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Typing Environment
In type theory a typing environment (or typing context) represents the association between variable names and data types. 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 programming languages these environments are used and maintained by typing rules to type check a given program or expression. See also * Type system 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 progr ... References Data types Program analysis Type theory {{type-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Theory
In mathematics, logic, and computer science, a type theory is the 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 theory as a foundation of mathematics. Two influential type theories that were proposed as foundations are Alonzo Church's typed λ-calculus and Per Martin-Löf's intuitionistic type theory. Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions. History Type theory was created to avoid a paradox in a mathematical foundation based on naive set theory and formal logic. Russell's paradox, which was discovered by Bertrand Russell, existed because a set could be defined using "all possible sets", which included itself. Between 1902 and 1908, Bertrand Russell proposed various "theories of type" to fix the problem. By 1908 Russell arrived at a "ramified" theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |