The Linear Algebra of UTP

  • Bernhard Möller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4014)


We show that the well-known algebra of matrices over a semiring can be used to reason conveniently about predicates as used in the Unifying Theories of Programming (UTP). This allows a simplified treatment of the designs of Hoare and He and the prescriptions of Dunne. In addition we connect the matrix approach with the theory of test and condition semirings and the modal operators diamond and box. This allows direct re-use of the results and proof techniques of Kleene algebra with tests for UTP as well as a connection to traditional wp/wlp semantics. Finally, we show that matrices of predicate transformers allow an even more streamlined treatment and removal of a restricting assumption on the underlying semirings.


Linear Algebra Boolean Algebra Composition Operator Galois Connection State Predicate 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bernhard Möller
    • 1
  1. 1.Institut für InformatikUniversität AugsburgAugsburgGermany

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