Functional logic overloading is a novel approach to userdefined overloading that extends Haskell’s concept of type classes in significant ways. Whereas type classes are conceptually predicates on types in standard Haskell, they are type functions in our approach. Thus, we can base type inference on the evaluation of functional logic programs. Functional logic programming provides a solid theoretical foundation for type functions and, at the same time, allows for programmable overloading resolution strategies by choosing different evaluation strategies for functional logic programs. Type inference with type functions is an instance of type inference with constrained types, where the underlying constraint system is defined by a functional logic program. We have designed a variant of Haskell which supports our approach to overloading, and implemented a prototype frontend for the language.

Haskell has a sophisticated mechanism for overloading identifiers with multiple definitions at distinct types. Object-oriented programming has a similar notion of overriding and overloading for methods names. Unfortunately, it is not possible to encode object-oriented overloading directly using Haskell overloading. This deficiency becomes particularly tiresome when Haskell programs wish to call methods imported from an object-oriented library. We present two refinements of Haskell’s type class system: Closed classes and overlapping instances. We demonstrate how we may exploit the refined system so as to be able to encode object-oriented classes within Haskell. This encoding allows us to mimic, within Haskell, the overloading resolution rules employed by object-oriented languages without the need for additional type annotations or name mangling. As a consequence, object-oriented class libraries are very convenient to import and use within Haskell. 1 The problem The purpose of this paper is to make it easy to import libraries from Java[9] or.NET[18], into a Haskell program. By “easy ” we mean that it should be as easy to use the library from Haskell than from its native language. Indeed, Haskell’s higher order features and first-class monadic values make it a powerful glue language, so if we succeed it might even be easier to use the library from Haskell than from its native language. However, these advantages will not be persuasive if things that are easy in the native language are clumsy in Haskell. That is the challenge we address here.

. This article presents a type system based on the DamasMilner system[DM82], that supports overloading. Types of overloaded symbols are constrained polymorphic types. The work is related to Haskell type classes[Wad89,NP93,HHJW96], System O[OWW95] and other similar type systems[Kae88,Smi91,Jon94,DCO96]. Restrictions imposed in these systems with respect to overloading are eliminated. User-defined global and local overloading is supported without restrictions. There is no need for declarations or annotations of any sort. No language construct is added in order to cope with overloading. The type system uses a context-dependent overloading policy, specified by a predicate used in a single inference rule. Overloading of functions defined over different type constructors is supported, as done with Haskell's constructor classes. No monomorphism restriction is required in order to solve ambiguity problems. The system uses an open-world approach, in which new overloaded definition...

We propose an extension of Haskell's type class system with lambda abstractions in the type language. Type inference for our extension relies on a novel constrained unification procedure called guided higher-order unification. This unification procedure is more general than Haskell's kind-preserving unification but less powerful than full higher-order unification.

Haskell has a sophisticated mechanism for overloading identifiers with multiple de nitions at distinct types. Object-oriented programming has a similar notion of overriding and overloading for methods names. Unfortunately, it is not possible to encode object-oriented overloading directly using Haskell overloading. This deficiency becomes particularly tiresome when Haskell programs wish to call methods imported from an object-oriented library. We present two refinements of Haskell's type class system: Closed classes and overlapping instances. We demonstrate how we may exploit the refined system so as to be able to encode object-oriented classes within Haskell. This encoding allows us to mimic, within Haskell, the overloading resolution rules employed by object-oriented languages without the need for additional type annotations or name mangling. As a consequence,...