Systematic software development using VDM (2nd ed.)
Systematic software development using VDM (2nd ed.)
Programming from specifications (2nd ed.)
Programming from specifications (2nd ed.)
The B-book: assigning programs to meanings
The B-book: assigning programs to meanings
ACM Transactions on Programming Languages and Systems (TOPLAS)
Refinement Calculus: A Systematic Introduction
Refinement Calculus: A Systematic Introduction
MPC '00 Proceedings of the 5th International Conference on Mathematics of Program Construction
From Kleene Algebra to Refinement Algebra
MPC '02 Proceedings of the 6th International Conference on Mathematics of Program Construction
A predicative semantics for real-time refinement
Programming methodology
Reasoning about real-time programs using idle-invariant assertions
APSEC '00 Proceedings of the Seventh Asia-Pacific Software Engineering Conference
Science of Computer Programming - Special issue on mathematics of program construction (MPC 2002)
Unifying theories of programming that distinguish nontermination and abort
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
Termination of real-time programs: definitely, definitely not, or maybe
UTP'06 Proceedings of the First international conference on Unifying Theories of Programming
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Program algebras abstract the essential properties of programming languages in the form of algebraic laws. The proof of a refinement law may be expressed in terms of the algebraic properties of programs required for the law to hold, rather than directly in terms of the semantics of a language. This has the advantage that the law is then valid for any programming language that satisfies the required algebraic properties. By characterised the important properties of programming languages algebraically we can devise simple proofs of common refinement laws. In this paper we consider standard refinement laws for sequential programs. We give simple characterisations of program invariants and well foundedness of statements.