Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-28T02:13:45.246Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalized implication equation languages

Published online by Cambridge University Press:  09 April 2009

Norman Y. Foo  and
Roslyn B. Riley
Norman Y. Foo
Affiliation:
Basser Department of Computer ScienceUniversity of SydneySydney, N.S.W. 2006, Australia
Roslyn B. Riley
Affiliation:
Basser Department of Computer ScienceUniversity of SydneySydney, N.S.W. 2006, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The calculus for equational implication languages given by Selman is generalized to handle the logical equivalent if the if…then…else… construct of high level programming languages. The relevance of these results to current investigations in the algebraic specifications of data types is discussed.

Keywords

implication languagealgebraic theorydecidabilitycompleteness.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 1 , August 1985 , pp. 101 - 106
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Buchi, J. R., ‘Weak second order arithmetic and finite automata’, Z. Math. Logik Grundlag. Math. 6 (1960), 66–92.CrossRefGoogle Scholar
[2]Goguen, J. A., Thatcher, J. W. and Wagner, E. G., ‘An initial algebra approach to the specification, correctness and of abstract data types’, Current Trends in programming methodology iv, Yeh, R. T. (ed.), pp. 80–149 (Prentice Hall, New Jersey, 1978).Google Scholar
[3]Guttag, J. V., ‘Some extensions to algebraic specifications’, pp. 63–67, Proceedings of ACM conference (Sigplan Notices 12, 1977).CrossRefGoogle Scholar
[4]Majster, M. E., ‘Limits of the ‘algebraic’ specification of abstract data types’, (ACM-Sigplan Notices 12, 1977).CrossRefGoogle Scholar
[5]Samet, H., ‘Effective on-line proofs of equalities and inequalities of formulas’, pp. 28–32, IEEE Transactions on Computers 29 (1980).CrossRefGoogle Scholar
[6]Selman, A., ‘Completeness of calculi for axiomatically defined classes of algebras’, J. Symbolic Logic 37 (1972), 433.Google Scholar
[7]Selman, A., ‘Completeness of calculi for axiomatically defined classes of algebras’, Algebra Universalis 2 (1) (1972), 20–32.CrossRefGoogle Scholar
[8]Thatcher, J. W., Wagner, E. and Wright, J., ‘Data types specification: parametrization and the power of specification techniques’, pp. 119–132, 10th ACM Symposium on the Theory of Computing, 1978.CrossRefGoogle Scholar