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

35 被引用数 (Scopus)

## 抄録

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.

本文言語 English Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, ISSAC 1989 G. H. Gonnet Association for Computing Machinery 357-363 7 0897913256 https://doi.org/10.1145/74540.74582 Published - 1989 7月 17 1989 ACM-SIGSAM International Symposium on Symbolic and Algebraic Computation, ISSAC 1989 - Portland, United States継続期間: 1989 7月 17 → 1989 7月 19

### 出版物シリーズ

名前 Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC Part F130182

### Other

Other 1989 ACM-SIGSAM International Symposium on Symbolic and Algebraic Computation, ISSAC 1989 United States Portland 89/7/17 → 89/7/19

• 数学 (全般)

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