Advertisement

Correctness of recursive flow diagram programs

  • J. A. Goguen
  • J. Meseguer
Appendix
Part of the Lecture Notes in Computer Science book series (LNCS, volume 53)

Abstract

This paper presents a simple algebraic description of the semantics of non-deterministic recursive flow diagram programs with parallel assignment, culminating in a method for proving their partial correctness which generalizes the well-known Floyd-Naur method for ordinary flow diagram programs. Our treatment involves first considering a program scheme, and then interpreting it in an appropriate semantic model. The program schemes are conveniently viewed as diagrams in an algebraic theory, with semantic model a relational algebra. Some examples are given in a simple programming language whose features correspond precisely to our algebraic framework.

Keywords

Natural Transformation Partial Function Semantic Model Target Node Universal Property 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    ADJ (coauthored by J. A. Goguen, J. W. Thatcher, E.C. Wagner and J. B. Wright) (1975) "An introduction to categories, algebraic theories and algebras," IBM Research Report RC 5369.Google Scholar
  2. 2.
    (1976) "A junction between computer science and category theory: I, Basic definitions and examples," Part 2, IBM Research Report RC 5908.Google Scholar
  3. 3.
    Burstall, R. M. (1972) "An algebraic description of programs with assertions, verification, and simulation," Proc ACM Confr. Proving Assertions about programs, Las Cruces, New Mexico, 7–14.Google Scholar
  4. 4.
    Eilenberg, S., and Wright, J. B. (1967) "Automata in general algebras," Inf. Control 11, 452–470.CrossRefGoogle Scholar
  5. 5.
    Goguen, J. A. (1974) "On homomorphisms, correctness termination, unfoldments and equivalence of flow diagram programs," J. Comp. Sys. Sci. 8, 333–365.Google Scholar
  6. 6.
    (1974a) "Set theoretic correctness proofs," Semantics and Theory of Computation Report No. 1, UCLA Computer Science Dept.Google Scholar
  7. 7.
    Lawvere, F. W. (1963) "Functorial semantics of algebraic theories," thesis, Columbia University; summarized in Proc. Ntl. Acad. Sci. U.S.A. 50, 869–872.Google Scholar
  8. 8.
    Mac Lane, S. (1971) Category Theory for the Working Mathematician, Springer-Verlag.Google Scholar
  9. 9.
    Pareigis, B. (1970) Categories and functors, Academic Press, New York.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • J. A. Goguen
    • 1
  • J. Meseguer
    • 2
  1. 1.Computer Science DepartmentUCLALos AngelesUSA
  2. 2.Departamento de Algebra y Fundamentos, Facultad de CienciasSantiago de CompostelaSpain

Personalised recommendations