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Beyond conditional equations

Quasi-initial semantics for parametric algebraic specifications
  • Uwe Wolter
  • Michael Löwe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 581)

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.

Keywords

Minimal Covering Forgetful Functor Initial Covering Conditional Equation Consistent Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Uwe Wolter
    • 1
  • Michael Löwe
    • 1
  1. 1.FB InformatikTechnische Universität BerlinBerlin 10

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