## Full Abstraction for PCF (Extended Abstract) (1994)

Venue: | THEORETICAL ASPECTS OF COMPUTER SOFTWARE. INTERNATIONAL SYMPOSIUM TACS'94, NUMBER 789 IN LECTURE NOTES IN COMPUTER SCIENCE |

Citations: | 68 - 11 self |

### BibTeX

@INPROCEEDINGS{Abramsky94fullabstraction,

author = {Samson Abramsky and Pasquale Malacaria and Radha Jagadeesan},

title = {Full Abstraction for PCF (Extended Abstract)},

booktitle = {THEORETICAL ASPECTS OF COMPUTER SOFTWARE. INTERNATIONAL SYMPOSIUM TACS'94, NUMBER 789 IN LECTURE NOTES IN COMPUTER SCIENCE},

year = {1994},

pages = {1--15},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

The Full Abstraction Problem for PCF [23, 20, 7, 11] is one of the longest-standing problems in the semantics of programming languages. There is quite widespread agreement that it is one of the most difficult; there is much less agreement as to what exactly the problem is, or more particularly as to the precise criteria for a solution. The usual formulation is that one wants a "semantic characterization" of the fully abstract model (by which we mean the inequationally fully abstract order-extensional model, which Milner proved to be uniquely specified up to isomorphism by these properties [20]). The problem is to understand what should be meant by a "semantic characterization". Our view is that the essential content of the problem, what makes it important, is that it calls for a semantic characterization of sequential, functional computation at hig...

### Citations

3682 | Communicating Sequential Processes
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Citation Context ...e write fxsy for ifx is de��ned and equal to yj. We write s v t if s is a pre��x of t, i.e. for some u, su = t. We always consider sequences under this pre��x ordering and use order-theore=-=tic notions [13] without-=- further comment. 2.1 Games The games we consider are between Player and Opponent. A play or run of the game consists of an alternating sequence of moves, which may be ��nite or in��nite. Our ... |

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LCF considered as a programming language
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Citation Context ...cterizationj of the fully abstract model (by which we mean the inequationally fully abstract orderextensional model, which Milner proved to be uniquely speci��ed up to isomorphism by these propert=-=ies [20]-=-). The problem is to understand what should be meant by a isemantic characterizationj. Our view is that the essential content of the problem, what makes it important, is that it calls for a semantic c... |

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Citation Context ...cribe composition in terms of the functions inducing strategies. Say we have oe f : A ! B; oe g : B ! C. We want to ��nd h such that oe f ; oe g = oe h . We shall compute h by the iexecution formu=-=laj [15, 16, 17]. Be-=-fore giving the formal de��nition, let us explain the idea, which is rather simple. We want to hook the strategies up so that Player's moves in B under oe get turned into Opponent's moves in B for... |

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Citation Context ...]; Berry's bidomains model based on stable functions [5]; and the Bucciarelli-Ehrhard model based on strongly stable functions [8]. The fourth is the Berry-Curien model based on sequential algorithms =-=[6]-=- (Cartwright and Felleisen's model turns out to be equivalent to the sequential algorithms model [9, 12]). Of these, we can say that the standard model gives a good account of functional computation a... |

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43 |
Geometry of Interaction 1: Interpretation of System F
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Citation Context ...cribe composition in terms of the functions inducing strategies. Say we have oe f : A ! B; oe g : B ! C. We want to ��nd h such that oe f ; oe g = oe h . We shall compute h by the iexecution formu=-=laj [15, 16, 17]. Be-=-fore giving the formal de��nition, let us explain the idea, which is rather simple. We want to hook the strategies up so that Player's moves in B under oe get turned into Opponent's moves in B for... |

41 |
Modèles complètement adéquats et stables des lambda-calculus typés. Thèse d’Etat, Université Paris VII
- BERRY
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Citation Context ...ls of PCF put forward as embodying some semantic analysis. Three are domain-theoretic: the istandard modelj based on Scott-continuous functions [23]; Berry's bidomains model based on stable functions =-=[5]-=-; and the Bucciarelli-Ehrhard model based on strongly stable functions [8]. The fourth is the Berry-Curien model based on sequential algorithms [6] (Cartwright and Felleisen's model turns out to be eq... |

29 |
Fully Abstract Models of Programming Languages
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Citation Context ...eorder at all types. In particular, it is reAEexive at all types. This says that all elements of the model have extensional (functional) behaviour��there is no junk. We can now apply Theorem 7.2.2=-= of [24]-=- to conclude that M can be collapsed by a continuous homomorphism to the fully abstract model. In short, the fully abstract model is the extensional collapse of any intensionally fully abstract model.... |

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Citation Context ...collapsing map is a homomorphism, and in particular preserves application. This contrasts sharply with icollapsesj of the standard model to obtain the fully abstract model, as in the work of Mulmuley =-=[21]-=- and Stoughton and Jung [19], which are only homomorphic on the iinductively reachablej subalgebra. Thus we propose that a reasonable factorization of the full abstraction problem is to look for a sem... |

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Citation Context ... to non-functional aspects of the behaviour of their arguments. The bidomains model also contains non-sequential functions; while the strongly stable model, in the light of a recent result by Ehrhard =-=[14]-=-, can be seen as the iextensional collapsej of the sequential algorithms model. In short, all these models are unsatisfactory because they contain ijunkj. On the other side of the coin, we have Milner... |

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Citation Context ...hism, and in particular preserves application. This contrasts sharply with icollapsesj of the standard model to obtain the fully abstract model, as in the work of Mulmuley [21] and Stoughton and Jung =-=[19]-=-, which are only homomorphic on the iinductively reachablej subalgebra. Thus we propose that a reasonable factorization of the full abstraction problem is to look for a semantic presentation of an int... |

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Citation Context ...cribe composition in terms of the functions inducing strategies. Say we have oe f : A ! B; oe g : B ! C. We want to ��nd h such that oe f ; oe g = oe h . We shall compute h by the iexecution formu=-=laj [15, 16, 17]. Be-=-fore giving the formal de��nition, let us explain the idea, which is rather simple. We want to hook the strategies up so that Player's moves in B under oe get turned into Opponent's moves in B for... |

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