G. Fil. Share x Free: Simple and correct. Technical Report 15, Diparti- mento di Matematica, Universitk di Padova, December 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... from a bi directional interaction between aliasing and freeness information was initially pointed out by Muthukumar and Hermenegildo [32, 33] Since then, several authors considered the integration of set sharing with freeness, sometimes also including additional explicit structural information [9, 10, 29, 18]. Building on the results obtained in [34] 11] and [32] but independently from [30] Hans and Winkler [20] proposed a combined integration of freeness and linearity information with set sharing. Similar combinations have been proposed in [5, 6, 7] From a more pragmatic point of view, Codish et ....

....free is also necessarily linear. All these redundancies can be removed by taking, as abstract domain, the image of the concrete domain under the abstraction function. Apart from the simple cases shown above, it is somehow di#cult to explicitly characterize such a set. For instance, as observed in [18], the element xy, yz, xz , x, y, z , x, y, z # SFL like # S does not correspond to the abstraction of any concrete computation state. It is worth stressing that these spurious elements do not compromise the correctness of the analysis and, although they can a#ect the ....

G. File. Share Free: Simple and correct. Technical Report 15, Dipartimento di Matematica, Universita di Padova, December 1994.

....possible aliasing of program variables is crucial. Aliasing information can also be used indirectly in the computation of other interesting program properties. For instance, the precision with which freeness information can be computed depends on the precision with which aliasing can be tracked [5,6,12,31,46,47,51]. Notice that, often, it is not a knowledge about possible aliasing that is required but its converse, called definite independence . Two variables are independent if they are bound to terms that have no variables in common. Thus, when an analysis concludes that two variables are not possibly ....

....freeness with a depth k component [48,54] King [45] shows also how a more refined tracking of linearity (essentially, pushing linearity at the levels of sharing groups) allows for further precision improvements. A remarkable piece of work, in terms of elegance and cleanliness, is constituted by [31]. Here File is the first to define formally the reduced product between Sharing and Free (the usual domain for freeness) identifying the elements of the Cartesian product that are redundant. The important merit of this work is due to the fact that it operates a clear distinction between the ....

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G. File. Share Free: Simple and correct. Technical Report 15, Dipartimento di Matematica, Universita di Padova, December 1994.

....freeness [4] Beside the need to consider accuracy with respect to the PSFree property (where indicates the reduced product operation [10] we have to reconsider the concept of redundancy. Our definition of redundancy disregards the interactions between the sharing and the freeness components [11]: a new definition should be given that induces a finer equivalence relation. To summarize, we cannot claim that X combined with Free is as accurate as SS combined with Free with respect to the PS Free property. However, from a practical point of view, we do claim that the results of our ....

....with Free with respect to the PS Free property. However, from a practical point of view, we do claim that the results of our implementation of the combination of X with Free are as accurate as all current implementations of SS plus Free. As a matter of fact, the abstract operators formalized in [11] appear to be characterized by an unfavorable cost precision ratio, and the optimal form of these operators has not been implemented. The same observations apply when comparing the combination X plus Free plus Lin with respect to SS plus Free plus Lin. ....

G. File. Share Free: Simple and correct. Technical Report 15, Dipartimento di Matematica, Universita di Padova, December 1994.

....Lin and Free are the usual domains for linearity and freeness. 5 We emphasize that this claim holds for the analysis (domain and operators) defined in [4] It is known that this analysis, though very accurate, is not optimal. A more powerful abstract unification operator has been defined in [10], which exploits some non trivial interactions between the sharing and the freeness components. When this refined operator is employed, it is no longer true that SS # plus Lin plus Free is as accurate as SS plus Lin plus Free. However, our experimentation has revealed that the abstract operator ....

....some non trivial interactions between the sharing and the freeness components. When this refined operator is employed, it is no longer true that SS # plus Lin plus Free is as accurate as SS plus Lin plus Free. However, our experimentation has revealed that the abstract operator formalized in [10] is characterized by an extremely unfavorable cost precision ratio. ....

G. File. Share Free: Simple and correct. Technical Report 15, Dipartimento di Matematica, Universita di Padova, December 1994.

