On Static Analysis for Expressive Pattern Matching

Pattern matching is a widespread programming language construct that enables definitions of values by cases, generalizing if-then-else and case statements. The cases in a pattern matching expression should be exhaustive: when the value does not match any of the cases, the expression throws a run-time exception. Similarly, each pattern should be reachable, and, if possible, patterns should be disjoint to facilitate reasoning. Current compilers use simple analyses to check patterns. Such analyses ignore pattern guards, use static types to approximate possible expression values, and do not take into account properties of user-defined functions. We present a design and implementation of a new analysis of pattern matching expressions. Our analysis detects a wider class of errors and reports fewer false alarms than previous approaches. It checks disjointness, reachability, and exhaustiveness of patterns by expressing these conditions as formulas and proving them using decision procedures and theorem provers. It achieves precision by propagating possible values through nested expressions and approximating pattern-matching guards with formulas. It supports user-defined ``extractor'' functions in patterns by relying on specifications of relationships between the domains of such functions. The result is the first analysis that enables verified, declarative pattern matching with guards in the presence of data abstraction. We have implemented our analysis and describe our experience in checking a range of pattern matching expressions in a subset of the Scala programming language.