Maurizio Proietti and Alberto Pettorossi. Semantics preserving transformation rules for Prolog. In Partial Evaluation and Semantics-Based Program Manipulation, New Haven, Connecticut. (Sigplan Notices, vol. 26, no. 9), 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... 2 O(P; Q) if j i then Q j ;P 2 Q Modelling the operational behaviour of a logic program as a sequence of answers rather than as a set (as e.g. in [12, 5] explicitly takes the order in which solutions are found into account, and allows for multiple occurrences of the same answers (e.g. [3, 22, 11, 4]) Example 3. If P represents the program in Fig. 1 and Q the query path(a; X) then we have that O(P; Q) fX=bg; fX=cg; fX=bg) Note that O(P; Q) may be an in nite sequence, modelling the case where the Prolog evaluation mechanism constructs an in nite number of derivations and returns an ....

....the meaning of a goal by a sequence of computed answers. The semantics handles programs with cut and contains a bottom element that represents in nite looping. The semantics characterises a program by functional equations and is mainly developed towards proving termination of logic programs. Also [22] de nes an operational semantics by means of a sequence of answers and uses it to show that a number of transformation rules (unfold fold) preserve this semantics. It does not deal with programs containing cuts. In [2] Prolog control is explicitly modelled in a constraint logic language and a ....

M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In Proceedings of PEPM'91, Sigplan Notices, Vol. 26, N. 9, pages 274-284, 1991.

..... we model folding explicitly (instead of viewing foldings as abbreviations) we do not formulate speedup theorems. Giving conditions for total correctness of unfold fold transformations is a rather hot topic in the logic programming community, see e.g. TS84] KK90] Sek91] GS91] PP91a] BCE92] This is unlike the situation in the functional community where Kott s work (cf. section 4.9) seems rather isolated. It is tempting to explain this di#erence by observing . operational semantics traditionally enjoy a more respectable status in the former community than in the latter ....

.... consider the program a b; a c; d e; d f Now consider the goal [a,d] By first unfolding a and then unfolding d we first get [b,d] c,d] and then B 1 = b,e] b,f] c,e] c,f] By first unfolding d and then unfolding a we first get [a,e] a,f] and then B 2 = b,e] c,e] b,f] c,f] In [PP91a] one wants to distinguish between B 1 and B 2 , and therefore unfolding of the leftmost atom only is allowed (unless extra conditions are satisfied. It is important to make the following observation: as configurations are multisets, backtracking is automatically accounted for in the model. On ....

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Maurizio Proietti and Alberto Pettorossi. Semantics preserving transformation rules for Prolog. In Partial Evaluation and Semantics-Based Program Manipulation, New Haven, Connecticut. (Sigplan Notices, vol. 26, no. 9), 1991.

....of logic programs unfolding is not problematic. For example, it preserves both the least Herbrand model and set of computed answer substitutions semantics and even in the context of the unfair Prolog selection rule it cannot worsen the (universal) termination behaviour of a program [21]. Under tabled execution, however, unfolding even determinate may transform a terminating program into a non terminating one Naturally, this is a situation that better be avoided. To reason about unfolding of tabled logic programs, we describe a framework that captures their termination ....

.... negation executed under SLD(NF) or variants thereof) any unfolding is totally correct and does not modify the termination behaviour of the program (see e.g. 18] In the context of a fixed, unfair selection rule, like Prolog s left to right rule, unfolding can even improve termination (cf. [21]) but never worsen it. In the Prolog setting (i.e. if we take clause order, depth first strategy into account) unrestricted unfolding can only affect the existential termination of programs, because unfolding can change the order of solutions. Moreover, determinate unfolding does not modify the ....

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M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In Proceedings of the ACM Symposium on Partial Evaluation and Semantics based Program Manipulation, PEPM'91, Sigplan Notices, Vol. 26, N. 9, pages 274-- 284, Yale University, New Haven, U.S.A., 1991.

