F. Benoy and A. King. Inferring Argument Size Relationships with CLP(R). In Proc. 6th International Workshop on Logic Program Synthesis and Transformation, pages 34--153. Stockholm University /Royal Intitute of Technology, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....systems of linear inequalities. These are naturally more expressive than equalities. However Van Gelder s work was incomplete because the analysis could fail to nd a xpoint. The work of Cousot and Cousot [7] addressed this failing and the technique was successfully applied by Benoy and King [2] to automatically derive interargument relationships expressed as systems of linear inequalities. In this thesis we present the design and implementation of a new automatic termination analyser for Mercury. The new analysis is more precise than that of [28] and can prove termination in many ....

....iteration before showing how the term size relationships in the goals of a Mercury program can be abstracted in terms of convex constraints. Finally we consider some examples analyses and discuss how to ensure that the analysis converges. The IR analysis is essentially that of Benoy and King in [2] extended to apply to Mercury, we refer the reader to that paper for correctness proofs of the basic operations over this domain. Actually, the major contribution of [11] was to show how all the aspects of a typical termination analysis system, mode analysis, norm inference, IR analysis and ....

[Article contains additional citation context not shown here]

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In J. Gallagher, editor, Logic Program Synthesis and Transformation: Proc. LOPSTR 96, volume 1207 of Lecture Notes in Computer Science, pages 204-223. Springer-Verlag, 1997.

.... [7, 19] and of linear hybrid automata (an extension of finite state machines that models time requirements) 21, 23] for the computer aided formal verification of concurrent and reactive systems based on temporal specifications [28] for inferring argument size relationships in logic languages [5], and for the automatic parallelization of imperative programs [31] Since the work of Cousot and Halbwachs, convex polyhedra have thus played an important role in the formal methods community and new uses continue to emerge (see, e.g. 12, 17] As a consequence, several critical tasks, such as ....

....improved in [15] Concerning the e#ciency of the PPL, at present no application can use both the PPL and another convex polyhedra library, so comparisons are not possible. However, the PPL has been integrated with the China analyzer [1] for the purpose of detecting linear argument size relations [5]. The performance of the combined system has been compared, on the same task, with the performance of the cTI analyzer [29] which uses an implementation of convex polyhedra based on the SICStus CLP(Q) package. The combined system China PPL outperformed that version of cTI in a significant way, ....

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In J. P. Gallagher, editor, Logic Programming Synthesis and Transformation: Proceedings of the 6th International Workshop, volume 1207 of Lecture Notes in Computer Science, pages 204--223, Stockholm, Sweden, 1997. Springer-Verlag, Berlin.

....we do not construct a particular norm for a term according to its type, but rather characterise the size of the term in several ways, by counting the number of subterms of a particular type it contains. Let us reconsider Example 1. Instead of characterising the size of terms like [1; 2; 3] and [[1]; 2] 3; 4] by the particularly constructed norms (k:k 1 and k:k 2 respectively) we characterise their sizes by counting the number of integer values occurring in them, the number of lists of integer values and the number of lists of lists of integer values. The rst two of these measurements ....

....norms (k:k 1 and k:k 2 respectively) we characterise their sizes by counting the number of integer values occurring in them, the number of lists of integer values and the number of lists of lists of integer values. The rst two of these measurements are applicable to both [1; 2; 3] and [[1]; 2] 3; 4] and enable to compare their sizes. This contrast with the diculties that are encountered when one has to compare their sizes when measured with di erent norms k:k 1 and k:k 2 . Our motivation is twofold: First of all, we believe the use of type information to be a powerful tool ....

[Article contains additional citation context not shown here]

Florence Benoy and Andy King. Inferring argument size relationships with CLP(R). In John P. Gallagher, editor, Logic Programming Synthesis and Transformation, LOPSTR'96, Proceedings, volume 1207 of LNCS, pages 204-223, 1997.

.... [6, 23] and of linear hybrid automata (an extension of finite state machines that models time requirements) 24, 27] for the computer aided formal verification of concurrent and reactive systems based on temporal specifications [29] for inferring argument size relationships in logic languages [4, 5], for the automatic parallelization of imperative programs [31] for detecting bu#er overflows in C [21] and for the automatic generation of the ranking functions needed to prove progress properties [10] Since the domain of convex polyhedra admits infinite ascending chains, it has to be used in ....

....idea suggested in [12] This amounts to delaying the application of the widening operator k times for some fixed parameter k N. A study of the e#ect of alternative values for k in the automatic determination of linear size relations between the arguments of logic programs has been conducted in [4, 5]. One application of this idea is in termination inference [30] In order to achieve reasonable precision, the cTI analyzer runs with k = 3 as a default, but there are simple programs (such as mergesort) whose termination can only be established with k 3. On the other hand, setting k = 4 as the ....

[Article contains additional citation context not shown here]

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In J. P. Gallagher, editor, Logic Program Synthesis and Transformation: Proceedings of the 6th International Workshop, volume 1207 of Lecture Notes in Computer Science, pages 204--223, Stockholm, Sweden, 1997. Springer-Verlag, Berlin.

.... [6, 18] and of linear hybrid automata (an extension of finite state machines that models time requirements) 20, 22] for the computeraided formal verification of concurrent and reactive systems based on temporal specifications [27] for inferring argument size relationships in logic languages [5], and for the automatic parallelization of imperative programs [30] Since the work of Cousot and Halbwachs, convex polyhedra have thus played an important role in the formal methods community and new uses continue to emerge (see, e.g. 11, 16] As a consequence, several critical tasks, such as ....

....improved in [14] Concerning the e#ciency of the PPL, at present no application can use both the PPL and another convex polyhedra library, so comparisons are not possible. However, the PPL has been integrated with the China analyzer [1] for the purpose of detecting linear argument size relations [5]. The performance of the combined system has been compared, on the same task, with the performance of the cTI analyzer [28] which uses an implementation of convex polyhedra based on the SICStus CLP(Q) package. The combined system China PPL outperformed that version of cTI in a significant way, ....

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In J. P. Gallagher, editor, Logic Programming Synthesis and Transformation: Proceedings of the 6th International Workshop, volume 1207 of Lecture Notes in Computer Science, pages 204--223, Stockholm, Sweden, 1997. Springer-Verlag, Berlin.

....do not construct a particular norm for a term according to its type, but rather characterise the term s size in several ways, by counting the number of subterms of a particular type it contains. Reconsider Example 1 from above. Instead of characterising the size of terms like [1; 2; 3] and [ 1] [2]; 3; 4] by the particularly constructed norms (k:k 1 , respectively k:k 2 ) we characterise their sizes by counting the number of integer values occurring in them, the number of lists of integer values and the number of lists of lists of integer values. The rst two of these measurements are ....

....norms (k:k 1 , respectively k:k 2 ) we characterise their sizes by counting the number of integer values occurring in them, the number of lists of integer values and the number of lists of lists of integer values. The rst two of these measurements are applicable to both [1; 2; 3] and [ 1] [2]; 3; 4] and enable to compare their sizes. This contrast with the diculties that are encountered when one has to compare their sizes when measured with di erent norms k:k 1 and k:k 2 . Our motivation is twofold: First of all, we believe the use of type information to be a powerful tool for ....

[Article contains additional citation context not shown here]

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In Proceedings of LOPSTR'96, volume 1207 of Lecture Notes in Computer Science, pages 204-223, 1997.

....state in which x is de nitely bound to a rigid term and there exists an instantiation dependency such that whenever y becomes bound to a rigid term then so does z. For details on Pos see [19] Size relations express linear information about the sizes of terms with respect to a given norm function [1, 4, 7, 16]. For example, the relation x z y z describes a program state in which the sizes of the terms associated with x and y are less or equal to the size of the term associated with z. Similarly, a relation of the form z = x y describes a state in which the sum of the sizes of the terms ....

....the size of the term associated with z. Similarly, a relation of the form z = x y describes a state in which the sum of the sizes of the terms associated with x and y is equal to the size of the term associated with z. Several methods for inferring size relations are described in the literature [1, 4, 7, 8]. They di er primarily in their approach to obtaining a nite analysis as the abstract domain of size relations contains in nite chains. This paper makes two contributions. First we address the situation where termination analysis should consider a combination of several norms. Namely, the size ....

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In Sixth International Workshop on Logic Program Synthesis and Transformation (LOPSTR '96), pages 204-223, 1996.

....whenever y becomes bound to a ground term then so does z. Similar analyses can be applied to infer dependencies with respect to other notions of instantiation. For details on Pos see [14] Size relations express linear information about the sizes of terms (with respect to a given norm function) [2, 3, 7, 11]. For example, the relation x z y z describes a program state in which the sizes of the terms associated with x and y are less or equal to the size of the term associated with z. Similarly, z = x y describes a state in which the sum of the sizes of the terms associated with x and y is ....

....y are less or equal to the size of the term associated with z. Similarly, z = x y describes a state in which the sum of the sizes of the terms associated with x and y is equal to the size of the term associated with z. Several methods for inferring size relations are described in the literature [2, 3, 7, 8]. They di er primarily in their approach to obtaining a nite analysis as the abstract domain of size relations contains in nite chains. Throughout this paper we will use the so called term size norm for size relations for which the corresponding notion of instantiation is groundness. We base our ....

