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    Algebraic Advances for Aliasing

    2nd BCS-FACS Northern Formal Methods Workshop

    Ilkley, UK. 14th - 15th July 1997

    AUTHORS

    A.P. Hughes & A. Donnelly

    ABSTRACT

    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.

    PAPER FORMATS

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