Gallagher, J.: 1991, `A System for Specialising Logic programs'. Technical Report TR-91-32, University of Bristol.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....as our specialization method does not depend on them. A partial evaluator and a regular approximation procedure capable of specializing and approximating pure logic programs are also assumed. Complete descriptions of one such partial evaluator and regular approximation procedure can be found in [5, 7]. 3.1 An Improved Decision Procedure In this section we show how approximate information derived through a regular approximation may be used to achieve useful specializations. The class of Regular Unary Logic Programs was defined by Yardeni and Shapiro [24] It is attractive to represent ....

....variables in resources are analyzed, we may need to take advantage of all the useful specializations. However, the partial evaluation step may assist in overcoming some of the problems posed by more complicated resource descriptions as it can factor out common structure at argument level (see [6, 5] for further details) ....

J. Gallagher. A system for specialising logic programs. Technical Report TR-9132, University of Bristol, November 1991.

.... dates back to at least [2] has been introduced to the logic programming community in a seminal paper of Tamaki and Sato [26] has since been the subject of considerable research (see e.g. the references in [18] and has been successfully used in many partial evaluators for Prolog style execution [20, 19, 25, 8]. Unfortunately, no methodology for the transformation or specialisation of tabled logic programs exists. All techniques stay within the context of untabled execution. Initially, one may expect that results established in the classic (S)LD setting more or less carry over. This, however, turns ....

J. Gallagher. A system for specialising logic programs. Technical Report TR-9132, University of Bristol, November 1991.

....the actual choice depends on the particular application. For a more detailed discussion we refer the reader to [35] 36, 8] 51] the conclusion of [66] or the 13 extended version of [56] Sometimes however, it is possible to combine both approaches. This was first exemplified by Gallagher in [29, 30], where a (declarative) meta interpreter for the ground representation is presented. From an operational point of view, this metainterpreter lifts the ground representation to the non ground one for resolution (an alternate declarative view is discussed below) We will call this approach the mixed ....

....are in non ground form while the object programs are in ground form. 10 With that technique we can use the versatility of the ground representation for representing object level programs (but not goals) while still remaining reasonably efficient. Furthermore, as demonstrated by Gallagher in [29] and by the experiments in this paper, partial evaluation can in this way sometimes completely remove the overhead of the ground representation. Performing a similar feat on a meta interpreter using the full ground representation with explicit unification is much harder and has, to the best of our ....

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J. Gallagher. A system for specialising logic programs. Technical Report TR-91-32, University of Bristol, November 1991.

....basic results of partial evaluation to the extension considered, as done for instance in [10] we would like to reduce our application to a special instance of the general case of partial evaluation in logic programming. Several program specialisers for logic programs have been developed (e.g. [18, 39, 44]) The majority of them is written in Prolog and employs extra logical features of the language, such as the cut operator and built in predicates like var, nonvar, assert, retract, and copy term. Unfortunately this spoils declarativeness, which is one of the distinguishing features of logic ....

....the obtained program New M w.r.t. partially instantiated object queries. In this perspective, we explored the possibility of combining our program specialiser with other existing general partial evaluators. In particular, we considered Mixtus [39] a partial evaluator for full Prolog, and SP [18], a system that is able to specialise declarative logic programs, written in Prolog s syntax. In order to evaluate the effectiveness of such a combination, we have compared the specialised programs obtained, respectively (see Fig. 3) I) By applying our program specialiser to the ....

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J.P. Gallagher. A System For Specialising Logic Programs. Technical Report TR-91-32, University of Bristol, 1991.

....operator. In addition to the conditions stated above, this abstraction operator should preserve as much of the specialisation that was (in principle) possible for the atoms in A. An approach which tries to achieve all these goals in an elegant and refined way is that of Gallagher and Bruynooghe [20, 17]. Its abstraction operator is based on the notions of characteristic path, characteristic tree and most specific generalisation. Intuitively, two atoms of A are replaced by their most specific generalisation in A 0 , if their (incomplete) SLDNFtrees under the given unfolding rule have an ....

....if the characteristic trees are preserved by the generalisation then a lot of the specialisation that was possible within A will still be possible within A 0 . Unfortunately, although the approach is conceptually appealing, several errors turn up in the arguments provided in [20] and [17]. In the current paper we show that these errors can lead to relevant precision losses and even to non termination of the partial deduction process. We will also show that these problems cannot be solved within the standard partial deduction approach based on [43] We therefore extend the standard ....

