R. Barbuti, M. Codish, R. Giacobazzi, and M. Maher. Oracle Semantics for PROLOG. In H. Kirchner and G. Levi, editors, Algebraic and Logic Programming, Proceedings of the Third International Conference, volume 632 of Lecture Notes in Computer Science, pages 100--114. Springer-Verlag, Berlin, 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the substitutions associated to a resolvent in any SLD refutation. The knowledge about partial answers is important for program analysis [11] to characterize the semantics of concurrent languages [16] and to characterize universal termination, which in turn is useful for the semantics of PROLOG [2, 4]. 6 ffl call patterns (denoted by pt) which are the atoms (procedure calls) selected in any SLD derivation, and correct call patterns (denoted by cpt) which are the atoms (procedure calls) selected in any SLD refutation. Call patterns make it possible to derive properties of procedure calls, ....

R. Barbuti, M. Codish, R. Giacobazzi, and M. Maher. Oracle Semantics for PROLOG. In H. Kirchner and G. Levi, editors, Algebraic and Logic Programming, Proceedings of the Third International Conference, volume 632 of Lecture Notes in Computer Science, pages 100--114. Springer-Verlag, Berlin, 1992.

....1. # 38 Byeong Mo Chang, Kwang Moo Choe and R. Giacobazzi ETRI Journal, volume 16, number 4, January 1995 IV. EFFICIENT EXECUTION MODELS OF LOGIC PROGRAMS We first consider the linear execution of logic program like Prolog. A model of linear execution is provided as a transition system in [20], which is a pair .X; R consisting of a set X of states and a transition relation R# X#X on states. Definition 9 [20] Let P be a logic program. The transition system 9 P is .Atom # ; P where P # Atom # # Atom # is the smallest relation such that G P G 0 iff 1. GD A 1 ; A i ....

....EXECUTION MODELS OF LOGIC PROGRAMS We first consider the linear execution of logic program like Prolog. A model of linear execution is provided as a transition system in [20] which is a pair .X; R consisting of a set X of states and a transition relation R# X#X on states. Definition 9 [20] Let P be a logic program. The transition system 9 P is .Atom # ; P where P # Atom # # Atom # is the smallest relation such that G P G 0 iff 1. GD A 1 ; A i ; A k ;1# i # k; 2. H B 1 ; B n G P such that D mgu.A i ; H ; and 3. G 0 D A 1 ; B 1 ; B n ; A ....

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R. Barbuti, M. Codish, R. Giacobazzi and M. Maher, "Oracle semantics for Prolog," in Proceedings of International Conferenceof Algebraic andLogic Programming,Lecture Notes in Computer Science 632, Springer-Verlag, 1992.

....to the case of approximations of real Prolog, featuring some non logical primitives. The idea is to base the construction on recently proposed extensions of the S semantics which allow us to handle constructive negation [35,16,7] some Prolog primitives [1,11,28] and the Prolog computation rule [2,4]. ....

R. Barbuti, M. Codish, R. Giacobazzi, and M. Maher. Oracle Semantics for PROLOG. In H. Kirchner and G. Levi, editors, Algebraic and Logic Programming, Proceedings of the Third International Conference, volume 632 of Lecture Notes in Computer Science, pages 100--114. Springer-Verlag, Berlin, 1992.

.... 1 (617)253 1922, Fax: 1(617)253 3480, Email: miccianc theory.lcs.mit.edu Modelling control is attractive because it would allow new kinds of analyses and would improve the precision of existing ones. Several attempts to enhance traditional semantics with control related features have been made [2, 3, 5], and abstract interpretation frameworks that handle prolog search rule and cut have started to appear [6] However, none of [2, 3, 5] was shown to be actually usable for abstract interpretation, and [6] is not completely satisfactory from a theoretical point of view. In fact in [6] it is argued ....

