Full Abstraction for PCF

@article{Abramsky1994FullAF,
  title={Full Abstraction for PCF},
  author={Samson Abramsky and Radha Jagadeesan and Pasquale Malacaria},
  journal={Inf. Comput.},
  year={1994},
  volume={163},
  pages={409-470}
}
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… 
Full Abstraction for PCF
TLDR
The effective version of the model is considered and it is proved that every element of the effective extensional model is definable in PCF, which is the first syntax-independent description of the fully abstract model for PCF.
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It is shown that Berry's conjecture is true for unary PCF, that the stable order is not bounded complete, already for finitary PCF of second-order types.
On Berry's conjectures about the stable order in PCF
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  • Mathematics
    Math. Struct. Comput. Sci.
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References

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TLDR
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TLDR
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TLDR
This work defines a category of games and a model of the lazy X-calculus, a type-free functional language based on evaluation to weak head normal form, yielding an extensional model in /spl Escr/ that is shown to be fully abstract with respect to applicative simulation.
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