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arXiv · 1703.10938

On repetitive right application of B-terms

Mirai Ikebuchi·Keisuke Nakano
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Abstract

B-terms are built from the B combinator alone defined by B f g x = f (g x), which is well-known as a function composition operator. This paper investigates an interesting property of B-terms, that is, whether repetitive right applications of a B-term circulates or not. We discuss conditions for B-terms to and not to have the property through a sound and complete equational axiomatization. Specifically, we give examples of B-terms which have the property and show that there are infinitely many B-terms which does not have the property. Also, we introduce a canonical representation of B-terms that is useful to detect cycles, or equivalently, to prove the property, with an efficient algorithm.

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Mirai Ikebuchi, Keisuke Nakano. 2017-03-31. On repetitive right application of B-terms. https://doi.org/10.4230/lipics.fscd.2018.18

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