## An abstract account of composition (1995)

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Venue: | MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE |

Citations: | 15 - 1 self |

### BibTeX

@INPROCEEDINGS{Abadi95anabstract,

author = {Martín Abadi and Stephan Merz},

title = {An abstract account of composition},

booktitle = {MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE},

year = {1995},

pages = {499--508},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

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### Abstract

We presentalogic of specifications of reactive systems. The logic is independent of particular computational models, but it captures common patterns of reasoning with assumption-commitment specifications. We use the logic for deriving proof rules for TLA and CTL specifications.

### Citations

1108 | Temporal and Modal Logic
- Emerson
- 1990
(Show Context)
Citation Context ... well-founded structures, for example in the context of branching-time logics. The next section introduces our abstract logic. Sections 3 and 4 apply the logic to justify rules for TLA [16] andforCTL =-=[8]-=-. Section 5, in conclusion, discusses the results. 2 A logic of speci cations Our logic of speci cations is a propositional intuitionistic logic. We use the standard connectives ^ and !. In addition, ... |

806 | The temporal logic of actions
- Lamport
- 1991
(Show Context)
Citation Context ...ider non-linear well-founded structures, for example in the context of branching-time logics. The next section introduces our abstract logic. Sections 3 and 4 apply the logic to justify rules for TLA =-=[16]-=- andforCTL [8]. Section 5, in conclusion, discusses the results. 2 A logic of speci cations Our logic of speci cations is a propositional intuitionistic logic. We use the standard connectives ^ and !.... |

179 |
What good is temporal logic
- Lamport
(Show Context)
Citation Context ... of the expressiveness of CTL , which allows many di erent styles of assumption-commitment speci cations. We restrict attention to the fragment ofCTLwhere formulas are invariant under nite stuttering =-=[15]-=-|speci cally, we do not allow the next-time operator. Formulas of branching-time temporal logics are normally interpreted over in nite trees. They include state formulas, which are evaluated at a stat... |

159 |
Proofs of networks of processes
- Misra, Chandy
- 1981
(Show Context)
Citation Context ...nts are postconditions and the assumptions are preconditions. In the broader realm of reactive systems, which we consider in this paper, there are several forms of assumption-commitment speci cations =-=[17, 11,18,1,2,19,6,22,7,12]-=-. An assumption-commitment speci cation for a component of a reactive system consists of a formula A, which expresses assumptions about the environment, and a formula C, which expresses the requiremen... |

139 |
Tentative steps toward a development method for interfering programs
- Jones
- 1983
(Show Context)
Citation Context ...nts are postconditions and the assumptions are preconditions. In the broader realm of reactive systems, which we consider in this paper, there are several forms of assumption-commitment speci cations =-=[17, 11,18,1,2,19,6,22,7,12]-=-. An assumption-commitment speci cation for a component of a reactive system consists of a formula A, which expresses assumptions about the environment, and a formula C, which expresses the requiremen... |

70 | Modular model checking
- Kupferman, Vardi
- 1998
(Show Context)
Citation Context ...served by composition. i2IJosko [13, 14] has suggested representing an assumption-commitment speci - cation as a pair (A� C) where A is a linear-time formula and C is a branching-time formula� Vardi =-=[21]-=- has studied the complexity of model-checking for speci cations of this form. With Josko's de nitions, a tree M satis es a speci cation (A� C) with assumption A and commitment C i M 0 j= C where M 0 i... |

43 |
Conjoining speci cations
- Abadi, Lamport
- 1995
(Show Context)
Citation Context ...nts are postconditions and the assumptions are preconditions. In the broader realm of reactive systems, which we consider in this paper, there are several forms of assumption-commitment speci cations =-=[17, 11,18,1,2,19,6,22,7,12]-=-. An assumption-commitment speci cation for a component of a reactive system consists of a formula A, which expresses assumptions about the environment, and a formula C, which expresses the requiremen... |

