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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Parametricity ： ウィキペディア英語版 Parametricity In programming language theory, parametricity is an abstract uniformity property enjoyed by parametrically polymorphic functions, which captures the intuition that all instances of a polymorphic function act the same way. == Idea == Consider this example, based on a set ''X'' and the type ''T''(''X'') = (→ ''X'' ) of functions from ''X'' to itself. The higher-order function ''twice''''X'' : ''T''(''X'') → ''T''(''X'') given by ''twice''''X''(''f'') = ''f'' ∘ ''f'', is intuitively independent of the set ''X''. The family of all such functions ''twice''''X'', parametrized by sets ''X'', is called a "parametrically polymorphic function". We simply write twice for the entire family of these functions and write its type as $\backslash forall$''X''. ''T''(''X'') → ''T''(''X''). The individual functions ''twice''''X'' are called the ''components'' or ''instances'' of the polymorphic function. Notice that all the component functions ''twice''''X'' act "the same way" because they are given by the same rule. Other families of functions obtained by picking one arbitrary function from each ''T''(''X'') → ''T''(''X'') would not have such uniformity. They are called "''ad hoc'' polymorphic functions". ''Parametricity'' is the abstract property enjoyed by the uniformly acting families such as twice, which distinguishes them from ''ad hoc'' families. With an adequate formalization of parametricity, it is possible to prove that the parametrically polymorphic functions of type $\backslash forall$''X''. ''T''(''X'') → ''T''(''X'') are one-to-one with natural numbers. The function corresponding to the natural number ''n'' is given by the rule ''f'' $\backslash mapsto$ ''f''''n'', i.e., the polymorphic Church numeral for ''n''. In contrast, the collection of all ''ad hoc'' families would be too large to be a set. 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「Parametricity」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.