....more than one live clause, where dead clauses are those that contain an immediately failing atom) This guarantees that the amount of nondeterminism is not increased, which would be harmful for the efficiency. Determinate unfolding is also used in the ECCE partial evaluation system [LMS98] In [PP91] Pettorossi and Proietti propose two restrictive definitions of unfold for definite programs: Unfold of the leftmost atom, which is clearly not harmful wrt any semantics (as it trivially cannot cause any left propagation) and deterministic non left propagating unfold. Definition 3.2 ....

....Prolog or pure Prolog programs, one has to give a definition for it which takes into account the order of the literals in clause bodies. A first relevant result in the direction of an unfold fold transformation system which preserves left termination was presented by Proietti and Pettorossi in [PP91] They propose a transformation system for definite programs which is similar to [TS84] with three additional conditions: a) no reordering of the atoms is allowed, b) unfolding is allowed only for the leftmost atom of a clause or in the case of a deterministic non left propagating atom, and (c) ....

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M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In ACM SIGPLAN Symposium on Partial Evaluation and Semantics-Based Program Manipulation (PEPM '91), New Haven, CT (U.S.A.) (SIGPLAN NOTICES, Vol.26 (9)), pages 274--284. ACM press, 1991.

....This for instance is not guaranteed by the partial deduction framework of [60] which only preserves the computed answers but not their sequence. However, the semantics of the if then else remains reasonably simple and a straightforward denotational semantics [38] in the style of [4] and [79], can be given to ITE Prolog. For example, suppose that we associate to each ITE Prologliteral L a denotation [jL]j P in the program P , which is a possibly infinite sequence of computed answer substitutions with an optional element at the end of (a finite sequence) to denote looping. Some ....

.... been solved in various ways in the partial evaluation literature [77, 76, 83, 82] as well as overlooked in some contributions (e.g. 27] In the context of unfold fold transformations of pure logic programs, preservation of the order of solutions, as well as left termination, is handled e.g. in [79, 7]. In the remainder, we will use the techniques we described in [48] to specialise ITE Prolog programs. The method of [48] tries to strictly enforce the Prolog left toright selection rule. However, sometimes one does not want to select the leftmost atom, for instance because it is a built in which ....

M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In Proceedings of the ACM Symposium on Partial Evaluation and Semantics based Program Manipulation, PEPM'91, Sigplan Notices, Vol. 26, N. 9, pages 274--284, Yale University, New Haven, U.S.A., 1991.

.... partial evaluation process is addressed in [Hol91] Upper bounds for the speedup possible by applying unfold fold transformations have been given in [Han91] Hon91] Several ways to guarantee total correctness have been proposed in the literature, e.g. TS84] KK90] Sek91] Kot85] GS91] [PP91a]. They all work by putting forward some restrictions on the types of foldings allowed. For a more detailed description (and comparison with our approach) see Sect. 5. The purpose of this paper is to present a model for unfold fold transformations which enables one to express conditions which are ....

....1. If 1 u C C 1 and 1 u C C 2 , with C 1 and C 2 pruned, then there exists D such that 1 u C 1 D and 1 u C 2 D. This proposition only holds because we imposed no ordering on the elements of a configuration, which thus is a multiset and not a sequence of basic configurations. In [PP91a] one wants to model the fact the standard PROLOG explores the branches in sequential order, and therefore unfolding of the leftmost atom only is allowed (unless extra conditions are satisfied) Suppose we have a function E which from a basic configuration B and a configuration C in normal form ....

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Maurizio Proietti and Alberto Pettorossi. Semantics preserving transformation rules for Prolog. In Partial Evaluation and Semantics-Based Program Manipulation, New Haven, Connecticut. (Sigplan Notices, vol. 26, no. 9), 1991.

....box model is related to the control flow, the Prolog subset of) this reformulation is a very good candidate to be the basis of our Prolog model specification. In the following, we briefly describe this semantics; more detailed descriptions can be found in [7] and [25] Pettorossi and Proietti [26, 28] also proposed an operational semantics for Prolog, but it does not handle the cut. The direct style semantics proposed by Jones and Mycroft [17] as well as the one of Debray and Mishra [12] do handle the cut. But we believe that the semantics of Nicholson and Foo is more elegant because the ....

