Type class

In computer science, a type class is a type system construct that supports ad hoc polymorphism in a programming language. 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 were first implemented in the language Haskell after first being proposed by Philip Wadler and Stephen Blott as an extension to eqtypes in Standard ML, 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 need extensive modification of the compiler frontend or the underlying type system.

Overview

Type classes are defined 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:

where a is one instance of the type class Eq, and a defines the function signatures for 2 functions (the equality and inequality functions), which each take 2 arguments of type a and return a Boolean.

The type variable a has kind

∗

{\displaystyle *}

(

∗

{\displaystyle *}

is also known as Type in the latest Glasgow Haskell Compiler (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:

The function elem has the type a -> [a] -> Bool with the context Eq a, which constrains the types which a can range over to those a which belong to the Eq type class. (Haskell => can be called a 'class constraint'.)

Any type t can be made a member of a given type class C by using an instance declaration that defines implementations of all of C's methods for the given type t. For example, if a new data type t is defined, this new type can be made an instance of Eq by providing an equality function over values of type t in any way that is useful.