Modal Design Algebra

  • Walter Guttmann
  • Bernhard Möller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4010)


We give an algebraic model of the designs of UTP based on a variant of modal semirings, hence generalising the original relational model. This is intended to exhibit more clearly the algebraic principles behind UTP and to provide deeper insight into the general properties of designs, the program and specification operators, and refinement. Moreover, we set up a formal connection with general and total correctness of programs as discussed by a number of authors. Finally we show that the designs form a left semiring and even a Kleene and omega algebra. This is used to calculate closed expressions for the least and greatest fixed-point semantics of the demonic while loop that are simpler than the ones obtained from standard UTP theory and previous algebraic approaches.


Boolean Algebra Great Element Formal Connection Galois Connection Order Isomorphism 


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Walter Guttmann
    • 1
  • Bernhard Möller
    • 2
  1. 1.Abteilung Programmiermethodik und Compilerbau, Fakultät für InformatikUniversität UlmUlmGermany
  2. 2.Institut für InformatikUniversität AugsburgAugsburgGermany

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