## Retractions in Comparing Prolog Semantics (1989)

Venue: | IN PROC. COMPUTING SCIENCE IN THE NETHERLANDS, PART 1, P.M.G. APERS |

Citations: | 2 - 1 self |

### BibTeX

@INPROCEEDINGS{Bruin89retractionsin,

author = {A. de Bruin and E. P. de Vink},

title = {Retractions in Comparing Prolog Semantics},

booktitle = {IN PROC. COMPUTING SCIENCE IN THE NETHERLANDS, PART 1, P.M.G. APERS},

year = {1989},

pages = {71--90},

publisher = {}

}

### OpenURL

### Abstract

We present an operational model O and a continuation based denotational model D for a uniform variant of Prolog, including the cut operator. The two semantical definitions make use of higher order transformations F and Y, respectively. We prove O and D equivalent in a novel way by comparing yet another pair of higher order transformations F and Y , that yield F and Y, respectively, by application of a suitable abstraction operator.

### Citations

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A calculus of communicating systems
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(Show Context)
Citation Context ...eliver observables s as the result of a 4. computation, but also additional information. The resulting states s are preceded by a number of clock ticks, a row of t's. (In algebraic approaches as e.g. =-=[Mi]-=- and [BeKl], t denotes a silent or internal step of a process.) Here the idea is that each t in this row corresponds with the execution of an elementary action by the abstract machine, i.e. one iterat... |

78 |
J.I.Zucker: Processes and the Denotational Semantics of Concurrency
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Citation Context ...t compact equivalence proofs could be realized using higher order transformations. To a great extent, we also benefit from the work on metric semantics of concurrency performed by De Bakker e.a. E.g. =-=[BZ]-=-, [BKMOZ], [BM]a, [Ba2]. It is a pleasure to thank the forum formed by the members of the working group on concurrency, - Jaco de Bakker, Frank de Boer, Joost Kok, Jan Rutten and others - for their co... |

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Mathematical Theory of Program Correctness
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Citation Context ...O, we have to derive the result that O[[ s ]] s = ^ implies D[[ s ]] s = ^. Unfortunately this takes at least as much effort as was needed to derive the previous result. See for example the proofs in =-=[Ba1]-=-. On the other hand if the operator F would have a unique fixed point then it would not be necessary to derive this additional result. Uniqueness is guaranteed for instance when one does not use cpo's... |

54 | Denotational and Operational Semantics for Prolog
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- 1988
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Citation Context ...at will be studied in the sequel - cannot be given a satisfactory direct semantics. (In order to model the cut operator this way one has to resort to cut-flags or other kinds of indicators. See [JM], =-=[DM]-=-, [Bd], [Vi].) Our meaning function D is defined as the least fixed point of a higher order operator Y. In fact, it does not matter much how D is defined (as long as it remains denotational), the more... |

53 |
Stepwise Development of Operational and Denotational Semantics for Prolog
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Citation Context ...B - that will be studied in the sequel - cannot be given a satisfactory direct semantics. (In order to model the cut operator this way one has to resort to cut-flags or other kinds of indicators. See =-=[JM]-=-, [DM], [Bd], [Vi].) Our meaning function D is defined as the least fixed point of a higher order operator Y. In fact, it does not matter much how D is defined (as long as it remains denotational), th... |

45 |
Algebra of communicating processes
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Citation Context ...servables s as the result of a 4. computation, but also additional information. The resulting states s are preceded by a number of clock ticks, a row of t's. (In algebraic approaches as e.g. [Mi] and =-=[BeKl]-=-, t denotes a silent or internal step of a process.) Here the idea is that each t in this row corresponds with the execution of an elementary action by the abstract machine, i.e. one iteration of the ... |

34 | Continuation semantics for Prolog with cut
- Bruin, Vink
- 1989
(Show Context)
Citation Context ...t in a novel way by comparing yet another pair of higher order transformations F and Y , that yield F and Y, respectively, by application of a suitable abstraction operator. Section 1 Introduction In =-=[BV]-=- we presented both an operational and a denotational continuation based semantics for the core of Prolog, and we proved these two semantics equivalent. We used a two step approach, by first deriving t... |

17 |
Metric Semantics for Concurrency
- Meyer
- 1988
(Show Context)
Citation Context ... operator F has been exploited successfully to derive compact equivalence proofs for operational and denotational meanings along the lines sketched above. A similar line of reasoning has been used in =-=[BM]-=-. The fact that our operatorsF admits more than one fixed point seems to be an essential consequence due to the fact that we abstracted away from the intermediate configurations. For instance, it is n... |