....kinds of analyses and would improve the precision of existing ones. Several attempts to enhance traditional semantics with control related features have been made [2, 3, 5] and abstract interpretation frameworks that handle prolog search rule and cut have started to appear [6] However, none of [2, 3, 5] was shown to be actually usable for abstract interpretation, and [6] is not completely satisfactory from a theoretical point of view. In fact in [6] it is argued that there is no natural idea of collecting semantics for PROLOG, and the abstract semantics is defined by resorting to a notion of ....

R. Barbuti, M. Codish, R. Giacobazzi, and M. Maher. Oracle Semantics for PROLOG. In H. Kirchner and G. Levi, editors, Algebraic and Logic Programming, Proceedings of the Third International Conference, volume 632 of Lecture Notes in Computer Science, pages 100--114, Berlin, 1992. Springer-Verlag.

.... top down and bottom up semantics can be derived as abstractions of O R R , including ffl the resultants semantics defined (for any local rule R) in [61, 59] where we don t care about the sequences of clauses, ffl the resultants semantics with depth defined (for the leftmost rule) in [11], where a sequence of clauses is abstracted by its length, ffl the partial answers semantics O PA R defined (for any local rule R) in [61, 59] where we only keep the heads of the resultants by labeling as partial those heads that were heads of a non unit resultant, ffl the call patterns ....

....property iff there exists a frontier of a partial SLD tree for G (obtainable using a suitable abstraction of the resultant semantics and theorem 5.14) such that all the atoms in the frontier are not labeled as partial answers. This information is very important for the semantics of PROLOG [11, 17] and of all solutions metapredicates [40] ffl A goal G finitely fails iff there exist a finite number of frontiers for G, all the atoms in the frontiers of G are labeled as partial. This information is useful to get a bottom up characterization of SLDNFresolution [95] The information in ....

[Article contains additional citation context not shown here]

R. Barbuti, M. Codish, R. Giacobazzi, and M. Maher. Oracle Semantics for PROLOG. In H. Kirchner and G. Levi, editors, Algebraic and Logic Programming, Proceedings of the Third International Conference, volume 632 of Lecture Notes in Computer Science, pages 100--114. SpringerVerlag, Berlin, 1992.

....of pure PROLOG in the s semantics style. There are three candidate proposals: ffl the modeling control semantics [2, 3] where a pure PROLOG program is transformed into an ask tell constraint program, with the ask constraints expressing the termination properties. ffl the oracle semantics in [4], which is parametric w.r.t. an oracle which embodies the control strategy (and the oracle can be specialized to the PROLOG case) ffl the fixpoint semantics in [6] which is simpler and closer to the s semantics and provides a direct modeling of the PROLOG control. We decided to choose the ....

....pure PROLOG computed answers. The semantics is given according to the s semantics style and is oriented towards abstract interpretation. The construction of abstract interpretations in the style of those developed for logic programs was indeed the aim of several other semantics for pure PROLOG [2, 4, 6]. However none of those semantics was shown to be actually usable for abstract interpretation. Our bottom up definition is essentially a reconstruction of the semantics in [6] obtained by instantiating an adaptation of the generalized semantics scheme [26, 27] A nice feature is that we don t ....

R. Barbuti, M. Codish, R. Giacobazzi, and M. Maher. Oracle Semantics for PROLOG. In H. Kirchner and G. Levi, editors, Algebraic and Logic Programming, Proceedings of the Third International Conference, volume 632 of Lecture Notes in Computer Science, pages 100--114. Springer-Verlag, Berlin, 1992.

....one, namely we generate all and only the LSLD refutations. Then, we add a condition that checks whether there is an infinite sequence of transitions of the first level, i.e. of unconstrained resolution steps. Our solution is similar to the one proposed by Barbuti, Codish, Giacobazzi and Maher [3], based on the notion of oracle. In this way, we specify all and only the refutations generated by a standard Prolog interpreter. In order to exemplify the advantages of the proposed cross fertilization, we outline a concurrent semantics of Prolog at the end of this note. A simple rule describes ....

