Parametric type classes

Abstract

We propose a generalization to Haskell's type classes where a class can have type parameters besides the placeholder variable. We show that this generalization is essential to represent cent airier classes with overloaded data constructor and selector operations. We also show that the resulting type system has principal types and present unification and type reconstruction algorithms.

A theory of overloading

“…As already observed by Jones, functional dependencies subsume parametric type classes [Chen et al 1992]. For example, the (parametric) declaration class a :: Foo b can be expressed by the functional dependency class Foo a b | a->b.…”

“…In particular, we considered functional dependencies [Jones 2000] and some of its variations [Duggan and Ophel 2002b;Chen et al 1992]. CHRs do not solve the termination problem in case of Example 25.…”

“…Each of these extensions required a careful reinvestigation of essential properties such as decidable type inference and coherent semantics. There is also a significant body of further closely related work, for example, Gasbichler et al [2002], Duggan and Ophel [2002b], Shields and Jones [2001], Camarao and Figueiredo [1999], Odersky et al [1995], Nipkow and Prehofer [1995], and Chen et al [1992].…”

Language and program design for functional dependencies

“…In fact, the original proposal for functional dependencies in Haskell was conceived as a generalization of the work on parametric type classes by Chen et al [5]. Functional dependencies were never intended to serve as an ultimate mechanism for improving qualified types, but were just one 'sweet spot', hitting a nice compromise between expressive power and tractability, while also leveraging results from database theory.…”

Type classes in Haskell

“…There has been closely related work by Rouaix [1990] and Cormack and Wright [1990]; Nipkow and Snelting [1991] and Nipkow and Prehofer [1993] also describe type inference algorithms for type classes based on sorts; and work directly inspired by Haskell type classes includes the closely related Gofer type system with its multiparameter classes [Jones 1992a;1992b;, an extension of ML with type classes [Volpano and Smith 1991], constructor classes [Jones 1995], first-class abstract data types [Läufer 1992;Läufer and Odersky 1994;Odersky and Läufer 1991], and parametric type classes [Chen 1994;Chen et al 1992].…”