### 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 language | English |
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Title of host publication | Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, ISSAC 1989 |

Publisher | Association for Computing Machinery |

Pages | 357-363 |

Number of pages | 7 |

Volume | Part F130182 |

ISBN (Electronic) | 0897913256 |

DOIs | |

Publication status | Published - 1989 Jul 17 |

Externally published | Yes |

Event | 1989 ACM-SIGSAM International Symposium on Symbolic and Algebraic Computation, ISSAC 1989 - Portland, United States Duration: 1989 Jul 17 → 1989 Jul 19 |

### Other

Other | 1989 ACM-SIGSAM International Symposium on Symbolic and Algebraic Computation, ISSAC 1989 |
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Country | United States |

City | Portland |

Period | 89/7/17 → 89/7/19 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*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

**Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system.** / Okada, Mitsuhiro.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, ISSAC 1989.*vol. Part F130182, Association for Computing Machinery, pp. 357-363, 1989 ACM-SIGSAM International Symposium on Symbolic and Algebraic Computation, ISSAC 1989, Portland, United States, 89/7/17. https://doi.org/10.1145/74540.74582

}

TY - GEN

T1 - Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system

AU - Okada, Mitsuhiro

PY - 1989/7/17

Y1 - 1989/7/17

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85028762708&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028762708&partnerID=8YFLogxK

U2 - 10.1145/74540.74582

DO - 10.1145/74540.74582

M3 - Conference contribution

AN - SCOPUS:85028762708

VL - Part F130182

SP - 357

EP - 363

BT - Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, ISSAC 1989

PB - Association for Computing Machinery

ER -