On counting untyped lambda terms
Pierre Lescanne (LIP)
TL;DR
This paper investigates methods for counting untyped lambda calculus terms based on their size and free variables, providing insights into their enumeration and classification.
Contribution
It offers new results on enumerating untyped lambda terms with respect to size and free variables, advancing understanding of their combinatorial properties.
Findings
Derived formulas for counting lambda terms by size
Analyzed the distribution of free variables in terms
Provided asymptotic estimates for term counts
Abstract
We present several results on counting untyped lambda terms, i.e., on telling how many terms belong to such or such class, according to the size of the terms and/or to the number of free variables.
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Taxonomy
TopicsLogic, programming, and type systems · Advanced Algebra and Logic · semigroups and automata theory