## Distributed Operational Semantics for the Object Paradigm (1997)

Venue: | Oxford University Computing Laboratory |

Citations: | 1 - 0 self |

### BibTeX

@INPROCEEDINGS{Malcolm97distributedoperational,

author = {Grant Malcolm and Corina Cirstea},

title = {Distributed Operational Semantics for the Object Paradigm},

booktitle = {Oxford University Computing Laboratory},

year = {1997}

}

### OpenURL

### Abstract

this paper we present an approach we call `Distributed Operational Semantics', which models systems of concurrent, interacting objects by diagrams which assign an operational semantics to each object in a system. The behaviour of the whole system is given by a limit construction. In modelling behaviour by limits we follow earlier work by Goguen on Categorical Systems Theory [4, 5, 6]. This approach pays particular attention to the hierarchical structure of systems, and provides means of constructing systems from component parts in a way that captures both complex objects and parallel composition with synchronisation [16]. The operational semantics of objects can be very general: for example, a semantics for the object-oriented specification language FOOPS has been given by modelling objects as unlabelled transition systems; this semantics is summarised in Section 4.2, and a full account is given in [2]. We shall also present examples of systems that use labelled transition systems. A useful property of the examples we present is that they can be readily translated into specifications in the logic programming language Eqlog [9], which provides both a simulator for the system and a logic for reasoning about systems. Like the sheaf semantics for concurrent objects originating with Goguen [8, 3] and further investigated in [22, 16, 2], our approach is essentially constraint based: interactions between objects constrain their possible behaviours, primarily by synchronising on shared subobjects. Constructing the behaviour of a system by taking its limit corresponds to solving those constraints. It is because of its constraint based nature that the translation into Eqlog is so natural. This paper provides a short introduction to Distributed Operational Semantics; a fuller acco...

### Citations

3423 | Communicating sequential processes
- HOARE
- 1978
(Show Context)
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479 |
Conditional rewriting logic as a unified model of concurrency
- Meseguer
- 1992
(Show Context)
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429 |
Higher Order Categorical Logic
- Lambek, Scott
- 1986
(Show Context)
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395 |
Category theory for computing science
- Barr, Wells
- 1990
(Show Context)
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263 | Models for Concurrency
- Winskel, Nielsen
- 1995
(Show Context)
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218 |
Categories for the working mathematician, volume 5 of Graduate Texts in Mathematics
- Lane
- 1998
(Show Context)
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172 |
Basic Category Theory for Computer Scientists
- PIERCE
- 1991
(Show Context)
Citation Context ...ries Category theory allows an attractively abstract treatment of many constructions in mathematics and computer science. We give only a few basic definitions here; good introductions can be found in =-=[1, 7, 13, 19]-=-. A category C consists of the following: ffl a class jCj of objects; ffl a class kCk of morphisms (sometimes called `arrows'); ffl two maps @ 0 ; @ 1 : kCk ! jCj, which give, respectively, the source... |

112 | A calculus of mobile processes (parts i and ii
- Milner, Parrow, et al.
- 1992
(Show Context)
Citation Context ... actions label the transitions from one state to another. We find it convenient to assume that there is always an `idle transition', an action that does nothing, similar to thesaction of Milner's CCS =-=[18, 20]-=- or the `skip' action of CSP [11]. The following definition gives us a notion of a set of actions which contains an idle transition. Definition 3 A pointed set is a set A with a distinguished element ... |

101 | A categorical manifesto
- Goguen
- 1991
(Show Context)
Citation Context |

101 |
Eqlog: Equality, Types and Generic Modules for Logic Programming
- Goguen, Meseguer
- 1986
(Show Context)
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99 |
Unifying functional, object-oriented and relational programming with logical semantics
- Goguen, Meseguer
- 1987
(Show Context)
Citation Context ...true and SB --[AB]-? SB' == true and aps(SA') == SP' and bps(SB') == SP' . endo 4.2 Distributed Semantics for FOOPS (Only a sketch. A full account is given in [2].) The distributed semantics of FOOPS =-=[10]-=- is given by the limit of a functor from the category sketched in Figure 1 to the category of unlabelled transition systems. In this figure, ffifl fflfi ME i i i i i i) i i i i i1 j OC1;1 h TC1;1 \Del... |

46 | Sheaf semantics for concurrent interacting objects
- Goguen
- 1992
(Show Context)
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24 |
Mathematical Representation of Hierarchically Organized Systems Global Systems Dynamics, Ed
- GOGUEN
- 1970
(Show Context)
Citation Context ...mantics to each object in a system. The behaviour of the whole system is given by a limit construction. In modelling behaviour by limits we follow earlier work by Goguen on Categorical Systems Theory =-=[4, 5, 6]-=-. This approach pays particular attention to the hierarchical structure of systems, and provides means of constructing systems from component parts in a way that captures both complex objects and para... |

11 | A compositional proof system on a category of labelled transition systems - Winskel - 1990 |

7 |
Amilcar Sernadas. A categorial theory of objects as observed processes
- Ehrich, Goguen
- 1991
(Show Context)
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4 |
A sheaf semantics for FOOPS expressions (extended abstract
- Wolfram, Goguen
- 1992
(Show Context)
Citation Context ...[9], which provides both a simulator for the system and a logic for reasoning about systems. Like the sheaf semantics for concurrent objects originating with Goguen [8, 3] and further investigated in =-=[22, 16, 2]-=-, our approach is essentially constraint based: interactions between objects constrain their possible behaviours, primarily by synchronising on shared subobjects. Constructing the behaviour of a syste... |

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- Cirstea
- 1995
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Citation Context ... for the object-oriented specification language FOOPS has been given by modelling objects as unlabelled transition systems; this semantics is summarised in Section 4.2, and a full account is given in =-=[2]-=-. We shall also present examples of systems that use labelled transition systems. A useful property of the examples we present is that they can be readily translated into specifications in the logic p... |

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Systems and minimal realization
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- 1972
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Citation Context ...mantics to each object in a system. The behaviour of the whole system is given by a limit construction. In modelling behaviour by limits we follow earlier work by Goguen on Categorical Systems Theory =-=[4, 5, 6]-=-. This approach pays particular attention to the hierarchical structure of systems, and provides means of constructing systems from component parts in a way that captures both complex objects and para... |

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- 1995
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Citation Context ...nstraint based nature that the translation into Eqlog is so natural. This paper provides a short introduction to Distributed Operational Semantics; a fuller account will be given in a companion paper =-=[15]-=- (in particular, that paper will show that, for certain operational semantics, systems give rise to a topos, whose internal language provides a logic for proving properties of systems' behaviours). Th... |

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Interconnection of object specifications. To appear
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Citation Context ...ion to the hierarchical structure of systems, and provides means of constructing systems from component parts in a way that captures both complex objects and parallel composition with synchronisation =-=[16]-=-. The operational semantics of objects can be very general: for example, a semantics for the object-oriented specification language FOOPS has been given by modelling objects as unlabelled transition s... |