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March 2003 The Church-Rosser property in dual combinatory logic
Katalin Bimbó
J. Symbolic Logic 68(1): 132-152 (March 2003). DOI: 10.2178/jsl/1045861508

Abstract

Dual combinators emerge from the aim of assigning formulas containing $\leftarrow$ as types to combinators. This paper investigates formally some of the properties of combinatory systems that include both combinators and dual combinators. Although the addition of dual combinators to a combinatory system does not affect the unique decomposition of terms, it turns out that some terms might be redexes in two ways (with a combinator as its head, and with a dual combinator as its head). We prove a general theorem stating that no dual combinatory system possesses the Church-Rosser property. Although the lack of confluence might be problematic in some cases, it is not a problem per se. In particular, we show that no damage is inflicted upon the structurally free logics, the system in which dual combinators first appeared.

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Katalin Bimbó. "The Church-Rosser property in dual combinatory logic." J. Symbolic Logic 68 (1) 132 - 152, March 2003. https://doi.org/10.2178/jsl/1045861508

Information

Published: March 2003
First available in Project Euclid: 21 February 2003

zbMATH: 1045.03017
MathSciNet: MR1959314
Digital Object Identifier: 10.2178/jsl/1045861508

Rights: Copyright © 2003 Association for Symbolic Logic

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Vol.68 • No. 1 • March 2003
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