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Ensuring Global Termination of Partial Deduction while Allowing Flexible Polyvariance
, 1995
"... The control of polyvariance is a key issue in partial deduction of logic programs. Certainly, only finitely many specialised versions of any procedure should be generated, while, on the other hand, overly severe limitations should not be imposed. In this paper, wellfounded orderings serve as a star ..."
Abstract

Cited by 60 (14 self)
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The control of polyvariance is a key issue in partial deduction of logic programs. Certainly, only finitely many specialised versions of any procedure should be generated, while, on the other hand, overly severe limitations should not be imposed. In this paper, wellfounded orderings serve as a starting point for tackling this socalled "global termination" problem. Polyvariance is determined by the set of distinct "partially deduced" atoms generated during partial deduction. Avoiding adhoc techniques, we formulate a quite general framework where this set is represented as a tree structure. Associating weights with nodes, we define a wellfounded order among such structures, thus obtaining a foundation for certified global termination of partial deduction. We include an algorithm template, concrete instances of which can be used in actual implementations, prove termination and correctness, and report on the results of some experiments. Finally, we conjecture that the proposed framewor...
Analysis and Transformation of Proof Procedures
, 1994
"... Automated theorem proving has made great progress during the last few decades. Proofs of more and more difficult theorems are being found faster and faster. However, the exponential increase in the size of the search space remains for many theorem proving problems. Logic program analysis and transfo ..."
Abstract

Cited by 8 (2 self)
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Automated theorem proving has made great progress during the last few decades. Proofs of more and more difficult theorems are being found faster and faster. However, the exponential increase in the size of the search space remains for many theorem proving problems. Logic program analysis and transformation techniques have also made progress during the last few years and automated theorem proving can benefit from these techniques if they can be made applicable to general theorem proving problems. In this thesis we investigate the applicability of logic program analysis and transformation techniques to automated theorem proving. Our aim is to speed up theorem provers by avoiding useless search. This is done by detecting and deleting parts of the theorem prover and theory under consideration that are not needed for proving a given formula. The analysis and transformation techniques developed for logic programs can be applied in automated theorem proving via a programming technique called ...