S. Decorte and D. De Schreye. Termination analysis: some practical properties of the norm and level mapping space. In J. Jaffar, editor, Proc. of the 1998 Joint Int. Conf. and Symp. on Logic Programming, pages 235--249. MIT Press, June 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....call in a program as either static or dynamic such that constructing an SLD derivation by unfolding the statically annotated calls leaving the dynamically annotated ones as they are terminates for every call that may occur during specialisation. As was suggested before in the literature [3, 7], it seems natural to base the decision whether or not to unfold a predicate call on the termination properties of the particular call. The motivation is obvious: if it can be shown that the (specialisation time instance of the) call terminates under normal evaluation, the call can safely be ....

S. Decorte and D. De Schreye. Termination analysis: Some practical properties of the norm and level mapping space. In Joxan Jaar, editor, Proceedings of the

....than the one used so far. Having for each predicate p n the original clauses with head p n and transformed clauses with head pt n, the transformed clauses could be derived from the original by replacing each call q m by: terminates q(t) q(t) unfold q(t) qt(t) memoise q(t) In [10], Decorte and De Schreye describe how the constraint based termination analysis of [11] can be adapted to generate a finite set of most general termination conditions (e.g. for append 3 they would generate rigidity w.r.t. the listlength norm of the first argument and rigidity w.r.t. the ....

S. Decorte and D. De Schreye. Termination Analysis: Some Practical Properties of the Norm and Level Mapping Space. TR, Dept. Comp. Science, K.U. Leuven.

....Mesnard [8] provides techniques for inferring termination conditions, but does not consider inherently non well founded CLP domains. In this paper we present a termination inference technique for numerical loops based on the well known constraints based approach [4] further extending [3], and on the adornments technique [6, 7] We restrict our interest only to integer loops, since termination of real number computations is often implementation dependent (see [5] Example 1. p(X) X 0; X 5; X1 is X 1; p(X) p(X) X 5 This example illustrates two possible sources of ....

S. Decorte and D. De Schreye. Termination analysis: some practical properties of the norm and level mapping space. In J. Jaffar, editor, Proc. of the 1998 Joint Int. Conf. and Symp. on Logic Programming, pages 235--249. MIT Press, June 1998.

....meta programming inside the logic programming community [1, 8, 10, 11] See also [6] for a survey. On the other hand, termination analysis is one of the most intensive research areas in logic programming as well. See [3] for the survey. More recent work on this topic can be found among others in [4, 5, 7, 9, 12, 14 16]. Traditionally, termination analysis of logic programs have been done either by the transformational approach or by the direct one. A transformational approach first transforms the logic program into an equivalent term rewrite system (or, in some cases, into an equivalent functional ....

S. Decorte and D. De Schreye. Termination analysis: some practical properties of the norm and level mapping space. In J. Jaffar, editor, Proc. of the 1998 Joint Int. Conf. and Symp. on Logic Programming, pages 235--249. MIT Press, June 1998.

....under such weak assumptions. Knowing these predicates is useful even for programs where not all predicates have this property. 1 Introduction Termination of logic programs has been widely studied for LD derivations, that is derivations where the leftmost atom in a query is always selected [1, 3, 7, 8, 9, 10, 12]. These works are based on the following idea: when an atom a in a query is selected, it is possible to pin down the size 1 of a. This size cannot change via further instantiation. It is then shown that for the atoms introduced in this derivation step, it is again possible to pin down their size ....

....justi cation for restricting our attention to one atom queries. Thus the question is how it can be shown that a predicate is atom terminating. 5 Showing that a Predicate is Atom Terminating Termination proofs usually rely, more or less explicitly, on measuring the size of the input in a query [1, 3, 7, 8, 9, 10, 12]. We agree with Etalle et al. 12] that it is reasonable to make this dependency explicit. This gives rise to the concept of moded level mapping [12] which is an instance of level mapping [6] B P denotes the set of ground atoms using predicates occurring in P . De nition 5.1 [moded level ....

[Article contains additional citation context not shown here]

S. Decorte and D. De Schreye. Termination analysis: Some practical properties of the norm and level mapping space. In J. Jaar, editor, Proceedings of the 15th JICSLP, pages 235-249. MIT Press, 1998.

No context found.

S. Decorte and D. De Schreye. Termination analysis: some practical properties of the norm and level mapping space. In J. Jaffar, editor, Proc. of the 1998 Joint Int. Conf. and Symp. on Logic Programming, pages 235--249. MIT Press, June 1998.

No context found.

