Information Processing Letters
Acta Informatica
A generalization of Dijkstra's calculus
ACM Transactions on Programming Languages and Systems (TOPLAS)
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
ACM Transactions on Programming Languages and Systems (TOPLAS)
Science of Computer Programming - Special issue on mathematics of program construction (MPC 2002)
Algebras of modal operators and partial correctness
Theoretical Computer Science - Algebraic methodology and software technology
ACM Transactions on Computational Logic (TOCL)
RelMiCS'05 Proceedings of the 8th international conference on Relational Methods in Computer Science, Proceedings of the 3rd international conference on Applications of Kleene Algebra
UTP'06 Proceedings of the First international conference on Unifying Theories of Programming
Recasting hoare and he's unifying theory of programs in the context of general correctness
IW-FM'01 Proceedings of the 5th Irish conference on Formal Methods
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Partial, total and general correctness
MPC'10 Proceedings of the 10th international conference on Mathematics of program construction
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
Unifying correctness statements
MPC'12 Proceedings of the 11th international conference on Mathematics of Program Construction
Extended designs algebraically
Science of Computer Programming
Linking Unifying Theories of Program refinement
Science of Computer Programming
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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.