Type classes

In computer science, a type class is a type system construct that supports ad hoc polymorphism. This is achieved by adding constraints to type variables in parametrically polymorphic types. Such a constraint typically involves a type class T and a type variable a, and means that a can only be instantiated to a type whose members support the overloaded operations associated with T.

Type classes first appeared in the Haskell programming language, and were originally conceived as a way of implementing overloaded arithmetic and equality operators in a principled fashion. In contrast with the "eqtypes" of Standard ML, overloading the equality operator through the use of type classes in Haskell does not require extensive modification of the compiler frontend or the underlying type system.

Since their creation, many other applications of type classes have been discovered.

The programmer defines a type class by specifying a set of function or constant names, together with their respective types, that must exist for every type that belongs to the class. In Haskell, types can be parameterized; a type class Eq intended to contain types that admit equality would be declared in the following way:

The type variable a has kind ${\displaystyle *}$ (also known as Type in the latest GHC release), meaning that the kind of Eq is

The declaration may be read as stating a "type a belongs to type class Eq if there are functions named (==), and (/=), of the appropriate types, defined on it." A programmer could then define a function elem (which determines if an element is in a list) in the following way:

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