....seems very unlikely that a well designed compoundness analysis can lose this kind of information, which stems from bindings of the form x = f(y; z) 10 Recovering Hidden Information As noted by several authors (see, e.g. 6] the standard combination of Sharing and Free is not optimal. G. Fil e [15] formally identi ed the reduced product of these domains and proposed an improved abstract uni cation operator. This new operator exploits two properties holding for the abstract description of a single concrete substitution: 1) each free variable occurs in exactly one sharing group; and (2) two ....

....we obtained for the rst of the two ideas by G. Fil e presented above are independent from the fact that structural information and or 4 The function Reduce also deals with some hidden interactions between sharing and freeness information: as these improvements are subsumed by the work of Fil e [15], we discuss them in Section 10. 5 This is possible even without decomposing the abstract description: as examples, consider the substitutions 1 = fx = f(u) y = g(v)g and 2 = fx = f(y)g together with an abstract description saying that x and y are both free and the only sharing group ....

G. File. Share  Free: Simple and correct. Technical Report 15, Dipartimento di Matematica, Universita di Padova, December 1994.

....seems very unlikely that a well designed compoundness analysis can lose this kind of information, which stems from bindings of the form x = f(y, z) 10 Recovering Hidden Information As noted by several authors (see, e.g. 6] the standard combination of Sharing and Free is not optimal. G. File [15] formally identified the reduced product of these domains and proposed an improved abstract unification operator. This new operator exploits two properties holding for the abstract description of a single concrete substitution: 1) each free variable occurs in exactly one sharing group; and (2) ....

....we obtained for the first of the two ideas by G. File presented above are independent from the fact that structural information and or 4 The function Reduce also deals with some hidden interactions between sharing and freeness information: as these improvements are subsumed by the work of File [15], we discuss them in Section 10. 5 This is possible even without decomposing the abstract description: as examples, consider the substitutions # 1 = x = f(u) y = g(v) and # 2 = x = f(y) together with an abstract description saying that x and y are both free and the only sharing group ....

G. File. Share Free: Simple and correct. Technical Report 15, Dipartimento di Matematica, Universita di Padova, December 1994.

....possible aliasing of program variables is crucial. Aliasing information can also be used indirectly in the computation of other interesting program properties. For instance, the precision with which freeness information can be computed depends on the precision with which aliasing can be tracked [8, 11, 19, 27, 28, 31]. Notice that, sometimes, the property under investigation is called de nite independence . Two variables are independent if they are bound to terms that have no variables in common. That is, if two variables are not possibly aliased then they are de nitely independent and vice versa. Thus ....

....ileanTAP, an intuitionistic theorem prover written by J. Otten. The program begins with the directive : set flag(occur check,on) 8 The function Reduce also deals with some hidden interactions between sharing and freeness information: as these improvements are subsumed by the work of G. Fil e [19], we discuss them in Section 10. that such a Reduce function is not part of the abstract uni cation algorithm presented in [8] and it is unclear where and when it should be applied. The authors suggest that the algorithm should start with reduced abstract descriptions. However, there is no ....

[Article contains additional citation context not shown here]

G. File. Share  Free: Simple and correct. Technical Report 15, Dipartimento di Matematica, Universita di Padova, Italy, 1994.

....possible aliasing of program variables is crucial. Aliasing information can also be used indirectly in the computation of other interesting program properties. For instance, the precision with which freeness information can be computed depends on the precision with which aliasing can be tracked [5,6,12,31,46,47,51]. Notice that, often, it is not a knowledge about possible aliasing that is required but its converse, called de nite independence . Two variables are independent if they are bound to terms that have no variables in common. Thus, when an analysis concludes that two variables are not possibly ....

....freeness with a depth k component [48,54] King [45] shows also how a more re ned tracking of linearity (essentially, pushing linearity at the levels of sharing groups) allows for further precision improvements. A remarkable piece of work, in terms of elegance and cleanliness, is constituted by [31]. Here Fil e is the rst to de ne formally the reduced product between Sharing and Free (the usual domain for freeness) identifying the elements of the Cartesian product that are redundant. The important merit of this work is due to the fact that it operates a clear distinction between the bene ....

