## Games and full abstraction for PCF: preliminary announcement (1993)

Citations: | 5 - 0 self |

### BibTeX

@MISC{Abramsky93gamesand,

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

title = {Games and full abstraction for PCF: preliminary announcement},

year = {1993}

}

### OpenURL

### Abstract

The Full Abstraction Problem for PCF [14, 12, 4, 8] 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 [12]). 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 higher types. The phrase "sequential functional computation " deserves careful consideration. On the one hand, sequentiality refers to a computational process extended over time, not a mere function; on the other hand, we want to capture just those sequential computations in which the different parts or "modules " interact with each other in a purely functional fashion.

### Citations

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(Show Context)
Citation Context ...shion. There have, to our knowledge, been just four models of PCF put forward as embodying some semantic analysis. Three are domain-theoretic: the "standard model" based on Scott-continuous =-=functions [14]-=-; Berry's bidomains model based on stable functions [2]; and the Bucciarelli-Ehrhard model based on strongly stable functions [5]. The fourth is the Berry-Curien model based on sequential algorithms [... |

209 | Games and full completeness for multiplicative linear logic
- Abramsky, Jagadeesan
- 1992
(Show Context)
Citation Context ...s sense that our results offer a "solution" to the full abstraction problem for PCF. The Game Model Our intensionally fully abstract model is based on the game semantics for Linear Logic pre=-=sented in [1]-=-, and subsequently extended to cover the exponential types as described in a previous note on this list (May 28th). A first, simple step is to drop the notion of winning plays and strategies, and to a... |

109 |
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(Show Context)
Citation Context ...terization" 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 proper=-=ties [12]). The pro-=-blem 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 c... |

84 |
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(Show Context)
Citation Context ...]; Berry's bidomains model based on stable functions [2]; and the Bucciarelli-Ehrhard model based on strongly stable functions [5]. The fourth is the Berry-Curien model based on sequential algorithms =-=[3]-=- (Cartwright and Felleisen's model turns out to be equivalent to the sequential algorithms model [6, 9]). Of these, we can say that the standard model gives a good account of functional computation at... |

53 | Full Abstraction for sequential languages: the state of the art - Berry, Curien, et al. - 1985 |

40 |
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- Berry
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(Show Context)
Citation Context ...ls of PCF put forward as embodying some semantic analysis. Three are domain-theoretic: the "standard model" based on Scott-continuous functions [14]; Berry's bidomains model based on stable =-=functions [2]-=-; and the Bucciarelli-Ehrhard model based on strongly stable functions [5]. The fourth is the Berry-Curien model based on sequential algorithms [3] (Cartwright and Felleisen's model turns out to be eq... |

29 |
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(Show Context)
Citation Context ...order at all types. In particular, it is reflexive 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 =-=[15]-=- 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.... |

27 |
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(Show Context)
Citation Context ...collapsing map is a homomorphism, and in particular preserves application. This contrasts sharply with "collapses" of the standard model to obtain the fully abstract model, as in the work of=-= Mulmuley [13] and Stoug-=-hton and Jung [11], which are only homomorphic on the "inductively reachable" subalgebra. Thus we propose that a reasonable factorization of the full abstraction problem is to look for a sem... |

22 | Projecting sequential algorithms on strongly stable functions
- Ehrhard
- 1996
(Show Context)
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 =-=[10], can be seen as the-=- "extensional collapse" of the sequential algorithms model. In short, all these models are unsatisfactory because they contain "junk". On the other side of the coin, we have Milner... |

18 |
Studying the fully abstract model of PCF within its continuous function model
- Jung, Stoughton
- 1993
(Show Context)
Citation Context ...hism, and in particular preserves application. This contrasts sharply with "collapses" of the standard model to obtain the fully abstract model, as in the work of Mulmuley [13] and Stoughton=-= and Jung [11], which ar-=-e only homomorphic on the "inductively reachable" subalgebra. Thus we propose that a reasonable factorization of the full abstraction problem is to look for a semantic presentation of an int... |

17 | Definability and full abstraction - Curien - 2007 |

7 |
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(Show Context)
Citation Context ...n-theoretic: the "standard model" based on Scott-continuous functions [14]; Berry's bidomains model based on stable functions [2]; and the Bucciarelli-Ehrhard model based on strongly stable =-=functions [5]-=-. The fourth is the Berry-Curien model based on sequential algorithms [3] (Cartwright and Felleisen's model turns out to be equivalent to the sequential algorithms model [6, 9]). Of these, we can say ... |