation, ISSAC 1989
CountryUnited States
CityPortland
Period89/7/1789/7/19

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ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Okada, M. (1989). Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system. In Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, ISSAC 1989 (Vol. Part F130182, pp. 357-363). Association for Computing Machinery. https://doi.org/10.1145/74540.74582