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In Sixth International Workshop on Logic Program Synthesis and Transformation (LOPSTR '96), pages 204-223, 1996.

....3. The abstract binary unfoldings are computed as in Fig. 4. To obtain a nitary analysis, di erent approaches exist to further approximate the abstract domain. Example 5. Reconsider the abstract binary unfoldings of append 3 from Example 4. Further abstracting using polyhedral approximations [2] (thereby ar (1) T k:k P ) 1 ( 8 : append(X; Y; Z) 1;1 X = 0; Z = Y: append(X; Y; Z) 2;1 X = 1 Xs;Z = 1 Zs; append(Xs; Y; Zs) 9 = 2) T k:k P ) 2 ( 8 : append(X; Y; Z) 2;1 X = 1; Z = 1 Y: append(X; ....

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In Proceedings of LOPSTR'96, volume 1207 of Lecture Notes in Computer Science, pages 204-223, 1997.

....and used to maintain a shared representation of the alternatives available in such choice point. This solution works fine on SMMs where mutual exclusion is easily implemented using locks. However, on a DMM this process is a source of overhead access to the shared area becomes a bottleneck [3]. Sharing of information in a DMM leads to frequent exchange of messages and hence considerable overhead. Centralized data structures, such as shared frames, are expensive to realize in a distributed setting. Nevertheless, stack copying has been recognized as the best representation methodology to ....

....US Department of Education. References [1] K.A.M. Ali and R. Karlsson. Full Prolog and Scheduling Or parallelism in MUSE. International Journal of Parallel Programming, 1991. 19(6) 445 475. 2] L. Araujo and J. Ruz. A Parallel Prolog System for Distributed Memory. J. Logic Programming, 1998. [3] H. Babu. Porting muse on ipsc860. Master s thesis, New Mexico State Univ. 1996. 20 [4] T. Beaumont and D.H.D. Warren. Scheduling Speculative Work in Or Parallel Prolog Systems. In Int l Conf. on Logic Programming, MIT Press, 1993. 5] V. Benjumea and J.M. Troya. An OR Parallel Prolog Model ....

[Article contains additional citation context not shown here]

F. BENOY and A. KING. Inferring argument size relationships with CLP(R). In Logic Program Synthesis and Transformation. Springer-Verlag, 1997.

....arithmetic constraints ignore the signs of coecients, so the systems of constraints (x y z = 0) x y = 3) and (x y z = 0) x y = 3) are both given the Pos description (x y) x z) We look at several possible solutions to the two problems. For groundness analysis, the use of size relations [3, 11, 23] addresses the multiplicity problem, and can provide groundness information. A substitution is approximated by a constraint on term sizes. For example, the inequality x y z describes a substitution for which the size of the term x is bound to is smaller than or equal to the sum of the sizes of ....

....the two systems is best described by (x y) z and (x y) x z) respectively. 1 The interest is xed at 5 to avoid the presence of non linear constraints. 4 3 Size Relations An interesting solution to the multiplicity problem for Pos is obtained by applying a size relations analysis [3, 23], more commonly known in the context of termination analysis [5, 16] The interpretation of this type of analysis is parametric to a given size function on terms, called a symbolic norm [16] Symbolic norms (j j) are similar to linear norms except that variables are mapped to variables. In this ....

[Article contains additional citation context not shown here]

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In J. Gallagher, editor, Logic Program Synthesis and Transformation, volume 1207 of Lecture Notes in Computer Science, pages 204-223. Springer, 1997.

....with respect to other notions of instantiation. We denote the approximation of the 2 success set in Pos for groundness of a program P by [ P ] suc gr . For details on Pos see [14] Size relations express linear information about the sizes of terms (with respect to a given norm function) [3, 4, 8, 11]. For example, the relation x z y z describes a program state in which the sizes of the terms associated with x and y are less or equal to the size of the term associated with z. Similarly, a relation of the form z = x y describes a state in which the sum of the sizes of the terms ....

....the size of the term associated with z. Similarly, a relation of the form z = x y describes a state in which the sum of the sizes of the terms associated with x and y is equal to the size of the term associated with z. Several methods for inferring size relations are described in the literature [3, 4, 8, 9]. They di er primarily in their approach to obtaining a nite analysis as the abstract domain of size relations contains in nite chains. Throughout this paper we will use the so called term size norm for size relations for which the corresponding notion of instantiation is groundness. We base our ....

