M. Codish, D. Dams, and E. Yardeni. Derivation and Safety of an Abstract Unification Algorithm for Groundness and Aliasing Analysis. In Koichi Furukawa, editor, Proceedings of the Eighth International Conference on Logic Programming, pages 79--93. The MIT Press, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and type analysis. By keeping track of type information, it is possible to infer more accurate sharing information. Conversely, more accurate type information can be deduced if sharing is traced. Specifically, by tracking freeness [23, 9, 26] or alternatively a type property called linearity [25, 7, 15]) a sharing analysis does not always have to assume that aliasing is transitive [7] If variables can be inferred to be free, worst case aliasing need not be assumed in an analysis. Share Pvar Theta Free Pvar , however, only captures shallow type information: it traces the freeness of terms to ....

....sharing information. Conversely, more accurate type information can be deduced if sharing is traced. Specifically, by tracking freeness [23, 9, 26] or alternatively a type property called linearity [25, 7, 15] a sharing analysis does not always have to assume that aliasing is transitive [7]. If variables can be inferred to be free, worst case aliasing need not be assumed in an analysis. Share Pvar Theta Free Pvar , however, only captures shallow type information: it traces the freeness of terms to which a variable can be bound but not the freeness of sub terms. The usefulness of ....

[Article contains additional citation context not shown here]

M. Codish, D. Dams, and E. Yardeni. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In ICLP'91, pages 79--93, Paris, France, 1991. MIT Press.

....structural properties of substitutions, it is possible to infer more accurate sharing information. Conversely, more accurate type information can be deduced if sharing is traced. Type information is often applied by combining sharing and freeness analysis [20, 7, 23] or by tracing linearity [22, 5]. Freeness information differentiates between a free variable, a variable which is definitely not bound to non variable term; and a non free variable, a variable which is possibly bound to a non variable term. Freeness information is useful in its own right, in fact it is essential in the ....

....not bound to non variable term; and a non free variable, a variable which is possibly bound to a non variable term. Freeness information is useful in its own right, in fact it is essential in the detection of non strict and parallelism [13] A more general notion than freeness is linearity [22, 5]. Linearity relates to the number of times a variable occurs in a term. A term is linear if it definitely does not contain multiple occurrences of a variable; otherwise it is non linear. Without exploiting linearity (or freeness) analyses have to assume that aliasing is transitive [5] The ....

[Article contains additional citation context not shown here]

M. Codish, D. Dams, and E. Yardeni. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In ICLP'91, pages 79--93, Paris, France, 1991. MIT Press.

....it is linear if it is not bound to a term containing multiple occurrences of another variable) As argued informally by S0ndergaard [36] the mutual interaction between linearity and aliasing information can improve the accuracy of a sharing analysis. This observation has been formally applied in [11] to the specification of the abstract mgu operator for the domain ASub. In his PhD thesis [32] Langen proposed a similar integration with linearity, but for the set sharing domain. He also shown how the aliasing information allows to compute freeness with a good degree of accuracy (however, ....

.... 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 et al. 12, 13] integrate the information captured ....

[Article contains additional citation context not shown here]

M. Codish, D. Dams, and E. Yardeni. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In Furukawa

....it is linear if it is not bound to a term containing multiple occurrences of another variable) As argued informally by Sndergaard [34] the mutual interaction between linearity and aliasing information can improve the accuracy of a sharing analysis. This observation has been formally applied in [11] to the specification of the abstract mgu operator for the domain ASub. In his PhD thesis [30] Langen proposed a similar integration with linearity, but for the set sharing domain. He also shown how the aliasing information allows to compute freeness with # The present work has been partly ....

.... 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 al. 12, 13] integrate the information captured ....

[Article contains additional citation context not shown here]

M. Codish, D. Dams, and E. Yardeni. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In Furukawa

....the term finiteness property, set sharing is strictly more precise than pair sharing, since a set sharing domain is strictly more precise when computing the functions share same var p and share lin p . 8 This observation holds regardless of the pair sharing variant considered, including ASub [9, 35], PSD [3] and Sh PSh [33] It remains for us to establish that the relations and functions given in Definition 12 satisfy all the requirements of Definitions 3 and 4. This will require a proof of the correctness, with respect to rational unification, of the abstract operators defined on the ....

