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Beyond conditional equations

Quasi-initial semantics for parametric algebraic specifications

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Book cover CAAP '92 (CAAP 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 581))

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Abstract

Inspired by the work of S. Kaplan about positive/negative conditional rewriting, we investigate initial semantics for algebraic specifications with Gentzen-formulas. Since the standard initial approach is limited to conditional equations (i.e. positive Horn-formulas), the notion of semi-initial and quasi-initial algebras is introduced and it is shown that all specifications with (positive) Gentzen-formulas admit quasi-initial models.

The whole approach is generalized to the parametric case where quasi-initiality generalizes to quasi-freeness. Since quasi-free objects need not be isomorphic, the persistency requirement is added to obtain a unique semantics for many interesting practical examples. Unique persistent quasi-free semantics can be described as a free construction when the parameter category is restricted to injective homomorphisms.

An example which does not admit a correct initial semantics but a correct unique persistent quasi-initial semantics demonstrates that the concepts introduced in this paper might be of some importance w.r.t. practical applications.

This work has been partly supported by the German Ministry of Research and Technology (BMFT) as part of the compound project ”KORSO — Korrekte Software“.

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Authors and Affiliations

  1. FB Informatik, Technische Universität Berlin, Sekr. FR 6-1, Franklinstr. 28/29, D-1000, Berlin 10

    Uwe Wolter & Michael Löwe

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  1. Uwe Wolter
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  2. Michael Löwe
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J. -C. Raoult

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© 1992 Springer-Verlag Berlin Heidelberg

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Wolter, U., Löwe, M. (1992). Beyond conditional equations. In: Raoult, J.C. (eds) CAAP '92. CAAP 1992. Lecture Notes in Computer Science, vol 581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55251-0_19

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  • DOI: https://doi.org/10.1007/3-540-55251-0_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55251-2

  • Online ISBN: 978-3-540-46799-1

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