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Partially-additive monoids, graph-growing, and the algebraic semantics of recursive calls

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Graph-Grammars and Their Application to Computer Science and Biology (Graph Grammars 1978)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 73))

Abstract

The way in which Pfn (sets and partial functions) provides a setting for the semantics of deterministic programs [and Rel (sets and relations) provides a setting for the semantics of nondeterministic programs] has led us to axiomatize the notion of a partially-additive monoid. We show that programs incorporating procedure calls may be represented by graph grammars, with one non-terminal and production for each distinct procedure (including the program itself). Program execution may be construed as a process of interpretation of graphs obtained by repeated graph substitution. We show that the resultant interpretive semantics yields the same result as our theory of the canonical fixpoint for abstract recursion schemes introduced in an earlier paper.

International Workshop on Graph Grammars and their Applications to Computer Science and Biology, October 30-November 3, 1978, Bad Honnef, West Germany.

The research reported in this paper was supported in part by the National Science Foundation under grant MCS 76-84477.

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References

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Authors and Affiliations

  1. Computer and Information Science, USA

    M. A. Arbib

  2. Mathematics Department, University of Massachusetts, 01003, Amherst, MA, USA

    E. G. Manes

Authors
  1. M. A. Arbib
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  2. E. G. Manes
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Volker Claus Hartmut Ehrig Grzegorz Rozenberg

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© 1979 Springer-Verlag Berlin Heidelberg

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Arbib, M.A., Manes, E.G. (1979). Partially-additive monoids, graph-growing, and the algebraic semantics of recursive calls. In: Claus, V., Ehrig, H., Rozenberg, G. (eds) Graph-Grammars and Their Application to Computer Science and Biology. Graph Grammars 1978. Lecture Notes in Computer Science, vol 73. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0025716

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  • DOI: https://doi.org/10.1007/BFb0025716

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09525-5

  • Online ISBN: 978-3-540-35091-0

  • eBook Packages: Springer Book Archive

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