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Partial algebras flow from algebraic specifications

  • Petri Nets, Algebraic Specification
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 267))

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Abstract

The aim of this paper is to introduce and to investigate a method for specifying algebras with partial functions, while maintaining the simpler framework of total algebras and conventional specifications. For this purpose, an ordinary algebraic specification SPEC is equipped with a subspecification BASE, and each SPEC-algebra is equipped with a BASE-homomorphism distinguishing a BASE-part of the SPEC-algebra. These modifications, yielding the notions of based specification and of based algebra, do not seriously affect the semantic properties of algebraic specifications. In particular, the initial SPEC-algebra can simply be transformed into an initial based algebra. Then one can restrict a SPEC-algebra to its distinguished BASE-part. In this way, one gets a SPEC-algebra with operations that may be partial. The construction applies especially to the initial based algebra, the operations of which can be shown to be computable in a certain sense. Conversely, it turns out that each computable function on natural numbers can be specified as an operation of the initial based algebra of a based specification.

The work was partly done while I participated in the IBM World Trade Visiting Faculty Program at the Thomas J. Watson Research Center in Yorktown Heights, New York.

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Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Universität Bremen, D-2800, Bremen 33

    Hans-Jörg Kreowski

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  1. Hans-Jörg Kreowski
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Thomas Ottmann

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© 1987 Springer-Verlag Berlin Heidelberg

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Kreowski, HJ. (1987). Partial algebras flow from algebraic specifications. In: Ottmann, T. (eds) Automata, Languages and Programming. ICALP 1987. Lecture Notes in Computer Science, vol 267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18088-5_45

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  • DOI: https://doi.org/10.1007/3-540-18088-5_45

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18088-3

  • Online ISBN: 978-3-540-47747-1

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