## A Fully Abstract Model for Sequential Computation (1998)

Citations: | 7 - 0 self |

### BibTeX

@TECHREPORT{Marz98afully,

author = {Michael Marz},

title = {A Fully Abstract Model for Sequential Computation},

institution = {},

year = {1998}

}

### OpenURL

### Abstract

In 1977, G. Plotkin pointed out the problem of finding a fully abstract model for the sequential programming language PCF [16], which had been originally developed by D. Scott [19]. This question turned out to be one of the most enduring problems of semantics. A very nice description of the different approaches

### Citations

468 | Domain Theory
- Abramsky, Jung
- 1994
(Show Context)
Citation Context ...f (order) extensionality. 2 Fundamental domain theoretic concepts and notations This section gives a short summary of the domain theory used in this paper. More details can be found, for instance, in =-=[1]-=- or [17]. A domain A is a partially ordered set that is closed under directed suprema and has a least element ⊥A. A function f : A → B is called continuous if it is monotone and preserves directed sup... |

210 |
On full abstraction for pcf
- Hyland, Ong
(Show Context)
Citation Context ...ract model for PCF [14] by applying the concept of Kripke relations [6]. A different concept was used by several research groups elaborating fully abstract models for PCF by using game semantics, see =-=[2,4,13]-=-. G. McCusker extended this approach to sum types and recursive types [10]. The domain theoretic approach was refined by J. Riecke and A. Sandholm who modified the O’Hearn/Riecke model and presented a... |

109 |
Fully abstract models of typed lambda-calculi
- Milner
- 1977
(Show Context)
Citation Context ...es can be found in [5]. In this rather brief overview, we mainly focus on those articles which are related to the work in this paper. The first fully abstract model for PCF was presented by R. Milner =-=[11]-=-. However, it was purely syntactic and did not provide a semantic description of sequentiality. In 1992, K. Sieber presented a syntax free characterisation of sequentiality for types up to order two a... |

67 | Full abstraction for PCF (extended abstract
- Abramsky, Jagadeesan, et al.
- 1994
(Show Context)
Citation Context ...ract model for PCF [14] by applying the concept of Kripke relations [6]. A different concept was used by several research groups elaborating fully abstract models for PCF by using game semantics, see =-=[2,4,13]-=-. G. McCusker extended this approach to sum types and recursive types [10]. The domain theoretic approach was refined by J. Riecke and A. Sandholm who modified the O’Hearn/Riecke model and presented a... |

61 | Hereditarily sequential functionals
- Nickau
- 1994
(Show Context)
Citation Context ...ract model for PCF [14] by applying the concept of Kripke relations [6]. A different concept was used by several research groups elaborating fully abstract models for PCF by using game semantics, see =-=[2,4,13]-=-. G. McCusker extended this approach to sum types and recursive types [10]. The domain theoretic approach was refined by J. Riecke and A. Sandholm who modified the O’Hearn/Riecke model and presented a... |

29 | Domains and denotational semantics: history, accomplishments, and open problems
- Jung
- 1996
(Show Context)
Citation Context ... D. Scott [19]. This question turned out to be one of the most enduring problems of semantics. A very nice description of the different approaches to this subject with many references can be found in =-=[5]-=-. In this rather brief overview, we mainly focus on those articles which are related to the work in this paper. The first fully abstract model for PCF was presented by R. Milner [11]. However, it was ... |

26 | Tiuryn, A New Characterization of Lambda Definability
- Jung, A
- 1993
(Show Context)
Citation Context ...]. Two years later, P. O’Hearn and J. Riecke used Sieber’s technique and gave the first domain theoretic description of a fully abstract model for PCF [14] by applying the concept of Kripke relations =-=[6]-=-. A different concept was used by several research groups elaborating fully abstract models for PCF by using game semantics, see [2,4,13]. G. McCusker extended this approach to sum types and recursive... |

25 | Finitary PCF is not decidable
- Loader
- 2001
(Show Context)
Citation Context ... given continuous function between two objects in SD is an SD-morphism. In particular, the exponentials in SD are not decidable. However, in the light of Loader’s undecidability result for finite PCF =-=[7]-=-, it seems to be unlikely that a substantial improvement can be achieved as it entails that the additional relational structure has to be infinite. Recently, the fully abstract model for PCF in the ca... |

22 |
Semantical paradigms: notes for an invited lecture
- Meyer, Cosmodakis
- 1988
(Show Context)
Citation Context ...sult if a given input term terminates. The approach in this paper to deal with this problem is to use two different kinds of SFL types. A similar approach was studied by A. Meyer and S. Cosmadakis in =-=[9]-=-, although they do not deal with smash products. Arbitrary types are denoted by the letters τ, τ1, τ2, . . .. Types whose termination is sequentially semidecidable are called computational types or SS... |

21 | Games and Full Abstraction for FPC
- McCusker
- 2000
(Show Context)
Citation Context ...ferent concept was used by several research groups elaborating fully abstract models for PCF by using game semantics, see [2,4,13]. G. McCusker extended this approach to sum types and recursive types =-=[10]-=-. The domain theoretic approach was refined by J. Riecke and A. Sandholm who modified the O’Hearn/Riecke model and presented a fully abstract model for FPC, an extension of call-by-value PCF with sum ... |

6 |
A relative PCF-definability result for strongly stable functions and some corollaries
- Ehrhard
- 1999
(Show Context)
Citation Context ...ational and the gametheoretic account of full abstraction. It might be interesting to give a direct proof that the relational model of SFL is the extensional collapse of its game model (in analogy to =-=[3]-=-). Acknowledgements I would like to thank the members of the Arbeitsgruppe 14 of the Fachbereich Mathematik at the Technische Universität Darmstadt and the ‘Theory Group’ of the School of Computer Sci... |

1 |
Full abstraction via realisability
- Marz, Rohr, et al.
- 1998
(Show Context)
Citation Context ...PCF in the category SD was reconstructed as a realisability model over the partial combinatory algebra A which is obtained as the canonical solution of the domain equation A ∼ = N⊕[A → A]⊥ in SD (see =-=[12]-=-). In particular, for every PCF type σ its interpretation in Mod(A) is isomorphic to the one given by the canonical retraction of A to its denotation in SD. This result can be refined to a solution of... |