type theory In mathematics, logic, and computer science, a type theory is the formal system, formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theor ...

a typing environment (or typing context) represents the association between variable names and

data type In computer science and computer programming, a data type (or simply type) is a set of possible values and a set of allowed operations on it. A data type tells the compiler or interpreter how the programmer intends to use the data. Most progra ...

s. More formally an environment

\Gamma

is a set or ordered list of pairs

\langle x,\tau \rangle

, usually written as

x:\tau

, where

x

is a variable and

\tau

its type. The judgement :

\Gamma \vdash e:\tau

is read as "

e

has type

\tau

in context

\Gamma

". In

statically typed In computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type to every "term" (a word, phrase, or other set of symbols). Usually the terms are various constructs of a computer program ...

programming language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming l ...

s these environments are used and maintained by

typing rule In type theory, a typing rule is an inference rule that describes how a type system assigns a type to a syntactic construction. These rules may be applied by the type system to determine if a program is well-typed and what type expressions have. ...

s to type check a given program or expression.

References

Data types Program analysis Type theory {{type-theory-stub

See also

References