Not all patterns, but enough: an automatic verifier for partial but sufficient pattern matching

Abstract

We describe an automated analysis of Haskell 98 programs to check statically that, despite the possible use of partial (or nonexhaustive) pattern matching, no pattern-match failure can occur. Our method is an iterative backward analysis using a novel form of pattern-constraint to represent sets of data values. The analysis is defined for a core first-order language to which Haskell 98 programs are reduced. Our analysis tool has been successfully applied to a range of programs, and our techniques seem to scale well. Throughout the paper, methods are represented much as we have implemented them in practice, again in Haskell.