Type Preservation as a Confluence Problem

Abstract

This paper begins with recent work by Kuan, MacQueen, and Findler, which shows how standard type systems, such as the simply typed lambda calculus, can be viewed as abstract reduction systems operating on terms. The central idea is to think of the process of typing a term as the computation of an abstract value for that term. The standard metatheoretic property of type preservation can then be seen as a confluence problem involving the concrete and abstract operational semantics, viewed as abstract reduction systems (ARSs). In this paper, we build on the work of Kuan et al. by showing show how modern ARS theory, in particular the theory of decreasing diagrams, can be used to establish type preservation via confluence. We illustrate this idea through several examples of solving such problems using decreasing diagrams. We also consider how automated tools for analysis of term-rewriting systems can be applied in testing type