A Word Sampler for Well-Typed Functions

TL;DR

This paper introduces an exact, uniform sampler for well-typed functions in a simply-typed language, leveraging automata and grammars to ensure type soundness and completeness.

Contribution

It presents a novel reduction from a syntax-directed type system to a context-free grammar that preserves type properties and enables efficient sampling.

Findings

Samples uniformly from well-typed functions

Maintains type soundness and completeness

Uses fixed-parameter tractable reduction

Abstract

We describe an exact sampler for a simply-typed, first-order functional programming language. Given an acyclic finite automaton, $\alpha_{\varnothing}$, it samples a random function uniformly without replacement from well-typed functions in $\mathcal{L}(\alpha_{\varnothing})$. 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. $\mathcal{L}(\alpha_{\varnothing})$, while retaining the robust metatheory of formal languages.