M. Codish, D. Dams, and E. Yardeni. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In K. Furukawa, editor, Logic Programming: Proceedings of the Eighth International Conference on Logic Programming, MIT Press Series in Logic Programming, pages 79--93, Paris, France, 1991. The MIT Press.

....groundness dependencies. The domains that have influenced 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 ....

M. Codish, D. Dams, and E. Yardeni. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In Furukawa [33], pages 79--93.

....structural properties of substitutions, it is possible to infer more accurate sharing information. Conversely, more accurate type information can be deduced if sharing is traced. Type information is often applied by combining sharing and freeness analysis [20, 7, 23] or by tracing linearity [22, 5]. Freeness information differentiates between a free variable, a variable which is definitely not bound to non variable term; and a non free variable, a variable which is possibly bound to a non variable term. Freeness information is useful in its own right, in fact it is essential in the ....

....not bound to non variable term; and a non free variable, a variable which is possibly bound to a non variable term. Freeness information is useful in its own right, in fact it is essential in the detection of non strict and parallelism [13] A more general notion than freeness is linearity [22, 5]. Linearity relates to the number of times a variable occurs in a term. A term is linear if it definitely does not contain multiple occurrences of a variable; otherwise it is non linear. Without exploiting linearity (or freeness) analyses have to assume that aliasing is transitive [5] The ....

[Article contains additional citation context not shown here]

M. Codish, D. Dams, and E. Yardeni. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In ICLP'91, pages 79--93, Paris, France, 1991. MIT Press.

....subset of D(V ) such that = ff(fl( Thus an alias partition contains at most one non linear share set. Clearly, the alias abstract domain over a set of variables V with the ordering OE, abstraction function ff, and concretisation function fl is an abstraction (as defined, for example, in [3]) of (2 D(V ) To illustrate these definitions, let E be the equations F (x; y; r) C; G(w; w) v; v = u; H(x; y) z; s = K(t) t = K(s) Then ff(E) is the set ffx; y; zg; f; w; v; u; s; tgg: An important property of ff is that unification of a set of equations does not increase the ....

M Codish, D Dams, and E Yardeni. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In K Furukawa, editor, 8th International Conference on Logic Programming, pages 79--93. MIT Press, 1991. 14

....for abstract interpretation of logic programs [3, 18, 23, 24] Specialising a framework for a particular analysis involves devising an abstract domain for descriptions of sets of substitutions and designing a number of abstract functions. One important abstract function is abstract unification [6, 17]. This paper puts forward an abstract domain and an abstract unification function for inferring type information together with sharing and aliasing information. The remainder of this paper is organised as follows. Section 2 briefly recalls some concepts and notations in logic programming and ....

....form corresponding to a substitution . eq(fail) def = fail. A number of collecting semantics have been developed [3, 18, 23, 24, 26, 28] for logic programs. These collecting semantics use different sets of primitive functions such as unification, composition and restriction. Just as those in [6, 15, 28], the collecting semantics for normal logic programs developed in [22] uses only one primitive function which is defined as follows. Let A;B be atoms and ; substitutions. unify(A; B; def = 8 : let ae be a renaming substitution such that vars(A ae) vars(B ) in ae ....

[Article contains additional citation context not shown here]

M. Codish, D. Dams, and Yardeni E. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In K. Furukawa, editor, Proceedings of the Eighth International Conference on Logic Programming, pages 79--93, Paris, France, 1991. The MIT Press.

....and type analysis. By keeping track of type information, it is possible to infer more accurate sharing information. Conversely, more accurate type information can be deduced if sharing is traced. Specifically, by tracking freeness [23, 9, 26] or alternatively a type property called linearity [25, 7, 15]) a sharing analysis does not always have to assume that aliasing is transitive [7] If variables can be inferred to be free, worst case aliasing need not be assumed in an analysis. Share Pvar Theta Free Pvar , however, only captures shallow type information: it traces the freeness of terms to ....

