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arXiv · 2504.19379

Y is a least fixed point combinator

Joseph Helfer
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Abstract

The theory of recursive functions is related in a well-known way to the notion of *least fixed points*, by endowing a set of partial functions with an ordering in terms of their domain of definition. When terms in the pure lambda-calculus are considered as partial functions on the set of reduced lambda-terms, they inherit such a partial order. We prove that Curry's well-known fixed point combinator Y produces least fixed points with respect to this partial order.

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Joseph Helfer. 2025-04-27. Y is a least fixed point combinator. https://arxiv.org/abs/2504.19379

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