Learning Structure-Aware Representations of Dependent Types

Abstract

Agda is a dependently-typed programming language and a proof assistant, pivotal in proof formalization and programming language theory.This paper extends the Agda ecosystem into machine learning territory, and, vice versa, makes Agda-related resources available to machine learning practitioners.We introduce and release a novel dataset of Agda program-proofs that is elaborate and extensive enough to support various machine learning applications -- the first of its kind.Leveraging the dataset's ultra-high resolution, which details proof states at the sub-type level, we propose a novel neural architecture targeted at faithfully representing dependently-typed programs on the basis of structural rather than nominal principles.We instantiate and evaluate our architecture in a premise selection setup, where it achieves promising initial results, surpassing strong baselines.