M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In Proc. of the Symp. on Partial Evaluation and Semantics-Based Program Manipulation. ACM Press, 1991. Sigplan Notices 26:9.

....into Prolog. We discuss further work and conclude in Section 5. 2 An operational continuation semantics for Prolog Since a trace should reAEect as much as possible the program execution, relying on an (existing) operational semantics to specify a trace seems natural. Pettorossi and Proietti [11] proposed an operational semantics for Prolog, but it does not take the cut into account. The one proposed by Debray and Mishra [4] does handle the cut, but is quite unpractical. Nicholson and Foo dene in [10] a continuation based semantics for Prolog which captures very elegantly the cut ....

M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In PEPM'91. ACM Press, 1991. Sigplan Notices 26:9.

....is slightly more restrictive than the one of [TS84] Our system is based on a modularization of the program which distinguishes the part which can be transformed and guides the transformation. Other approaches to preserving termination properties, while transforming a program, can be found in [PP91,CG94,BE94,BC94,BC97]. The work of Proietti and Pettorossi in [PP91] made an important step forward in the direction of the preservation of left termination. They proposed a transformation system which is more restrictive than the ordered version of [TS84] since only unfolding the leftmost atom or a deterministic ....

....is based on a modularization of the program which distinguishes the part which can be transformed and guides the transformation. Other approaches to preserving termination properties, while transforming a program, can be found in [PP91,CG94,BE94,BC94,BC97] The work of Proietti and Pettorossi in [PP91] made an important step forward in the direction of the preservation of left termination. They proposed a transformation system which is more restrictive than the ordered version of [TS84] since only unfolding the leftmost atom or a deterministic atom is allowed. They proved that such a system ....

M. Proietti and A. Pettorossi. Semantics preserving transformation rules for prolog. In ACM SIGPLAN Symposium on Partial Evaluation and SemanticsBased Program Manipulation (PEPM '91). ACM press, 1991.

....by implementation. By induction hypothesis, the predicate p(y) is healthy and returns only extensions of the input substitution. Because z is fresh, replacing y with it can not spoil any already computed substitution, but only extend it, so the resulting predicate is healthy too. The article [PP91] describes some related results on the sequence of answer substitutions semantics and set of answer substitutions semantics of logic programs, and discusses under which syntactical restrictions the transformation rules of Prolog preserve the first semantics. Other related work on the semantics ....

.... a stepwise development of operational and denotational semantics for Prolog is described in [JM84] and the use of algebraic semantics for proving Prolog termination and transformation is described in [Ros00] using CCS to model Prolog) Other interesting articles include: vEK76] GM87] and [PP91]. Egon Borger uses evolving algebras for a semantical analysis of the logic programs, with case studies on (full) Prolog, BABEL and Godel [Bor94, BLR94, BR94] For general background reading I have used the following books: ffl logic programming and Prolog: Spi96, Llo93, Apt97, SS86, AdBR93, ....

M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In Proceedings of PEPM91 (ACM Symposium on Partial Evaulation and Semantics Based Program Manipulation) , volume 26 of Sigplan Notices, pages 274--284. ACM, September 1991.

....helps to validate the extended specification is given in appendix. 2 An operational continuation semantics for Prolog Since a trace should reflect as much as possible the program execution, relying on an (existing) operational semantics to specify a trace seems natural. Pettorossi and Proeitti [16, 17] proposed an operational semantics for Prolog, but it does not take the cut into account. The one proposed by Debray and Mishra [6] does handle the cut, but is quite unpractical. Nicholson and Foo define in [15] a continuation based semantics for Prolog which captures 2 unify j t 1 t 2 i: ae ( ....

M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In PEPM'91, pages 274--284. ACM Press, 1991. Sigplan Notices 26:9.