[Article contains additional citation context not shown here]

G. File. Share  Free: Simple and correct. Technical Report 15, Dipartimento di Matematica, Universita di Padova, December 1994.

....need to consider accuracy with respect to the PS ThetaFree property (where Delta Theta Delta indicates the reduced product operation [10] we have to reconsider the concept of redundancy. Our definition of redundancy disregards the interactions between the sharing and the freeness components [11]: a new definition should be given that induces a finer equivalence relation. To summarize, we cannot claim that X combined with Free is as accurate as SS combined with Free with respect to the PS Theta Free property. However, from a practical point of view, we do claim that the results of our ....

....Free with respect to the PS Theta Free property. However, from a practical point of view, we do claim that the results of our implementation of the combination of X with Free are as accurate as all current implementations of SS plus Free. As a matter of fact, the abstract operators formalized in [11] appear to be characterized by an unfavorable cost precision ratio, and the optimal form of these operators has not been implemented. The same observations apply when comparing the combination X plus Free plus Lin with respect to SS plus Free plus Lin. ....

G. Fil'e. Share \Theta Free: Simple and correct. Technical Report 15, Dipartimento di Matematica, Universit`a di Padova, December 1994.

....where Lin and Free are the usual domains for linearity and freeness. 5 We emphasize that this claim holds for the analysis (domain and operators) defined in [4] It is known that this analysis, though very accurate, is not optimal. A more powerful abstract unification operator has been defined in [10], which exploits some non trivial interactions between the sharing and the freeness components. When this refined operator is employed, it is no longer true that SS ae plus Lin plus Free is as accurate as SS plus Lin plus Free. However, our experimentation has revealed that the abstract operator ....

....some non trivial interactions between the sharing and the freeness components. When this refined operator is employed, it is no longer true that SS ae plus Lin plus Free is as accurate as SS plus Lin plus Free. However, our experimentation has revealed that the abstract operator formalized in [10] is characterized by an extremely unfavorable cost precision ratio. ....

G. Fil'e. Share \Theta Free: Simple and correct. Technical Report 15, Dipartimento di Matematica, Universit`a di Padova, December 1994.

.... from a bi directional interaction between aliasing and freeness information was initially pointed out by Muthukumar and Her menegildo [34, 35] Since then, several authors considered the integration of set sharing with freeness, sometimes also including additional explicit structural information [9, 10, 31, 20]. Building on the results obtained in [36] 11] and [34] but independently from [32] Hans and Winklet [22] proposed a combined integration of freehess and linearity information with set sharing. Similar combinations have been proposed in [5, 6, 7] From a more pragmatic point of view, Codish ....

....is also necessarily linear. All these redundancies can be removed by taking, as abstract domain, the image of the concrete domain under the abstraction function. Apart from the simple cases shown above, it is somehow difficult to explicitly characterize such a set. For instance, as observed in [20], the element ( xy, yz, xz) x, y, z , x, y, z ) FL like Ls does not correspond to the abstraction of any concrete computation state. It is worth stressing that these spurious elements do not compromise the correctness of the analysis and, although they can affect the precision of the ....

G. Fil. Share x Free: Simple and correct. Technical Report 15, Diparti- mento di Matematica, Universitk di Padova, December 1994.

....need to consider accuracy with respect to the PS Theta Free property (where Delta Theta Delta indicates the reduced product operation [9] we have to reconsider the concept of redundancy. Our definition of redundancy disregards the interactions between the sharing and the freeness components [10]: a new definition should be given that induces a finer equivalence relation. To summarize, we cannot claim that X combined with Free is as accurate as SS combined with Free with respect to the PS Theta Free property. However, from a practical point of view, we do claim that the results of our ....

....Free with respect to the PS Theta Free property. However, from a practical point of view, we do claim that the results of our implementation of the combination of X with Free are as accurate as all current implementations of SS plus Free. As a matter of fact, the abstract operators formalized in [10] appear to be characterized by an unfavorable cost precision ratio, and the optimal form of these operators has not been implemented. The same observations apply when comparing the combination X plus Free plus Lin with respect to SS plus Free plus Lin. ....

G. Fil'e. Share \Theta Free: Simple and correct. Technical Report 15, Dipartimento di Matematica, Universit`a di Padova, December 1994.

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