Y is a least fixed point combinator
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915262333190144 |
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| author | Helfer, Joseph |
| author_facet | Helfer, Joseph |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19379 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Y is a least fixed point combinator Helfer, Joseph Logic 03B40 F.4.1 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. |
| title | Y is a least fixed point combinator |
| topic | Logic 03B40 F.4.1 |
| url | https://arxiv.org/abs/2504.19379 |