## OBJECT-ORIENTED SPECIFICATIONS: SET-THEORY BASED AND ALGEBRAIC APPROACHES. A REVIEW (2002)

### BibTeX

@MISC{Senoshenko02object-orientedspecifications:,

author = {Kirill O. Senoshenko and Им. А. П. Ершова and Сеношенко К. О},

title = {OBJECT-ORIENTED SPECIFICATIONS: SET-THEORY BASED AND ALGEBRAIC APPROACHES. A REVIEW},

year = {2002}

}

### OpenURL

### Abstract

In this review, the main trends in object-oriented dynamic system specification are discussed. A classification for the specification approaches is given basing on the underlying model of system state; several representatives from different categories are presented. For each approach, a special attention is given to the completeness of support of various OO concepts, ability to define not only static aspects of the system but also its behavior and the specification transparency. Finally, a comparative review of the selected languages and formalisms is provided and directions for further work are outlined.

### Citations

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Citation Context ...ystems. In terms of the standard life cycle, it supports expression of requirements, design and specification. Support for implementation is now possible only via translation to a notation, such as B =-=[13]-=-, which also allows the use of the semantic analysis facilities of the latter. The concrete syntax of the language is quite different from that of Z and Object-Z. It was chosen in order to stress the ... |

153 |
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Citation Context ...of states and operations — this group of languages seems to be well-suited for being adapted to the object-oriented paradigm. One of the most widely used set-theory based specification languages is Z =-=[10]-=-. Several object-oriented extensions of Z have been developed; among them, we focus on Object-Z and Z++. 3.1 Object-Z The specification language Object-Z is Z extended to facilitate specification in a... |

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Citation Context ...ir of Σ2-algebras A2’ and A2″ and any morphism g between them; uh: IDAlg(Σ2) → Vh ○ Freeh is called a universal transformation. For the proof of existence of uh and Freeh and further details refer to =-=[9]-=-. – An algebraic specification consists of a signature and a set of (positive conditional) equations E. The translation f # (E) induced by the signature morphism f is understood conventionally (in eac... |

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Citation Context ...xistence of axiomatic and denotational semantics and the first tools. Semantics of Object-Z is usually given on the basis of that of Z with the help of the metalanguage, such as the one introduced in =-=[11]-=-, which allows the meaning of Object-Z constructs to be formally expressed in terms of constructs of Z. Semantics of both Z and Object-Z are based on the set theory, and they use first-order logic to ... |

11 | An algebraic semantics for the object specification language TROLL light
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Citation Context ...vents of different objects, as well as object creation and destruction, cannot be expressed. The semantics of TROLL is mostly informal; in contrast, the algebraic semantics of TROLL light is given in =-=[17]-=-. The underlying model of an object community is an algebraic transition system, where both the state and the state transformation caused by finite sets of events are represented as algebras. A single... |

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Citation Context ...ly, object creation and deletion are modeled. 4.2 TROLL TROLL (Textual Representation of an Object Logic Language) is designed for the conceptual modeling and subsequent design of information systems =-=[15,16]-=-. The emphasis is on combining conceptual modeling and formal specification techniques with techniques for describing distribution and concurrency. As the main abstractions, TROLL supports classes, ro... |

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C.: Protocol specification and analysis
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Citation Context ... for detailed description of global relationships and constraints. The language allows more expressive data type definitions, component definitions and system behavior specifications. 4.3 Maude Maude =-=[19,20]-=- is an object-oriented executable specification language and a system supporting both equational and rewriting logic concurrent computation for a wide range of applications, including automated proof ... |

7 | A formal framework with late binding
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Citation Context ... a state. One of the most fundamental works on specifying classes and relations between them is done by F. Parisi-Presicce and A. Pierantonio. Late binding of object methods is formally introduced in =-=[6]-=-. These two works are presented below. 2.1 Relations between classes The approach proposed in [7,8] is intended to give a strict algebraic definition of the notion of a class and to formalize the conc... |

4 |
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Citation Context ...t theory (a state is a family of sets and bags), – the algebraic approach (a state is an algebra), – Petri nets / algebraic nets (a state is a net). There are representatives for each of these groups =-=[1,2]-=- that additionally involve the temporal logic in describing dynamic properties of a system though it is not always the case. Because of the limited size of this review, only the languages from the fir... |

