Systematic software development using VDM (2nd ed.)
Systematic software development using VDM (2nd ed.)
The Z notation: a reference manual
The Z notation: a reference manual
A logical approach to discrete math
A logical approach to discrete math
Category theory for computing science, 2nd ed.
Category theory for computing science, 2nd ed.
Proceedings of the 9th International Conference of Z Usres on The Z Formal Specification Notation
ZUM '95 Proceedings of the 9th International Conference of Z Usres on The Z Formal Specification Notation
ZUM '95 Proceedings of the 9th International Conference of Z Usres on The Z Formal Specification Notation
A VDM Study of Fault-Tolerant Stable Storage - Towards a Computer Engineering Mathematics
FME '93 Proceedings of the First International Symposium of Formal Methods Europe on Industrial-Strength Formal Methods
Tutorial on the Irish School of the VDM
VDM '91 Proceedings of the 4th International Symposium of VDM Europe on Formal Software Development-Volume 2: Tutorials
IW-FM'98 Proceedings of the 2nd Irish conference on Formal Methods
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Using algebraic structures and techniques alone we derive an intuitive result concerning updates to a system of aliases. Specifically, we use the kernel relation of a map to characterise the system of aliases; we express the inverse image of map override as a new operation, called "underride", which we define; we provide an important theorem relating map composition, override and underride in a very natural way; and finally we identify another satisfying and insightful algebraic approach to the same problem based on algebraic properties of the solution space. We thereby illustrate our contention that this use of abstract algebra extends the mathematical foundations of software engineering, provides a conveniently high level at which to reason about models (shorter intuitive proofs) and promotes increased mathematical insight on the part of practitioners.