Comparing Two Different Approaches to Products in Abstract Relation Algebra

  • R. Berghammer
  • A. Haeberer
  • G. Schmidt
  • P. Veloso
Part of the Workshops in Computing book series (WORKSHOPS COMP.)


During the development of relation algebra as a formal programming tool, the need of some form of “categorical product” of relations became apparent, whether as a type or as an operation. Two approaches arose in the late 70’s and the early 80’s which will be referred here as the “Munich approach” (see, e.g., [18, 7]) and the “Rio approach” (see, e.g., [13, 12, 22]).




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. C. Backhouse, P. J. DE Bruin, P. Hoogendijk, G. Malcolm, J. Van Der Woude: Polynomial relators. Computing Science Notes, Dept. Mathematics and Computing Science, Eindhoven Univ. of Technology, May 1991Google Scholar
  2. [2]
    G. Baum, A. Haeberer, P. Veloso: On the Representability of the Abstract Relational Algebra, IGPL Newsletter 1, 3 (September 1992) European Foundation for Logic, Language, and Information, Interest Group on Programming LogicGoogle Scholar
  3. [3]
    A. R. Bednarek, S. Ulam: Projective algebra and the calculus of relations. J. Symb. Logic 43, 56–64 (1978)CrossRefMATHMathSciNetGoogle Scholar
  4. [4]
    R. Berghammer, G. Schmidt: A relational view on gotos and dynamic logic. In: Schneider, H.J., Göttler, H. (eds.): Proc. Conf. Graphtheoret. Concepts in Corn-put. Sci., June 16–18, 1982, Neunkirchen a. Br., 13–24, Hanser 1982Google Scholar
  5. [5]
    R. Berghammer, G. Schmidt: The RELVTEW-System. Notes to a system presentation. In: Choffrut, C., Jantzen, M. (Eds.): Proc. 8th Ann. Symp. Theo-ret. Aspects of Comput. Sci. Lect. Notes Comput. Sci. 480, 535–536, Springer 1991Google Scholar
  6. [6]
    R. Berghammer, G. Schmidt, H. Zierer: Symmetrie quotients and domain constructions. Inform. Proc. Letters 33, 3, 163–168 (1989/90)CrossRefMATHMathSciNetGoogle Scholar
  7. [7]
    R. Berghammer, H. Zierer: Relational algebraic semantics of deterministic and nondeterministic programs. Theoret. Comput. Sci. 43, 123–147 (1986)CrossRefMATHMathSciNetGoogle Scholar
  8. [8]
    R. Brethauer: Ein Formelmanipulationssystem zur computergestützten Beweisführung in der Relationenalgebra, Univ. der Bundeswehr München, Diplomarb. (1991)Google Scholar
  9. [9]
    L. Chin, A. Tarski: Distributive and modular laws in the arithmetic of relation algebras. University of California Publications in Mathematics (new series) 1 (1951)Google Scholar
  10. [10]
    W. P. De roever: Recursive program schemes: semantics and proof theory. Ph. D.-Thesis, Math. Centrum Tracts, Amsterdam, 1974Google Scholar
  11. [11]
    C. J. Everett, S. Ulam: Projective algebra I. Amer. J. Math. 68, 77–88 (1946)MATHMathSciNetGoogle Scholar
  12. [12]
    A. Haeberer, P. Veloso: Partial relations for program derivation: Adequacy, Inevitability, and Expressiveness. In: Möller, B. (ed.): Constructing programs from specifications. Proc. IFIP TC 2/WG 2.1, Pacific Grove, USA, North-Holland 1991Google Scholar
  13. [13]
    A. Haeberer, P. Veloso, P. Elustondo: Towards a relational calculus for software construction. Doc. 640-BUR-5, 41st IFIP WG 2.1, Chester, GB (1990)Google Scholar
  14. [14]
    B. Jónsson, A. Tarski: Boolean algebras with operators, Part II. Amer. J. Math. 74, 127–167 (1952)MATHGoogle Scholar
  15. [15]
    R. Maddux: On the derivation of identities involving projection functions. Draft paper July 29, 1993Google Scholar
  16. [16]
    G. Schmidt, T. Ströhlein: Relation and Graphs—Discrete Mathematics for Computer Scientists. EATCS Monographs on Theoret. Comput. Sci., Springer 1993Google Scholar
  17. [17]
    G. Schmidt, T. Ströhlein: Relation algebras: Concept of points and representability, Discrete Math. 54, 83–92 (1985)CrossRefMATHMathSciNetGoogle Scholar
  18. [18]
    G. Schmidt: Programs as partial graphs I: Flow equivalence and correctness. Theoret. Comput. Sci. 15, 1–25 (1981)CrossRefMATHMathSciNetGoogle Scholar
  19. [19]
    A. Tarski: On the calculus of relations. J. Symb. Logic 6, 73–89 (1941)CrossRefMATHMathSciNetGoogle Scholar
  20. [20]
    A. Tarski, S. GIVANT: A formalization of set theory without variables. Amer. Math. Soc. Coll. Publ. 41, Providence, Rhode Island, 1987Google Scholar
  21. [21]
    P. Veloso, A. Haeberer: A unitary relational algebra for classical first-order logic. Bull, of the Section on Logic of the Polish Academy of Sciences 20, 52–62 (1991)MathSciNetGoogle Scholar
  22. [22]
    P. Veloso, A. Haeberer, G. Baum: Formal program construction within an extended calculus of binary relations. J. Symb. Comp. (to appear)Google Scholar
  23. [23]
    H. Zierer: Relation algebraic domain constructions. Theoret. Comput. Sci. 87, 163–188 (1991)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© British Computer Society 1994

Authors and Affiliations

  • R. Berghammer
    • 2
  • A. Haeberer
    • 1
  • G. Schmidt
    • 2
  • P. Veloso
    • 1
  1. 1.Departamento de InformáticaPUC, Rio de JaneiroBrazil
  2. 2.Fakultät für Informatik, Bundeswehr-Univ.NeubibergGermany

Personalised recommendations