Relational algebraic semantics of deterministic and nondeterministic programs
Theoretical Computer Science
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
Embedding a demonic semilattice in a relation algebra
Theoretical Computer Science
ACM Transactions on Programming Languages and Systems (TOPLAS)
Refinement and demonic semantics
Relational methods in computer science
A generalized control structure and its formal definition
Communications of the ACM
A Relational Model of Programs Without the Restriction to Egli-Milner-Monotone Constructs
PROCOMET '94 Proceedings of the IFIP TC2/WG2.1/WG2.2/WG2.3 Working Conference on Programming Concepts, Methods and Calculi
Semantics of Nondeterministic and Noncontinuous Constructs
Program Construction, International Summer Schoo
MPC '00 Proceedings of the 5th International Conference on Mathematics of Program Construction
Algebras of modal operators and partial correctness
Theoretical Computer Science - Algebraic methodology and software technology
ACM Transactions on Computational Logic (TOCL)
Non-termination in unifying theories of programming
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
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
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
Science of Computer Programming
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
Lifting general correctness into partial correctness is ok
IFM'07 Proceedings of the 6th international conference on Integrated formal methods
Partial, total and general correctness
MPC'10 Proceedings of the 10th international conference on Mathematics of program construction
Reasoning about loops in total and general correctness
UTP'08 Proceedings of the 2nd international conference on Unifying theories of programming
Unifying recursion in partial, total and general correctness
UTP'10 Proceedings of the Third international conference on Unifying theories of programming
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
Non-termination in unifying theories of programming
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
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
Omega algebra, demonic refinement algebra and commands
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
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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.