Proof-relevant Horn Clauses for Dependent Type Inference and Term Synthesis

Abstract

First-order resolution has been used for type inference for many years, including in Hindley- Milner type inference, type-classes, and constrained data types. Dependent types are a new trend in functional languages. In this paper, we show that proof-relevant first-order resolution can play an important role in automating type inference and term synthesis for dependently typed languages. We propose a calculus that translates type inference and term synthesis problems in a dependently typed language to a logic program and a goal in the proof-relevant first-order Horn clause logic. The computed answer substitution and proof term then provide a solution to the given type inference and term synthesis problem. We prove the decidability and soundness of our method. The paper is under consideration for acceptance in TPLP.

Paper presented at the 34nd International Conference on Logic Programming (ICLP 2018), Oxford, UK, July 14 to July 17, 2018 18 pages, LaTeX, 0 PDF figures