D. Boulanger and M. Bruynooghe. Deriving unfold/fold transformations of logic programs using extended OLDT-based abstract interpretation. Journal of Symbolic Computation, 15:495521, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....via a nite amount of computation. The interpretation domains vary according to the property to be analyzed and the degree of information one would like to obtain [41] A general framework where program transformation strategies are supported by abstract interpretation techniques, is de ned in [17]. Among the many transformation techniques which depend on program analysis techniques, we would like to mention: i) compiling control (see Section 3.2.1) where the information about the ow of computation is used for generating the unfolding tree, ii) the specialization method of [75] which ....

D. Boulanger and M. Bruynooghe. Deriving unfold/fold transformations of logic programs using extended OLDT-based abstract interpretation. Journal of Symbolic Computation, 15:495521, 1993.

.... analysis , which tells us which expressions should be unfolded when part of the input data is known at compile time [Launchbury 91, Mycroft 81, Nielson Nielson 88, Jones et al. 93] A general framework for the use of abstract interpretations when transforming logic programs is presented in [Boulanger Bruynooghe 93] As an example of use of abstract interpretations we now present the socalled Matrix of Lengths method for the derivation of on line programs. Given a program which produces a string as output, this method allows us to derive an equivalent program with on line behaviour, that is, a program ....

Boulanger, D., Bruynooghe, M.: Deriving Unfold /Fold Transformations of Logic Programs Using Extended OLDTbased Abstract Interpretation. Journal of Symbolic Computation 15 (1993) 495--521

....also be used for other purposes, such as program analysis, synthesis, specialization, and veri cation. Indeed, for instance, in [19] we can nd a method based on unfold fold rules, for proving the equivalence of functional expressions. This method can also be adapted to the case of logic programs [4, 26] for proving equivalences of goals, that is, equivalences of conjunctions of atoms. In this paper, which builds upon [26] we formalize this method, called unfold fold proof method, for the case of de nite logic programs w.r.t. the least Herbrand model semantics. We also present a method for ....

D. Boulanger and M. Bruynooghe. Deriving unfold/fold transformations of logic programs using extended OLDT-based abstract interpretation. Journal of Symbolic Computation, 15:495-521, 1993.

....to guide folding. Maher described a system that permits only reversible folding [Mah87] The basic Tamaki Sato system itself was extended in several directions (e.g. to handle folding with multiple clauses [GK94] negation [AD95, Sek91, Sek93] and applied to practical problems (e.g. BCD90, BB93, PPR97] All the above systems di er from each other mainly in terms of the fold operations they permit. Research done while on leave from Chennai Mathematical Institute, Chennai, India. 1 Correctness of Unfold Fold Transformations Consider the sequence of programs in Figure 1. In the ....

D. Boulanger and M. Bruynooghe. Deriving unfold/fold transformations of logic programs using extended OLDT-based abstract interpretation. Journal of Symbolic Computation, pages 495-521, 1993.

....that can be applied to our deduction system in order to completely automate the deductive process. 1. 1 Related Work Related Work : Program Transformations Unfold fold logic program transformation systems have been extensively used for program synthesis, specialization and optimization [BCD90, BB93, LSW96, PPR97, PP99a] 4 However, relatively little work has been done on using such systems for constructing proofs. Hsiang and Srivas [HS87] extended Prolog s evaluation with limited forward chaining to perform inductive theorem proving. This limited forward chaining step is in fact a ....

....to guide folding. Maher described a system that permits only reversible folding [Mah87] The basic Tamaki Sato system itself was extended in several directions (e.g. to handle folding with multiple clauses [GK94] negation [AD95, Sek91, Sek93] and applied to practical problems (e.g. BCD90, BB93, PPR97] See [PP98] for an excellent survey of research on this topic over the past decade) 8 Correctness of Unfold Fold Transformations Correctness proofs for unfold fold transformations consider transformation sequences of the form P 0 ; P 1 ; where P 0 is an initial program and P ....

D. Boulanger and M. Bruynooghe. Deriving unfold/fold transformations of logic programs using extended OLDT-based abstract interpretation. Journal of Symbolic Computation, pages 495-521, 1993.

....transformations are correct with respect to various semantics of negation including the well founded model and stable model semantics. 1 Introduction Unfold fold transformation systems for logic programs have been used for automated deduction [8, 17] and program specialization and optimization [2, 4, 10, 15]. Normal logic programs consist of definitions of the form A: Gamma OE where A is an atom and OE is a boolean formula over atoms. Unfolding replaces an occurrence of A in a program with OE while folding replaces an occurrence of OE with A. Folding is called reversible if its effects can be undone ....

D. Boulanger and M. Bruynooghe. Deriving unfold/fold transformations of logic programs using extended OLDT-based abstract interpretation. Journal of Symbolic Computation, pages 495--521, 1993.

....an appendix with supplementary reference material for the convenience of the referees, and is not a part of the main paper. 1 Introduction Unfold fold transformation systems for logic programs have been used for and automated deduction [7, 16] and program specialization and optimization [2, 3, 9, 14]. Normal logic programs consist of definitions of the form A: Gamma OE where A is an atom and OE is a boolean formula over atoms. Unfolding replaces an occurrence of A in a program with OE while folding replaces an occurrence of OE with A. Folding is called reversible if its effects can be ....

D. Boulanger and M. Bruynooghe. Deriving unfold/fold transformations of logic programs using extended OLDT-based abstract interpretation. Journal of Symbolic Computation, pages 495--521, 1993.

....on maintaining counters to guide folding. Maher described a system that permits only reversible folding [8] The basic Tamaki Sato system itself was extended in several directions (e.g. to handle folding with multiple clauses [5] negation [1, 12, 13] and applied to practical problems (e.g. [2, 3, 10]) See [9] for an excellent survey of research on this topic over the past decade) Correctness of Unfold Fold Transformations Correctness proofs for unfold fold transformations consider transformation sequences of the form P 0 ; P 1 ; where P 0 is an initial program and P i 1 is ....

D. Boulanger and M. Bruynooghe. Deriving unfold/fold transformations of logic programs using extended OLDT-based abstract interpretation. Journal of Symbolic Computation, pages 495--521, 1993.

....on maintaining counters to guide folding. Maher described a system that permits only reversible folding [10] The basic Tamaki Sato system itself was extended in several directions (e.g. to handle folding with multiple clauses [7] negation [1, 18, 19] and applied to practical problems (e.g. [2, 3, 12]) See [11] for an excellent survey of research on this topic over the past decade) Correctness of Unfold Fold Transformations Correctness proofs for unfold fold transformations consider transformation sequences of the form P 0 ; P 1 ; where P 0 is an initial program and P i 1 is ....

D. Boulanger and M. Bruynooghe. Deriving unfold/fold transformations of logic programs using extended OLDT-based abstract interpretation. Journal of Symbolic Computation, pages 495--521, 1993.

....for definite programs. An unfold fold transformation system for definite logic programs was first described in a seminal paper by Tamaki and Sato [23] Since then their system has been substantially extended and expanded [1, 8, 12, 22, 24] and applied to practical problems of importance (e.g. see [2, 4, 14, 17]) An excellent survey of research on this topic appears in [16] Unfold fold logic program transformation systems have been extensively used for program synthesis and program optimization. However, relatively little work has been done on using such systems for constructing proofs. Hsiang and ....

D. Boulanger and M. Bruynooghe. Deriving unfold/fold transformations of logic programs using extended OLDTbased abstract interpretation. Journal of Symbolic Computation, pages 495--521, 1993.

....be used for other purposes, such as program analysis, synthesis, specialization, and verification. Indeed, for instance, in [19] we can find a method based on unfold fold rules, for proving the equivalence of functional expressions. This method can also be adapted to the case of logic programs [4, 26] for proving equivalence of goals, that is, conjunctions of atoms. In this paper, which builds upon [26] we formalize this method, called unfold fold proof method, for the case of definite logic programs w.r.t. the least Herbrand model semantics. We also present a method for program synthesis ....

D. Boulanger and M. Bruynooghe. Deriving unfold/fold transformations of logic programs using extended OLDT-based abstract interpretation. Journal of Symbolic Computation, 15:495--521, 1993.

....Proietti Section 7) As an alternative approach, one can use a simple method based on unfold fold transformations which we call unfold fold proof method. This proof method was introduced by Kott for recursive equation programs [ Kott, 1982 ] and its application to logic programs is described in [ Boulanger and Bruynooghe, 1993; Proietti and Pettorossi, 1994a; Proietti and Pettorossi, 1994b ] The unfold fold proof method can be described as follows. Given a program P , a semantics function SEM, and a replacement law G 1 j V G 2 , with V = fX 1 ; Xm g, we consider the clauses D 1 . newp 1 (X 1 ; Xm ) ....

D. Boulanger and M. Bruynooghe. Deriving unfold/fold transformations of logic programs using extended OLDT-based abstract interpretation. Journal of Symbolic Computation, 15:495--521, 1993.

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