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## Aspects quantitatifs des lambda termes affines et linéaires

(1)
1
Pierre Lescanne

#### 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.

### Dates and versions

ensl-01464047 , version 1 (09-02-2017)
ensl-01464047 , version 2 (14-02-2017)
ensl-01464047 , version 3 (24-02-2017)
ensl-01464047 , version 4 (03-04-2017)
ensl-01464047 , version 5 (21-05-2017)

### Identifiers

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

### Cite

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

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