Semantics, orderings and recursion in the weakest precondition calculus:
Abstract: "An extension of Dijkstra's guarded command language is studied, including sequential composition, demonic choice and a backtrack operator. We consider three orderings on this language: a refinement ordering defined by Back, a new deadlock ordering, and an approximation ordering...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1992
|
| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS
92,67 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "An extension of Dijkstra's guarded command language is studied, including sequential composition, demonic choice and a backtrack operator. We consider three orderings on this language: a refinement ordering defined by Back, a new deadlock ordering, and an approximation ordering of Nelson. The deadlock ordering is in between the two other orderings. All operators are monotonic in Nelson's ordering, but backtracking is not monotonic in Back's ordering and sequential composition is not monotonic for the deadlock ordering. At first sight recursion can only be added using Nelson's ordering By extending the theory of fixed points in partial orderings we show that, under certain circumstances, least fixed points for non monotonic functions can be obtained by iteration from the least element. This permits us the addition of recursion even using Back's ordering or the deadlock ordering. In order to give a semantic characterization of the three orderings that relates initial states to possible outcomes of the computation, the relations between predicate transformers and discrete powerdomains is studied. Three powerdomains are considered: two versions of the Smyth powerdomain and the Egli-Milner powerdomain. For each of them an isomorphism is proved with a suitable domain of predicate transformers. |
| Beschreibung: | 58 S. |
Internformat
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| 100 | 1 | |a Bonsangue, Marcello M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Semantics, orderings and recursion in the weakest precondition calculus |c Marcello Bonsague ; Joost N. Kok |
| 264 | 1 | |a Amsterdam |c 1992 | |
| 300 | |a 58 S. | ||
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| 490 | 1 | |a Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS |v 92,67 | |
| 520 | 3 | |a Abstract: "An extension of Dijkstra's guarded command language is studied, including sequential composition, demonic choice and a backtrack operator. We consider three orderings on this language: a refinement ordering defined by Back, a new deadlock ordering, and an approximation ordering of Nelson. The deadlock ordering is in between the two other orderings. All operators are monotonic in Nelson's ordering, but backtracking is not monotonic in Back's ordering and sequential composition is not monotonic for the deadlock ordering. At first sight recursion can only be added using Nelson's ordering | |
| 520 | 3 | |a By extending the theory of fixed points in partial orderings we show that, under certain circumstances, least fixed points for non monotonic functions can be obtained by iteration from the least element. This permits us the addition of recursion even using Back's ordering or the deadlock ordering. In order to give a semantic characterization of the three orderings that relates initial states to possible outcomes of the computation, the relations between predicate transformers and discrete powerdomains is studied. Three powerdomains are considered: two versions of the Smyth powerdomain and the Egli-Milner powerdomain. For each of them an isomorphism is proved with a suitable domain of predicate transformers. | |
| 650 | 4 | |a Recursion theory | |
| 700 | 1 | |a Kok, Joost N. |e Verfasser |4 aut | |
| 810 | 2 | |a Department of Computer Science: Report CS |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 92,67 |w (DE-604)BV008928356 |9 92,67 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-005976658 | ||
Datensatz im Suchindex
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| any_adam_object | |
| author | Bonsangue, Marcello M. Kok, Joost N. |
| author_facet | Bonsangue, Marcello M. Kok, Joost N. |
| author_role | aut aut |
| author_sort | Bonsangue, Marcello M. |
| author_variant | m m b mm mmb j n k jn jnk |
| building | Verbundindex |
| bvnumber | BV009033870 |
| ctrlnum | (OCoLC)29452378 (DE-599)BVBBV009033870 |
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| id | DE-604.BV009033870 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:28:58Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005976658 |
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| physical | 58 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
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| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS |
| spelling | Bonsangue, Marcello M. Verfasser aut Semantics, orderings and recursion in the weakest precondition calculus Marcello Bonsague ; Joost N. Kok Amsterdam 1992 58 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS 92,67 Abstract: "An extension of Dijkstra's guarded command language is studied, including sequential composition, demonic choice and a backtrack operator. We consider three orderings on this language: a refinement ordering defined by Back, a new deadlock ordering, and an approximation ordering of Nelson. The deadlock ordering is in between the two other orderings. All operators are monotonic in Nelson's ordering, but backtracking is not monotonic in Back's ordering and sequential composition is not monotonic for the deadlock ordering. At first sight recursion can only be added using Nelson's ordering By extending the theory of fixed points in partial orderings we show that, under certain circumstances, least fixed points for non monotonic functions can be obtained by iteration from the least element. This permits us the addition of recursion even using Back's ordering or the deadlock ordering. In order to give a semantic characterization of the three orderings that relates initial states to possible outcomes of the computation, the relations between predicate transformers and discrete powerdomains is studied. Three powerdomains are considered: two versions of the Smyth powerdomain and the Egli-Milner powerdomain. For each of them an isomorphism is proved with a suitable domain of predicate transformers. Recursion theory Kok, Joost N. Verfasser aut Department of Computer Science: Report CS Centrum voor Wiskunde en Informatica <Amsterdam> 92,67 (DE-604)BV008928356 92,67 |
| spellingShingle | Bonsangue, Marcello M. Kok, Joost N. Semantics, orderings and recursion in the weakest precondition calculus Recursion theory |
| title | Semantics, orderings and recursion in the weakest precondition calculus |
| title_auth | Semantics, orderings and recursion in the weakest precondition calculus |
| title_exact_search | Semantics, orderings and recursion in the weakest precondition calculus |
| title_full | Semantics, orderings and recursion in the weakest precondition calculus Marcello Bonsague ; Joost N. Kok |
| title_fullStr | Semantics, orderings and recursion in the weakest precondition calculus Marcello Bonsague ; Joost N. Kok |
| title_full_unstemmed | Semantics, orderings and recursion in the weakest precondition calculus Marcello Bonsague ; Joost N. Kok |
| title_short | Semantics, orderings and recursion in the weakest precondition calculus |
| title_sort | semantics orderings and recursion in the weakest precondition calculus |
| topic | Recursion theory |
| topic_facet | Recursion theory |
| volume_link | (DE-604)BV008928356 |
| work_keys_str_mv | AT bonsanguemarcellom semanticsorderingsandrecursionintheweakestpreconditioncalculus AT kokjoostn semanticsorderingsandrecursionintheweakestpreconditioncalculus |