Counting and generating terms in the binary lambda calculus

In a paper entitled Binary lambda calculus and combinatory logic, John Tromp presents a simple way of encoding lambda calculus terms as binary sequences. In what follows, we study the numbers of binary strings of a given size that represent lambda terms and derive results from their generating functions, especially that the number of terms of size n grows roughly like 1:963447954::: n . In a second part we use this approach to generate random lambda terms using Boltzmann samplers.

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