H. Seki. On the Power of Alexander Templates. In Proc. of PODS'89. pp. 150-159. ACM Press.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and to provide optimizations such as avoiding the computation of duplicated facts, and the memoization of intermediate results. As examples, we have the transformations called Generalized Magis Sets [5, 12] Generalized Supplementary Magic Sets [5] Magic Templates [19] Alexander Templates [24], Counting Methods [23] and recently Induced Magic Sets [6] Although bottom up evaluation based on magic sets has been studied in the context of logic programming, there are some approaches (for instance [13] which consider bottom up evaluation of constraint logic programs, showing a new ....

....predicate associated to p, ends and obtains p(0) as fact. Later [19] the well formed condition was removed but no general result of termination for bottom up evaluation was presented by allowing function symbols (and therefore for general Horn logic programs) although some attempts were done [24, 19]. In the presence of function symbols, the Herbrand model of a logic program can be in nite and thus, in the general case, the bottom up evaluation of the original and transformed program cannot end. Therefore, the introduction of function symbols causes uncompleteness for negative information. In ....

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H. Seki. On the Power of Alexander Templates. In Proc. of PODS'89. pp. 150-159. ACM Press.

....such as avoiding the computation of duplicated facts, and the memoization of intermediate results. As examples, we have the transformations called Generalized Magis Sets [RSS90, BR91, RSS92, Bra95, KSS95] Generalized Supplementary Magic Sets [BR91] Magic Templates [Ram91] Alexander Templates [Sek89] Counting Methods [SZ88] and recently Induced Magic Sets [Cod97] Although bottom up evaluation based on magic sets has been studied in the context of logic programming, there are some approaches (for instance [Tom95, KS96] which consider bottom up evaluation of constraint logic programs, ....

....associated to p, ends and obtains p(0) as fact. Later [Ram91] the well formed condition was removed but no general result of termination for bottom up evaluation was presented by allowing function symbols (and therefore for general Horn logic programs) although some attempts were done [RSS92, Sek89, Ram91] In the presence of function symbols, the Herbrand model of a logic program can be in nite and thus, in the general case, the bottom up evaluation of the original and transformed program cannot end. Therefore, the introduction of function symbols causes uncompleteness for negative ....

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H. Seki. On the Power of Alexander Templates. In Proc. of PODS. pp. 150-159. ACM Press, 1989.

....version, and also additional discussion and material on functional dependency inference. 2 The work of R. Ramakrishnan was supported in part by an IBM Faculty Development Award and NSF grant IRI 8804319. Part of the work was done while visiting IBM Thomas J. Watson Research Center. 1 mind [5, 6, 8, 13, 20, 22, 23, 26]. In principle, bottom up methods can also be used to evaluate programs with function symbols and few, possibly non ground, facts [20, 26] Our central thesis, and the motivation for this work, is that the bottom up approach has the potential to be comparable to or superior in efficiency to ....

....Development Award and NSF grant IRI 8804319. Part of the work was done while visiting IBM Thomas J. Watson Research Center. 1 mind [5, 6, 8, 13, 20, 22, 23, 26] In principle, bottom up methods can also be used to evaluate programs with function symbols and few, possibly non ground, facts [20, 26]. Our central thesis, and the motivation for this work, is that the bottom up approach has the potential to be comparable to or superior in efficiency to top down methods for a wide range of logic programs. Given the soundness and completeness of the approach, in contrast to the incompleteness ....

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H. Seki, On the Power of Alexander Templates. In Proc. 8th ACM SIGMOD-SIGACT Symposium on Principles of Database Systems, 1989.

....costs of memoing set oriented evaluations, and suggests an important direction for future research. 1 Introduction The following example demonstrates that Prolog with last call optimization (see, e.g. MW88] can beat bottom up evaluation using Magic Sets Magic Templates optimization ([RLK86, Sek89, BMSU86, BR87b, Ram88]) for some Datalog programs. Example 1.1 This example is from [Ros91] Let P be the program p(X; Z) e(X; Y ) p(Y; Z) p(n; X) t(X) e(1; 2) e(n Gamma 1; n) t(1) t(m) Query: p(1; X) Given the subgoal p(1; X) Prolog sets up subgoal e(1; X) and gets an answer ....

