Intensional datatype refinement: with application to scalable verification of pattern-match safety

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.

Contextual Refinement Types

“…Jones and Ramsay [15] used refinement types to validate termination of functional programs in the presence of non-exhaustive pattern matching. Their notion of an intensional refinement is obtained by removing some of the constructors from a datatype, but the remaining constructors cannot be assigned new sorts.…”