Browsing by Author "Rewitzky, Ingrid Moira"

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    A topological framework for program semantics
    (1995) Rewitzky, Ingrid Moira; Brink, Chris
    Program semantics can be viewed relationally as in relational semantics, algebraically as in predicate transformer semantics, logically as in information systems and order-theoretically as in denotational semantics. This can be compared to a common situation in non-classical logics. Namely, a logic can often be presented as a formal deductive system, as an algebra and as a relational structure, with each of the presentations derivable from each of the other two. The central hypothesis of this thesis is that this situation can serve as a paradigm for unifying the various versions of program semantics. Starting with a relational semantics based on certain ordered topological spaces, called Priestley spaces, and invoking the techniques of Priestley duality, an algebraic. a logical and an order-theoretic presentation of program semantics are derived. Each of these four presentations are also derivable from each of the other three. The topological model of program semantics based on Priestley spaces thus serves as a unifying framework for other versions of program semantics, essentially as in the logic-algebra-semantics paradigm.
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    Modelling the algebra of weakest preconditions
    (1991) Rewitzky, Ingrid Moira; Brink, Chris
    In expounding the notions of pre- and postconditions, of termination and nontermination, of correctness and of predicate transformers I found that the same trivalent distinction played a major role in all contexts. Namely: Initialisation properties: An execution of a program always, sometimes or never starts from an initial state. Termination/nontermination properties: If it starts, the execution always, sometimes or never terminates. Clean-/messy termination properties: A terminating execution always, sometimes or never terminates cleanly. Final state properties: All, some or no final states of α from s have a given property.