Abstract
An approach is described for the generation of certain mathematical objects (like sets, correspondences, mappings) in terms of relations using relation-algebraic descriptions of higher-order objects. From non-constructive characterizations executable relational specifications are obtained. We also show how to develop more efficient algorithms from the frequently inefficient specifications within the calculus of binary relations.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Abold-Thalmann H., Berghammer R., Schmidt G.: Manipulation of concrete relations: The RELVIEW-system. Report Nr. 8905, Fakultät für Informatik, Universität der Bundeswehr München (1989)
Backhouse R.C., Hoogendijk P., Voermans E., van der Woude J.C.S.P: A relational theory of datatypes. Eindhoven University of Technology, Dept. of Mathematics and Computer Science (1992)
Berghammer R.: Computing the cut completion of a partially ordered set — An example for the use of the RELVIEW-system. Report Nr. 9205, Fakultät für Informatik, Universität der Bundeswehr München (1992)
Berghammer R., Schmidt G.: The RELVIEW-system. In: Choffrut C., Jantzen M. (eds.): Proc. STACS '91, Lect. Notes Comput. Sci. 480, Springer, 535–536 (1991)
Berghammer R., Schmidt G.: Relational specifications. In: Rauszer C. (ed.): Algebraic Methods in Logic and Computer Science, Banach Center Publications, Volume 28, Institute of Mathematics, Polish Academy of Sciences, 167–190 (1993)
Berghammer R., Zierer H.: Relational algebraic semantics of deterministic and nondeterministic programs. Theoret. Comput. Sci. 43, 123–147 (1986)
Berghammer R., Schmidt G., Zierer H.: Symmetric quotients and domain constructions. Inform. Proc. Letters 33, 3, 163–168 (1989/90)
Berghammer R., Gritzner T.F., Schmidt G.: Prototyping relational specifications using higher-order objects. Report Nr. 9304, Fakultät für Informatik, Universität der Bundeswehr München (1993)
Brook T.: Order and recursion in topoi. Notes on Pure Mathematics, Vol. 9, Australian National University of Canberra (1977)
Budde R., Kuhlenkamp K., Matthiassen H., Züllinghoven H. (eds.): Approaches to prototyping. Springer (1984)
Chin L.H., Tarski A.: Distributive and modular laws in the arithmetic of relation algebras. University of California Publications in Mathematics (new series) 1, 341–384 (1951)
De Bakker J.W., de Roever W.P.: A calculus for recursive program schemes. In: Nivat M. (ed.): Proc. ICALP 73, North-Holland, 167–196 (1973)
De Roever W.P.: Recursion and parameter mechanisms: An axiomatic approach. In: Loeckx J. (ed.): Proc. ICALP 74, Lect. Notes Comput. Sci. 14, Springer, 34–65 (1974)
Desharnais J., Jaoua A., Mili F., Boudriga N., Mili A.: Conjugate kernels: An operator for program construction. Theoret. Comput. Sci., to appear
Freyd P.J., Ščedrov A.: Categories, allegories. Mathematical Library, Vol. 39, North-Holland (1990)
Haralick R.M.: The diclique representation and decomposition of binary relations. J. ACM 21, 3, 356–366 (1974)
Hoare C.A.R., He J.: The weakest prespecification, Parts I&II, Fundamenta Informaticae IX, 51–84 & 217–252 (1986)
Jónsson B., Tarski A.: Boolean algebras with operators, Part II. Amer. J. Math. 74, 127–167 (1952)
Mili A.: A relational approach to the design of deterministic programs. Acta Informatica 20, 315–328 (1983)
Mili A., Desharnais J., Mili F.: Relational heuristics for the design of deterministic programs. Acta Informatica 24, 239–276 (1987)
Möller B.: Relations as a program development language. In: Möller B. (ed.): Proc. IFIP TC2/WG2.1 Working Conference on Constructing Programs from Specifications, North-Holland, 373–397 (1991)
Reisig W.: Petri nets — An introduction. EATCS Monographs on Theoret. Comput. Sci., Springer (1985)
Schmidt G.: Programs as partial graphs I: Flow equivalence and correctness. Theoret. Comput. Sci. 15, 1–25 (1981)
Schmidt G., Ströhlein T.: On kernels of graphs and solutions of games: A synopsis based on relations and fixed points. SIAM J. Alg. Disc. Meth. 6, 1, 54–65 (1985)
Schmidt G., Ströhlein T.: Relationen und Graphen. Springer (1989); English version: Relations and graphs. Discrete Mathematics for Computer Scientists, EATCS Monographs on Theoret. Comput. Sci., Springer (1993)
Spivey J.M.: The Z notation: A reference manual. Prentice Hall (1989)
Ströhlein T.: Untersuchungen über kombinatorische Spiele. Doctoral Thesis, Technische Universität München (1970)
Tarski A.: On the calculus of relations. Journal of Symbolic Logic 6, 73–89 (1941)
Veloso P., Haeberer A.: A finitary relational algebra for classical first-order logic. Bull. of the Section on Logic of the Polish Academy of Sciences 20, 52–62 (1991)
Veloso P., Haeberer A., Baum G.: Formal program construction within an extended calculus of binary relations. J. Symbolic Comp., to appear
Zierer H.: Relation algebraic domain constructions. Theoret. Comput. Sci. 87, 163–188 (1991)
Zierer H., Schmidt G., Berghammer R.: An interactive graphical manipulation system for higher objects based on relation algebra. In: Tinhofer G., Schmidt G. (eds.): Proc. 12th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 86), Bernried/Starnberger See, 17.6.–19.6. 1986, Lect. Notes Comput. Sci. 246, Springer: Berlin-Heidelberg-New York, 68–81 (1987)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Berghammer, R., Gritzner, T.F., Schmidt, G. (1994). Prototyping relational specifications using higher-order objects. In: Heering, J., Meinke, K., Möller, B., Nipkow, T. (eds) Higher-Order Algebra, Logic, and Term Rewriting. HOA 1993. Lecture Notes in Computer Science, vol 816. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58233-9_4
Download citation
DOI: https://doi.org/10.1007/3-540-58233-9_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58233-5
Online ISBN: 978-3-540-48579-7
eBook Packages: Springer Book Archive