....(such as a unification of a subgoal with the head of a rule, or generation of a subquery) and no more than 2 different derivations are mapped on to the same action of Prolog . 2 By taking last call optimization into account, this theorem extends earlier results of Ramakrishnan [Ram88] and Seki [Sek89] which compare the number of inferences made by bottom up evaluation with the number of inferences made by specific top down strategies. We observe again that the number of inferences is only one aspect of the cost of an evaluation strategy. To obtain a more accurate comparison, the cost of each ....

H. Seki. On the power of Alexander templates. In Proc. of the ACM Symposium on Principles of Database Systems, pages 150--159, 1989. 13

.... We use a term representation based on persistent versioning to greatly reduce the cost of copying (Section 4) The second cause for inefficiency is less obvious, and is present with Magic Templates rewriting as well as with its variants (MTTR rewriting [14] and Alexander Templates [16]) The unifications in the first two derivations in the evaluation shown above have corresponding unifications in a Prolog evaluation. But there are no unifications in a Prolog evaluation corresponding to the unifications in the third derivation the derivation corresponds to a step in the ....

....these facts. We present one such program in Example 7.2. For such programs Opt NGBU combines the best features of Prolog evaluation and bottom up evaluation. The question of how bottom up and top down methods compare is considered important, and has been under investigation by several researchers [20, 3, 9, 16]. Our result carries the comparison of top down and bottom up methods farther than earlier results in three important ways: a) it extends the class of programs considered from safe Datalog to full logic programs, b) it compares bottom up evaluation with a sophisticated model of Prolog ....

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H. Seki. On the power of Alexander templates. In Procs. of the ACM Symposium on Principles of Database Systems, pages 150--159, 1989.

....negation [3, 7] into our framework, we treat positive and negative literals symmetrically. This means that we do not impose a positivistic computation rule [14, 17] i.e. one that always prefers positive literals) Moreover, in contrast to extensions of OLDT resolution for stratified programs [9, 19], we maintain only one table, where the entry for an atom can be used either positively or negatively. This is the main point where our research deviates from [4, 5] Acknowledgments We thank W lodzimierz Drabent, Ulf Nilsson, Halina Przymusinska, Teodor Przymusinski and David S. Warren for many ....

H. Seki. On the power of Alexander Templates. In Proc. of the 8th Symposium on Principles of Database Systems. ACM SIGACT-SIGMOD, 1989.

....inefficient, often solving previously solved goals over and over again. OLDT resolution, due to Tamaki and Sato [34] is a technique which caches previously derived solutions in a table. The theory and implementation of OLDT has been studied extensively by several researchers including Seki [28, 27] and Warren and his colleagues [9, 10] Furthermore, it is known that OLDT and magic set computations [5, 6, 26] are essentially equivalent, though they differ in many (relatively minor) details. We will use the OLDT technique as our starting point, and extend it as follows: 1) Multiple ....

H. Seki. (1989) On the Power of Alexander Templates, Proc. 8th ACM Symp. on Principles of Database Systems, pps 150--159.

....Tel: 516) 632 8470 Fax: 516) 632 8334 1 Introduction SLG resolution [4, 6] is emerging as a powerful technique for combining Deductive Databases, Non monotonic Reasoning and Logic Programming. SLG is a generalization of SLD resolution with tabling. A form of SLD with tabling has been shown in [13] to be asymptotically equivalent to a variant of magic templates [11] Among properties relevant to deductive databases, SLG evaluates programs according to the well founded model [16] terminates for programs with bounded term size, and has polynomial data complexity for Datalog programs with ....