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In Sixth International Workshop on Logic Program Synthesis and Transformation (LOPSTR '96), pages 204-223, 1996.

No context found.

F. Benoy and A. King. Inferring Argument Size Relationships with CLP(R). In Logic-based Program Synthesis and Transformation (Selected Papers), volume 1207 of Lecture Notes in Computer Science, pages 204-223. Springer-Verlag, 1997.

....Analysis As before, Kleene iteration can be used to compute lfp( T P ) However, the chain of iterates T P k may not stabilise in a finite number of steps. In order to obtain convergence, widening (a fixpoint acceleration technique) 5] is applied. Given a standard widening on polyhedra [3], 5] 6] or equivalently, on linear constraints) O : C Lin C Lin C Lin , a widening, O : B Lin , where = B Lin [ f g) on the interpretation base is induced as follows: p(x) c 1 ] O [p(x) c 2 ] p(x) c 1 Oc 2 ] p(x) c 1 ] O [q(y) c 2 ] if p 6= q [p(x) ....

....the following simple example, projecting onto the single variable z: x y 4 x y 6 x 6 y 0 2 2y y 1 y z ; z 1 4.2 Convex Hull The convex hull of two polyhedra is the smallest polyhedron containing both polyhedra. The convex hull calculations are performed as in [3]. Polyhedra are represented as a set of linear inequalities. The convex hull, PC , of two polyhedra, P 1 and P 2 , is given by the following (where x is a vector and A i ; B i are matrices, together giving the linear inequalities that define the polyhedra) P 1 = fx 1 2 Q jA 1 x 1 B 1 g; P 2 ....

[Article contains additional citation context not shown here]

F. Benoy and A. King. Inferring Argument Size Relationships with CLP(R). In J. Gallagher, editor, Logic Program Synthesis and Transformation, volume 1207 of Lecture Notes in Computer Science, pages 204--224. Springer, 1996.

No context found.

F. Benoy and A. King. Inferring Argument Size Relationships with CLP(R). In Proc. 6th International Workshop on Logic Program Synthesis and Transformation, pages 34--153. Stockholm University /Royal Intitute of Technology, 1996.

No context found.

F. Benoy and A. King. Inferring Argument Size Relationships with CLP(R). Proc. 6th International Workshop on Logic Program Synthesis and Transformation, Stockholm University/Royal Intitute of Technology, 1996, pp. 134-153.

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F. Benoy, A. King, Inferring argument size relationships with CLP(R), in: J. P. Gallagher (Ed.), Logic Program Synthesis and Transformation: Proceedings of the 6th International Workshop, Vol. 1207 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, Stockholm, Sweden, 1997, pp. 204--223.

No context found.

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In J. P. Gallagher, editor, Logic Program Synthesis and Transformation: Proceedings of the 6th International Workshop, volume 1207 of Lecture Notes in Computer Science, pages 204--223, Stockholm, Sweden, 1997. Springer-Verlag, Berlin.

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F. Benoy and A. King. Inferring argument size relationships with clp(r). In Proc. of LOPSTR'96. Springer Verlag, 1996.

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F. Benoy and A. King. Inferring argument size relationships with CLP(R). In J. P. Gallagher, editor, Logic Program Synthesis and Transformation: Proceedings of the 6th International Workshop, volume 1207 of Lecture Notes in Computer Science, pages 204--223, Stockholm, Sweden, 1997. Springer-Verlag, Berlin.

No context found.

F. Benoy, A. King, Inferring argument size relationships with CLP(R), in: J. P. Gallagher (Ed.), Logic Program Synthesis and Transformation: Proceedings of the 6th International Workshop, Vol. 1207 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, Stockholm, Sweden, 1997, pp. 204--223.

No context found.

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In J. P. Gallagher, editor, Logic Program Synthesis and Transformation: Proceedings of the 6th International Workshop, volume 1207 of Lecture Notes in Computer Science, pages 204--223, Stockholm, Sweden, 1997. Springer-Verlag, Berlin.

No context found.

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In J. P. Gallagher, editor, Logic Program Synthesis and Transformation: Proceedings of the 6th International Workshop, volume 1207 of Lecture Notes in Computer Science, pages 204--223, Stockholm, Sweden, 1997. Springer-Verlag, Berlin.

No context found.

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In Sixth International Workshop on Logic Program Synthesis and Transformation (LOPSTR'96), pages 204--223, 1996.

No context found.

F. Benoy and A. King. Inferring argument size relationships with CLP(R). In Sixth International Workshop on Logic Program Synthesis and Transformation (LOPSTR'96), pages 204-223, 1996.

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