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In computer science and logic, a dependent type is a type that depends on a value. It is an overlapping feature of type theory and type systems. In intuitionistic type theory, dependent types are used to encode logic's quantifiers like "for all" and "there exists". In functional programming languages like ATS, Agda, Idris and Epigram, dependent types prevent bugs by allowing extremely expressive types. Two common examples of dependent types are dependent functions and dependent pairs. A dependent function's return type may depend on the ''value'' (not just type) of an argument. A function that takes a positive integer "n" may return an array of length "n". (Note that this is different from polymorphism and generic programming, both of which include the type is an argument.) A dependent pair may have a second value that depends on the first. It can be used to encode a pair of integers where the second one is greater than the first. Dependent types add complexity to a type system. Deciding the equality of dependent types in a program may require computations. If arbitrary values are allowed in dependent types, then deciding type equality may involve deciding whether two arbitrary programs produce the same result; hence type checking may become undecidable. ==History== Dependent types were created to deepen the connection between programming and logic. In 1934, Haskell Curry noticed that the types used in mathematical programming languages followed the same pattern as axioms in propositional logic. Going further, for every proof in the logic, there was a matching function (term) in the programming language. One of Curry's examples was the correspondence between simply typed lambda calculus and intuitionistic logic. Predicate logic is an extension of propositional logic, adding quantifiers. Howard and de Bruijn extended lambda calculus to match this more powerful logic by creating types for dependent functions, which correspond to "for all", and dependent pairs, which correspond to "there exists". (Because of this and other work by Howard, propositions-as-types is known as the Curry-Howard correspondence.) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dependent type」の詳細全文を読む スポンサード リンク
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