H. Seki. On the power of Alexander templates. In ACM Symposium on Principles of Database Systems, pages 150--159, 1989.

....programs, but many programs that are hard to think of in Prolog are very natural in HiLog. These advances in LP and DD are converging. It turns out that OLDT and Magic Template evaluation are very closely related, essentially slightly different implementations of the same underlying algorithm [Sek89] Also higher order extensions have been found to be important in the DD area as well (see the NAIL GLUE project at Stanford [PDR91] One difference between LP and DD efforts is that LP tends to assume data is memory resident and DD worries about disk accesses. It is a clear trend that memory ....

Hirohisa Seki. On the power of Alexander templates. In Proceedings of the Eighth Symposium on Principles of Database Systems, pages 150--159. ACM Press, 1989. Philadelphia, PA.

.... database community, primarily on ramifications and generalizations of the magic set notation (see [BMSU86, BR87] Concern there is with passing relevant goal and binding information within a Horn clause setting (without function symbols) Further work incorporating this approach appears in [Sek89] and [Bry90] for example. Stickel [Sti] addresses non Horn clause sets, interpreting the goal oriented Model Elimination procedure within a forwardchaining paradigm. Demolombe [Dem91] likewise introduces a methodology for non Horn sets using a variant of the magic set concept together with a ....

....relevancy mechanism introduced here provides the needed goal oriented search to allow the advantages of both goal oriented procedures and data driven procedures to be realized in one procedure. Of course, this was the original intent of the magic set [BMSU86, BR87] and Alexander template devices [Sek89] introduced into the database community in the 1980 s. SATCHMORE is in this spirit. As mentioned earlier, the ideas introduced here have been put in the declarative format of magic sets and Alexander templates in [HOI93] 23 7 Summary We have provided an extension to the SATCHMO prover that ....

H. Seki. On the power of Alexander templates. In Proc. of the Eighth ACM Symposium on Principles of Database Systems, 1989.

....prepass of Magic Templates rewriting can be used to avoid the generation of non ground facts at the cost of computing irrelevant facts. 2 Prolog systems, such as tail recursion optimization, were ignored ( Ull89] or (3) the cost of operations such as unification and indexing were ignored ([Bry90, Ram88, Sek89]) Since we remove all these restrictions, our work represents a major advance on earlier work. Opt NGBU evaluation can be much faster than Prolog evaluation if redundant computation is avoided through subsumption checks; the time complexity of evaluation may be significantly better, and infinite ....

.... scheme for binding environments to permit modification of shared variables without damaging stored facts (Section 3) The second cause for inefficiency is less obvious, and is present with Magic Templates rewriting as well as with its variants (MTTR rewriting [Ros91] and Alexander Templates [Sek89]) The sequence of unification operations in the evaluation shown above is as follows: the given query(paths( fact is unified with the body of rule QR1:1 to generate a query(dappend( fact. The query(dappend( fact is unified with the body of rule R2 0 to generate an answer ....

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H. Seki. On the power of Alexander templates. In Proc. of the ACM Symposium on Principles of Database Systems, pages 150--159, 1989.

.... in a number of negative contexts that is exponential in the size of the Herbrand base of a function free programs [11] Techniques for effective set at a time query evaluation have been studied in deductive databases, including magic sets [4, 5] magic templates [33] and Alexander templates [39]. The main idea is to simulate top down SLD resolution to avoid generation of tuples irrelevant to the given goal. In fact, tuples of magic predicates correspond to subgoals maintained in OLDT resolution [43] For definite programs, it has been shown [8, 39] that the top down with memoing and the ....

....templates [33] and Alexander templates [39] The main idea is to simulate top down SLD resolution to avoid generation of tuples irrelevant to the given goal. In fact, tuples of magic predicates correspond to subgoals maintained in OLDT resolution [43] For definite programs, it has been shown [8, 39] that the top down with memoing and the set at a time approaches are essentially equivalent. Methods of query processing have been investigated for stratified and modularly stratified programs [3, 34, 37] With negation, the major issue becomes maintaining dependencies among magic tuples (or ....

H. Seki. On the power of Alexander templates. In ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 150--159, March 1989.

....in the context of bottom up parallel evaluation [CW89] We think that on the contrary much can be gained by a careful study of the literature of both top down and bottom up approaches. There is a strong relationship between the structure of top down and bottom up computations, as demonstrated in [Ra88, Se89] and also [BMSU86, BeR87, Br89, Ul89b, Ul89a, Vi89, KL86, KL88] etc. While the details of an implementation of a top down method would differ considerably from that of a bottom up method, we believe that many ideas, such as schemes for structure sharing, are likely to work in either approach. ....

.... and expositions presented in [BaR86, Br89, NR89, Ul89a] We note that while most of this literature deals with the implementation of Datalog, which is a subset of logic programs without function symbols, and also does not deal with nonground terms, recent proposals treat full logic programs [Ra88, Se89]. We will examine one of these proposals ( Ra88] in detail later. The following brief discussion should be supplemented by consulting Section 5. The fundamental operation in bottom up approaches is the application of a rule to a set of facts to generate new facts, which is similar to the use of ....

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H. Seki, On the Power of Alexander Templates. In Proc. 8th ACM SIGMOD-SIGACT Symposium on Principles of Database Systems, pages 150-159, 1989.

....between tuple at a time behavior and set at a time can be viewed as one of scheduling. Accordingly, we define a breadth first set at a time tabling strategy and prove it iteration equivalent to a form of semi naive magic evaluation. That is, we extend the well known asymptotic results of Seki [10] by proving that each iteration of the tabling strategy produces the same information as semi naive magic. Further, this set at a time scheduling is amenable to implementation in an engine that uses Prolog compilation. We describe both the engine and its performance, which is comparable with the ....

....added features of database evaluation to logic programming languages. Magic evaluation closely resembles tabling. Both magic and tabling combine top down goal orientation with bottom up redundancy checking. Indeed, for rangerestricted programs, they have been proven to be asymptotically equivalent [10, 8] under certain assumptions. Despite these well known equivalences, magic style systems have traditionally differed from tabling systems. Magic style systems, such as Aditi [15] CORAL [7] and LDL [3] are built upon set at a time semi naive engines, while tabling systems, such as XSB [9] use a ....

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H. Seki. On the power of Alexander templates. In Proceedings of PODS, pages 150--159, 1989.

....answers and result in unacceptable inefficiency. The problem of evaluating recursive (Datalog) queries has been extensively studied and a number of techniques have been proposed (see e.g. BR86] Vie89] CW96] Recently, two approaches have gained special attention: 1) magic sets [BMSU86, Sek89, BR91, Ram91] which adds goal directedness to bottom up evaluation, and (2) tabling (or memoization) CW96, TS86, Vie89, BD93] which adds features of database evaluation to logic programming languages. These two approaches resemble each other in that they combine top down goal orientation with ....

....BD93] which adds features of database evaluation to logic programming languages. These two approaches resemble each other in that they combine top down goal orientation with bottom up redundancy checking. In fact, under certain assumptions they have been proved to be asymptotically equivalent [Sek89] Despite these well known equivalences, magic style systems have traditionally differed from tabling systems. Magic style systems, such as LDL [CGK 90] CORAL [RSS92b] Glue Nail [DMP93] and Aditi [VRK 94] are built upon set at a time engines, and can use set at a time operations like ....

[Article contains additional citation context not shown here]

H. Seki. On the power of Alexander templates. In Proceedings of PODS, pages 150--159, 1989.

....between tuple at a time behavior and set at a time can be viewed as one of scheduling. Accordingly, we define a breadth first set at a time tabling strategy and prove it iteration equivalent to a form of semi naive magic evaluation. That is, we extend the well known asymptotic results of Seki [15] by proving that each iteration of the tabling strategy produces the same information as semi naive magic. Further, this set at a time scheduling is amenable to implementation in an engine that uses Prolog compilation. We describe both the engine, which is freely available, and its performance, ....

....features of database evaluation to logic programming languages. Magic evaluation closely resembles tabling. Both magic and tabling combine top down goal orientation with bottom up redundancy checking. Indeed, for range restricted programs, they have been proven to be asymptotically equivalent [15, 13] under certain assumptions. Despite these well known equivalences, magic style systems have traditionally differed from tabling systems. Magic style systems, such as LDL [4] CORAL [12] Glue Nail [5] are built upon set at a time semi naive engines, while tabling systems, such as XSB [14] use a ....

[Article contains additional citation context not shown here]

H. Seki. On the power of Alexander templates. In Proc. of 8th PODS, pages 150--159. ACM, 1989.

....between tuple at a time behavior and set at a time can be viewed as one of scheduling. Accordingly, we define a breadth first set at a time tabling strategy and prove it iteration equivalent to a form of semi naive magic evaluation. That is, we extend the well known asymptotic results of Seki [13] by proving that each iteration of the tabling strategy produces the same information as semi naive magic. Further, this set at a time scheduling is amenable to implementation in an engine that uses Prolog compilation. We describe both the engine, which is freely available, and its performance, ....

....features of database evaluation to logic programming languages. Magic evaluation closely resembles tabling. Both magic and tabling combine top down goal orientation with bottom up redundancy checking. Indeed, for range restricted programs, they have been proven to be asymptotically equivalent [13, 11] under certain assumptions. Despite these well known equivalences, magic style systems have traditionally differed from tabling systems. Magic style systems, such as LDL [4] CORAL [10] Glue Nail [5] are built upon set at a time semi naive engines, while tabling systems, such as XSB [12] use a ....

[Article contains additional citation context not shown here]

H. Seki. On the power of Alexander templates. In Proc. of 8th PODS, pages 150--159. ACM, 1989.

....logic programs with tabling. Tabling methods [18, 21, 4, 3] have emerged as a powerful technique for incorporating Deductive Database and Non monotonic Reasoning capabilities within the framework of logic programming. In terms of deductive databases, a form of SLD with tabling has been shown in [17] to be asymptotically equivalent to a variant of Magic Templates [2] while having the same termination properties. In terms of non monotonic reasoning, the tabling methods of SLG [4] and of Bol and Degerstedt [3] evaluate programs according to the well founded model ( 20] with polynomial data ....

H. Seki. On the power of Alexander templates. In ACM Symposium on Principles of Database Systems, pages 150--159, 1989.

....of program transformations that includes the magic set and Alexander transformations. We call these query answer transformations. These transformations were introduced as recursive query evaluation techniques [2] 26] but have since been adapted for use in program analysis [6] 10] 17] [28], 14] They allow top down computation to be performed in a bottom up manner. The regular approximations introduced so far do not take into account possible queries to a program. By analysing the computation of a general call to a predicate p(x 1 ; xn ) we may get a more precise result ....

H. Seki. On the power of Alexander templates. In Proceedings of the 8 th ACM SIGACT-SIGMODSIGART Symposium on Principles of Database Systems, Philadelphia, Pennsylvania, 1989.

....Dynamic Programming also offers a solution to completeness problems one encounters with standard depth first strategies (as in PROLOG) It improves termination by avoiding those loops which correspond to infinite recomputations. Our approach is related to tabulation[TS86, Vie87] or magic set[Sek89] techniques proposed for Logic Programming,but encompasses them by being more flexible. Indeed, Dynamic Programming works for various automata which This work has been partly supported by the Eureka Software Factory (ESF) project. can encode all kinds of resolution strategies (e.g. SLD, ....

H. Seki. On the power of alexander templates. In Proc. of the 8th ACM symps. on principles of Databases Systems, 1989.

....through computation sharing. The first approach consists in adding a memoing mechanism to a standard PROLOG evaluator [TS86, Vie87, War89, LCMVH91] We will not discuss this approach in this paper. The second approach is provided by the so called Magic Set transformation and its extensions [BR87, BMSU86, Ram88, Sek89]. It relies on a semi naive (i.e. with tabulation) bottom up evaluation of a transformed version of the original program that includes magic predicates to restrict the computation to a useful part of the search space. We propose a third approach which, we believe, generalizes and explains ....

