Embedding Non-linear Pattern Matching with Backtracking for Non-free Data Types into Haskell

Pattern matching is an important language construct for data abstraction. Many pattern-match extensions have been developed for extending the range of data types to which pattern matching is applicable. Among them, the pattern-match system proposed by Egi and Nishiwaki features practical pattern matching for non-free data types by providing a user-customizable non-linear pattern-match facility with backtracking. However, they implemented their proposal only in dynamically typed programming languages, and there were no proposals that allow programmers to benefit from both static type systems and expressive pattern matching. This paper proposes a method for implementing this pattern-match facility by meta-programming in Haskell. There are two technical challenges: (i) we need to design a set of typing rules for the pattern-match facility; (ii) we need to embed these typing rules in Haskell to make types of the pattern-match expressions inferable by the Haskell type system. We propose a set of typing rules and show that several GHC extensions, such as multi-parameter type classes, datatype promotion, GADTs, existential types, and view patterns, play essential roles for embedding these typing rules into Haskell. The implementation has already been distributed as a Haskell library miniEgison via Hackage.