C. Braem, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality analysis of Prolog. In ILPS, pages 457--471. The MIT Press, 1994. 15  Home/Search   Document Details and Download   Summary   Related Articles   Check

....not need the delay directive (see [11, 23] Finiteness of the number of solutions: The analysis is based on complexity and execution cost to determine if a goal has a finite number of solutions (even none) or there are a potential infinite number of answers. The interested reader can consult [17, 4]. 3 Management of disequality constraints The first step in our management of negation is to handle disequalities between terms t 1 6= t 2 . Most Prolog implementations can work with disequalities if both terms are ground (built in predicate = However, they cannot work in the presence of ....

C. Braem, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality analysis of Prolog. In I. S. on Logic Programming, pages 457--471. The MIT Press, 1994.

.... of literals, as described in [9, 20] Finally, in order to determine finiteness in the number of solutions, the upper bounds complexity and execution cost analysis has been used [15] note that an upper bound cost that is not infinity implies a finite number of solutions (an alternative is [3]) The transformations have been implemented using the specializer in CiaoPP. The source programs always make calls to a version of the generic predicate similar to the neg predicate presented in section 2. The specializer creates specialized versions of the generic predicate for each literal ....

C. Braem, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality analysis of Prolog. In ILPS, pages 457--471. The MIT Press, 1994. 15

....is an integer solution to an arbitrary set of linear equalities and inequalities, referred to as a problem. We have tested the prototype first on a number of simple standard benchmarks, and then on more complex ones. The latter are taken from those used in the cardinality analysis of Braem et al. [2], which is the closest related previous work that we are aware of. Some relevant results of these tests are presented in Table 1. Program lists the program names, N the number of predicates in the program, F the number of predicates detected by the analysis as non failing, Cov the number of ....

....of these tests are presented in Table 1. Program lists the program names, N the number of predicates in the program, F the number of predicates detected by the analysis as non failing, Cov the number of predicates detected to cover their type, C the number of non failing predicates detected in [2], TF the time required by the covering analysis (SPARCstation 10, 55MHz, 64Mbytes of memory) TM the time required to derive the modes and types, and T T the total analysis time (all times are given in milliseconds) Averages (per predicate in the case of analysis time) are also provided in the ....

[Article contains additional citation context not shown here]

C. Braem, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality analysis of prolog. In Proc. International Symposium on Logic Programming, pages 457--471, Ithaca, NY, November 1994. MIT Press.

....overhead, since the maximum length is computed at run time. Sucient (semi )automatic methods to approximate the number of computed instances by means of lower and upper bounds have been studied in the context of cost analysis of logic programs [8] and of cardinality analysis of Prolog programs [6]. Of course, if 1 is a lower bound to the number of computed instances of P and Q then they have not bounded nondeterminism. Dually, if n 2 N is an upper bound then P and Q have bounded nondeterminism. In this case, however, we are still left with the problem of determining a level of the SLD tree ....

C. Braema, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality analysis of prolog. In M. Bruynooghe, editor, Proceedings of the 1994 International Logic Programming Symposium, pages 457|471, 1994.

....methods, based on cuts in the program, to determine if a query to a predicate has more than one solution. Debray and Warren [8] describe a technique to detect functional predicates in 17 a program predicates that have at most one answer to every query. Cardinality analysis by Braem et al. [2] extends functionality analysis by estimating the number of answers to queries (instead of whether is more or less than 1) The determinacy analysis implemented in Mercury compiler [10] also estimates the cardinality of each query. Non failure analysis proposed by Debray and Hermenegildo [7] ....

C. Braem, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality analysis of Prolog. In International Logic Programming Symposium (ILPS), pages 457--471, 1994.

....methods, based on cuts in the program, to determine if a query to a predicate has more than one solution. Debray and Warren [8] describe a technique to detect functional predicates in a program predicates that have at most one answer to every query. Cardinality analysis by Braem et al. [2] extends functionality analysis by estimating the number of answers to queries (instead of whether is more or less than 1) The determinacy analysis implemented in Mercury compiler [10] also estimates the cardinality of each query. Non failure analysis proposed by Debray and Hermenegildo [7] ....

C. Braem, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality analysis of Prolog. In International Logic Programming Symposium (ILPS), pages 457--471, 1994.

....more suitable for subgoal reordering than Prolog. It has no non logical constructs that could destroy the declarative semantics which give logic programs their power; in Mercury even I O is declarative. The third type of relevant SA is the cost analysis of logic programs (Debray Lin, 1993; Braem et al. 1994; Debray et al. 1997) Cortesi et al. 1997) describe a cost formula similar to Equation 5 to select a lowest cost ordering. However, they used a generate andtest approach which can sometimes be prohibitively expensive. Static analysis of cost and number of solutions can be used to obtain the ....

Braem, C., Le Charlier, B., Modar, S., & Van Hentenryck, P. (1994). Cardinality Analysis of Prolog. In Bruynooghe, M. (Ed.), Logic Programming - Proceedings of the 1994 International Symposium, pp. 457--471, Massachusetts Institute of Technology. The MIT Press.

.... [8,29,34,36] These analyses have been applied to the detection of both strict and non strict independence [8,9] Analyses have been developed also to derive other impor tant properties beyond variable instantiation states such as determinism [39] non failure [13] and number of answers [6]. Dealing with Irregularity and Speculation Dynamic Solutions: The preceding discussion has on purpose avoided the issue of run time overheads. The obvious practical implication of the existence of overheads (task creation, scheduling, data movement, etc. is that even if a task is known to be ....

C. Braem, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality analysis of prolog. In Proc. International Symposium on Logic Programming, pages 457--471, Ithaca, NY, November 1994. MIT Press.

....detection methods are heavily dependent on user supplied cuts, which essentially encourages less declarative style of programming. The dependence on operational constructs like cuts is much reduced in the notion of functionality by Debray and Warren [7] Cardinality analysis by Braem et al. [1] extends on the idea of functionality analysis where they estimate the numbers of answers of predicates. Among the different existing Prolog systems, Mercury has integrated determinacy analysis into its compiler [9] This notion of determinacy analysis, where again, the number of answers of a ....

C. Braem, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality analysis of prolog. In Proceedings of International Symposium on Logic Programming, pages 457--471, 1994.

....in a list are floating point numbers. We use redundant tests to propagate information between proof tree branches while retaining a simple analysis framework. This approach is quite limited in its scope and it might be useful to consider approaches such as the cardinality analysis of Braems et al. [2] For instance, propagating assertions X Y through the program is orthogonal to our range arithmetic and may provide opportunities for further optimizations. 7 Conclusion and future work We proposed a simple structure analysis domain, type jungles. The domain can be viewed as a restriction of ....

C. Braem, B. Le Charlier, S. Modart, P. Van Hentenryck, Cardinality analysis of Prolog, in Proc. ILPS'94.

....Z Y 2. r(X,Y) Gamma X Y 2. Figure 1: A simple CLP( Lin ) program. perform the optimizations safely. In particular, it uses the generic abstract interpretation algorithm GAIA [11] instantiated to three abstract domains: Prop [13, 20] to deduce information on fixed variables, RatOrder [1] to remove redundant constraints, and LSign [16, 19] to reorder constraints and to determine unconstrained variables. The preliminary experimental results indicate that substantial speedups can be obtained. In particular, on most of the benchmarks, the speedups are asymptotic, i.e. they depend on ....

C. Braem, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality Analysis of Prolog. In Proceedings of the International Symposium on Logic Programming (ILPS-94), pages 457--471, Ithaca, NY, November 1994.

....specification; this requires more information from the programmer but allows for more general termination proofs. The analyzer computes information about the number of solutions using the notion of abstract sequence introduced in [14] This is related to the cardinality analysis described in [2]. However, we do not perform an 1 Partly supported by European Community HCM Network Logic Program Synthesis and Transformation Contract Nr. CHRX CT93 00414 , and by MURST NRP Modelli della Computazione e dei Linguaggi di Programmazione abstract interpretation in the usual sense since ....

....abstract interpretation in the usual sense since we use the formal specification of the subproblems instead of their code; moreover, we allow the number of solutions to be expressed as a function of the input argument sizes. This enhances the expressiveness of cardinality analysis with respect to [2]. Based on the new analyzer, we get al..most for free an automatic complexity analysis, in the spirit of the framework proposed by Debray and Lin in [8] In our context, this analysis is useful to choose the most efficient version of a procedure. The paper is organized as follows. In Section 1, we ....

[Article contains additional citation context not shown here]

C. Braem, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality Analysis of Prolog. In Proc. Int'l Logic Programming Symposium, (ILPS'94), Ithaca, NY. The MIT Press, Cambridge, Mass., 1994.

....UNION for all but one component, namely E sol ; this is because the number of solutions of a procedure is the sum of the numbers of solutions of its clauses, not an upper bound of them. To obtain a good precision in the computation of E sol , it is important to detect mutual exclusion of clauses [9, 46]. In our implementation, we generalize this idea. First, we compute the greatest lower bound of the fi ref component of the two abstract sequences. Then, we compute the sum of the numbers of solutions for this greatest lower bound only. In particular, when the greatest lower bound is equal to , ....

.... and other built in predicates) Second, the notion of abstract sequence that we use is more elaborated than the abstract substitution notion used in the various applications of GAIA (e.g. 16, 17, 47, 48, 64] A simpler notion of abstract sequence has been introduced in GAIA recently [9, 45, 46] but it is less convenient than ours to express relations between input terms, output terms, and the number of solutions to a goal as well as to detect mutual exclusion of clauses. The abstract domain for substitutions that we use in this paper is related to the abstract equation system (AES) ....

[Article contains additional citation context not shown here]

C. Braem, B. Le Charlier, S. Modard, and P. Van Hentenryck. Cardinality Analysis of Prolog. In M. Bruynooghe, editor, Proceedings of the International Logic Programming Symposium (ILPS'94), Ithaca NY, USA, November 1994. MIT Press.

....program variables and p 2 P k or a constraint of the form c 0 op P m i=1 c i x i where c i are rational numbers, op 2 f ; g, and x 1 ; xm are all the clause variables. A typical CLP( lin ) program is the factorial program 1 This was motivated by our previous work on sequences [12, 1] which separates properties of the elements of the sequences from properties of the sequence. 2 Note that Marriott and Stuckey use an abstraction function for constraints and an approximation relation for the remaining semantic objects. fact(x 1 ,x 2 ) x 1 = 0, x 2 = 1. fact(x 1 ,x 2 ) x ....

C. Braem, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality Analysis of Prolog. In Proceedings of the International Symposium on Logic Programming (ILPS-94), pages 457-- 471, Ithaca, NY, November 1994.

....experiments, it is worth mentioning the reexecution semantics [20] which is a collecting semantics that is very different from the standard semantics of Prolog, as it allows one to improve the accuracy of the analysis in a tremendous way for some abstract domains. A more recent version of GAIA [1, 17, 18] is based on a denotational semantics of Prolog and allows one to derive precise information about the cut and the number of solutions to a goal. It is interesting to note that, although this version of the system uses a completely different standard semantics, most of the abstract operations ....

C. Braem, B. Le Charlier, S. Modard, and P. Van Hentenryck. Cardinality analysis of Prolog. In M. Bruynooghe, editor, Proceedings of the International Logic Programming Symposium (ILPS'94), Ithaca NY, USA, November 1994. MIT Press.

....like modes, sharing and types, that can be automatically inherited from previous works [14] but on the automatic verification of assumptions like the number of solutions, or the size relations between input and output arguments. Our analyser is built upon the notion of abstract sequence [2, 3, 12]. Abstract sequences describe pairs h ; Si, where is a substitution and S is the sequence of answer substitutions resulting from executing a program (a procedure, a clause, etc. with input substitution . In this paper, we revisit this notion so that ffl the new notion includes an ....

....substitutions into a single one. In fact, CONC differs from UNION only for the computation of the number of solutions to a procedure which is the sum of the numbers of solutions of its clauses, not an upper bound of them. To obtain a good precision, we detect mutual exclusion of clauses [2, 13] by computing the greatest lower bound of the fi ref component of the two abstract sequences. If it is , then the clauses are exclusive: in this case, we only collect the numbers of solutions of the two clauses. Otherwise, we compute the sum of the numbers of solutions for the greatest lower ....