....0 h i 6 s , p ; h i) ha : g 0 ; OEi Gamma P hg : g 0 ; OE 0 i The rule End above can be applied only if g is nil or if its first atom cannot be unified with any rule of P . Thus, it describes the termination of a computation. The new rule Sel 0 uses an oracle in the style of [3] and permits to derive all and only the solutions of a standard Prolog interpreter. Theorem 3.4 (Equivalence with Prolog) Given a Prolog program P ; g, the unfolding of its p T SP is (isomorphic to) the computation sub tree of a standard Prolog interpreter made of all and only paths leading to ....

R. Barbuti, M. Codish, R. Giacobazzi, and M. Maher. Oracle semantics for Prolog. Technical Report TR 5/94, University of Pisa, 1994.

....used in [7] to obtain a semantics compositional wrt the union of programs, here our aim was to model resultants and other observables such as call patterns and partial answers. These observables were considered also in [15] without taking into account the selection rule. Also related are the works [3, 4] which, using a more complex semantic domain, aim at a semantics modeling the Prolog deep first search strategy. More recently, the paper [9] constructs an algebraic framework which, starting from a semantics similar to our resultants semantics, allows to derive several different semantics ....

R. Barbuti, M. Codish, R. Giacobazzi, and M. Maher. Oracle Semantics for PROLOG. In H. Kirchner and G. Levi, editors, Algebraic and Logic Programming, Proceedings of the Third International Conference, volume 632 of Lecture Notes in Computer Science, pages 100--114. Springer-Verlag, Berlin, 1992.

....An ES semantics sem for a set of goals G Goals is a mapping G EventSeq. If G = Goals then sem will be called complete. An oracle is an ES semantics for G = f(A) j A is a built in atom g. The concept of oracle as it is presented here, has nothing to do with the concept as presented in [1] where an oracle is used to abstract away from the sequential depth first strategy of Prolog. We use an oracle to provide us with the meaning of the built in s. Starting in the next section we will try to develop a partial evaluation procedure which preserves the semantics of a given RLP program ....

R. Barbuti, M. Codish, R. Giacobazzi, and M. Maher. Oracle semantics for Prolog. In H. Kirchner and G. Levi, editors, Proceedings of the Third International Conference on Algebraic and Logic Programming, Lecture Notes in Computer Science 632, pages 100--114. Springer Verlag, 1992.

....corresponding components: 1) a standard analysis for the logic component of the program; and (2) a termination analysis for the control component. An approximate model for the control component (termination) can be provided either by applying techniques of abstract interpretation, as described in [6], or by applying proof procedures as proposed by [26] It is interesting to note that a precise model for the control component provides a result which reflects the standard Prolog semantics; while the worst approximation (which specifies that all termination conditions are possibly true) reflects ....

R. Barbuti, M. Codish, R. Giacobazzi, and M. Maher. Oracle Semantics for PROLOG. In H. Kirchner and G. Levi, editors, Algebraic and Logic Programming, Proceedings of the Third International Conference, volume 632 of Lecture Notes in Computer Science, pages 100--114. Springer-Verlag, Berlin, 1992.

....Prolog (although there have been suggestions to use dependency directed backtracking [71] Since depth first search is incomplete on infinite trees, not all answers are computed. The depth first search can be incorporated in the semantics in the same way as is done for Prolog (see, for example, [18, 17]) but we will not go into details here. In Section 8 we will discuss a class of CLP languages which use a top down execution similar to the one outlined above, but do not use backtracking. 21 Consider the transition hA; C; Si g hA; C 0 ; i where C 0 is a set of equations in L such that ....

R. Barbuti, M. Codish, R. Giacobazzi & M.J. Maher, Oracle Semantics for Prolog, Proc. 3rd Conference on Algebraic and Logic Programming, LNCS 632, 100-- 115, 1992.

