Programming Computable Functions: Difference between revisions

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The '''Programming language for Computable Functions''', or '''PCF''', is a typed [[Functional programming|functional language]] introduced by [[Gordon Plotkin]] in [[1977]]. It is based on the [[Logic of Computable FunctionFunctions]] ([[LCF]]) by [[Dana Scott]]. It can be considered as a simplified version of modern typed functional languages such as [[ML programming language|ML]].

A [[fully abstract]] model for PCF was first given by [[Robin Milner|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.