34 | A logical view of composition
- Abadi, Plotkin
- 1992
(Show Context)
Citation Context ...methods. However, we do not attempt to capture every aspect of these speci cation methods� we focus on simple, basic results with broad applicability. Our logic borrows from that of Abadi and Plotkin =-=[5]-=-. In particular, we take the idea of using intuitionistic reasoning for assumption-commitment speci cations. However, for the sake of simplicity and generality, we do not adopt some non-standard const... |

26 | Composition of assumption-commitment specifications in a UNITY style. Science of Computer Programming, 23:107–126
- Collette
- 1994
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Citation Context |

21 |
Logic with truth values in a linearly ordered Heyting algebra
- Horn
- 1969
(Show Context)
Citation Context ...istically valid, for example: i2I ((P1 ! P2) ! Q) ^ ((P2 ! P1) ! Q) ! Q This formula is a disjunction-free version of the traditional formula (P1 ! P2)_ (P2 ! P1), which expresses a kind of linearity =-=[10]-=-. In the previous work on TLA, the composition of speci cations is their conjunction, and re nement is implication. The assumption-commitment speci cation with assumption A and commitment C is either ... |

15 |
Verifying the correctness of AADL modules using model checking
- Josko
- 1990
(Show Context)
Citation Context ...ion of the speci cations of the modules. The application of our theorems as composition rules will therefore require additional arguments. This complication is not unique to our work� several authors =-=[13, 9]-=- have advocated restricting commitments to the fragment 8CTL in order to ensure that speci cations are preserved by composition. i2IJosko [13, 14] has suggested representing an assumption-commitment ... |

9 |
Model checking and modular veri cation
- Grumberg, Long
- 1994
(Show Context)
Citation Context ...ion of the speci cations of the modules. The application of our theorems as composition rules will therefore require additional arguments. This complication is not unique to our work� several authors =-=[13, 9]-=- have advocated restricting commitments to the fragment 8CTL in order to ensure that speci cations are preserved by composition. i2IJosko [13, 14] has suggested representing an assumption-commitment ... |

9 |
Assumption/commitment rules for networks of asynchronously communicating agents
- len, Dederichs, et al.
- 1993
(Show Context)
Citation Context |

8 | A Logic for
- Plotkin, Abadi
- 1993
(Show Context)
Citation Context ...perty ifF holds of an in nite sequence whenever it holds of all its nite pre xes. The connective ^ and ) are the usual, classical ones� several interesting, additional connectives are de nable in TLA =-=[3]-=-: { C(F ) holds of a sequence i F holds of all nite pre xes of . { F ;. Gholds of i , for all ( nite or in nite) pre xes of ,ifF holds of then so does G. Although ;. is strictly stronger than ), F ) G... |

6 |
A logical view of composition and re nement
- Abadi, Plotkin
- 1991
(Show Context)
Citation Context ... of P1�:::�P n implies P . Proposition2. The following sequents are derivable: P + ! Q� P + ! (Q ! R) ` P + ! R (1) ^ (P +! i Qi) ` ( ^ Pi) + ! ( ^ Qi) (2) i2I i2I i2I P + ! Q ` P ! Q (3) P + ! P ` P =-=(4)-=- Sequents (1) and (2) state implication-like properties of + !.Sequent(3)says that + ! is stronger than !. Sequent (4) can be understood as an abstract formulation of computational induction. Beyond t... |

6 | On unifying assumption-commitment style proof rules for concurrency
- Xu, Cau, et al.
- 1994
(Show Context)
Citation Context |

1 |
Assumption/guarantee speci cations in lineartime temporal logic
- Jonsson, Tsay
- 1995
(Show Context)
Citation Context |

1 |
Modular speci cation and veri cation of reactive systems
- Josko
- 1993
(Show Context)
Citation Context ...mplication is not unique to our work� several authors [13, 9] have advocated restricting commitments to the fragment 8CTL in order to ensure that speci cations are preserved by composition. i2IJosko =-=[13, 14]-=- has suggested representing an assumption-commitment speci - cation as a pair (A� C) where A is a linear-time formula and C is a branching-time formula� Vardi [21] has studied the complexity of model-... |