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Volume 5 - September 1995

Contents

Page 2 of 2

Research Article

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

  • Egidio Astesiano, Elena Zucca
  • Published online by Cambridge University Press:
    04 March 2009, pp. 257-282

  • 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.

  • A note on the structure of bilattices

  • A. Avron
  • Published online by Cambridge University Press:
    04 March 2009, pp. 431-438

  • A notion of bilattice was first proposed by Ginsberg as a general framework for many applications. Related notions were further investigated and applied for various goals by Fitting. In the present paper a general definition of bilattices is proposed, which covers all particular cases that have actually been used in the literature. It is shown also that in the finite case every bilattice in our sense is graphically representable by a special type of a two-dimensional diagram.

Front matter

  • MSC volume 5 issue 1 Cover and Front matter

  • Published online by Cambridge University Press:
    04 March 2009, pp. f1-f2
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Research Article

  • Order-enrichment for categories of partial maps

  • Marcelo P. Fiore
  • Published online by Cambridge University Press:
    04 March 2009, pp. 533-562

  • Motivated by a desire to treat non-termination directly in the semantics of computation, the notion of approximation between programs is studied in the context of categories of partial maps. In particular, contextual approximation and specialisation are considered and shown to coincide. Moreover, after exhibiting the approximation between total maps as a primitive notion, from an arbitrary (or axiomatic) approximation order on total maps a computationally natural approximation order on partial maps is derived. The main technical contribution is a characterisation of when this approximation order between partial maps is domain-theoretic (in the sense that the category of partial maps Cpo-enriches) provided that the approximation order between total maps is also.

Author Index

Front matter

  • MSC volume 5 issue 3 Cover and Front matter

  • Published online by Cambridge University Press:
    04 March 2009, pp. f1-f2
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Back matter

  • MSC volume 5 issue 1 Cover and Back matter

  • Published online by Cambridge University Press:
    04 March 2009, pp. b1-b5
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Research Article

  • Compositionality and compatibility of parameterization and parameter passing in specification languages

  • Rosa M. Jiménez, Fernando Orejas, Hartmut Ehrig
  • Published online by Cambridge University Press:
    04 March 2009, pp. 283-314

  • In this paper we continue previous work by Sannella, Sokolowski and Tarlecki on parameterization in specification languages. Within the loose approach, we define specification and model level semantics for two kinds of parameterizations (parameterized specifications and specifications of parameterized data types) and describe, in a compositional manner, parameter passing at both levels. Moreover, the specification and the model level semantics of parameter passing are shown to be compatible. We also show that the results obtained do not only apply to the loose approach but can also be directly applicable to the initial framework, and in general to any other kind of monomorphic framework (i.e., a framework where all specifications are monomorphic). In particular, the results obtained generalize and extend previous results for the initial approach. Finally, to obtain our results, new categorical constructions of multiple pushouts, amalgamations and extensions, which generalize standard notions of pushouts, amalgamations and extensions, had to be introduced.

Back matter

  • MSC volume 5 issue 3 Cover and Back matter

  • Published online by Cambridge University Press:
    04 March 2009, pp. b1-b4
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Front matter

  • MSC volume 5 issue 2 Cover and Front matter

  • Published online by Cambridge University Press:
    04 March 2009, pp. f1-f2
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  • MSC volume 5 issue 4 Cover and Front matter

  • Published online by Cambridge University Press:
    04 March 2009, pp. f1-f2
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Back matter

  • MSC volume 5 issue 4 Cover and Back matter

  • Published online by Cambridge University Press:
    04 March 2009, pp. b1-b4
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  • MSC volume 5 issue 2 Cover and Back matter

  • Published online by Cambridge University Press:
    04 March 2009, pp. b1-b4
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Page 2 of 2