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J. Gallagher. A system for specialising logic programs. Technical Report TR-91-32, University of Bristol, November 1991.

....seems much harder than handling the local level. So, in this paper, it is to the latter, global, level that we turn our attention. The concept of characteristic trees has been advocated as a suitable and refined basis for the global control of partial deduction by Gallagher and Bruynooghe in [21, 18]. The main idea is, instead of using the syntactic structure to decide upon polyvariance, to examine the specialisation behaviour of the atoms to be specialised: only if this behaviour is sufficiently different from one atom to the other should different specialised versions be generated. However, ....

....2.3 Let A and A 0 be sets of atoms. Then A 0 is an abstraction of A iff every atom in A is an instance of an atom in A 0 . An abstraction operator is an operator which maps every finite set of atoms to a finite abstraction of it. The following generic scheme, based on a similar one in [18, 19], describes the basic layout of practically all algorithms for controlling partial deduction. Algorithm 2.4 Input: A program P and a goal G Output: A specialised program P 0 Initialise: i = 0 , A i = fA j A is an atom in G g repeat for each A k 2 A i , compute a finite SLDNF tree k for P ....

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J. Gallagher. A system for specialising logic programs. Technical Report TR-91-32, University of Bristol, November 1991.

....predicate definition will be generated) Under the conditions stated in [52] namely closedness (all leaves are an instance of an atom in S) and independence (no two atoms in S have a common instance) correctness of the specialised program is guaranteed. In a lot of practical approaches (e.g. [18, 19, 21, 42, 45, 39, 49]) independence is ensured by using a renaming transformation which maps dependent atoms to new predicate symbols. Adapted correctness results can be found in [4] 49] and [46] Renaming is often combined with argument filtering to improve the efficiency of the specialised program (see e.g. 20, 4] ....

.... can be found in [4] 49] and [46] Renaming is often combined with argument filtering to improve the efficiency of the specialised program (see e.g. 20, 4] and also [50] Closedness can be ensured by using the following outline of a partial deduction algorithm (similar to the ones used in e.g. [18, 19, 39, 44]) 5 Algorithm3. Partial deduction) Input: a program P and an initial set S0 of atoms to be specialised Output: a set of atoms S Initialisation: Snew : abstract(S0 ) repeat Sold : Snew Snew : fsn j sn 2 leaves(UP (so) so 2 Sold g Snew : abstract(Sold [ Snew ) until Sold = Snew ....

J. Gallagher. A system for specialising logic programs. Technical Report TR-9132, University of Bristol, November 1991.

....as our specialization method does not depend on them. A partial evaluator and a regular approximation procedure capable of specializing and approximating pure logic programs are also assumed. Complete descriptions of one such partial evaluator and regular approximation procedure can be found in [5, 7]. 3.1 An Improved Decision Procedure In this section we show how approximate information derived through a regular approximation may be used to achieve useful specializations. The class of Regular Unary Logic Programs was defined by Yardeni and Shapiro [24] It is attractive to represent ....

....variables in resources are analyzed, we may need to take advantage of all the useful specializations. However, the partial evaluation step may assist in overcoming some of the problems posed by more complicated resource descriptions as it can factor out common structure at argument level (see [6, 5] for further details) ....

J. Gallagher. A system for specialising logic programs. Technical Report TR-9132, University of Bristol, November 1991.

....as our specialization method does not depend on them. A partial evaluator and a regular approximation procedure capable of specializing and approximating pure logic programs is also assumed. Complete descriptions of one such partial evaluator and regular approximation procedure can be found in [12, 14]. 3.1 An Improved Specialization Procedure In this section we show how approximate information derived through a regular approximation may be used to achieve useful specializations. First, we introduce Regular Unary Logic Programs. This class of programs was defined by Yardeni and Shapiro [48] ....

....can be used. It is also not compulsory to have a partial evaluation step, as our small example in Figure 2 illustrates, but it has been shown in [9, 7] that it usually improves the analysis results to such an extent that we now always include it in the specialization process. The SP System [12] utilizing a determinate unfolding rule with some renaming was used to obtain the partially evaluated programs. As a second step we approximate with respect to the query goal( d; q] l] P lan; Resources) An empty approximation is computed 5 , which proves that it is impossible to obtain a ....

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J. Gallagher. A system for specialising logic programs. Technical Report TR-91-32, University of Bristol, November 1991.

....evaluator to make better use of the static information available from the first order theories. A minimal partial evaluator is then defined, suitable for the specialisation of proof procedures, that preserves the structure of the meta program. The terminology used is consistent with that in [65, 10, 36]. 3.1 Introduction Partial evaluation is ideally suited for removing most of the overheads incurred by the writing of meta interpreters, especially when using the ground representation. It is debatable if many useful meta interpreters can be written using this representation without the aid of a ....

....the specialisation of arbitrary meta programs. In this thesis we wish to show how significant improvements can be made on state of the art partial evaluations for the specialisation of meta programs. During the last few years many partial evaluators for various subsets of Prolog have been written [93, 36, 78, 62, 88]. Gurr presented a self applicable partial evaluator for Godel in [46] Most of these partial evaluators are based on the theory developed by Lloyd and Shepherdson [65] and the algorithm by Benkerimi and Lloyd [10] We repeat from [65] the basic definitions and main theorems that are used. ....

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J. Gallagher. A system for specialising logic programs. Technical Report TR-91-32, University of Bristol, November 1991.

....in the ground representation. We return to the relevance of performing specialisation at the object level at the end of this section. 1 A declarative style of writing meta interpreters in which the program is in the ground representation and the goals are lifted to the non ground one (see [20, 12, 30]) solve(empty) solve(X and Y ) solve(X) solve(Y ) solve(X) clause(X; Y ) solve(Y ) Figure 2: Non ground Vanilla solve Let us first examine what happens when we specialise the non ground representation. Suppose for instance that we use the standard vanilla solve in figure 2. Let the ....

.... L; L) append( HjX] Y; HjZ] append(X; Y; Z) last( X] X) last( HjT ] X) last(T; X) 2 The same general picture will also be obtained when specialising a meta interpreter written in the mixed style which lifts the ground representation to the non ground one for resolution (see [12, 20, 30]) Let G be the goal append(L; a] R) last(R; X) Thus R is a list of which we only know that the last element is a and if last(R; X) succeeds then X must be bound to the constant a. Unfortunately, partial deduction is unable to do so because, no matter how deep one unfolds G, there is ....

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J. Gallagher. A system for specialising logic programs. Technical Report TR-91-32, University of Bristol, November 1991.

....refinement which goes beyond mere heuristic strategies, as we find in unfold fold. Indeed, formal frameworks have been developed, analysing issues of termination and of code and search explosion, and efficiency gains have been obtained [11, 58, 23, 24, 40, 50] Several fully automated systems (sp [22], sage [27] paddy[63] mixtus [67] ecce [40, 50, 51, 53] as well as semi automated ones (logimix [60] leupel [39, 46] cogen [30] have been developed and successfully applied to at least medium size applications [46, 49, 18, 37] A similar development of automated techniques and systems has ....

....for selecting atoms to unfold, and unfold until no more atoms are select by the rule. Requirements are: termination, good specialisation, and avoiding search space explosion as well as work duplication. Existing approaches have been based on one or more of the following elements: ffl determinacy [23, 22] Only (except once) select atoms that match a single clause head. The strategy can be refined with a so called look ahead to detect failure at a deeper level. Methods solely based on this heuristic, apart from not guaranteeing termination, are often somewhat too conservative. ffl well founded ....

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J. Gallagher. A system for specialising logic programs. Technical Report TR-91-32, University of Bristol, 1991.

....of the System In this section we present some other aspects of the ecce system. 5.1 Global Control: Characteristic Trees and Atoms The global control is often considered to be the more difficult part of controlling partial deduction. A refined approach is the one based on characteristic trees [11, 9], which capture the specialisation behaviour of atoms. An abstraction operator like the most specific generalisation 4 (msg) is just based on the syntactic structure of the atoms to be specialised. This is generally not such a good idea. Indeed, two atoms can be specialised very similarly in the ....

....4 (msg) is just based on the syntactic structure of the atoms to be specialised. This is generally not such a good idea. Indeed, two atoms can be specialised very similarly in the context of one program P 1 and very dissimilarly in the context of another one P 2 . Characteristic trees [11, 9], however, capture (to some depth) how the atoms are specialised and how they behave computationally in the context of the respective programs. An abstraction operator which takes these trees into account will notice their similar behaviour in the context of P 1 and their dissimilar behaviour ....