4 |
Structured inheritance for algebraic class specifications
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Citation Context ...one by F. Parisi-Presicce and A. Pierantonio. Late binding of object methods is formally introduced in [6]. These two works are presented below. 2.1 Relations between classes The approach proposed in =-=[7,8]-=- is intended to give a strict algebraic definition of the notion of a class and to formalize the concepts of inheritance, actualization, combination, etc., which are considered as binary relations bet... |

3 |
Making static dynamic: Towards an axiomatization for dynamic ADT's
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Citation Context ...atic part of a dynamic system and cannot be regarded as a complete model of it. One of possible extensions of this approach that supports complex evolving object communities is formally introduced in =-=[14]-=-. The intent is to define an object transition system (OTS) in which every state is represented by an algebra that contains both objects and object values. The set of possible values is determined by ... |

2 |
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Citation Context ...t theory (a state is a family of sets and bags), – the algebraic approach (a state is an algebra), – Petri nets / algebraic nets (a state is a net). There are representatives for each of these groups =-=[1,2]-=- that additionally involve the temporal logic in describing dynamic properties of a system though it is not always the case. Because of the limited size of this review, only the languages from the fir... |

1 |
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Citation Context .... Because of the limited size of this review, only the languages from the first two groups, which are most widely used nowadays, are discussed below. Approaches representing the system state as a net =-=[3,4,5]-=- are rather specific and have a limited range of application while the intent is to compare generalpurpose object-oriented specification languages. The paper is organized as follows. A pure algebraic ... |

1 |
Cooperative Nets // Lect
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Citation Context .... Because of the limited size of this review, only the languages from the first two groups, which are most widely used nowadays, are discussed below. Approaches representing the system state as a net =-=[3,4,5]-=- are rather specific and have a limited range of application while the intent is to compare generalpurpose object-oriented specification languages. The paper is organized as follows. A pure algebraic ... |

1 |
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Citation Context ...one by F. Parisi-Presicce and A. Pierantonio. Late binding of object methods is formally introduced in [6]. These two works are presented below. 2.1 Relations between classes The approach proposed in =-=[7,8]-=- is intended to give a strict algebraic definition of the notion of a class and to formalize the concepts of inheritance, actualization, combination, etc., which are considered as binary relations bet... |

1 |
Saake G. Specifying Information System Dynamics
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Citation Context ...ly, object creation and deletion are modeled. 4.2 TROLL TROLL (Textual Representation of an Object Logic Language) is designed for the conceptual modeling and subsequent design of information systems =-=[15,16]-=-. The emphasis is on combining conceptual modeling and formal specification techniques with techniques for describing distribution and concurrency. As the main abstractions, TROLL supports classes, ro... |

1 |
Futatsugi K., Jouannaud J.-P. Introducing OBJ
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Citation Context ...hic protocols and network applications. Maude uses and extends the algebraic specification paradigm, and its equational logic sublanguage essentially includes a well-known specification language OBJ3 =-=[21]-=-. The language consists of the basic part (Core Maude) and its reflection called Full Maude. Core Maude supports module hierarchies consisting of (nonparameterized) functional and system modules and p... |

1 |
Object-Oriented Specification by Typed Gurevich
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(Show Context)
Citation Context ...isfied in the model. The exchange equation states that rewrite rules can be applied in any order, sequentially or simultaneously. 4.4 Object-Oriented Abstract State Machines The approach presented in =-=[22]-=- uses the mechanism of Typed Abstract State Machines (TASMs) [23] to provide means of object-oriented specification of complex evolving systems. The specification of such a system includes specificati... |

1 |
Typed Gurevich Machines Revisited // Joint NCC
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Citation Context ...les can be applied in any order, sequentially or simultaneously. 4.4 Object-Oriented Abstract State Machines The approach presented in [22] uses the mechanism of Typed Abstract State Machines (TASMs) =-=[23]-=- to provide means of object-oriented specification of complex evolving systems. The specification of such a system includes specifications of data types representing the static part of a system, objec... |

1 |
Generic Facilities in Object-Oriented ASMs // Lect. Notes Comput
- Zamulin
(Show Context)
Citation Context ...ures of the object-oriented paradigm (inheritance, polymorphism, subtyping) are fully supported. The above approach can be extended to provide means of specifying the constrained generic object types =-=[24]-=-. 36s5 CONCLUSIONS In this review, the main trends in object-oriented dynamic system specification have been discussed. Now we briefly summarize the results of the discussion. Pure algebraic specifica... |