2 research outputs found

    Sequence-Based Abstract Interpretation of Prolog

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    Many abstract interpretation frameworks and analyses for Prolog have been proposed, which seek to extract information useful for program optimization. Although motivated by practical considerations, notably making Prolog competitive with imperative languages, such frameworks fail to capture some of the control structures of existing implementations of the language. In this paper we propose a novel framework for the abstract interpretation of Prolog which handles the depth-first search rule and the cut operator. It relies on the notion of substitution sequence to model the result of the execution of a goal. The framework consists of (i) a denotational concrete semantics, (ii) a safe abstraction of the concrete semantics defined in terms of a class of post-fixpoints, and (iii) a generic abstract interpretation algorithm. We show that traditional abstract domains of substitutions may easily be adapted to the new framework, and provide experimental evidence of the effectiveness of our approach. We also show that previous work on determinacy analysis, that was not expressible by existing abstract interpretation frameworks, can be seen as an instance of our framework.Comment: 62 pages. To appear in the journal "Theory and Practice of Logic Programming

    Reduction types and intensionality in the lambda-calculus

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    In this thesis I introduce a new approach to the automated analysis of the reduction behaviour of A-calculus terms. This new approach improves on earlier analysers in several ways, not least in its treatment of higher-order terms and polymorphism, two notably troublesome issues. In addition, this thesis introduces a stronger notion of reduction behaviour than strictness. This concept, called strong head neededness, forms the basis for a new notation for describing the reduction behaviour of terms. This notation is a kind of type, elements of which are built using a Boolean algebra of function type constructors. Thus the form of the methodology proposed is that of a type system. Consideration is given to a variety of type assignment systems for the new type system. This supports the hypothesis that the approach proposed is suitable as a framework for building a range of analyses. Having established this framework it is then a matter of engineering to determine the appropriate trade off between information derived and performance achieved. An investigation is conducted into the formal semantics of all the constructs introduced. In particular, the investigation proves a range of soundness and completeness results. Also examined is the semantics of the new notion of type and the development of a model for reduction types. The model is of interest in its own right, as it gives further insight into the reduction behaviour of A-terms. The thesis includes detailed implementations of all the type assignment systems and ascertains the correctness of these implementations
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