R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In M. Alpuente, R. Barbuti, and I. Ramos, editors, Proceedings of the \1994 Joint Conference on Declarative Programming (GULP-PRODE '94)", pages 312-326, Pe~nscola, Spain, September 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....sections can potentially reduce the complexity of convex hull calculations, can be implemented easily without CLP(R) support, but are likely to sacrifice a lot of precision. Moreover, the representation is likely to become intractable for predicates of larger arity. Interval Approximations China [1, 2, 3] is an analyser for CLP(R) and CLP(FD) that approximates conjunctions of constraints with bounding boxes. Bounding boxes are rectangular regions with sides parallel to the axes that are obtained by projecting variables onto their axes in order to represent each variable with the interval that ....

....parallel to the axes that are obtained by projecting variables onto their axes in order to represent each variable with the interval that results from the projection. Interval widening is required for termination and constraints are solved by propagating constraints around a constraint network [1, 2]. The bounding box approximation has been chosen for tractability, but our work suggests that, with some thought, it is not difficult to implement a more precise analysis with polyhedral approximations. To be fair, however, China [2] introduces some nice ideas like, for example, the way ....

R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In GULP-PRODE'94, pages 312--326, 1994.

....programs can be built. For instance, one can express unbounded lists where interpreted terms occur. Independently of the need for unbounded containers , it is a common CLP idiom to embed interpreted terms into Herbrand terms. From the experience gained with the rst prototype version of China [2] it was clear that, in order to attain a signi cant precision in the analysis of numerical constraints in CLP(H N ) languages, one must keep at least part of the uninterpreted terms in concrete form. Note that almost any analysis is much more precise when this kind of structural information is ....

R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In M. Alpuente, R. Barbuti, and I. Ramos, editors, Proceedings of the \1994 Joint Conference on Declarative Programming (GULP-PRODE '94)", pages 312-326, Pe~nscola, Spain, September 1994.

....fX ff Y g Y ff X; fX ff Y; Y ff Zg X ff Z; fX; X ff Y g Y: 4 Beware not to confuse CLP(R) the idealized language over the reals [28] with CLP(R) the (far from ideal) implemented language and system [27] 18 4. 2 Bounds and relations analysis for numeric domains The analysis described in [5,6,3] is based on constraint inference, a variant of constraint propagation [18] This technique, developed in the field of artificial intelligence, has been applied to temporal and spatial reasoning [1,38] Let us focus our attention to arithmetic domains, where the constraints are binary relations ....

....characterizes precisely the combination of the above techniques. Other techniques, such as interval refinement, can be easily incorporated. What we have just presented is a watered down version of the 20 numerical component (presented as a simple constraint system) employed in the China analyzer [3]. 5 Determinate constraint systems Determinate constraint systems are at the bottom of the hierarchy. Such a construction is uniquely determined by a simple constraint system together with appropriate merge operator and diagonal elements. Notice that, for simplicity, we only present the finite ....

[Article contains additional citation context not shown here]

R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In M. Alpuente, R. Barbuti, and I. Ramos, editors, Proceedings of the "1994 Joint Conference on Declarative Programming (GULPPRODE '94)", pages 312--326, Pe~n'iscola, Spain, September 1994.

....standard constraint domain with one suitable for expressing the desired information. This fundamental aspect was brought to light in [5] and elaborated in [12] For languages of the kind of CLP(N ) where N is some numerical domains, the first steps towards pattern analysis were moved in [3, 4] [2] describes some of the more important applications of such analyses. The work done in this field is being generalized to CLP(H, N) languages, integrating numerical and symbolic pattern analysis. This is done with a variety of techniques, including depth k abstraction. A more restricted kind of ....

....pattern analysis. This is done with a variety of techniques, including depth k abstraction. A more restricted kind of integration has recently been described in [17] Here, the numerical part is essentially the one proposed in [3] Now, instead of directly describing the techniques employed in [3, 4, 2, 17], we concentrate on what is missing from them: a general notion of constraint domain which allows one to adequately describe both the logical part of concrete computations (e.g. answer constraints) and as much pattern analyses (e.g. the shape of those answer constraints) we can think about. We ....

[Article contains additional citation context not shown here]

R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In Proc. GULP--PRODE'94, 1994.

....Y # X; X # Y, Y # Z # X # Z; X, X # Y # Y. 4 Beware not to confuse CLP(R) the idealized language over the reals [29] with CLP(R) the (far from ideal) implemented language and system [28] 18 4. 2 Bounds and relations analysis for numeric domains The analysis described in [6,7,3] is based on constraint inference, a variant of constraint propagation [19] This technique, developed in the field of artificial intelligence, has been applied to temporal and spatial reasoning [1,38] Let us focus our attention to arithmetic domains, where the constraints are binary relations ....

....characterizes precisely the combination of the above techniques. Other techniques, such as interval refinement, can be easily incorporated. What we have just presented is a watered down version of the 20 numerical component (presented as a simple constraint system) employed in the China analyzer [3]. 5 Determinate constraint systems Determinate constraint systems are at the bottom of the hierarchy. Such a construction is uniquely determined by a simple constraint system together with appropriate merge operator and diagonal elements. Notice that, for simplicity, we present only the finite ....

[Article contains additional citation context not shown here]

R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In M. Alpuente, R. Barbuti, and I. Ramos, editors, Proceedings of the "1994 Joint Conference on Declarative Programming (GULPPRODE '94)", pages 312--326, Penscola, Spain, September 1994.

....programs can be built. For instance, one can express unbounded lists where interpreted terms occur. Independently of the need for unbounded containers , it is a common CLP idiom to embed interpreted terms into Herbrand terms. From the experience gained with the first prototype version of China [2] it was clear that, in order to attain a significant precision in the analysis of numerical constraints in CLP(H N ) languages, one must keep at least part of the uninterpreted terms in concrete form. Note that almost any analysis is much more precise when this kind of structural information is ....

R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In M. Alpuente, R. Barbuti, and I. Ramos, editors, Proceedings of the "1994 Joint Conference on Declarative Programming (GULP-PRODE '94)", pages 312--326, Penscola, Spain, September 1994.

....programs can be built. For instance, one can express unbounded lists where interpreted terms occur. Independently of the need for unbounded containers , it is a common CLP idiom to embed interpreted terms into Herbrand terms. From the experience gained with the first prototype version of China [2] it was clear that, in order to attain a significant precision in the analysis of numerical constraints in CLP(H N ) languages, one must keep at least part of the uninterpreted terms in concrete form. Note that almost any analysis is much more precise when this kind of structural information is ....

R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In M. Alpuente, R. Barbuti, and I. Ramos, editors, Proceedings of the "1994 Joint Conference on Declarative Programming (GULP-PRODE '94)", pages 312--326, Pe~n'iscola, Spain, September 1994.

....In programs where many variables are ground the ROBDDs generated will be kept small, and so also the cost of searching will be diminished. 3 Experimental Evaluation The ideas presented in this paper have been experimentally validated in the context of the development of the China analyzer [2]. China is a data flow analyzer for CLP(H, N ) languages (i.e. Prolog, CLP(R) clp(FD) and so forth) written in Prolog and C . It performs bottom up analysis deriving information on both call and success patterns by means of program transformations and optimized fixpoint computation ....

R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In Proceedings GULP-PRODE '94, pages 312--326, Penscola, Spain, September 1994.

....this process, the ROBDD package is invoked over the simpli ed arguments. Only then we search for further true variables in the resulting ROBDD. 8 Experimental Evaluation The ideas presented in this paper have been experimentally validated in the context of the development of the China analyzer [2]. China is a data ow analyzer for CLP(H, N ) languages (i.e. Prolog, CLP(R) clp(FD) and so forth) written in Prolog and C . It performs bottom up analysis deriving information on both call and success patterns by means of program transformations and optimized xpoint computation ....

R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In M. Alpuente, R. Barbuti, and I. Ramos, editors, Proceedings of the \1994 Joint Conference on Declarative Programming (GULP-PRODE '94)", pages 312-326, Pe~nscola, Spain, September 1994.

....this process, the ROBDD package is invoked over the simplified arguments. Only then we search for further true variables in the resulting ROBDD. 8 Experimental Evaluation The ideas presented in this paper have been experimentally validated in the context of the development of the China analyzer [2]. China is a data flow analyzer for CLP(H, N ) languages (i.e. Prolog, CLP(R) clp(FD) and so forth) written in Prolog and C . It performs bottom up analysis deriving information on both call and success patterns by means of program transformations and optimized fixpoint computation ....

R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In M. Alpuente, R. Barbuti, and I. Ramos, editors, Proceedings of the "1994 Joint Conference on Declarative Programming (GULP-PRODE '94)", pages 312--326, Penscola, Spain, September 1994.

....ROBDD package is invoked over the simplified arguments. Only then the searching for further true variables in the resulting ROBDD is performed. 8 Experimental Evaluation The ideas presented in this paper have been experimentally validated in the context of the development of the China analyzer [2]. China is a data flow analyzer for CLP(H, N ) languages (i.e. Prolog, CLP(R) clp(FD) and so forth) written in Prolog and C . It performs bottom up analysis deriving information on both call and success patterns by means of program transformations and optimized fixpoint computation ....

R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In M. Alpuente, R. Barbuti, and I. Ramos, editors, Proceedings of the "1994 Joint Conference on Declarative Programming (GULP-PRODE '94)", pages 312--326, Pe~n'iscola, Spain, September 1994.

....In programs where many variables are ground the ROBDDs generated will be kept small, and so also the cost of searching will be diminished. 3 Experimental Evaluation The ideas presented in this paper have been experimentally validated in the context of the development of the China analyzer [2]. China is a data flow analyzer for CLP(H, N ) languages (i.e. Prolog, CLP(R) clp(FD) and so forth) written in Prolog and C . It performs bottom up analysis deriving information on both call and success patterns by means of program transformations and optimized fixpoint computation ....

R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In Proceedings GULP-PRODE '94, pages 312--326, Pe~n'iscola, Spain, September 1994.

....standard constraint domain with one suitable for expressing the desired information. This fundamental aspect was brought to light in [5] and elaborated in [12] For languages of the kind of CLP(N ) where N is some numerical domains, the first steps towards pattern analysis were moved in [3, 4] [2] describes some of the more important applications of such analyses. The work done in this field is being generalized to CLP(H, N ) languages, integrating numerical and symbolic pattern analysis. This is done with a variety of techniques, including depth k abstraction. A more restricted kind of ....

....pattern analysis. This is done with a variety of techniques, including depth k abstraction. A more restricted kind of integration has recently been described in [17] Here, the numerical part is essentially the one proposed in [3] Now, instead of directly describing the techniques employed in [3, 4, 2, 17], we concentrate on what is missing from them: a general notion of constraint domain which allows one to adequately describe both the logical part of concrete computations (e.g. answer constraints) and as much pattern analyses (e.g. the shape of those answer constraints) we can think about. We ....

[Article contains additional citation context not shown here]

R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In Proc. GULP--PRODE'94, 1994.

....this process, the ROBDD package is invoked over the simplified arguments. Only then we search for further true variables in the resulting ROBDD. 8 Experimental Evaluation The ideas presented in this paper have been experimentally validated in the context of the development of the China analyzer [2]. China is a data flow analyzer for CLP(H, N ) languages (i.e. Prolog, CLP(R) clp(FD) and so forth) written in Prolog and C . It performs bottom up analysis deriving information on both call and success patterns by means of program transformations and optimized fixpoint computation ....

R. Bagnara. On the detection of implicit and redundant numeric constraints in CLP programs. In M. Alpuente, R. Barbuti, and I. Ramos, editors, Proceedings of the "1994 Joint Conference on Declarative Programming (GULP-PRODE '94)", pages 312--326, Pe~n'iscola, Spain, September 1994.

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