....oracle showing how the oracle semantics can be abstracted for semantics based program analysis. We close with a short conclusion. For continuity and ease of readability, the proofs together with auxiliary lemmata, have been moved to the appendix. This paper is an extended and revised version of [Barbuti, Codish, Giacobazzi and Maher 92] in particular the ideas of [Barbuti, Codish, Giacobazzi and Maher 92] are reported in Sections 3 and 4.1. 2 Preliminaries In the following we assume familiarity with the standard definitions and notation for logic programs. The standard reference works by Apt [Apt 90] and Lloyd [Lloyd 87] ....

....program analysis. We close with a short conclusion. For continuity and ease of readability, the proofs together with auxiliary lemmata, have been moved to the appendix. This paper is an extended and revised version of [Barbuti, Codish, Giacobazzi and Maher 92] in particular the ideas of [Barbuti, Codish, Giacobazzi and Maher 92] are reported in Sections 3 and 4.1. 2 Preliminaries In the following we assume familiarity with the standard definitions and notation for logic programs. The standard reference works by Apt [Apt 90] and Lloyd [Lloyd 87] provide the necessary background material. Given a possibly infinite set X ....

R. Barbuti, M. Codish, R. Giacobazzi, and M. J. Maher. Oracle semantics for Prolog. In [Levi and Kirchner 92], pages 100--114.

....of SLD , with arbitrary elements . 0 denotes the first element of the trace . s 2 State s 2 TP (SLD) s c Gamma 0 2 TP (SLD) s c Gamma 2 TP (SLD) It is a common practice in logic program semantics to restrict the interest to ANDcompositional execution traces only (e.g. in [3, 15, 23]) Intuitively a set of traces is AND compositional if the execution trace of any (possibly non atomic) goal can be reconstructed by composing traces for atomic goals in the set. The inductive definition of the set E of AND compositional execution traces for atomic goals is in Table 1. It is a ....

....model complete wrt. H. ffl The trace abstraction ff t is obtained by approximating finite traces by the pair of their initial and final state enhanced with the sequence of clauses used in the trace, ff t (X ) fhh; B ; oei j h oe Gamma B 2 X g. This semantics has been recently used in [3] to model Prolog depth first search. ffl The sequence abstraction ff is obtained by approximating finite traces by the pair of their initial and final states in a clause like form: ff : T P (SLD) Clause) is such that ff (X ) fh b j h c Gamma b 2 X g. This ....

R. Barbuti, M. Codish, R. Giacobazzi, and M. Maher. Oracle semantics for PROLOG. In Proc. ALP'92 , LNCS 632, pp. 100-114, 1992. To appear in Inf. & Comp..

....oracle showing how the oracle semantics can be abstracted for semantics based program analysis. We close with a short conclusion. For continuity and ease of readability, the proofs together with auxiliary lemmata, have been moved to the appendix. This paper is an extended and revised version of [Barbuti, Codish, Giacobazzi and Maher 92] in particular the ideas of [Barbuti, Codish, Giacobazzi and Maher 92] are reported in Sections 3 and 4.1. 2 Preliminaries In the following we assume familiarity with the standard definitions and notation for logic programs. The standard reference works by Apt [Apt 90] and Lloyd [Lloyd 87] ....

....program analysis. We close with a short conclusion. For continuity and ease of readability, the proofs together with auxiliary lemmata, have been moved to the appendix. This paper is an extended and revised version of [Barbuti, Codish, Giacobazzi and Maher 92] in particular the ideas of [Barbuti, Codish, Giacobazzi and Maher 92] are reported in Sections 3 and 4.1. 2 Preliminaries In the following we assume familiarity with the standard definitions and notation for logic programs. The standard reference works by Apt [Apt 90] and Lloyd [Lloyd 87] provide the necessary background material. Given a possibly infinite set X ....

R. Barbuti, M. Codish, R. Giacobazzi, and M. Maher. Oracle semantics for Prolog. In [Levi and Kirchner 92], pages 100--114.

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