....sharing information. Conversely, more accurate type information can be deduced if sharing is traced. Specifically, by tracking freeness [23, 9, 26] or alternatively a type property called linearity [25, 7, 15] a sharing analysis does not always have to assume that aliasing is transitive [7]. If variables can be inferred to be free, worst case aliasing need not be assumed in an analysis. Share Pvar Theta Free Pvar , however, only captures shallow type information: it traces the freeness of terms to which a variable can be bound but not the freeness of sub terms. The usefulness of ....

[Article contains additional citation context not shown here]

M. Codish, D. Dams, and E. Yardeni. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In ICLP'91, pages 79--93, Paris, France, 1991. MIT Press.

....a framework for a particular analysis involves devising an abstract domain for descriptions of sets of substitutions, called abstract substitutions, and corresponding abstract operators on abstract substitutions. One important abstract operator commonly required is abstract unification [9, 25] which mainly abstracts the normal unification. Another important abstract operator commonly required is an operator that computes (an approximation of) the least upper bound of abstract substitutions. In fact, these two abstract operators are the only abstract operators required by the frameworks ....

....abstracts the normal unification. Another important abstract operator commonly required is an operator that computes (an approximation of) the least upper bound of abstract substitutions. In fact, these two abstract operators are the only abstract operators required by the frameworks proposed in [9, 23, 30, 40]. The polymorphic type analysis will be presented as an abstract domain for polymorphic type descriptions of sets of substitutions together with its associated abstract unification operator and least upper bound operator as required by the framework in [30] The adaptation to the frameworks in ....

[Article contains additional citation context not shown here]

M. Codish, D. Dams, and Yardeni E. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In K. Furukawa, editor, Proceedings of the Eighth International Conference on Logic Programming, pages 79--93, Paris, France, 1991. The MIT Press.

....contains no variables. This is useful not only to an optimising compiler that attempts to speed up unification but also to other program manipulation tools that apply dataflow analyses. Groundness analysis has also been used to improve precisions of other dataflow analyses such as sharing analysis [41, 21, 22, 7, 11, 37, 44, 26] and type analysis [30] There have been many methods proposed for groundness analysis [35, 17, 7, 44, 12, 33, 12, 1, 2, 5, 27, 19, 8, 10, 42] This paper present a new groundness analysis, called polymorphic groundness analysis, whose input and output are parameterised by a number of mode ....

....to other program manipulation tools that apply dataflow analyses. Groundness analysis has also been used to improve precisions of other dataflow analyses such as sharing analysis [41, 21, 22, 7, 11, 37, 44, 26] and type analysis [30] There have been many methods proposed for groundness analysis [35, 17, 7, 44, 12, 33, 12, 1, 2, 5, 27, 19, 8, 10, 42]. This paper present a new groundness analysis, called polymorphic groundness analysis, whose input and output are parameterised by a number of mode parameters. These mode parameters represent groundness information that is not available before analysis but can be provided after analysis. When the ....

[Article contains additional citation context not shown here]

M. Codish, D. Dams, and Yardeni E. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In Furukawa [18], pages 79--93.

....these difficulties. The analysis requires a fairly sophisticated domain to capture enough knowledge to recognize the above cases. The components of the analysis domain combine earlier works: sharing information is based on that presented by S ndergaard [12] and expanded by Codish et al. [1], groundness information is based on that Marriott and S ndergaard [7] The nonlinear information is completely novel. The analysis shares some similarity of purpose with work of Mulkers et al. [8, 9, 10] for PROLOG. Here they are interested in determining dead variables and dead structure for ....

....call alive variables are those passed in from an upper level call to the predicate whose body we are executing together with those variables appearing later in the body. They may have further access after the call terminates. ffl Sharing information is similar to that used by Codish et al. [1]. Variables are said to share if the structures they represent are bound to terms containing a common variable. We add to the sharing domain an element , which is used to represent some variable outside the scope of the current clause, so sharing with variables not in the current clause can still ....

[Article contains additional citation context not shown here]

M. Codish, D. Dams, and E. Yardeni. Derivation and safety of an abstract unification algorithm for aliasing analysis. In K. Furukawa, editor, Logic Programming: Proc. Eighth Int. Conf., pp. 79--93, MIT Press, 1990.

....on logic programs consult [7] or [16] S ndergaard [19] sketched the manipulations (the abstract versions of unification and composition) of abstract substitutions, including the fixpoint computation necessary to reach a stable and correct set of program point annotations. Codish, Dams and Yardeni [6] subsequently provided the details of abstract unification and proved its correctness. We have implemented an abstract interpretation based method which is faithful to the basic ideas in those two papers but differs in two important ways: 1. The groundness information captured by Asub is limited ....

M. Codish, D. Dams, and E. Yardeni. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In K. Furukawa, editor, Logic Programming: Proc. Eighth Int. Conf., pages 79--93. MIT Press, 1991.

No context found.

M. Codish, D. Dams, and E. Yardeni. Derivation and Safety of an Abstract Unification Algorithm for Groundness and Aliasing Analysis. In Koichi Furukawa, editor, Proceedings of the Eighth International Conference on Logic Programming, pages 79--93. The MIT Press, 1991.

....present paper are a definition of the preorder relation and the abstract solved form for this composite domain, and the presentation of a revised unification algorithm able to handle equations involving mixed terms in a uniform way, and its correctness proof. The basic strategy, also applied in [6, 7], is to systematically mimic each step in the Martelli Montanari unification algorithm [29] Equations on mixed terms are rewritten by the algorithm to a set of equations which are either in solved form or involve abstract terms only; the latter equations are then solved in the set sharing domain ....

....A similar (symmetric) property holds for Y j (1 j m) Similar but weaker properties hold in the case that only one of the independent terms being unified is linear. The properties specified by the next lemma partially overlap with those of Lemma 5 in [23] which slightly improved Lemma 2. 2 in [7]) and Lemma 5.7 in [2] Lemma 4.6 Let t[X 1 ; X n ] be a linear concrete term and s[Y 1 ; Ym ] a non linear concrete term such that the terms are unifiable and fX 1 ; X n g fY 1 ; Ym g = i.e. the terms do not share) It then holds for an idempotent and ....

[Article contains additional citation context not shown here]

M. Codish, D. Dams, and E. Yardeni. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In K. Furukawa, editor, Proceedings of the Eighth International Conference on Logic Programming, pages 79--93, Paris, France, 1991. The MIT Press, Cambridge, Mass.

....compilation scheme for sharing information. 2) Most of the recent work on sharing analyses for logic programs attempts to justify the correctness of the proposed abstract operations (e.g. unification) by mimicking the behavior of a suitable corresponding concrete algorithm (for example as in [5, 6]) In contrast, in this paper we focus on algebraic properties (e.g. of a most general unifier) For example, we first characterize the algebraic properties of an abstract most general unifier in the context of a sharing analysis, and then provide an abstract unification algorithm and prove that ....

....Unification of abstract atoms is defined as usual by incremental unification of corresponding abstract terms. mgu A lin (E) 8 : if E = ffi mgu A lin (E 0 ) if E = f = 0 g [ E 0 and = lin mgu ACI1 ( 0 ) 21) Example 25 In the following examples, adapted from [6], we solve at each step the first (upper) equation in the set and apply the result to the other equations: 36 lin mgu ACI1 ( 1 ; 2 ) v 1 = vars( 1 ) v 2 = vars( 2 ) if (v 1 = v 2 = then return x 2 (v 1 [ v 2 ) else if 1 is linear and 2 is linear and v 1 v 2 = then S = ....

M. Codish, D. Dams, and E. Yardeni. Derivation and Safety of an Abstract Unification Algorithm for Groundness and Aliasing Analysis. In Furukawa

....approach in the specification of such algorithms should be taken. More specifically, when attempting to mimic the process of concrete unification for data descriptions, it is productive to systematically mimic each step in a suitable concrete algorithm. This approach has been illustrated in [4] which provides the first proof of correctness for abstract unification over S ndergaard s domain for sharing analysis described in [20] This paper applies a similar approach and describes the first systematic derivation of an abstract unification algorithm for freeness analysis. On the bottom ....

....algorithm, given a suitable notion of data descriptions. A main contribution of the paper is in the novel choice of data descriptions called abstract equation systems which fuse concrete and abstract equations. It is this choice which facilitates the application of the methodology adopted from [4]. While this paper focuses primarily on correctness of abstract unification, the results provide a good foundation for the continuing development of precise and efficient freeness analyses for logic programs [2, 3, 18] The rest of this paper is organized as follows: Section 2 provides some ....

[Article contains additional citation context not shown here]

M. Codish, D. Dams, and E. Yardeni. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In Furukawa [11], pages 79--93.

....t 2 ) Independence is a very important property in work on AND parallelization of logic programs [21, 23] The above notion of sharing is often referred to as pair sharing since it specifies the sharing of a pair of terms. Together with groundness and linearity it forms the pair sharing domain of [9, 42]. A pair (X; Y ) 2 V 2 represents that X and Y may be bound to terms with common variables. A reflexive pair (X; X) represents possibly non linear bindings. However in [16] reflexive pairs are used to represent possible non ground bindings. Another useful notion is that of set sharing which is ....

....in ) i.e. 8X; Y 2 V: X 6= Y share oe (X; Y ) X; Y ) 2 d share in and (following the approach of [42] 8X 2 V: linear oe (X) X; X) 2 d share in . It must be proven that, if X 6= Y share (X; Y ) then (X; Y ) 2 d share out . We borrow the structure of a soundness proof presented in [9]. First note that share (X; Y ) iff share (Xoe; Y oe) The sharing between Xoe and Y oe under the substitution is related to the sharing between X, Y , and the variables of s and t under the initial substitution oe, and can be expressed as follows: share (Xoe; Y oe) share oe (X; Y ) 8 ....

[Article contains additional citation context not shown here]

M. Codish, D. Dams, and E. Yardeni. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In K. Furukawa, editor, Proceedings of the Eighth International Conference on Logic Programming, pages 79--93, Paris, France, 1991. The MIT Press, Cambridge, Mass.

No context found.

M. Codish, D. Dams, and E. Yardeni. Derivation and Safety of an Abstract Unification Algorithm for Groundness and Aliasing Analysis. In ICLP'91, pages 79--96, Paris, France, June 1991. MIT Press.

No context found.

M. Codish, D. Dams, E. Yardeni, Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis, in: K. Furukawa 39 (Ed.), Logic Programming: Proceedings of the Eighth International Conference on Logic Programming, MIT Press Series in Logic Programming, The MIT Press, Paris, France, 1991, pp. 79--93.

No context found.

M. Codish, D. Dams, E. Yardeni, Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis, in: K. Furukawa 39 (Ed.), Logic Programming: Proceedings of the Eighth International Conference on Logic Programming, MIT Press Series in Logic Programming, The MIT Press, Paris, France, 1991, pp. 79--93.

No context found.

M. Codish, D. Dams, E. Yardeni, Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis, in: K. Furukawa 39 (Ed.), Logic Programming: Proceedings of the Eighth International Conference on Logic Programming, MIT Press Series in Logic Programming, The MIT Press, Paris, France, 1991, pp. 79--93.

No context found.

M. Codish, D. Dams, E. Yardeni, Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis, in: K. Furukawa 39 (Ed.), Logic Programming: Proceedings of the Eighth International Conference on Logic Programming, MIT Press Series in Logic Programming, The MIT Press, Paris, France, 1991, pp. 79--93.

No context found.

M. Codish, D. Dams, and E. Yardeni. Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis. In K. Furukawa, editor, Logic Programming: Proceedings of the Eighth International Conference on Logic Programming, MIT Press Series in Logic Programming, pages 79--93, Paris, France, 1991. The MIT Press.

First 50 documents

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