Refinement Algebra with Operators for Enabledness and Termination

in: Universität Augsburg in: T. Uustalu (Ed.), Mathematics of Program Construction 8th International Conference (MPC 2006), LNCS 4014.
pp. 397-415, 2006.
Springer.

Abstract:
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