## From Partial Orders with Projections to Domains (Extended Abstract) (1999)

Venue: | Mathematical Foundations of Programming Semantics, Fifteenth Conference, volume 20 of Electronic Notes in Theoretical Computer Science |

Citations: | 8 - 8 self |

### BibTeX

@INPROCEEDINGS{Kummetz99frompartial,

author = {Ralph Kummetz},

title = {From Partial Orders with Projections to Domains (Extended Abstract)},

booktitle = {Mathematical Foundations of Programming Semantics, Fifteenth Conference, volume 20 of Electronic Notes in Theoretical Computer Science},

year = {1999},

pages = {pages.}

}

### OpenURL

### Abstract

Ralph Kummetz 1 Institut fur Algebra Technische Universitat Dresden D-01062 Dresden, Germany Abstract We study approximating partial orders with projections (approximating pop's). These are triples (D; ; P) consisting of a poset (D; ) and a directed set P of projections such that the supremum of P exists and sup P = id D . We derive a canonical uniformity U on D and relate properties of U such as completeness and compactness to properties of the poset and the projection set. We show that each monotone net in D is convergent if and only if (D; ) is an algebraic domain such that the images of the projections are precisely the compact elements of (D; ). Furthermore, the bifinite domains arise exactly as approximating pop's where U is compact. 1 Introduction In the theory of denotational semantics of programming languages, various classes of domains and their approximations have been intensively investigated. Scott [11] constructed a domain-theoretic model of the type-free -calculus ...

### Citations

472 | Domain theory
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- 1994
(Show Context)
Citation Context ...hain of finite posets. These and other cartesian closed categories were further investigated e.g. by Gunter [7] and Jung [8]. For an excellent and recent survey on domain theory see Abramsky and Jung =-=[1]-=-. On the other hand, Ehrig et al. [4] and Groe-Rhode [5], see also [6], introduced and investigated the concept of projection spaces as a basic model for algebraic specifications of nonterminating pro... |

221 | A Powerdomain Construction
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(Show Context)
Citation Context ...and their approximations have been intensively investigated.sScott [11] constructed a domain-theoretic model of the type-free -calculus using an approximating chain of suitable Scott-domains. Plotkin =-=[10]-=- introduced SFP-domains, which form a convenient mathematical model for the semantics of nondeterministic programming languages, as limits of a chain of finite posets. These and other cartesian closed... |

36 |
Continuous lattices. In Toposes, algebraic geometry and logic
- Scott
- 1972
(Show Context)
Citation Context ...op's where U is compact. 1 Introduction In the theory of denotational semantics of programming languages, various classes of domains and their approximations have been intensively investigated.sScott =-=[11]-=- constructed a domain-theoretic model of the type-free -calculus using an approximating chain of suitable Scott-domains. Plotkin [10] introduced SFP-domains, which form a convenient mathematical model... |

15 | Profinite solutions for recursive domain equations
- Gunter
- 1985
(Show Context)
Citation Context ...ematical model for the semantics of nondeterministic programming languages, as limits of a chain of finite posets. These and other cartesian closed categories were further investigated e.g. by Gunter =-=[7]-=- and Jung [8]. For an excellent and recent survey on domain theory see Abramsky and Jung [1]. On the other hand, Ehrig et al. [4] and Groe-Rhode [5], see also [6], introduced and investigated the conc... |

11 |
Cartesian Closed Categories of Domains. CWI Tracts 66, Centrum voor Wiskunde en Informatica
- Jung
- 1989
(Show Context)
Citation Context ...l for the semantics of nondeterministic programming languages, as limits of a chain of finite posets. These and other cartesian closed categories were further investigated e.g. by Gunter [7] and Jung =-=[8]-=-. For an excellent and recent survey on domain theory see Abramsky and Jung [1]. On the other hand, Ehrig et al. [4] and Groe-Rhode [5], see also [6], introduced and investigated the concept of projec... |

10 | Metric semantics from partial order semantics - Baier, Majster-Cederbaum - 1997 |

7 |
Transformation of combined data type and process specifications using projection algebras
- Groe-Rhode, Ehrig
- 1990
(Show Context)
Citation Context ...r cartesian closed categories were further investigated e.g. by Gunter [7] and Jung [8]. For an excellent and recent survey on domain theory see Abramsky and Jung [1]. On the other hand, Ehrig et al. =-=[4]-=- and Groe-Rhode [5], see also [6], introduced and investigated the concept of projection spaces as a basic model for algebraic specifications of nonterminating processes. A projection 1 Supported by D... |

6 |
On functions preserving levels of approximation: a refined model construction for various lambda calculi
- Spreen
- 1999
(Show Context)
Citation Context ...al order on the given space such that all projections are !-continuous mappings. In [2] it is shown that SFP-domains can be characterized as special kinds of rank ordered cpo's. Very recently, Spreen =-=[12]-=- used rank orderings on dI-domains to obtain models of the fip-calculus. In this paper we study in a general way how elements of partially ordered sets can be approximated when a certain family of pro... |

4 |
Parameterized data type and process specifications using projection algebras
- Groe-Rhode
- 1989
(Show Context)
Citation Context ...categories were further investigated e.g. by Gunter [7] and Jung [8]. For an excellent and recent survey on domain theory see Abramsky and Jung [1]. On the other hand, Ehrig et al. [4] and Groe-Rhode =-=[5]-=-, see also [6], introduced and investigated the concept of projection spaces as a basic model for algebraic specifications of nonterminating processes. A projection 1 Supported by DFG/Graduiertenkolle... |