# 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…

## 585 Citations

Full Abstraction for PCF

- Computer Science
- 2000

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.

Inductive Definition and Domain Theoretic Properties of Fully Abstract Models for PCF and PCF+

- Computer ScienceLog. Methods Comput. Sci.
- 2007

A construction of fully abstract typed models for PCF and PCF^+ (i.e., PCF +
"parallel conditional function"), respectively, is presented. It is based on
general notions of sequential computational…

A Simple Adequate Categorical Model for PCF

- PhilosophyTLCA
- 1997

An axiomatic approach to adequacy for PCF is presented, in the sense that categorical axioms enabling an adequate semantics to be given are introduced, which takes the point of view that partiality is the fundamental notion from which order-structure should be derived.

A universal realizability model for sequential functional computation

- Computer Science, Mathematics
- 2002

It is shown that every closed FPC-term of type U can be defined in the untyped language lambda+Error and it follows that the combinatory algebras l U and L are applicatively equivalent.

Linearity and PCF: a semantic insight!

- Computer ScienceICFP
- 2011

This work introduces a language, named SlPCF*, that increases the higher-order expressivity of a linear core of PCF by means of new operators related to exception handling and parallel evaluation, and formalizes two evaluation machineries for the language.

On Berry's conjectures about the stable order in PCF

- MathematicsLog. Methods Comput. Sci.
- 2011

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

- Mathematics
- 2011

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.

Full abstraction, totality and PCF

- MathematicsMath. Struct. Comput. Sci.
- 1999

This work considers the interaction of totality and full abstraction, asking whether full abstraction holds for Scott's model of cpos and continuous functions if one restricts to total programs and total observations, and investigates how totality differs between these models.

A semantic analysis of control

- Computer Science
- 1999

This thesis examines the use of denotational semantics to reason about control flow in sequential, basically functional languages, and establishes decidability of observational equivalence for finitary PCF, contrasting with the undecidable of the analogous relation in pure PCF.

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