Intensional Datatype Refinement

TL;DR

This paper introduces a refinement type system that automatically verifies pattern-match safety in functional programs, combining algebraic datatypes with structural subtyping and intersection, enabling efficient analysis.

Contribution

It presents a novel, fully automatic, sound, and complete type inference system for pattern-match safety, with linear-time complexity and a prototype implementation for Haskell.

Findings

Prototype analyzes Haskell packages in milliseconds

Type inference is linear-time and fully automatic

System extends ML-style types with structural subtyping and intersection

Abstract

The pattern-match safety problem is to verify that a given functional program will never crash due to non-exhaustive patterns in its function definitions. We present a refinement type system that can be used to solve this problem. The system extends ML-style type systems with algebraic datatypes by a limited form of structural subtyping and environment-level intersection. We describe a fully automatic, sound and complete type inference procedure for this system which, under reasonable assumptions, is worst-case linear-time in the program size. Compositionality is essential to obtaining this complexity guarantee. A prototype implementation for Haskell is able to analyse a selection of packages from the Hackage database in a few hundred milliseconds.