A Simple Algorithm and Proof for Type Inference

Mitchell Wand. A Simple Algorithm and Proof for Type Inference. Fundamenta Infomaticae, 10:115-122, 1987.

Abstract

We present a simple proof of Hindley’s Theorem: that it is decidable whether a term of the untyped lambda calculus is the image under type-erasing of a term of the simply typed lambda calculus. The proof proceeds by a direct reduction to the unification problem for simple terms. This arrangement of the proof allows for easy extensibility to other type inference problems.