K. Verschaetse and D. De Schreye. Deriving termination proofs for logic programs using abstract procedures. In K. Furukawa, editor, Proceedings of the 8th International Conference on Logic Programming, pages 301-315. MIT Press, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....11] LD resolution [10, 23] LDNF resolution [9, 12] SLD resolution with dynamic scheduling [14, 26] or with tabling [30, 29] The second one is intended to automatize the veri cation by de ning sucient conditions for termination wrt. a speci c interpreter, e.g. the standard Prolog interpreter [31, 20, 13, 22, 19, 21]. In this paper we follow the rst approach: we de ne and characterize the class of well typed typed terminating programs, namely well typed general programs terminating wrt. LDNF resolution for any well typed general query. These programs and queries may contain negated literals; they are moded ....

K. Verschaetse and D. De Schreye. Deriving termination proofs for logic programs using abstract procedures. In K. Furukawa, editor, Proceedings of the 8th International Conference on Logic Programming, pages 301-315. MIT Press, 1991.

.... generated by different procedures can be used to improve the performance of deductive database programs, e.g. to plan the order in which subgoals are evaluated [10] In addition, knowledge about the size relationships between arguments is important for reasoning about program termination [32, 38, 40]. The remainder of this paper is organized as follows: Section 2 introduces some preliminary notions on the subject. Section 3 presents the method for the inference of argument size relationships. Section 1 4 describes the analysis for estimating the number of solutions generated by each ....

.... be determined by examining the types of argument positions, the general idea being to use the back edges in the type graph of a predicate to determine how that predicate recursively traverses its input terms (or constructs its output terms) and thereby synthesize a measure for the predicate [32, 40]. Type information may be inferred via program analysis [13, 29, 36, 42] and is not discussed further here. We first discuss how to determine the size of ground terms. Let j Delta j m : H N be a function that maps ground terms to their sizes under a specific measure m, where H is the ....

K. Verschaetse and D. De Schreye, "Deriving Termination Proofs for Logic Programs, using Abstract Procedures," Proc. Eighth International Conference on Logic Programming, Paris, June 1991, pp. 301--315.

....programs (up to 450 lines of Prolog) It also shows that type graphs can be practical and this is of importance for many applications such 2 GAIA is available by anonymous ftp from Brown University. 1 as compile time garbage collection (e.g. 17] and automatic termination analysis (e.g. [21]) The technical contributions to obtain this result are (1) a novel widening operator for type graphs which appears to be accurate and effective in keeping the sizes of the graphs, and hence the computation time, reasonably small; 2) the use of the pattern domain to obtain a compact ....

K. Verschaetse and D. De Schreye. Deriving Termination Proofs for Logic Programs Using Abstract Procedures. In Eighth International Conference on Logic Programming (ICLP-91), Paris (France), June 1991.

....input of another so the available parallelism in this program is limited. We will now consider a method for breaking the data dependencies of this program. Assume that we can compute the relative sizes of certain terms in the program at compile time (several algorithms for this task are known [7, 15]) Hence we can infer that if size( A j X] n 1, then size(Z) size(X) n. We can, therefore, rewrite the program as follows, where the goal length(X; N) computes the number of elements N in the list X. nrev(X,Y) length(X,N) nrev(N,X,Y) nrev(0, nrev(N 1, A X] Y) ....

K. Verschaetse & D. De Schreye, Deriving termination proofs for logic programs using abstract procedures, Proc. 8th Int. Conf. Logic Programming, MIT Press, 1991.

....the previous section on declarative semantics. 3.1 Termination and Confluence Termination is a highly desirable property which has been studied in many different contexts. In particular, termination proofs for sets of SiRs can benefit from work in rewriting systems [Der87] and logic programming [Plu90, VeDe91, Bez89, ApPe90]. If a set of SiRs is terminating, then there is no simplification step from any resolvent consisting of infinitely many derivation steps. Finding a suitable termination order may need user intervention. Termination for a class of SiRs is proved by giving an ordering on atoms showing that the ....

K. Verschaetse and D. De Schreye, Deriving Termination Proofs for Logic Programs using Abstract Procedures, 8th Int Conf on Logic Programming, MIT Press 1991, pp. 301-315.

....of the level mapping under instantiation) which allows to extend termination analysis techniques beyond beyond the variable free case. An important objective of present and future research is the automation of proving termination of logic programs, already touched upon by [UvG] P] BCF] and [VS]. In the rest of this section we review closely related research in some more detail. Together with Apt we extend in [AB] the ideas of this paper to the case of logic programs with negation, with A = A as the obvious extension of the level mapping. The resulting class of general ....

....but not acyclic are a quicksort program and a cycle avoiding transitive closure program for finite graphs. General transitive closure is not acceptable, since it can lead to recursive enumerability (see the discussion in Section 4) In a separate development, Verschaetse and de Schreye in [VS], and together with Bruynooghe in [SVB] study termination and left termination with respect to an arbitrary set S of (not necessarily variable free) atoms. They introduce relativizations with respect to S of the notions (left) terminating program, level mapping, recurrent and acceptable program. ....

K. VERSCHAETSE, D. DE SCHREYE, Deriving termination proofs for logic programs using abstract procedures, in: K. FURUKAWA, (editor), Proceedings of the international conference on logic programming, Paris, pp. 301-315, MIT Press, 1991. 16 -- --

....in this field is the work by CousotHalbwachs [10] The subject has known a renewal of interest with the development of logic programming and deductive databases with arithmetical constraints. Several new applications were then possible in these frameworks: proof of termination of logic programs[16, 24, 28], compilation of recursive queries in temporal databases [2, 20] verification of safety properties of concurrent systems[18] However almost all these works are interested in finding not the least fixpoint but rather an approximation of it using some techniques of Abstract Interpretation (convex ....

K. Verschaetse and D. De Schreye. "Deriving Termination Proofs for Logic Programs using Abstract Procedures", Proc. 8th Intl. Conf. on Logic Programming, Paris, 1991, pp. 301-315.

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Verschaetse, K. and D. De Schreye, "Deriving Termination Proofs for Logic Programs using Abstract Procedures". Proc. 8th Intl. Conf. on Logic Programming, Paris, 1991, pp. 301-315.

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