## 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

3643 | Communicating Sequential Processes
- Hoare
- 1985
(Show Context)
Citation Context ...ne 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 skip A 2 A. Given two pointed set... |

511 |
Conditional rewriting logic as a unified model of concurrency
- Meseguer
- 1992
(Show Context)
Citation Context ...ch can make it difficult to reason about systems and their components, although algebraic and categorical approaches to comparing classes of models promise to improve the situation (see, for example, =-=[17, 20]-=-). In 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 o... |

449 |
Introduction to Higher Order Categorical Logic
- Lambek, Scott
- 1986
(Show Context)
Citation Context ...lications. One interesting result is that for any small category C, the functor category LTS C is a topos. This means that any topology of a system gives rise, via the internal language of this topos =-=[12, 14]-=- to a logic in which properties of systems can be expressed and proved. A pleasant property of this logic is that it is `compositional' in the following sense: each sentence of the logic states some p... |

419 |
Category Theory for Computer Science
- Barr, Wells
- 1990
(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... |

273 | A classification of models for concurrency
- Sassone, Nielsen, et al.
- 1993
(Show Context)
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237 |
Categories for the working mathematician, volume 5 of Graduate Texts in Mathematics
- Lane
- 1998
(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... |

185 |
Basic category theory for computer scientists, Foundations of Computing Series
- 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... |

120 | 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 ... |

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

104 |
Eqlog: equality, types and generic modules for logic programming
- Goguen, Meseguer
- 1986
(Show Context)
Citation Context ...amples 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... |

103 |
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... |

49 | Sheaf semantics for concurrent interacting objects
- Goguen
- 1992
(Show Context)
Citation Context ...e 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 subobject... |

24 |
Mathematical representation of hierarchically organized systems
- Goguen
- 1971
(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... |

12 | 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)
Citation Context ...e 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 subobject... |

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... |

3 | A distributed semantics for FOOPS
- Cirstea
- 1995
(Show Context)
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... |

3 |
Systems and minimal realization
- Goguen
- 1972
(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... |

1 |
Distributed operational sematics
- Malcolm
- 1995
(Show Context)
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... |

1 |
Interconnection of object specifications. To appear
- Malcolm
- 1995
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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... |