Abstract
In this paper, we first review a bottom-up abstract interpretation framework for finite approximations of definite programs that are characterised by abstraction functions. For each such abstraction function a, a finite approximation of the least fixpoint semantics is given as the least fix-point of a function Φ P,α over an abstract domain in a similar way that the least fixpoint semantics is given as the least fixpoint of a function T P over the concrete domain. Then the derivation of an algorithm for the computation of lfp(Φ P,α ) is detailed and its implementation in Prolog is presented. The final algorithm is efficient in both storage usage and time usage. The efficiency in its storage usage is obtained by formulating another function Ψ P,α and establishing that lfp(Ψ P,α ) = lfp(Φ P,α ). The time efficiency is obtained by using heuristic knowledge derived from program text and information accumulated during the computation of lfp(Φ P,α ). The time efficiency is exemplified through depth abstractions and stump abstractions.
Supported by the Sino-British Friendship Scholarship Scheme.
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© 1993 British Computer Society
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Lu, L., Greenfield, P. (1993). An Algorithm for Finite Approximations of Definite Programs and its Implementation in Prolog. In: Broda, K. (eds) ALPUK92. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3421-3_4
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DOI: https://doi.org/10.1007/978-1-4471-3421-3_4
Publisher Name: Springer, London
Print ISBN: 978-3-540-19783-6
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