Abstract
An algebraic analogue to domain equations as known from denotational semantics is presented. A set of mutually recursive algebraic domain equations is roughly speaking a set of parameterized algebraic specifications applying instances of each other in a recursive fashion. The solution to a set of algebraic domain equations can be constructed by using a new parameter passing technique called recursive parameter passing. The theory also covers the notion of parameterized algebraic domain equations and it is shown that the result of successive actualization and recursive parameter passing is independent of the order. The specification method makes sense under an arbitrary institution.
Keywords
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.
References
M. A. Arbib and E. G. Manes. Arrows, Structures and Functors. The Categorical Imperative. Academic Press, Inc., 1975.
D. Bjørner and C. B. Jones. Formal Specification and Software Development. Prentice-Hall International, Inc., 1982.
H-D. Ehrich and U. Lipeck. Algebraic domain equations. Theoretical Computer Science, (27):167–196, 1983.
H. Ehrig and E. Mahr. Fundamentals of Algebraic Specification 1: Equations and Initial Semantics. Springer-Verlag, 1985.
J.A. Goguen and R.M. Burstall. Institutions: Abstract Model Theory for Computer Science. SRI International, 1985.
J.A. Goguen, J.W. Thatcher, E.G. Wagner, and J.B. Wright, Initial Algebra Semantics and Continuous Algebras. Journal of Association Computing Machinery, (24):68–95, 1977.
A. E. Haxthausen. Mutually Recursive Algebraic Specifications. Technical Report ID-TR:1988-41, Department of Computer Science, Technical University of Denmark, April 1988.
A. E. Haxthausen. Mutually Recursive Algebraic Domain Equations. In Proceedings of VDM'88. Lecture Notes of Computer Science, 328, 1988.
A. E. Haxthausen. Structuring Mechanisms in Formal Specification Languages. Ph.D. thesis ID-TR:1988-42, Department of Computer Science, Technical University of Denmark, July 1988.
B. Möller and W. Dosch. On the algebraic specification of domains. In Proceedings of 3rd Workshop on Specification of Abstract Data Types, Bremen, 1984.
D. Sannella and A. Tarlecki. Specifications in an Arbitrary Institution. Technical Report, Department of Computer Science, University of Edinburgh, 1985.
J. E. Stoy. Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory. MIT Press, 1977.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Haxthausen, A.E. (1989). Parameterized algebraic domain equations. In: Ehrig, H., Herrlich, H., Kreowski, H.J., Preuß, G. (eds) Categorical Methods in Computer Science With Aspects from Topology. Lecture Notes in Computer Science, vol 393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51722-7_12
Download citation
DOI: https://doi.org/10.1007/3-540-51722-7_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51722-1
Online ISBN: 978-3-540-46787-8
eBook Packages: Springer Book Archive