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Abstractions of data types

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Abstract

The use of abstraction in the context of abstract data types, is investigated. Properties to be checked are formulas in a first order logic under Kleene's 3-valued interpretation. Abstractions are defined as pairs consisting of a congruence and a predicate interpretation. Three types of abstractions are considered,∀∀, ∀∃ and ∃0,1∀, and for each of them corresponding property preservation results are established. An abstraction refinement property is also obtained. It shows how one can pass from an existing abstraction to a (less) finer one. Finally, equationally specified abstractions in the context of equationally specified abstract data types are discussed and exemplified.

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Authors and Affiliations

  1. School of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL, 32816, USA

    Ferucio Laurenţiu Ţiplea

  2. Department of Computer Science, “Al. I. Cuza” University, Iaşi, 740083, Romania

    Constantin Enea

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  1. Ferucio Laurenţiu Ţiplea
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  2. Constantin Enea
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Correspondence to Ferucio Laurenţiu Ţiplea.

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On leave from the Department of Computer Science, “Al. I. Cuza” University, Iaşi 740083, Romania

The research reported in this paper was partially supported by the program ECO-NET 08112WJ/2004-2005 and by the National University Research Council of Romania, grants CNCSIS 632(28)/2004 and CNCSIS 632(50)/2005.

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Ţiplea, F.L., Enea, C. Abstractions of data types. Acta Informatica 42, 639–671 (2006). https://doi.org/10.1007/s00236-006-0010-3

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  • DOI: https://doi.org/10.1007/s00236-006-0010-3

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