M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. of the ACM Symposium on Principles of Programming Languages, pages 451--464. ACM Press, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....in [15] and the semantic based approximation in [32] can be easily extended to CLP languages in view of the present paper. The machinery of partial answers instead may require We thank an anonymous referee for this comment. an additional layer of abstraction, like the one applied in [16] for the compositional analysis of modular logic programs. We believe that our constraint system notion and abstraction can be easily applied to semantic constructions characterizing different observable behaviours, like those described in [10] 8. CONCLUSIONS We have defined an algebraic ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

.... upon part P j if and only if # X j , # X # j : F # Y , # X 1 , # X j , # # #= Y , # X 1 , # X # j , # #) It is often the case that this dependency graph is built before the analysis and parts are analyzed in sequence by their topological order (see e.g. [8, 57]) As in most incremental compilation systems, circular dependency may not be considered (i.e. all circularly dependent parts are grouped into a single part since an iterative analysis is necessary) At the limit, the analysis will degenerate into a global analysis as considered in Sec. 2, the ....

M. Codish, S. Debray, and R. Giacobazzi. Compositional analysis of modular logic programs. In 20 POPL, 451464, Charleston, 1993. ACM Press.

....An appendix thus details how our analyser handles various builtins. It is intended to help other developers in the analysis community. Other issues that have not be discussed in this note, however, are more problematic. For example, supporting programs that are broken across several les [4,5,9] is a study within its own right. At present, our analyser has no support for modules. It also cannot handle term mutating setarg 3 goals. 6 ....

M. Codish, S. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Principles of Programming Languages, pages 451-464. ACM Press, 1993.

....its body contains the constant a as the result of an earlier bottom up propagation. Recently, an integration between partial deduction and abstract interpretation (both top down) has been established [13] A similar integration between our framework and bottom up abstract interpretation (see e.g. [3]) might be feasible and is a topic of further research. Also the exact relation between bottom up and top down partial deduction needs to be scrutinised, as well as an integration between the two techniques. Examples in [21] indicate that a combination of the described bottom up transformation ....

Michael Codish, Saumya K. Debray, and Roberto Giacobazzi. Compositional analysis of modular logic programs. In Conference Record of the Twentieth ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 451--464, Charleston, South Carolina, January 10--13, 1993. ACM Press.

....the rst attempt to achieve this bottom up propagation in a completely general way. Recently, an integration between partial deduction and abstract interpretation (both top down) was established [Leu98] A similar integration between our framework and bottom up abstract interpretation (see, e.g. CDG93] might be feasible and is a topic of further research. Acknowledgments We thank anonymous referees for extremely helpful comments on previous versions of this paper. We also thank Karel De Vlaminck for his continuing support and interest in this work. Acknowledgment of support Vanhoof was ....

Michael Codish, Saumya K. Debray, and Roberto Giacobazzi. Compositional analysis of modular logic programs. In Conference Record of the Twentieth ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 451-464, Charleston, South Carolina, January 10-13, 1993. ACM Press.

.... G, L, F, M, # ; L is finite output S: array[N ] of L declare H: array[N ,L] of L; initial values # W : list of (n,x) n#N , x#L; initially empty [1] H[#,#] #; W : #,#) 2] while W #= # do [3] remove (n,x) from W ; y: H[n,x] 4] if n is not a call node or an exit node then [5] foreach m#Succ(n) do propagate(m,x,fm (y) 6] if n is a call node then [7] e : called entry(n) propagate(e,y,fe(y) 8] if n is an exit node then [9] foreach r#Succ(n) and l #L do [10] if H[call node(r) l] x then propagate(r,l,fr (y) 11] foreach n#N do [12] S[n] V l#L ....

.... n#N # , x#L # ; initially empty [1a ] if ##N # then [1b] H[#,# # ] # # ; add (#,# # ) to W ; 1c ] foreach n#BoundaryEntries do [1d ] H[n,#e(n) #e(n) add (n,#e(n) to W ; 2] while W #= # do [3] remove (n,x) from W ; y: H[n,x] 4] if n is not a call node or an exit node then [5] foreach m#Succ(n) do propagate(m,x,f # m (y) 6a ] if n is a call node and n #BoundaryCalls then [7a] e : called entry(n) propagate(e,y,f # e (y) 6b ] if n is a call node and n#BoundaryCalls then [7b ] r : ret node(n) propagate(r,x,f # r (#c(n) y) 8] if n is an exit node ....

[Article contains additional citation context not shown here]

M. Codish, S. Debray, and R. Giacobazzi. Compositional analysis of modular logic programs. In Proc. Symp. on Principles of Prog. Lang., pages 451--464, 1993.

.... Abstract interpretation of CLP programs has been considered in a denotational semantics framework in [38] while by using suitable abstract versions of the immediate consequence operators T 3 P we can generalize the bottom up approach in [3] The compositional semantics in [7] has been used in [10] to develop a modular analysis for pure logic programs. Analogously, our F Omega semantics and its operator T Omega P can be taken as the basis to define a framework for the compositional abstract interpretation of CLP programs, thus providing the same benefits discussed in [10] in terms of ....

....been used in [10] to develop a modular analysis for pure logic programs. Analogously, our F Omega semantics and its operator T Omega P can be taken as the basis to define a framework for the compositional abstract interpretation of CLP programs, thus providing the same benefits discussed in [10] in terms of complexity and reusability of the analysis. It is worth noting that in many applications based on abstract interpretation the set of (possibly abstract) values for variables is finite. In such a case, by a slight modification of the definition of F Omega (analogous to that one in ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

....4. As for call patterns, both the magic like transformation in [15] and the semantic based approximation in [32] can be easily extended to CLP languages in view of the present paper. The machinery of partial answers instead may require an additional layer of abstraction, like the one applied in [16] for the compositional analysis of modular logic programs. We believe that our constraint system notion and abstraction can be easily applied to semantic constructions characterizing different observable behaviours, like those described in [10] 8. CONCLUSIONS We have defined an algebraic ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

.... input values (actually, it is not clear what is input and what it is output to start with) so in order to implement such an intelligent selection strategy, one would need some sophisticated analysis tools which might either be based on abstract interpretation (with tools similar to the ones of [CDG93]) or on re ned versions of modes such as the ones described in [BM97, EG96] Other works related to this subjects are [LK92, EvR98] 17 We have also discussed the fact that logic programs allow backtracking. We have seen that strictly speaking backtracking computations can be easily ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional analysis of modular logic programs. In ACM, editor, Twentieth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 451-464. ACM Press, 1993.

....model. Having noted the above, we note there do exist examples in the literature where abstraction on syntax generates small step rule schemes that can be used to generate useful program models. The best known example is the Kleene star abstraction technique of Codish, Falaschi, and Marriott [12, 11], where the size of an unfolded Prolog program is controlled by joining together goal clauses that use the same predicate symbol. A Prolog program is therefore abstracted into a syntax of regular expressions. Schmidt [42] uses a similar regular expression language to abstract the syntax of ....

M. Codish and S. Debray and R. Giacobazzi. Compositional analysis of modular logic programs. Proc. 20th ACM Symp. on Principles of Programming Languages, 1993, pp. 451-464.

....it is not clear that it can be implemented efficiently, as for some practical programs analyzed by hand, the resulting equations are very large. This blow up is caused by applying quantifier elimination to the missing descriptions, and it is difficult to see how it can be reduced. Codish et al. [3] have given a general framework for incremental analysis based on an unfolding semantics. The particular analysis sketched here differs from analyses in their framework in two ways. First, because of the use of quantifier elimination, there is no need to introduce star abstractions as our ....

