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Constrained partial deduction and the preservation of characteristic trees

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Abstract

Partial deduction strategies for logic programs often use an abstraction operator to guarantee the finiteness of the set of goals for which partial deductions are produced. Finding an abstraction operator which guarantees finiteness and does not lose relevant information is a difficult problem. In earlier work Gallagher and Bruynooghe proposed to base the abstraction operator oncharacteristic paths andtrees, which capture the structure of the generated incomplete SLDNF-tree for a given goal.

In this paper we exhibit the advantages of characteristic trees over purely syntactical measures: if characteristic trees can be preserved upon generalisation, then we obtain an almost perfect abstraction operator, providing just enough polyvariance to avoid any loss of local specialisation. Unfortunately, the abstraction operators proposed in earlier work do not always preserve the characteristic trees upon generalisation. We show that this can lead to important specialisation losses as well as to non-termination of the partial deduction algorithm. Furthermore, this problem cannot be adequately solved in the ordinary partial deduction setting.

We therefore extend the expressivity and precision of the Lloyd and Shepherdson partial deduction framework by integrating constraints. We provide formal correctness results for the so obtained generic framework ofconstrained partial deduction. Within this new framework we are, among others, able to overcome the above mentioned problems by introducing an alternative abstraction operator, based on so calledpruning constraints. We thus present a terminating partial deduction strategy which, for purely determinate unfolding rules, induces no loss of local specialisation due to the abstraction while ensuring correctness of the specialised programs.

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  1. Department of Computer Science, K. U. Leuven, Celestijnenlaan 200 A, B-3001, Heverlee, Belgium

    Michael Leuschel & Danny de Schreye

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  1. Michael Leuschel
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  2. Danny de Schreye
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Michael Leuschel, Ph.D.: He currently works as a postdoctoral researcher at the Department of Computer Science of the Katholieke Universiteit Leuven. His present research focuses on program transformation and specialisation for declarative programming languages. Other research interests include abstract interpretation, optimised integrity checking and meta-programming. He received his degree (“Licence”) in Computer Science from the Université Libre de Bruxelles in 1990 and a Master of Artificial Intelligence from the Katholieke Universiteit Leuven in 1993, where he also received his Ph.D in 1997.

Danny De Schreye, Ph.D: He is a professor at the Department of Computer Science of the Katholieke Universiteit Leuven and a senior research associate of the Belgian National Fund for Scientific Research. He obtained his Ph.D from K.U. Leuven in 1983, on the topic of operator algebras. His research interests are in the field of Logic Programming, and include program transformation and termination, knowledge representation and reasoning, and constraint programming.

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Leuschel, M., de Schreye, D. Constrained partial deduction and the preservation of characteristic trees. New Gener Comput 16, 283–342 (1998). https://doi.org/10.1007/BF03037483

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