Counting and generating terms in the binary lambda calculus

Abstract

Abstract 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.