Learning Structure-Aware Representations of Dependent Types
Keywords: premise selection, agda, structured attention, theorem proving, proof assistant
TL;DR: A novel, hyper-articulated dataset for AI&TP, and a first model to go with it.
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.
Primary Area: Machine learning for other sciences and fields
Submission Number: 4102
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