S. Decorte and D. De Schreye. Termination analysis: some practical properties of the norm and level mapping space. In J. Jaffar, editor, Proceedings of the 1998 Joint International Conference and Symposium on Logic Programming, pages 235--249. MIT Press, June 1998.

No context found.

S. Decorte and D. De Schreye. Termination analysis: some practical properties of the norm and level mapping space. In J. Jaffar, editor, Proc. of the 1998 Joint Int. Conf. and Symp. on Logic Programming, pages 235--249. MIT Press, June 1998.

No context found.

S. Decorte and D. De Schreye. Termination analysis: some practical properties of the norm and level mapping space. In J. Jaffar, editor, Proceedings of the 1998 Joint International Conference and Symposium on Logic Programming, pages 235--249. MIT Press, June 1998.

No context found.

Stefaan Decorte and Danny De Schreye. Termination analysis: some practical properties of the norm and level mapping space. In Joxan Jaar, editor, Proc. of the 1998 Joint Int. Conf. and Symp. on Logic Programming, pages 235-249. MIT Press, June 1998.

....with respect to a set. Here, the generalisation of rigidity was less complicated, so that in the end we obtained the strongest results for this variant of acceptability. Therefore, we first present order acceptability with respect to a set of goals. We need the following notion. Definition 5. [12] Let P be a definite program and S be a set of atomic queries. The call set, Call(P; S) is the set of all atoms A, such that a variant of A is a selected atom in some derivation for P [f Qg, for some Q 2 S and under the left to right selection rule. To illustrate this definition recall the ....

.... nil terminated listg: Such information about S could for instance be expressed in terms of the rigid types of Janssens and Bruynooghe [21] and Call(P; S) could be computed using the type inference of [21] 2 6 The following definition generalises the notion of acceptability with respect to a set [12] in two ways: 1) it generalises it to general quasi orderings, 2) it generalises it to mutual recursion, using the standard notion of mutual recursion [2] Definition 6. Let S be a set of atomic queries and P a definite program. P is order acceptable with respect to S if there exists a ....

[Article contains additional citation context not shown here]

S. Decorte and D. De Schreye. Termination analysis: some practical properties of the norm and level mapping space. In J. Jaffar, editor, Proc. of the 1998 Joint Int. Conf. and Symp. on Logic Programming, pages 235--249. MIT Press, June 1998.

....w q, if (p; q) is in the transitive closure of the relation refers to. p and q are mutually recursive and write p q, if p w q and q w p. We recall some basic notions, related to termination analysis with respect to sets of queries. A level mapping is a function j j: B P N . The call set [11], Call(P; S) is the set of all atoms A, such that a variant of A is a selected atom in some branch of the LD tree for P[f Qg, for some Q 2 S. The following de nition [24] generalises the notion of acceptability with respect to a set [10, 11] by extending it to mutual recursion. De nition 2. ....

....level mapping is a function j j: B P N . The call set [11] Call(P; S) is the set of all atoms A, such that a variant of A is a selected atom in some branch of the LD tree for P[f Qg, for some Q 2 S. The following de nition [24] generalises the notion of acceptability with respect to a set [10, 11] by extending it to mutual recursion. De nition 2. Let S be a set of atomic queries and P a de nite program. P is acceptable with respect to S if there exists a level mapping j j such that for any A 2 Call(P; S) for any clause A B 1 ; B n in P , such that mgu(A; A ) ....

S. Decorte and D. De Schreye. Termination analysis: some practical properties of the norm and level mapping space. In J. Jaar, editor, Proc. of the 1998 Joint Int. Conf. and Symp. on Logic Programming, pages 235-249. MIT Press, June 1998.

....with respect to a set. Here, the generalisation of rigidity was less complicated, so that in the end we obtained the strongest results for this variant of acceptability. Therefore, we first present term acceptability with respect to a set of goals. We need the following notion. Definition 6. [9] Let P be a definite program and S be a set of atomic queries. The call set, Call(P; S) is the set of all atoms A, such that a variant of A is a selected atom in some derivation for P [f Qg, for some Q 2 S and under the left to right selection rule. To illustrate this definition recall the ....

....t 3 are free variables and t 2 is a nil terminated listg. Such information about S could for instance be expressed in terms of the rigid types of [16] and Call(P; S) could be computed using the type inference of [16] 2 The following definition generalises the notion of acceptability w.r.t. a set [9] in two ways: 1) it generalises it to general term orders, 2) it generalises it to mutual recursion, using the standard notation of mutual recursion [1] the original definition of acceptability required decrease only for calls to the predicate that appears in the head of the clause. This ....