C. Braem, B. Le Charlier, S. Modard, and P. Van Hentenryck. Cardinality Analysis of Prolog. In M. Bruynooghe, editor, Proc. of the International Logic Programming Symposium (ILPS'94), Ithaca NY, USA, November 1994. MIT Press.

....and combine all kinds of useful information about Prolog program executions. To the best of our knowledge, no previous framework was able to incorporate such information in a single analysis. 3. The notion of abstract sequence used by the analyser is novel with respect to the one introduced in [4, 16, 17]. It describes a set of pairs of the form h ; Si, where and S respectively denote an (input) substitution and the sequence of answer substitutions resulting from executing (part of) a program with this input. Such notion is more relational than the one in [4, 16, 17] since it allows us to ....

....to the one introduced in [4, 16, 17] It describes a set of pairs of the form h ; Si, where and S respectively denote an (input) substitution and the sequence of answer substitutions resulting from executing (part of) a program with this input. Such notion is more relational than the one in [4, 16, 17] since it allows us to relate and S explicitly, contrary to the old notion which only abstracts sets of sequences. So, we may relate the number of solutions and the size of output terms to the size of input terms in full generality (e.g. we can relate the input and output sizes of the same 1 ....

[Article contains additional citation context not shown here]

C. Braem, B. Le Charlier, S. Modard, and P. Van Hentenryck. Cardinality Analysis of Prolog. In M. Bruynooghe, editor, Proceedings of the International Logic Programming Symposium (ILPS'94), Ithaca NY, USA, November 1994. MIT Press.

....like modes, sharing and types, that can be automatically inherited from previous works [14] but on the automatic verification of assumptions like the number of solutions, or the size relations between input and output arguments. The analyser is built upon the notion of abstract sequence [2, 4, 12]. Abstract sequences describe pairs h ; Si, where is a substitution and S is the sequence of answer substitutions resulting from executing a program (a procedure, a clause, etc. with input substitution . In this paper, we revisit this notion. The main novelties are: ffl the new notion ....

C. Braem, B. Le Charlier, S. Modard, and P. Van Hentenryck. Cardinality Analysis of Prolog. In M. Bruynooghe, editor, ILPS'94, Ithaca NY, USA, November 1994. MIT Press.

....static analysis techniques in order to verify the correctness criteria for a Prolog procedure. This is a refinement and an extension of the analyzer presented in [3] which only performs mode and type verification. The main novelties of our analyzer are the following: 1: abstract sequences (see [1, 10]) are used instead of abstract substitutions: this allows us to infer information about the number of solutions and termination; 2: completeness and termination analyses are performed (they were not considered in [3] we adapt the framework proposed by De Schreye, Verschaetse and Bruynooghe in ....

....an infinite number of solutions and if this is not the last one then the executions of all the following clauses in P are finitely failed. When computing the sequence of answers for the whole procedure, input output patterns are used to determine whether some clauses are mutually exclusive (see [1]) 4 The Synthesizer The synthesizer receives the same inputs as the analyzer. First, for each clause of P all correct permutations of the literals in its body are computed and one correct permutation is selected according to some minimality criteria (e.g. minimum number of solutions) Then, a ....

C. Braem, B. Le Charlier, S. Modart, P. Van Hentenryck. Cardinality Analysis of Prolog. In Proc. Int'l Logic Programming Symposium, (ILPS'94), Ithaca, NY. The MIT Press, Cambridge, Mass., 1994.

No context found.

C. Braem, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality analysis of Prolog. In ILPS, pages 457--471. The MIT Press, 1994. 15

No context found.

C. Braem, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality analysis of prolog. In Proc. International Symposium on 131 Logic Programming, pages 457--471, Ithaca, NY, November 1994. MIT Press.

No context found.

C. Braem, B. Le Charlier, S. Modart, and P. Van Hentenryck. Cardinality analysis of Prolog. In M. Bruynooghe, editor, Proc. of the International Logic Programming Symposium, pages 457---471. MIT Press, 1994.

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