The Algebra of Patterns (Extended Version)

Pattern matching is a popular feature in functional, imperative and object-oriented programming languages. Language designers should therefore invest effort in a good design for pattern matching. Most languages choose a first-match semantics for pattern matching; that is, clauses are tried in the order in which they appear in the program until the first one matches. As a consequence, the order in which the clauses appear cannot be arbitrarily changed, which results in a less declarative programming model. The declarative alternative to this is an order-independent semantics for pattern matching, which is not implemented in most programming languages since it requires more verbose patterns. The reason for this verbosity is that the syntax of patterns is usually not expressive enough to express the complement of a pattern. In this paper, we show a principled way to make order-independent pattern matching practical. Our solution consists of two parts: First, we introduce a boolean algebra of patterns which can express the complement of a pattern. Second, we introduce default clauses to pattern matches. These default clauses capture the essential idea of a fallthrough case without sacrificing the property of order-independence.