In type theory and

programming language A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually def ...

s, a type variable is a mathematical variable ranging over

types Type may refer to: Science and technology Computing * Typing, producing text via a keyboard, typewriter, etc. * Data type, collection of values used for computations. * File type * TYPE (DOS command), a command to display contents of a file. * Ty ...

. Even in programming languages that allow mutable variables, a type variable remains an abstraction, in the sense that it does not correspond to some memory locations.

Programming language A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually def ...

s that support parametric polymorphism make use of universally quantified type variables. Languages that support existential types make use of existentially quantified type variables. For example, the following OCaml code defines a polymorphic identity function that has a universally quantified type, which is printed by the interpreter on the second line: # let id x = x;; val id : 'a -> 'a = In mathematical notation, the type of the function id is

\forall a.a \to a

, where

a

is a type variable.

See also