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Quantitative aspects of linear and affine closed lambda terms

Abstract : Affine $λ$-terms are $λ$-terms in which each bound variable occurs at most once and linear $λ$-terms are $λ$-terms in which each bound variables occurs once. and only once. In this paper we count the number of closed affine $λ$-terms of size $n$, closed linear $λ$-terms of size $n$, affine $β$-normal forms of size $n$ and linear $β$-normal forms of ise $n$, for different ways of measuring the size of $λ$-terms. From these formulas, we show how we can derive programs for generating all the terms of size $n$ for each class. For this we use a specific data structure, which are contexts taking into account all the holes at levels of abstractions.
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Contributor : Pierre Lescanne Connect in order to contact the contributor
Submitted on : Monday, April 3, 2017 - 5:13:22 PM
Last modification on : Friday, September 10, 2021 - 2:34:04 PM
Long-term archiving on: : Tuesday, July 4, 2017 - 1:52:49 PM


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  • HAL Id : ensl-01464047, version 4
  • ARXIV : 1702.03085


Pierre Lescanne. Quantitative aspects of linear and affine closed lambda terms. 2017. ⟨ensl-01464047v4⟩



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