17 |
Comparative semantics for flow of control in logic programming without logic
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Citation Context ...proofs could be realized using higher order transformations. To a great extent, we also benefit from the work on metric semantics of concurrency performed by De Bakker e.a. E.g. [BZ], [BKMOZ], [BM]a, =-=[Ba2]-=-. It is a pleasure to thank the forum formed by the members of the working group on concurrency, - Jaco de Bakker, Frank de Boer, Joost Kok, Jan Rutten and others - for their comments and the good sci... |

16 |
Contrasting Themes in the Semantics of Imperative Concurrency
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Citation Context ...act equivalence proofs could be realized using higher order transformations. To a great extent, we also benefit from the work on metric semantics of concurrency performed by De Bakker e.a. E.g. [BZ], =-=[BKMOZ]-=-, [BM]a, [Ba2]. It is a pleasure to thank the forum formed by the members of the working group on concurrency, - Jaco de Bakker, Frank de Boer, Joost Kok, Jan Rutten and others - for their comments an... |

12 |
The category of complete partial ord.ers: ø tool of mo,lci,ng meaning
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Citation Context ... The relationsi, j between cpo's is - roughly speaking - one half of the subdomain ordering in the category CPO . For the subdomain ordering there is the additional requirement that i �� jsid Ds. =-=See [Pl]-=-. Given cpo's D, D the pair of continuous functions i, j such that Dsi, j D is not unique. It is already the case (contrary to the subdomain ordering) that for fixed inclusion i there exist several re... |

11 |
Uniform abstraction, atomicity and contractions in the comparative semantics of concurrent
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- 1988
(Show Context)
Citation Context ...act backtracking language B. This uniform language was studied also in [BV]a for it captures the control flow of Prolog with cut, the latter being the main interest of the particular paper. (See also =-=[BaKo]-=-, [Vi]a, [Ba2]a for similar uses of intermediate abstracta in deriving sound denotational semantics for logic programming languages.) In the present paper however, we will focus on the residue B itsel... |

10 |
J.J.C.: Linear time and branching time semantics for recursion with merge
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- 1984
(Show Context)
Citation Context ...chine, i.e. one iteration of the step function. Similarly for a nonterminating computation, we do not deliver ^ but an infinite row of t's instead. So ^ is reformulated as internal divergence, (as in =-=[BBKM]-=-). Now, for the corresponding meaning functions O and D a compact equivalence proof can be given. In order to establish from this the equivalence of our original functions O and D it is sufficient to ... |

9 |
Contractions in Comparing Concurrency Semantics
- Kok, Rutten
- 1988
(Show Context)
Citation Context ...e the existence of the fixed points, but when complete metric spaces are used instead and the operators are contracting functions on these spaces. For in that case Banach's theorem can be applied. In =-=[KR]-=- unicity of the fixed point of the operational higher order operator F has been exploited successfully to derive compact equivalence proofs for operational and denotational meanings along the lines sk... |

7 |
Programming Calculi Based on Fixed Point Transformations
- Meyer
- 1985
(Show Context)
Citation Context ...hereof like the ones discussed above. We show that the abstract domains can be considered as so called retracts of the more concrete ones. We will derive a few theorems, related to those of [BMZ] and =-=[Me]-=- that enable us to prove results as in (*) in a more smooth and elegant way. In the remaining sections this theory is tested using the above described language B: Section 4 describes the operational a... |

2 |
Proving Termination Properties of Prolog Programs: A Semantic Approach
- Badinet
- 1988
(Show Context)
Citation Context ...l be studied in the sequel - cannot be given a satisfactory direct semantics. (In order to model the cut operator this way one has to resort to cut-flags or other kinds of indicators. See [JM], [DM], =-=[Bd]-=-, [Vi].) Our meaning function D is defined as the least fixed point of a higher order operator Y. In fact, it does not matter much how D is defined (as long as it remains denotational), the more usual... |

2 |
Comparative Semantics for Prolog with Cut," Report IR-166, Vrije Universiteit
- Vink
- 1988
(Show Context)
Citation Context ...tudied in the sequel - cannot be given a satisfactory direct semantics. (In order to model the cut operator this way one has to resort to cut-flags or other kinds of indicators. See [JM], [DM], [Bd], =-=[Vi]-=-.) Our meaning function D is defined as the least fixed point of a higher order operator Y. In fact, it does not matter much how D is defined (as long as it remains denotational), the more usual appro... |