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In computer science, Programming Computable Functions,〔"PCF is a programming language for computable functions, based on LCF, Scott’s logic of computable functions" . ''Programming Computable Functions'' is used by . It is also referred to as ''Programming with Computable Functions'' or ''Programming language for Computable Functions''.〕 or PCF, is a typed functional language introduced in an unpublished 1969 manuscript by Dana Scott. It can be considered to be an extended version of the typed lambda calculus or a simplified version of modern typed functional languages such as ML. A fully abstract model for PCF was first given by Milner (1977). However, since Milner's model was essentially based on the syntax of PCF it was considered less than satisfactory (Ong, 1995). The first two fully abstract models not employing syntax were formulated during the 1990s. These models are based on game semantics (Hyland and Ong, 2000; Abramsky, Jagadeesan, and Malacaria, 2000) and Kripke logical relations (O'Hearn and Riecke, 1995). For a time it was felt that neither of these models was completely satisfactory, since they were not effectively presentable. However, Ralph Loader demonstrated that no effectively presentable fully abstract model could exist, since the question of program equivalence in the finitary fragment of PCF is not decidable. ==Syntax== The ''types'' of PCF are inductively defined as * nat is a type * For types ''σ'' and ''τ'', there is a type ''σ'' → ''τ'' A ''context'' is a list of pairs ''x : σ'', where ''x'' is a variable name and ''σ'' is a type, such that no variable name is duplicated. One then defines typing judgments of terms-in-context in the usual way for the following syntactical constructs: * Variables (if ''x : σ'' is part of a context ''Γ'', then ''Γ'' ⊢ ''x'' : ''σ'') * Application (of a term of type ''σ'' → ''τ'' to a term of type ''σ'') * λ-abstraction * The Y fixed point combinator (making terms of type ''σ'' out of terms of type ''σ'' → ''σ'') * The successor (succ) and predecessor (pred) operations on nat and the constant 0 * The conditional if with the typing rule: : : (nats will be interpreted as booleans here with a convention like zero denoting truth, and any other number denoting falsity) 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「Programming Computable Functions」の詳細全文を読む スポンサード リンク
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