D. Jacobs and A. Langen. Accurate and E#cient Approximation of Variable Aliasing in Logic Programs. In 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....computable operators on substitutions. The groundness operator gvars captures the set of variables that are mapped to ground rational trees by rt. We define it by means of the occurrence operator occ . This was introduced in [40] as a replacement for the sharing group operator sg of [44]. In [40] the occ operator is used to define a new abstraction function for set sharing analysis that, di#erently from the classical ones [22, 44] maps equivalent substitutions in rational solved form to the same abstract element. Definition 9. Occurrence and groundness operators. For each ....

....trees by rt. We define it by means of the occurrence operator occ . This was introduced in [40] as a replacement for the sharing group operator sg of [44] In [40] the occ operator is used to define a new abstraction function for set sharing analysis that, di#erently from the classical ones [22, 44], maps equivalent substitutions in rational solved form to the same abstract element. Definition 9. Occurrence and groundness operators. For each n N, the occurrence function occ n : RSubst # f (Vars) is defined, for each # RSubst and each v Vars, by occ n (#, v) v ....

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D. Jacobs and A. Langen. Accurate and e#cient approximation of variable aliasing in logic programs. In E. L. Lusk and R. A. Overbeek, editors, Logic Programming: Proceedings of the North American Conference, MIT Press Series in Logic Programming, pages 154--165, Cleveland, Ohio, USA, 1989. The MIT Press.

....# defined on uco(C) formalizes the intuition of an abstract domain being more precise than another one; moreover, given two elements # 1 , # 2 # uco(C) their reduced product, denoted # 1 # # 2 , is their glb on uco(C) 2. 5 The Set Sharing Domain The set sharing domain of Jacobs and Langen [24], encodes both aliasing and groundness information. Let VI # f Vars be a fixed and finite set of variables of interest. An element of the set sharing domain (a sharing set) is a set of subsets of VI (the sharing groups) Note that the empty set is not a sharing group. Definition 3 (The ....

.... dependency lattice is PSD def = # PSD (SH ) 3 The Domain SFL The abstract domain SFL is made up of three components, providing di#erent kinds of sharing information regarding the set of variables of interest VI : the first component is the set sharing domain SH of Jacobs and Langen [24]; the other two components provide freeness and linearity information, each represented by simply recording those variables of interest that are known to enjoy the corresponding property. Definition 7 (The domain SFL. Let F def = #(VI ) and L def = #(VI ) be partially ordered by reverse ....

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D. Jacobs and A. Langen. Accurate and e#cient approximation of variable aliasing in logic programs. In E. L. Lusk and R. A. Overbeek, editors, Logic Programming: Proceedings of the North American Conference, MIT Press Series in Logic Programming, pages 154--165, Cleveland, Ohio, USA, 1989. The MIT Press.

....trees. This poses a non trivial problem when trying to define a good abstraction function, since it would be really desirable for this function to map any two equivalent concrete elements to the same abstract element. As shown in [23] the classical abstraction function for set sharing analysis [12, 25], which was defined for idempotent substitutions only, does not enjoy this property when applied, as it is, to arbitrary substitutions in rational solved form. A possibility is to look for a more general abstraction function that allows to obtain the desired property. For example, in [23] the ....

....idempotent substitutions only, does not enjoy this property when applied, as it is, to arbitrary substitutions in rational solved form. A possibility is to look for a more general abstraction function that allows to obtain the desired property. For example, in [23] the sharing group operator sg of [25] is replaced by an occurrence operator, occ, defined by means of a fixpoint computation. We now provide a similar fixpoint construction defining the finiteness operator. Definition 3.4 (Finiteness functions. For each n # N, the finiteness function hvars n : RSubst # #(Vars) is defined, for ....

D. Jacobs and A. Langen. Accurate and e#cient approximation of variable aliasing in logic programs. In E. L. Lusk and R. A. Overbeek, editors, Logic Programming: Proceedings of the North American Conference, MIT Press Series in Logic Programming, pages 154--165, Cleveland, Ohio, USA, 1989. The MIT Press.

