A Word Sampler for Well-Typed Functions

We describe an exact sampler for a simply-typed, first-order functional programming language. Given an acyclic finite automaton, ${\alpha }_{\mathrm{\varnothing }}$, it samples a random function uniformly without replacement from well-typed functions in $\mathcal{L}({\alpha }_{\mathrm{\varnothing }})$. This is achieved via a fixed-parameter tractable reduction from a syntax-directed type system to a context-free grammar, preserving type soundness and completeness w.r.t. $\mathcal{L}({\alpha }_{\mathrm{\varnothing }})$, while retaining the robust metatheory of formal languages.