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J. Gallagher. A system for specialising logic programs. Technical Report TR-91-32, University of Bristol, November 1991.

....SLD trees for the atoms to be partially deduced. In essence, it consists of an unfolding strategy. Requirements are: termination, good specialisation, avoiding search space explosion as well as work duplication. Approaches have been based on one or more of the following elements: ffl determinacy [13, 14] Only (except once) select atoms that match a single clause head. The strategy can be refined with a so called look ahead to detect failure at a deeper level. Methods solely based on this heuristic, apart from not guaranteeing termination, tend not to worsen a program, but are often somewhat too ....

....ensured and the degree of polyvariance is decided: For which atoms should partial deductions be produced Obviously, again, termination is an important issue, as well as obtaining a good overall specialisation. The following ingredients are important in recent approaches: ffl characteristic trees [13, 14, 21, 19] A characteristic tree is an abstraction of an SLD tree. It registers which atoms have been selected and which clauses were used for resolution. As such, it provides a good characterisation of the computation and specialisation connected with a certain atom (or goal) Its use in partial deduction ....

[Article contains additional citation context not shown here]

J. Gallagher. A system for specialising logic programs. Technical Report TR-9132, University of Bristol, November 1991.

....basic results of partial evaluation to the extension considered, as done for instance in [10] we would like to reduce our application to a special instance of the general case of partial evaluation in logic programming. Several program specialisers for logic programs have been developed (e.g. [16, 21, 32, 35]) The majority of them is written in Prolog and employs extra logical features of the languages, such as the cut operator and built in predicates like var, nonvar, assert, retract, and copy term. While most of these specialisers yield notable speed ups, the adoption of Prolog s extra logical ....

....it is interesting to consider the possibility of combining our program specialiser with other existing general partial evaluators. In particular, we have experimented the possibility of using Mixtus [32] a partial evaluator for full Prolog that is able to specialise any Prolog program, and SP [16], a more general system that is able to specialise declarative logic programs, written according to Prolog s syntax. In order to evaluate the usefulness of combining our program specialisation technique with Mixtus or SP, we have compared the specialised programs obtained, respectively: I) By ....

J.P. Gallagher. A System For Specialising Logic Programs. Technical report, University of Bristol, 1991.

....of each tree, which synthesises the computation in that branch. In the remainder of this paper we will restrict our attention to definite logic programs (possibly with some declarative built ins like n= is, In that context, the following generic scheme (based on a similar one presented in [6, 5]) describes the basic layout of practically all proposed algorithms for computing the sets S and f 1 ; n g (see also e.g. 13, 19] Algorithm 1.1 (Standard Partial Deduction) Initialise i = 0 , S i = fAg repeat for each A k 2 S i , compute a finite SLD tree k for A k ; let S 0 ....

....the redundant branch. Finally, the success information, X=a, would be propagated up to the p(x) call, yielding a specialised program: p(a) q(a) r(a) which is correct for all instances of the considered query p(x) Note that this particular example could be solved by the techniques in [5]. There, a limited success propagation, restricted to only one resolution step, is introduced and referred to as a more specific resolution step. The particular example can of course also be solved by standard partial deduction and a sufficiently refined unfolding rule. More difficult and ....

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J. Gallagher. A system for specialising logic programs. Technical Report TR-91-32, University of Bristol, November 1991.

....versions of a given predicate should be generated. A good abstraction operation should, while guaranteeing termination, produce enough polyvariance to ensure satisfactory specialisation. An approach which aims at achieving all these goals in a refined way is that of Gallagher and Bruynooghe ([7, 4]) Its abstraction operation is based on the notions of characteristic paths and characteristic trees. Intuitively, two atoms of A are replaced by their msg 1 in A 0 , if their (incomplete) SLDNF trees have an identical structure (this structure is referred to as the characteristic tree) ....

.... two atoms of A are replaced by their msg 1 in A 0 , if their (incomplete) SLDNF trees have an identical structure (this structure is referred to as the characteristic tree) Unfortunately, although the approach is conceptually appealing, several errors turn up in arguments provided in [7, 4]. These errors invalidate the termination proofs as well as the arguments regarding precision and preservation of specialisation under the abstraction operation. In [12, 13] Leuschel and De Schreye have significantly adapted the approach to overcome these problems. An alternative abstraction ....

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J. Gallagher. A system for specialising logic programs. Technical Report TR-9132, University of Bristol, November 1991.