....terms. This poses a non trivial problem when trying to define a good abstraction function, since it would be really desirable for this function to map any two equivalent concrete elements to the same abstract element. As shown in [24] the classical abstraction function for set sharing analysis [13, 26], which was defined for idempotent substitutions only, does not enjoy this property when applied, as it is, to arbitrary substitutions in rational solved form. A possibility is to look for a more general abstraction function that allows to obtain the desired property. For example, in [24] the ....

....idempotent substitutions only, does not enjoy this property when applied, as it is, to arbitrary substitutions in rational solved form. A possibility is to look for a more general abstraction function that allows to obtain the desired property. For example, in [24] the sharing group operator sg of [26] is replaced by an occurrence operator, occ, defined by means of a fixpoint computation. We now provide a similar fixpoint construction defining the finiteness operator. 6 As usual, this is modulo the possible renaming of variables. 10 Definition 5. Finiteness functions. For each n # N, ....

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D. Jacobs and A. Langen. Accurate and e#cient approximation of variable aliasing in logic programs. In E. L. Lusk and R. A. Overbeek, editors, Logic Programming: Proceedings of the North American Conference, MIT Press Series in Logic Programming, pages 154--165, Cleveland, Ohio, USA, 1989. The MIT Press.

....most of the recent research on sharing analysis are the following: the domain ASub of Sndergaard [55] which combines elementary information on groundness, pair sharing, and linearity. The abstract operators were formalized rigorously in [13] the domain Sharing of Jacobs and Langen [42,43,47], which is based on the concept of sharing set (in contrast with the concept of sharing pair adopted by ASub) While ASub takes advantage of linearity information, Sharing is more accurate in capturing groundness dependencies. See Section 8 for a brief review of the research work that has been ....

....can be found in Appendix A, while some details on the programs used in the experimental evaluation are given in Appendix B. 2 Preliminaries In this section we introduce some mathematical notation that will be used in the paper, as well as recalling the set sharing domain of Jacobs and Langen [42,43,47]. 2.1 Basic Concepts and Notation For a set S, #S is the cardinality of S, #(S) is the powerset of S, whereas # f (S) is the set of all the finite subsets of S. A preorder # over a set P is a binary relation that is reflexive and transitive. If # is also antisymmetric, then it is called a ....

D. Jacobs and A. Langen. Accurate and e#cient approximation of variable aliasing in logic programs. In E. L. Lusk and R. A. Overbeek, editors, Logic Programming: Proceedings of the North American Conference, MIT Press Series in Logic Programming, pages 154--165, Cleveland, Ohio, USA, 1989. The MIT Press.

....1 Introduction In logic programming, a knowledge of sharing between variables is important for optimizations such as the exploitation of parallelism. Today, talking about sharing analysis for logic programs is almost the same as talking about the set sharing domain Sharing of Jacobs and Langen [12, 13]. The adequacy of this domain is not normally questioned. Researchers appear to be more concerned as to which add ons are best: linearity, freeness, depth k abstract substitutions and so on [3, 4, 5, 14, 15, 17] rather than whether it is the optimal domain for the sharing information under ....

....thus # is identified with # x ## #(x) # # x # dom(#) # . A substitution # is idempotent if vars # #(x) # # dom(#) # for each x # dom(#) The set of all the idempotent substitutions is denoted by Subst . 2. 2 The Sharing Domain The Sharing domain is due to Jacobs and Langen [12]. Definition 1 (The set sharing lattice. Let 1 SG def = # S # # f (Vars) # # S #= # # 1 The literature on Sharing is almost unanimous in defining sharing sets so that they always contain the empty set. We deviate from this de facto standard: in our approach sharing sets never ....

D. Jacobs and A. Langen. Accurate and e#cient approximation of variable aliasing in logic programs. In Proceedings of the North American Conference on Logic Programming, pages 154--165. The MIT Press, 1989.

....1 Introduction In logic programming, a knowledge of sharing between variables is important for optimizations such as the exploitation of parallelism. Today, talking about sharing analysis for logic programs is almost the same as talking about the set sharing domain Sharing of Jacobs and Langen [11,12]. The adequacy of this domain is not normally questioned. Researchers appear to be more concerned as to which add ons are best: linearity, freeness, depth k abstract substitutions and so on [3 5,13,14,16] rather than whether it is the optimal domain for the sharing information under ....

....thus # is identified with # x ## #(x) # # x # dom(#) # . A substitution # is idempotent if vars # #(x) # #dom(#) # for each x # dom(#) The set of all the idempotent substitutions is denoted by Subst . 2. 2 The Sharing Domain The Sharing domain is due to Jacobs and Langen [11]. Definition 1. The set sharing lattice. Let 1 SG def = # S # # f (Vars) # # S #= # # and let SH def = #(SG) The set sharing lattice is given by the set SS def = # (sh, U) # # sh # SH , U # # f (Vars) #S # sh : S # U # # #, # ordered by # SS defined as ....

D. Jacobs and A. Langen. Accurate and e#cient approximation of variable aliasing in logic programs. In E. L. Lusk and R. A. Overbeek, editors, Proceedings of the North American Conference on Logic Programming, pages 154--165. The MIT Press, Cambridge, Mass., 1989.

....on page 48. A An implementation for the parameter domain P As discussed in Section 3, several abstract domains for sharing analysis can be used to implement the parameter component P . As a basic implementation, one could consider the well known set sharing domain of Jacobs and Langen [JL89]. In such a case, all the non trivial correctness results have already been established in [HBZ01] in particular, the abstraction function provided in [HBZ01] satisfies the requirement of Definition 3 and the abstract unification operator has been proven correct with respect to rational tree ....

D. Jacobs and A. Langen, Accurate and e#cient approximation of variable aliasing in logic programs, Logic Programming: Proceedings of the North American Conference (Cleveland, Ohio, USA) (E. L. Lusk and R. A. Overbeek, eds.), MIT Press Series in Logic Programming, The MIT Press, 1989, pp. 154--165. 48

....occur check. The results for safeness, idempotence and commutativity for abstract unification using this abstraction function are given. 1 Introduction Today, talking about sharing analysis for logic programs is almost the same as talking about the set sharing domain Sharing of Jacobs and Langen [6, 7]. Key properties such as commutativity and soundness of this domain and its associated abstract operations are normally assumed to hold. The main reason for this is that [7] not only includes a proof of the soundness but also refers the reader to the thesis of Langen [11] for proofs of ....

.... # = vars(t i,j ) Therefore, for each i = 1, j, vars(t i,j # j ) vars(t i,j ) It then follows (using the alternative characterisation of variable idempotence) that # j is variable idempotent. # 4 Set Sharing 4. 1 The Sharing Domain The Sharing domain is due to Jacobs and Langen [6]. However, we use the definition as presented in [1] Definition 4 (The set sharing lattice. Let SG def = # S # # f (Vars) # # S #= # # and let SH def = #(SG) The set sharing lattice is given by the set SS def = # (sh, U) # # sh # SH , U # # f (Vars) #S # sh : S # ....

[Article contains additional citation context not shown here]

D. Jacobs and A. Langen. Accurate and e#cient approximation of variable aliasing in logic programs. In E. L. Lusk and R. A. Overbeek, editors, Logic Programming: Proceedings of the North American Conference, MIT Press Series in Logic Programming, pages 154--165, Cleveland, Ohio, USA, 1989. The MIT Press.

....of hidden information in the combination of Sharing with the usual domain for freeness. Keywords: Mode Analysis, Sharing Analysis, Abstract Interpretation. 1 Introduction In this paper, we present one of the final steps in our revamp of the set sharing domain, Sharing, of Jacobs and Langen [17]. We have first questioned the adequacy of Sharing with respect to the property of interest, that is, pair sharing. In [4] we have proved that Sharing is redundant for pair sharing and we have identified the weakest abstraction of Sharing that can capture pair sharing with the same degree of ....

D. Jacobs and A. Langen. Accurate and e#cient approximation of variable aliasing in logic programs. In E. L. Lusk and R. A. Overbeek, editors, Logic Programming: Proceedings of the North American Conference, MIT Press Series in Logic Programming, pages 154--165, Cleveland, Ohio, USA, 1989.

....are used to provide more precise groundness information. Indeed, we are requiring a quite complicated interaction between domains. Another application of groundness analysis with fast access to ground variables is for aliasing analysis. The most popular domain for this kind of analysis is Sharing [13]. Without going into details, its strength over the previous approaches [15, 12] comes from the fact that it keeps track of groundness dependencies. In fact, Sharing has, as far as groundness information is concerned, the same power of Def. When Pos is used for groundness, using Sharing for ....

D. Jacobs and A. Langen. Accurate and e#cient approximation of variable aliasing in logic programs. In E. Lusk and R. Overbeek, editors, Proc. North American Conf. on Logic Programming'89, pages 154--165. The MIT Press, Cambridge, Mass., 1989.

....this abstraction function are given. Keywords: abstract interpretation, logic programming, occur check, rational trees, set sharing. 1 Introduction Today, talking about sharing analysis for logic programs is almost the same as talking about the set sharing domain Sharing of Jacobs and Langen [8, 9]. Researchers are primarily concerned with extending the domain with linearity, freeness, depth k abstract substitutions and so on [2, 4, 12, 13, 16] Key properties such as commutativity and soundness of this domain and its associated abstract operations are normally assumed to hold. The main ....

....## f(g(x 3 , x 4 ) # , # 3 = # x 1 ## f(g(f(g(x 3 , x 4 ) x 4 ) x 2 ## g(f(g(x 3 , x 4 ) x 4 ) x 3 ## f(g(x 3 , x 4 ) # . Note that # 3 is variable idempotent and that T # # 0 ## # 3 . 4 Set Sharing 4. 1 The Sharing Domain The Sharing domain is due to Jacobs and Langen [8]. However, we use the definition as presented in [1] Definition 2. The set sharing lattice. Let SG def = # S # # f (Vars) # # S #= # # and let SH def = #(SG) The set sharing lattice is given by the set SS def = # (sh, U) # # sh # SH , U # # f (Vars) #S # sh : S # ....

[Article contains additional citation context not shown here]

D. Jacobs and A. Langen. Accurate and e#cient approximation of variable aliasing in logic programs. In E. L. Lusk and R. A. Overbeek, editors, Logic Programming: Proceedings of the North American Conference, MIT Press Series in Logic Programming, pages 154--165, Cleveland, Ohio, USA, 1989. The MIT Press.

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D. Jacobs and A. Langen. Accurate and E#cient Approximation of Variable Aliasing in Logic Programs. In 1989.

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D. Jacobs and A. Langen. Accurate and E#cient Approximation of Variable Aliasing in Logic Programs. In 1989 North American Conference on Logic Programming. MIT Press, October 1989.

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D. Jacobs and A. Langen. Accurate and e#cient approximation of variable aliasing in logic programs. In Ewing L. Lusk and Ross A. Overbeek, editors, Proceedings of the North American Conference on Logic Programming, pages 154--165. MIT Press, 1989.

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D. Jacobs, A. Langen, Accurate and e#cient approximation of variable aliasing in logic programs, Proc. North-American Conf. on Logic Programming (NACLP-89), Cleveland, OH, October 1989.

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D. Jacobs, A. Langen, Accurate and e#cient approximation of variable aliasing in logic programs, in: E. L. Lusk, R. A. Overbeek (Eds.), Logic Programming: Proceedings of the North American Conference, MIT Press Series in Logic Programming, The MIT Press, Cleveland, Ohio, USA, 1989, pp. 154--165.

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D. Jacobs, A. Langen, Accurate and e#cient approximation of variable aliasing in logic programs, in: E. L. Lusk, R. A. Overbeek (Eds.), Logic Programming: Proceedings of the North American Conference, MIT Press Series in Logic Programming, The MIT Press, Cleveland, Ohio, USA, 1989, pp. 154--165.

No context found.

D. Jacobs, A. Langen, Accurate and e#cient approximation of variable aliasing in logic programs, in: E. L. Lusk, R. A. Overbeek (Eds.), Logic Programming: Proceedings of the North American Conference, MIT Press Series in Logic Programming, The MIT Press, Cleveland, Ohio, USA, 1989, pp. 154--165.

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D. Jacobs, A. Langen, Accurate and e#cient approximation of variable aliasing in logic programs, in: E. L. Lusk, R. A. Overbeek (Eds.), Logic Programming: Proceedings of the North American Conference, MIT Press Series in Logic Programming, The MIT Press, Cleveland, Ohio, USA, 1989, pp. 154--165.

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