.... in unfold fold transformation [TS84,GS91,KF86,PP93] Methods for constraining unfold fold transformations (of logic programs) to guarantee correctness under various semantic interpretations have been widely studied see Tamaki and Sato s work [TS84] and its many derivatives e.g. Sek93] Sat90][PP91]. See [Amt92] for a technical framework in which many of these conditions can be expressed, and [PP93] for an overview of the methods. There are (informal) similarities between our method of constraining unfold fold using ticks and the method of counters of Kanamouri and Fujita 7 [KF86] a ....

M Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In Proceedings of the symposium on Partial Evaluation and Semantics-Based Program Manipulation. ACM press, SIGPLAN notices, 26(9), September 1991.

....by computing specializations for all of the procedure calls in the main procedure body, and then defining these new specialized procedures by recursively specializing their bodies. This was the approach we used in [19, 31] and is similar to the work of Proietti and Pettorossi for Prolog and Lisp [28, 27]. The correctness of these systems is entirely dependent on the correctness of the specializers, and these in turn are constraint simplifiers. The bulk of our work on partial evaluation will consist in defining the constraint language and implementing and verifying the correctness of the ....

M. Proietti, A. Pettorossi. Semantics Preserving Transformation Rules for Prolog, Proceedings of the Symposium on Partial Evaluation and Semantics-Based Program Manipulation, Yale University, New Haven, CT, pp. 274-284, ACM Press, Jun. 17-19, 1991.

....of the calls to p before applying eventually several times the simplification transformation. While performing our transformation, we want to preserve an operational equivalence between programs similar to this preserved by Mixtus and Paddy, or proposed by M. Proietti and A. Pettorossi [PP91]. Our equivalence, named strong operational equivalence in [PDL91] means to have between two pairs (program, goal) same answer substitutions; in the same order; and that there exists a bijection on infinite derivations in the SLD trees of the original and the transformed program, at the same ....

M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In ACM Symposium on Partial Evaluation and Semantics Based Program Manipulation, New-Haven, U.S.A., June 1991.

....of the if then else has its price in terms of a more complex partial evaluation procedure. In turn however, the if then else, is much better suited for partial evaluation than the full blown cut. For instance, a simple denotational semantics, along the line of the semantics described in [2] and [69], can be given to RLP and the unfolding techniques are also much simpler (see [42] and the example below) Using the if then else instead of the cut was already advocated by O Keefe in [64] and performed by Takeuchi and Furukawa in [79] 5.2 Specialising RLP In order to preserve the sequence of ....

.... has been solved in various ways in the partial evaluation literature [66,67,72,73] as well as overlooked in some contributions (e.g. 24] In the context of unfold fold transformations of pure logic programs, preservation of the order of solutions, as well as left termination, is handled e.g. in [5, 69]. The solution that has been used in [42] for RLP, is to strictly enforce the Prolog leftto right selection rule. However, sometimes one does not want to select the leftmost atom, for instance because it is a built in which is not sufficiently instantiated, or simply to ensure termination of the ....

M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In Proceedings of the ACM Symposium on Partial Evaluation and Semantics based Program Manipulation, PEPM'91, Sigplan Notices, Vol. 26, N. 9, pages 274--284, Yale University, New Haven, U.S.A., 1991.

.... built in s cannot always be specified logically (var 1 for instance) and that built in s can generate side effects which have no impact on the computed answers (print 1 for example) We fulfilled all the above requirements by adapting the denotational semantics of pure Prolog as defined in [2] and [17]. In these papers the semantics semP of a pure Prolog program P is a mapping from goals to (possibly infinite) sequences of computed answers. These sequences can be terminated by a least element which captures divergence (non termination producing no computed answer) Our semantics is based ....

....construction. Let us just state that the equivalence notion j for event sequences induces an equivalence on ES semantics and we thus obtain an equivalence relation between programs. All further details will be made available in an upcoming technical report. 3 This definition avoids a mistake of [17] which uses equivalence up to a renaming substitution (for which, contrary to what is stated in [17] fY=X1g and fY=X2g are not equivalent) 4 On page 48 of [19] it is stated that It is a question open to future research whether it is feasible to execute assert 1 and retract 1 by a partial ....