....allowing more precise descriptions of sets of terms, such as sorted lists. Arithmetic constraints with the convex hull upper bound, and Boolean constraints are potentially useful constraint domains. 5. 1 Implementation The implementation of the algorithm presented here was based on the SP system [4] for the basic partial evaluation algorithm and the regular approximation tools [6] for the operations concerning the handling of RUL programs. The code runs in SICStus Prolog and is available from the authors. Acknowledgements We thank the PEPM 00 referees for their constructive and insightful ....

J. Gallagher. A system for specialising logic programs. Technical Report TR-91-32, University of Bristol, November 1991.

....indicates the permutation program with first argument a list of integers, and Permutation 2 is the same except that the second argument is a list of integers. The query answer transformations were performed with respect to a top goal for each program. A SPARC station IPC running the SP system [12] in Sicstus Prolog was used in all the experiments and all timings are in seconds. Approximation Results No. of No. of Bottom Left Program Clauses Literals Up Op Left Op Right Op naive reverse 4 7 0.10 non 0.51 op 0.83 op permutation 1 7 14 0.16 non 0.29 op 0.83 op permutation 2 7 14 0.16 non ....

J. Gallagher. A System for Specialising Logic Programs. Technical Report TR-91-32, Dept. of Computer Science, University of Bristol, November 1991.

....and answers generated during the computation of P [ f Ag. From this information, an optimised version of P can be derived (e.g. some clauses in P may not be needed to compute answers for A) Our current research is to integrate regular approximations in an algorithm for program specialisation [9], and analyse the behaviour of constraint interpreters. The method of integration is described in [6] 5.5 Machine Learning Regular approximation of a program can be regarded as an example of inductive learning, in which the regular definitions are generalisations of the information given in the ....

....transformed version of a unification algorithm for a ground representation, which contains approximately 80 clauses, the procedure takes several minutes to reach a fixed point. Further research will be aimed at incorporating the regular approximation procedure into a program specialisation system [9]. By getting more precise descriptions of call and answer patterns during partial evaluation, more specialised programs can be obtained. Acknowledgements Thanks to Ian Holyer, Bristol University, for useful discussions about regular programs. ....

J. Gallagher. A System for Specialising Logic programs. Technical Report TR-91-32, University of Bristol, November 1991.

....of Example 1 where any(t) is true for any term t in the Herbrand Universe of the program. The predicates t1 to t4 are ordinary logic program predicates and x1, x2 and x3 logic program variables. The program in Example 2 was produced automatically by the logic program specialisation system SP [6] at the University of Bristol. 3.3 Approximation in Problem Solving The use of approximation to solve problems is common. In its simplest form it means that when trying to show that some property p(x) holds for every element x of a set S, it is sufficient to show that p(x) holds for every ....

....[27] and [1] and has close links with type checking and other branches of program analysis. 4 Analysis Method The analysis method consists of two stages. Let the theorem prover be a normal program P , and the theory and theorem be represented by a normal goal G. 1. Partially evaluate [5] 14] [6], 20] P wrt G (or some G 0 such that G is an instance of G 0 ) Call the partially evaluated program P 1 . 2. Compute a regular approximation of clauses in P 1 with respect to P 1 [fGg. This yields P 2 which is used to delete useless clauses from P 1 , giving P 3 . By the correctness of ....

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J. Gallagher. A system for specialising logic programs. Technical Report TR-91-32, University of Bristol, November 1991.

....prover can be partially evaluated with respect to a given object theory. This is the same idea as partially evaluating a meta interpreter for logic programs with respect to a fixed object program [5] 7] 23] The partial evaluator (called SP) used for our experiments is fully described in [6]. In principle we could use any partial evaluator based on the theory in [14] augmented with a method of renaming predicates in the final partially evaluated program) In the next sections, the inherent limitations of partial evaluation for specialisation of the proof procedure are shown. 3.1 ....

J. Gallagher. A System for Specialising Logic programs. Technical Report TR-91-32, University of Bristol, November 1991.

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Gallagher, J.: 1991, `A System for Specialising Logic programs'. Technical Report TR-91-32, University of Bristol.

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J. Gallagher. A system for specialising logic programs. Technical Report TR-91-32, University of Bristol, November 1991.

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J. Gallagher. A system for specialising logic programs. Technical Report TR-91-32, Computer Science Department, University of Bristol, U.K., November 1991.

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