Declarative Algorithms for Term Generation, Counting

We design a declarative variant of Rémy’s algorithm, for uniform ran7 dom generation of binary trees. 8 Using the same basic mechanism as in the case of binary trees, we derive a gen9 eralization to term algebras of an arbitrary signature. With trees seen as sets of 10 edges connecting vertices labeled with logic variables, we use Prolog’s multiple11 answer generation mechanism to derive a generic algorithm that counts terms of 12 a given size, generates them all, or samples a random term given the signature of 13 a term algebra. 14 As applications, we implement generators for term algebras defining Motzkin 15 trees, use all-term and random-term generation for mutual cross-testing and de16 scribe an extension mechanism that transforms a random sampler for Motzkin 17 trees into one for closed lambda terms. 18