## Object-oriented refinement and proof using behaviour functions (2000)

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Venue: | Proc. 3rd Workshop Rigorous Object-Oriented Methods |

Citations: | 1 - 0 self |

### BibTeX

@INPROCEEDINGS{Clark00object-orientedrefinement,

author = {Tony Clark},

title = {Object-oriented refinement and proof using behaviour functions},

booktitle = {Proc. 3rd Workshop Rigorous Object-Oriented Methods},

year = {2000}

}

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### Abstract

This paper proposes a new calculus for expressing the behaviour of object-oriented systems. The semantics of the calculus is given in terms of operators from computational category theory. The calculus aims to span the gulf between abstract specification and concrete implementation of object-oriented systems using mathematically verifiable properties and transformations. The calculus is compositional and can be used to express the behaviour of partial system views. The calculus is used to specify, analyse and refine a simple case study. 1

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Citation Context ...tension of, or complimentary to, [Cla97] [Eva98] [Eva99] and [Lan98]. The builtin operators of theso -calculus arise from Computational Category Theory. The reader is directed to [Bar90], [Ryd88] and =-=[Gog89]-=- for definitions 1 of the appropriate constructs and to [Cla99a] for a discussion of how these constructs are used in the development of object-oriented systems. This work differs from other approache... |

53 | The Structure and Semantics of Actor Languages - Agha - 1991 |

51 | Foundations of the unified modeling language
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Citation Context ...ormations. Theso -calculus can express partial views of a system and is therefore suitable as the basis for a semantics of UML [UML98] and as such can be seen as an extension of, or complimentary to, =-=[Cla97]-=- [Eva98] [Eva99] and [Lan98]. The builtin operators of theso -calculus arise from Computational Category Theory. The reader is directed to [Bar90], [Ryd88] and [Gog89] for definitions 1 of the appropr... |

49 | Sheaf semantics for concurrent interacting objects
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(Show Context)
Citation Context ...nd Proof using Behaviour Functions Tony Clark Department of Computing University of Bradford West Yorkshire BD7 1DP UK a.n.clark@scm.brad.ac.uk October 20, 1999 1 Introduction In [Gog75], [Ehr91] and =-=[Gog90]-=- Goguen et al. propose an abstract model of object systems based on standard constructions in Category Theory. They show how to use the constructions to build systems but do not propose a calculus for... |

45 |
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(Show Context)
Citation Context ...tructs but uses a logic rather than a -calculus to express models. Following Goguen, we propose that the behaviour of a system is a limit on a diagram of behaviours; diagrams are also used in [Ken99] =-=[Ken97]-=- where the aim is to express logical properties of data. Other calculi have been proposed as the basis for object-oriented systems, notably those defined in [Aba98]. Theso -calculus differs from other... |

43 | Reasoning with UML class diagrams
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(Show Context)
Citation Context ...s. Theso -calculus can express partial views of a system and is therefore suitable as the basis for a semantics of UML [UML98] and as such can be seen as an extension of, or complimentary to, [Cla97] =-=[Eva98]-=- [Eva99] and [Lan98]. The builtin operators of theso -calculus arise from Computational Category Theory. The reader is directed to [Bar90], [Ryd88] and [Gog89] for definitions 1 of the appropriate con... |

26 |
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Citation Context ...sing, verifying and transforming object-oriented system designs. 3 Theso -Calculus Theso -calculus is a notation for expressing object-oriented system designs. It is a standard normal order -calculus =-=[Han94]-=- [Plo75] extended with builtin operators [Lan64] for constructing behaviour functions in terms of behaviour products, coproducts, equalizers and morphisms. The syntax of theso -calculus is given in fi... |

18 |
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(Show Context)
Citation Context ...structs and to [Cla99a] for a discussion of how these constructs are used in the development of object-oriented systems. This work differs from other approaches with similar aims. The Object Calculus =-=[Bic97]-=- uses similar categorical constructs but uses a logic rather than a -calculus to express models. Following Goguen, we propose that the behaviour of a system is a limit on a diagram of behaviours; diag... |

7 | Rigorous development in uml
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- 1999
(Show Context)
Citation Context ... -calculus can express partial views of a system and is therefore suitable as the basis for a semantics of UML [UML98] and as such can be seen as an extension of, or complimentary to, [Cla97] [Eva98] =-=[Eva99]-=- and [Lan98]. The builtin operators of theso -calculus arise from Computational Category Theory. The reader is directed to [Bar90], [Ryd88] and [Gog89] for definitions 1 of the appropriate constructs ... |

6 | Visualizing Action Contracts in Object-Oriented Modeling
- Kent, Gil
(Show Context)
Citation Context ...cal constructs but uses a logic rather than a -calculus to express models. Following Goguen, we propose that the behaviour of a system is a limit on a diagram of behaviours; diagrams are also used in =-=[Ken99]-=- [Ken97] where the aim is to express logical properties of data. Other calculi have been proposed as the basis for object-oriented systems, notably those defined in [Aba98]. Theso -calculus differs fr... |

4 |
A Semantics for Object-Oriented Systems. Presented at the Third Northern Formal Methods Workshop
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- 1998
(Show Context)
Citation Context ...of object systems based on standard constructions in Category Theory. They show how to use the constructions to build systems but do not propose a calculus for expressing and reasoning about them. In =-=[Cla99a]-=-, [Cla99b] and [Cla99c] a calculus is proposed for expressing object systems based on Goguen's work. The calculus was shown to support incremental system development based on features of Computational... |

4 |
Sernadas, A.: A Categorical Model of Objects as Observed Processes
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- 1991
(Show Context)
Citation Context ...Refinement and Proof using Behaviour Functions Tony Clark Department of Computing University of Bradford West Yorkshire BD7 1DP UK a.n.clark@scm.brad.ac.uk October 20, 1999 1 Introduction In [Gog75], =-=[Ehr91]-=- and [Gog90] Goguen et al. propose an abstract model of object systems based on standard constructions in Category Theory. They show how to use the constructions to build systems but do not propose a ... |

3 | N.: A Semantics for Object-Oriented Design Notations
- Clark
- 1999
(Show Context)
Citation Context ...systems based on standard constructions in Category Theory. They show how to use the constructions to build systems but do not propose a calculus for expressing and reasoning about them. In [Cla99a], =-=[Cla99b]-=- and [Cla99c] a calculus is proposed for expressing object systems based on Goguen's work. The calculus was shown to support incremental system development based on features of Computational Category ... |

3 | N.: A Semantic Framework for Object-Oriented Development
- Clark
- 1999
(Show Context)
Citation Context ... on standard constructions in Category Theory. They show how to use the constructions to build systems but do not propose a calculus for expressing and reasoning about them. In [Cla99a], [Cla99b] and =-=[Cla99c]-=- a calculus is proposed for expressing object systems based on Goguen's work. The calculus was shown to support incremental system development based on features of Computational Category Theory [Ryd88... |