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by Samson Abramsky, Radha Jagadeesan, Pasquale Malacaria
Information and Computation
http://www.dcs.qmul.ac.uk/~pm/Papers/Final/fapcf.ps
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Abstract:
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 denability in PCF. More precisely, every compact strategy in the model is denable in a certain simple extension of PCF. We then introduce an intrinsic preorder on strategies, and show that it satises some remarkable 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 rst syntax-independent description of the fully abstract model for PCF. (Hyland and Ong have obtained very similar results by a somewhat dierent route, independently and at the same time.) We then consider the eective version of our model, and prove a Universality Theorem: every element of the eective extensional model is
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