Type checking through unification

Abstract

In this paper we describe how to leverage higher-order unification to type check a dependently typed language with meta-variables. The literature usually presents the unification algorithm as a standalone component, however the need to check definitional equality of terms while type checking gives rise to a tight interplay between type checking and unification. This interplay is a major source of complexity in the type-checking algorithm for existing dependently typed programming languages. We propose an algorithm that encodes a type-checking problem entirely in the form of unification constraints, reducing the complexity of the type-checking code by taking advantage of higher order unification, which is already part of the implementation of many dependently typed languages.