[Article contains additional citation context not shown here]

S. Decorte and D. De Schreye. Termination analysis: some practical properties of the norm and level mapping space. In J. Jaffar, editor, Proc. of the 1998 Joint Int. Conf. and Symp. on Logic Programming, pages 235--249. MIT Press, June 1998.

....technique is not a fully conservative extension of standard acceptability. For the moment, our approach is limited to well moded programs and goals only. Another line of future work is to develop an extension to term orderings for the notion of acceptability with respect to a set of atoms of [7, 8]. We expect that this extension may be much easier in the non ground case, because acceptability with respect to a set does not require any notion of boundedness. 52 6 Acknowledgement Alexander Serebrenik is supported by GOA: LP : a second generation logic programming language . Danny De ....

S. Decorte and D. De Schreye. Termination analysis: some practical properties of the norm and level mapping space. In J. Jaffar, editor, Proceedings of the 1998 Joint International Conference and Symposium on Logic Programming, pages 235--249. MIT Press, June 1998.

....than the size of p(X1) 6 Gamma X, thus, proving termination. We present a transformation that allows us to define such a level mappings in an automatic way by incorporating techniques of [8] such as level mapping inference, in the well known framework of the acceptability with respect to a set [5, 6]. This integration provides not only a better understanding of termination behaviour of integer computations, but also the possibility to perform the analysis automatically as in Decorte et al. 7] The rest of the paper is organised as follows. After making some preliminary remarks, we present ....

....basic notions, related to termination analysis. A level mapping is a function j Delta j: B E P N , where N is the set of the naturals. We study termination of programs with respect to sets of queries. The following notion is one of the most basic notions in this framework. Definition 2. [6] Let P be a definite program and S be a set of atomic queries. The call set, Call(P; S) is the set of all atoms A, such that a variant of A is a selected atom in some derivation for P [ f Qg, for some Q 2 S and under the left to right selection rule. The following definition [14] generalises ....

[Article contains additional citation context not shown here]

S. Decorte and D. De Schreye. Termination analysis: some practical properties of the norm and level mapping space. In J. Jaffar, editor, Proc. of the 1998 Joint Int. Conf. and Symp. on Logic Programming, pages 235--249. MIT Press, June 1998.

....can easily be inferred to ensure termination. As such, the approach has the advantage that the set of queries of interest does not need to be speci ed. Maximal sets of terminating queries are automatically inferred. Note though that the technique is again restricted to use of a speci c norm. In [Decorte and Schreye 1998], we adapt our approach to also support this extended functionality. There, we automatically generate a nite set of norms, such that the set of queries that can be proved to terminate using these norms (and our termination condition) is maximized. However, in the process, the termination ....

....under which the third phase is solvable. An example of an application here is the inference of sets of terminating queries for the speci c program under consideration. They are obtained by considering as input only those systems corresponding to the rigid acceptability and the validity condition. [Decorte and Schreye 1998] shows how a minor extension of the technique provides this functionality. The approach is applicable with no further diculties in modular program development systems, mainly because the rigid acceptability condition is expressed completely at clause level. Here, the information obtained for one ....

Decorte, S. and Schreye, D. D. 1998. Termination analysis: some practical properties of the norm and level mapping space. In Proceedings IJCSLP98, the International Joint Conference and Symposium on Logic Programming, J. Jafar, Ed. MIT press, Manchester, 235-249.

....q, if p w q and q w p. We also abbreviate p w q, q 6w p by p A q. Results for termination of meta interpreters presented in this paper are based on notion of order acceptability, introduced in [25] This notion of order acceptability generalises the notion of acceptability with respect to a set [13] in two ways: 1) it generalises it to general term orderings, 2) it generalises it to mutual recursion, using the standard notion of mutual recursion [1] the original definition of acceptability required decrease only for calls to the predicate that appears in the head of the clause. This ....

....original definition of acceptability required decrease only for calls to the predicate that appears in the head of the clause. This restriction limited the approach to programs only with direct recursion. Before introducing the order acceptability we need the following notion. Definition 2. [13] Let P be a definite program and S be a set of atomic queries. The call set, Call(P; S) is the set of all atoms A, such that a variant of A is a selected atom in some derivation for P [ f Qg, for some Q 2 S and under the left to right selection rule. 3 Definition 3. Let S be a set of atomic ....

[Article contains additional citation context not shown here]

S. Decorte and D. De Schreye. Termination analysis: some practical properties of the norm and level mapping space. In J. Jaffar, editor, Proc. of the 1998 Joint Int. Conf. and Symp. on Logic Programming, pages 235--249. MIT Press, June 1998.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC