Full Abstraction for PCF

An intensional model for the programming language PCF is described in which the types of PCF are interpreted by games and the terms by certain history-free strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable in a certain si...

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Vydáno v:Information and computation Ročník 163; číslo 2; s. 409 - 470
Hlavní autoři: Abramsky, Samson, Jagadeesan, Radha, Malacaria, Pasquale
Médium: Journal Article
Jazyk:angličtina
Vydáno: San Diego, CA Elsevier Inc 15.12.2000
Elsevier
Témata:
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
full abstraction
functional computation
game semantics
General logic
Language theory and syntactical analysis
linear logic
Logic and foundations
Mathematical logic, foundations, set theory
Mathematics
PCF
programming language semantics
Sciences and techniques of general use
sequentiality
Theoretical computing
PCF
functional computation
linear logic
full abstraction
game semantics
programming language semantics
sequentiality
Functional computationFunctional calculus
Linear logic
Programming language
Semantics
Game semantics
Programming language semantics
Abstraction
Logic
ISSN:0890-5401, 1090-2651
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Popis
Shrnutí:An intensional model for the programming language PCF is described in which the types of PCF are interpreted by games and the terms by certain history-free strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable in a certain simple extension of PCF. We then introduce an intrinsic preorder on strategies and show that it satisfies some striking properties such that the intrinsic preorder on function types coincides with the pointwise preorder. We then obtain an order-extensional fully abstract model of PCF by quotienting the intensional model by the intrinsic preorder. This is the first syntax-independent description of the fully abstract model for PCF. (Hyland and Ong have obtained very similar results by a somewhat different route, independently and at the same time.) We then consider the effective version of our model and prove a universality theorem: every element of the effective extensional model is definable in PCF. Equivalently, every recursive strategy is definable up to observational equivalence.
ISSN:0890-5401
1090-2651
DOI:10.1006/inco.2000.2930