Polymorphic variants in Haskell

Abstract

In languages that support polymorphic variants, a single variant value can be passed to many contexts that accept different sets of constructors. Polymorphic variants can be used in order to introduce extensible algebraic datatypes into functional programming languages and are potentially useful for application domains such as interpreters, graphical user interface (GUI) libraries and database interfaces, where the number of necessary constructors cannot be determined in advance. Very few functional languages, however, have a mechanism to extend existing datatypes by adding new constructors. In general, for polymorphic variants to be useful, we would need some mechanisms to reuse existing functions and extend them for new constructors.Actually, the type system of Haskell, when extended with parametric type classes (or multi-parameter type classes with functional dependencies), has enough power not only to mimic polymorphic variants but also to extend existing functions for new constructors.This paper, first, explains how to do this in Haskell's type system (Haskell 98 with popular extensions). However, this encoding of polymorphic variants is difficult to use in practice. This is because it is quite tedious for programmers to write mimic codes by hand and because the problem of ambiguous overloading resolution would embarrass programmers. Therefore, the paper proposes an extension of Haskell's type classes that supports polymorphic variants directly. It has a novel form of instance declarations where records and variants are handled symmetrically.This type system can produce vanilla Haskell codes as a result of type inference. Therefore it behaves as a preprocessor which translates the extended language into plain Haskell. Programmers would be able to use polymorphic variants without worrying nasty problems such as ambiguities.