On Termination, Confluence and Consistent CHR-based Type Inference

TL;DR

This paper explores conditions under which CHR-based type inference remains consistent even when the underlying CHR programs do not terminate, addressing practical challenges in Haskell's type system.

Contribution

It introduces and verifies relaxed criteria like range-restrictedness, local confluence, and ground termination to ensure consistency in non-terminating CHR programs.

Findings

Identifies conditions ensuring consistency without termination

Verifies criteria for non-terminating but consistent CHR programs

Addresses practical issues in Haskell's type inference system

Abstract

We consider the application of Constraint Handling Rules (CHR) for the specification of type inference systems, such as that used by Haskell. Confluence of CHR guarantees that the answer provided by type inference is correct and consistent. The standard method for establishing confluence relies on an assumption that the CHR program is terminating. However, many examples in practice give rise to non-terminating CHR programs, rendering this method inapplicable. Despite no guarantee of termination or confluence, the Glasgow Haskell Compiler (GHC) supports options that allow the user to proceed with type inference anyway, e.g. via the use of the UndecidableInstances flag. In this paper we formally identify and verify a set of relaxed criteria, namely range-restrictedness, local confluence, and ground termination, that ensure the consistency of CHR-based type inference that maps to potentially non-terminating CHR programs.