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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