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Summary: Full Abstraction for PCF1
Samson.Abramsky2
University of Edinburgh
and
Radha Jagadeesan3
Loyola University Chicago
and
Pasquale Malacaria4
Queen Mary and Westfield College
An intensional model for the programming language PCF is described,
in which the types of PCF are interpreted by games, and the terms by cer-
tain "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 pre-
order. 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. (Hy-
land and Ong have obtained very similar results by a somewhat different
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