# 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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Cited literature [21 references]

https://hal-ens-lyon.archives-ouvertes.fr/ensl-01464047
Contributor : Pierre Lescanne <>
Submitted on : Sunday, May 21, 2017 - 3:22:31 PM
Last modification on : Thursday, February 7, 2019 - 3:56:01 PM
Long-term archiving on : Wednesday, August 23, 2017 - 10:53:02 AM

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counting_affine.pdf
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### Identifiers

• HAL Id : ensl-01464047, version 5
• ARXIV : 1702.03085

### Citation

Pierre Lescanne. Quantitative aspects of linear and affine closed lambda terms. 2017. ⟨ensl-01464047v5⟩

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