## Relating State Transformation Semantics and Predicate Transformer Semantics for Parallel Programs (1993)

Citations: | 3 - 0 self |

### BibTeX

@TECHREPORT{Breugel93relatingstate,

author = {Franck Van Breugel and Franck Van Breugel},

title = {Relating State Transformation Semantics and Predicate Transformer Semantics for Parallel Programs},

institution = {},

year = {1993}

}

### OpenURL

### Abstract

A state transformation semantics and a predicate transformer semantics for programs built from atomic actions, sequential composition, nondeterministic choice, parallel composition, atomisation, and recursion are presented. Both semantic models are derived from some SOS-style labelled transition system. The state transformation semantics and the predicate transformer semantics are shown to be isomorphic extending results of Plotkin and Best. AMS Subject Classification (1991): 68Q55 CR Subject Classification (1991): D.3.1, F.3.2 Keywords & Phrases: state transformation, predicate transformer, isomorphism, labelled transition system, parallelism Note: This work was partially supported by the Netherlands Nationale Faciliteit Informatica programme, project Research and Education in Concurrent Systems (REX).

### Citations

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Citation Context ... lost when introducing parallel composition is that the programs x := 2 and x := 1 ; x := x + 1 are semantically equivalent, but x := 2 k x := 3 and (x := 1 ; x := x + 1) k x := 3 are not (see, e.g., =-=[Mil93]-=-). The state transformation semantics and the predicate transformer semantics to be presented are mappings from statements to state transformations and predicate transformers, respectively. Before we ... |

78 |
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Citation Context ...e postulate a denumerable set (oe 2) \Sigma of states (cf. page 212 of [Wan77] and page 529 of [Plo79]). State transformations are defined as mappings from \Sigma to the so-called Smyth power domain (=-=[Smy78]-=-) of \Sigma in Definition 1.1 The partial order (ff 2) ST of state transformations is the set \Sigma ! P S (\Sigma ? ); where P S (\Sigma ? ) = f S ` \Sigma j S is nonempty and finite g [ f\Sigma ? g ... |

75 |
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Citation Context ...l programs built from atomic actions, sequential composition, nondeterministic choice, parallel composition, atomisation (atomicity being a key notion in reasoning about parallel programs, see, e.g., =-=[LL90]-=-), and recursion. (In order to introduce recursion we will consider a program to be a statement and a declaration. The statement is built from atomic actions, procedure variables, and the operators me... |

52 | An operational semantics for CSP - Plotkin - 1983 |

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Citation Context ...Remark 2.14 The above definition shows some similarities with the definition of the weakest invariant in terms of the weakest liberal precondition, i.e. win (oe; Q) = 2oeswlp (; Q); as at page 408 of =-=[Lam90]-=-. By means of the above defined predicate transformer semantics O pt , the predicate transformer semantics O pt , which maps statements to predicate transformers, is defined. Definition 2.15 The predi... |

24 | domains and predicate transformers: a topological view , Techincal monograph 126 - Power - 1983 |

19 |
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Citation Context ...ntics is considered by De Roever in [Roe76]. In [Bak77], De Bakker shows that there is a homomorphism from the state transformation semantics to the predicate transformer semantics. Plotkin shows, in =-=[Plo79]-=-, that by refining the definitions this homomorphism can be strengthened to an isomorphism. Predicate transformer semantics for partial correctness of parallel programs are studied by Van Lamsweerde a... |

12 |
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(Show Context)
Citation Context ...fining the definitions this homomorphism can be strengthened to an isomorphism. Predicate transformer semantics for partial correctness of parallel programs are studied by Van Lamsweerde and Sintzoff =-=[LS79]-=-, Haase [Haa81], Flon and Suzuki [FS81], Elrad and Francez [EF84], Best [Bes82, Bes89], and Scholefield and Zedan [SZ92]. In [Bes89], a predicate transformer semantics and a state transformation seman... |

7 |
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(Show Context)
Citation Context ...dition semantics, to deal with partial correctness of sequential programs. The relation between this predicate transformer semantics and a state transformation semantics is considered by De Roever in =-=[Roe76]-=-. In [Bak77], De Bakker shows that there is a homomorphism from the state transformation semantics to the predicate transformer semantics. Plotkin shows, in [Plo79], that by refining the definitions t... |

7 |
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(Show Context)
Citation Context ...e refinements and endowments with orders can be done in various ways. Here, we will follow [Plo79]. Other isomorphism results of state transformations and predicate transformers are presented by Wand =-=[Wan77]-=-, Majster-Cederbaum [MC80], Best [Bes82], Smyth [Smy83, Smy92], Apt and Plotkin [AP86], and Bonsangue and Kok [BK92, BK93]. For an overview of these isomorphism results we refer the reader to [BK92]. ... |

4 |
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(Show Context)
Citation Context ...ial correctness of parallel programs are studied by Van Lamsweerde and Sintzoff [LS79], Haase [Haa81], Flon and Suzuki [FS81], Elrad and Francez [EF84], Best [Bes82, Bes89], and Scholefield and Zedan =-=[SZ92]-=-. In [Bes89], a predicate transformer semantics and a state transformation semantics are related. However, only parallel programs without recursion are considered. In this paper, we present a state tr... |

3 |
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- 1980
(Show Context)
Citation Context ...s with orders can be done in various ways. Here, we will follow [Plo79]. Other isomorphism results of state transformations and predicate transformers are presented by Wand [Wan77], Majster-Cederbaum =-=[MC80]-=-, Best [Bes82], Smyth [Smy83, Smy92], Apt and Plotkin [AP86], and Bonsangue and Kok [BK92, BK93]. For an overview of these isomorphism results we refer the reader to [BK92]. Introduction 3 Having disc... |

1 |
Sur les correspondences multivoques des emsembles
- Konig
- 1926
(Show Context)
Citation Context ...ation c 0 . Because IN is well-founded and by Property 2.6, all transition sequences are finite, i.e. all paths in the tree are finite. By induction, the tree is finitely branching. By Konig's lemma (=-=[Kon26]-=-), the tree has only a finite number of paths. Consequently, the set (2.1) is finite. Obviously, (2.1) is a nonempty set. ut The well-definedness of the state transformation semantics O st is conclude... |