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D-oids: a model for dynamic data-types †

Published online by Cambridge University Press:  04 March 2009

Egidio Astesiano  and
Elena Zucca
Egidio Astesiano
Affiliation:
Dipartimento di Informatica e Scienze dell’Informazione, Via Dodecaneso 35, 16146 Genova (Italy) Email: {astes, zucca}@disi.unige.it
Elena Zucca
Affiliation:
Dipartimento di Informatica e Scienze dell’Informazione, Via Dodecaneso 35, 16146 Genova (Italy) Email: {astes, zucca}@disi.unige.it
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Abstract

We propose a semantic framework for dynamic systems, which, in a sense, extends the well-known algebraic approach for modelling static data structures to the dynamic case. The framework is based on a new mathematical structure, called a d-oid, consisting of a set of instant structures and a set of dynamic operations. An instant structure is a static structure, e.g. an algebra; a dynamic operation is a transformation of instant structures with an associated point to point map, which allows us to keep track of the transformations of single objects and thus is called a tracking map. By an appropriate notion of morphism, the d-oids over a dynamic signature constitute a category.

It is shown that d-oids can model object systems and support an abstract notion of possibly unique object identity; moreover, for a d-oid satisfying an identity preserving condition, there exists an essentially equivalent d-oid where the elements of instant structures are just names.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 5 , Issue 2 , June 1995 , pp. 257 - 282
Copyright
Copyright © Cambridge University Press 1995

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