[Article contains additional citation context not shown here]

M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In Proceedings of the ACM Symposium on Partial Evaluation and Semantics based Program Manipulation, PEPM'91, Sigplan Notices, Vol. 26, N. 9, pages 274-- 284, Yale University, New Haven, U.S.A., 1991.

....several extensions of the original Tamaki and Sato s rules have been studied. It has also been 15 proved that, under suitable hypotheses, the unfold fold rules preserve several semantics of de nite logic programs, such as computed answers, nite failure, pure Prolog, and left termination (see [14, 39, 77, 92, 100, 105, 123]) The transformational approach has also been considered in the case of various extensions of de nite logic programs, such as logic programs with negation (see Section 5) constraint logic programs [8, 64, 106] and concurrent constraint programs [65, 148] General methods for proving the ....

M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In ACM Symposium on Partial Evaluation and Semantics Based Program Manipulation, PEPM '91, Yale University, New Haven, Connecticut, USA, pages 274284. ACM Press, 1991.

....completeness. Variants of the above transformation rules can be shown to be correct w.r.t. richer logic languages and other program semantics (see, for instance, Aravindan Dung 93, Bossi Cocco 93, Bossi Cocco Etalle 92, GardnerShepherdson 91, Kanamori Horiuchi 87, Kawamura Kanamori 88, Maher 93, Proietti Pettorossi 91a, Sato 92, Seki 91, Seki 93] and [Pettorossi Proietti 94] for an overview) 3.2 Transformation Strategies for Logic Programs Here we list some of the strategies we use for transforming logic programs. i) Predicate Tupling Strategy. This strategy, also called tupling, for short, consists in ....

Proietti, M., Pettorossi, A.: Semantics Preserving Transformation Rules for Prolog. Proc. ACM Symposium on Partial Evaluation and Semantics Based Program Manipulation, PEPM '91, New Haven USA, Sigplan Notices 26 9 (1991) 274--284

....and Prolog[P 1 ; p] hi. Transformation of Logic Programs 39 We also have that the use of the folding rule does not necessarily preserve the Prolog semantics. In order to overcome this inconvenience, several researchers have proposed restricted versions of the unfolding and folding rules [ Proietti and Pettorossi, 1991; Sahlin, 1993 ] The following two instances of the unfolding rule can be shown to be totally correct w.r.t. Prolog. Rule R1.1 Leftmost Unfolding. The unfolding of a clause C w.r.t. the leftmost atom of its body is said to be a leftmost unfolding of C. Rule R1.2 Single Non left propagating ....

M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In ACM Symposium on Partial Evaluation and Semantics Based Program Manipulation, PEPM '91, Yale University, New Haven, Connecticut, USA, pages 274--284. ACM Press, 1991.

....other termination properties, such as left termination, when we use the enhanced rules we have introduced, is left for future studies. However, we believe that one can provide versions of our rules which preserve such properties, by extending the approaches proposed for Tamaki and Sato s rules in [1, 3, 18]. Finally, notice that for an efficient evaluation of the specialized programs, one may remove during a post processing phase the inequalities which have been introduced by the application of the case split rule. This can be done by replacing inequalities in favour of cuts as specified by the ....

M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In ACM Symposium on Partial Evaluation and Semantics Based Program Manipulation, PEPM '91, Yale University, New Haven, Connecticut, USA, pages 274--284. ACM Press, 1991.

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Maurizio Proietti and Alberto Pettorossi. Semantics preserving transformation rules for Prolog. In Partial Evaluation and Semantics-Based Program Manipulation, New Haven, Connecticut. (Sigplan Notices, vol. 26, no. 9), 1991.

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M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In Proceedings of the ACM Symposium on Partial Evaluation and Semantics based Program Manipulation, PEPM'91, Sigplan Notices, Vol. 26, N. 9, pages 274-284, Yale University, New Haven, U.S.A., 1991.

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M. Proietti and A. Pettorossi. Semantics preserving transformation rules for Prolog. In Proceedings of PEPM'91, Sigplan Notices, Vol. 26, N. 9, pages 274-284, 1991.

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