.... than the gain it procures [Shi85] The better known description of this technique is the Magic Set transformation for DATALOG programs [BMSU86, BR87, Ram88] It has been extended to PROLOG programs as the Magic Templates transformation [Ram88] and the Alexander Templates transformations [RLK86, Sek89]. The formulation of the transformation rules differs slightly from [BR87] and takes after [Nil91] In particular, the atoms call(A) resp. ret(A) are used in place of magic(A) resp. of A) 1. Each clause fl k of P is replaced by the n k 1 following clauses: ff) ret(A k:0 ) Gammacall(A k:0 ....

H. Seki. On the power of alexander templates. In Proc. of the 8th ACM symps. on principles of Databases Systems, 1989.

....to those presented in [18] 5. 3 Regular Approximations of Call Answer Programs The oddly named magic set and Alexander transformations were introduced as recursive query evaluation techniques [2] 3] and [16] They have since been adapted for use in program analysis [5] 7] 12] 14] and [17]. The motivation for using the transformations is the following: we want to examine particular computations rather than the model of the program. If we analyse a program (as it is) we get the success set of the program, which is in general larger than the information we want for a particular call ....

H. Seki. On the power of Alexander templates. In Proceedings of the 8 th ACM SIGACTSIGMOD -SIGART Symposium on Principles of Database Systems, Philadelphia, Pennsylvania, 1989.

....have been proposed for extending or replacing the standard WAM based implementation of PROLOG. For instance, one may cite the parallel models (independent AND parallelism[DeG84, HG90] OR parallelism[War87] the tabular models (OLDT[TS86] SLDAL[Vie87] XWAM[War89] or the magic set models[BMSU86, Sek89, UOKT84]. These models dif This work has been partially supported by the Eureka Software Factory (ESF) project. fer from the original one essentially in that they simultaneously maintain several computation branches instead of only one. This implies in particular that a variable may have multiple ....

H. Seki. On the power of alexander templates. In Proc. of the 8th ACM symps. on principles of Databases Systems, 1989.

....them seems to be able to guarantee the termination of bottom up evaluation of finite answer Datalog nS queries. Some of the methods, e.g. Magic Sets defined by Bancilhon, Maier, Sagiv and Ullman [3] introduce additional termination problems of their own, as noticed by Ramakrishnan [33] and Seki [39]. Therefore, we obtain termination in a different way. Essentially, we show that in the context of Datalog nS , it is sufficient to consider ground refutations containing terms of bounded depth. Consequently, in bottom up evaluation only facts with terms of bounded depth have to be generated. We ....

....like the one in Example 4.3 has been noticed in the literature. Kifer and Lozinskii [20] call it a diverging cycle feeding into a converging one . They present a technique, called signatures, that is helpful in the opposite situation, i.e. a converging cycle feeding into a diverging one. Seki [39] presents a variant of the same technique in the context of Magic Sets. The technique actually originates in the work of Sato and Tamaki [38, 43] Finally, Ramakrishnan [33] also recognizes the additional sources of non termination introduced by the Magic Sets transformation. Clearly, for some ....

H. Seki. On the Power of Alexander Templates. In ACM SIGACT-SIGMODSIGART Symposium on Principles of Database Systems, pages 150--159, Philadelphia, Pennsylvania, March 1989.

....LR ones, differentiate the syntactic contexts in function of the state where the parsing process is, by virtue of the application of a predictive technique in the generation of the parser. The idea to consider bottom up evaluation with a top down predictive control is not new. The Magic Set [5, 6, 7, 8] techniques reduce the number of useless intermediate results produced by using a goal oriented bottom up evaluation. The main drawback of this approach is the extra cost these methods require. In effect, the addition of predictive control is made by re writing logic programs and introducing new ....

H. Seki, "On the power of Alexander templates", in Proc. of the 8th ACM symp. on principle of Database Systems, 1989.

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