Pattern matching with abstract data types

TL;DR: This work views pattern matching as a bundling of case recognition and component selection functions instead of a method for inverting data construction, and removes the implied equivalence between data constructors and pattern constructors.

Abstract: Pattern matching in modern functional programming languages is tied to the representation of data. Unfortunately, this is incompatible with the philosophy of abstract data types.Two proposals have been made to generalize pattern matching to a broader class of types. The laws mechanism of Miranda allows pattern matching with non-free algebraic data types. More recently, Wadler proposed the concept of views as a more general solution, making it possible to define arbitrary mappings between a physical implementation and a view supporting pattern matching. Originally, it was intended to include views in the new standard lazy functional programming language Haskell.Laws and views each offer important advantages, particularly with respect to data abstraction. However, if not used with great care, they also introduce serious problems in equational reasoning. As a result, laws have been removed from Miranda and views were not included in the final version of Haskell.We propose a third approach which unifies the laws and views mechanisms while avoiding their problems. Philosophically, we view pattern matching as a bundling of case recognition and component selection functions instead of a method for inverting data construction. This can be achieved by removing the implied equivalence between data constructors and pattern constructors. In practice, we allow automatic mapping into a view but not out of the view. We show that equational reasoning can still be used with the resulting system. In fact, equational reasoning is easier, since there are fewer hidden traps.