....the use of quantifier elimination, there is no need to introduce star abstractions as our analysis will always terminate. Second, performing the analysis incrementally never loses precision. This is because Pos is condensing, and because star abstraction is not used. In the more general case of [3] no assumption of condensation can be made, so that performing an analysis incrementally may lose precision. 7 Conclusion Groundness analysis is an important component of most dataflow analyses for (constraint) logic programs. In general, combination of dataflow analyses is not easy, but for ....

Codish, M., Debray, S., and Giacobazzi, R. Compositional analysis of modular logic programs. Proc. Twentieth ACM Symp. Principles of Programming Languages, pages 451--464. Charleston, South Carolina, 1993.

....of which are discussed in the following paragraphs. One advantage of modules is that they help encapsulate the propagation of complex situations such as with globalcall dynamic predicates. Compositional Analysis. Modular analyses based on compositional semantics (such as, for example, that of [9]) can be used to analyze programs split in modules. Such analyses leave the abstract substitutions for the predicates whose definitions are not available open, in the sense that some representation of the literals and their interaction with the abstract substitution is incorporated as a handle ....

M. Codish, S. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages POPL'93, pages 451--464, ACM, 1993.

....of a widening operator on the lattice of abstract Omega Gamma interpretations. Some proposals are in the literature; e.g. in [5] sequences of process calls in a cc configuration are handled by applying another approximation layer, called abstraction; the same technique has been applied in [4] for the compositional analysis of pure logic programs; this solution enforces termination but must pay in terms of accuracy. An interesting result has been achieved in [15] for the case of finite abstract domains. In this case a finite characterization of the compositional semantics of a ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

....conditions for using T ff 0 to eliminate false candidates. Yet another interesting topic on incremental refinement of success patterns is to combine domain refinement such as that proposed in this paper with compositional approach towards logic program analysis proposed by Codish et. al [3] since compositional approach is the only feasible way to analyse large programs. It is necessary to study the interaction between analysis refinement and analysis composition. ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional analysis of modular logic programs. In Proceedings of the Nineteenth Annual ACM Symposium on Principles of Programming Languages, pages 451--464. The ACM Press, 1993.

....we describe how the fixpoint algorithm in the generic analysis engines can be extended to support incremental analysis. Surprisingly, there has been little research into incremental analysis for logic programs. Several researchers have looked at compositional analysis of modules in logic programs [5]. There has been much research into incremental analysis for other programming paradigms (see for example the bibliography of Ramalingam and Reps [16] However, to our knowledge this is the first paper to identify the different types of incremental change which are useful in logic program ....

M. Codish, S. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages POPL'93, pages 451--464, Charleston, South Carolina, 1993. ACM.

....for logic programs. 3 In the sense of abstract interpretation ( 10] i.e. ff(lfp( P ) D lfp(ffffi P ffifl) The following is a list of some well known semantics for logic programs that can all be derived by abstract interpretation from h(T a P (SLD) P i. Some of them have been used in [4, 8, 18] for data flow analysis of logic programs. Each semantics is provided with the corresponding abstraction, hence with a G.c. indeed insertion) A more complete treatment for semantics derivable by abstract interpretation from a reference semantics is in [9, 21] In what follows, we denote fl x the ....

....interpretation I 2 (T a P (SLD) is abstracted by ff s Gammac into an object in S r Call such that ff s Gammac (I ) Y 2 (Atom) T Call ff s (I ) Y ) A semantic interpretation for S r Call can be obtained in modular logic programming by the following result. We adopt the notation in [8], and say that for a logic program (or module) P , open(P) denotes the set of predicates that occur in the body of a clause in P but are not defined in P . A program Q extends P if Q defines open(P) Let fl s Gammac be the upper adjoint of ff s Gammac , and T s Gammac P = ff s Gammac ffi P ....

M. Codish, S. Debray, and R. Giacobazzi. Compositional analysis of modular logic programs. In Proc. ACM POPL '93, pp. 451--464, 1993.

....inheritance mechanisms [18] see section 6. 6) O Omega (P ) can be considered as the semantic basis for modular program analysis, since by using suitable abstractions of O Omega (P ) we can analyze program components and then combine the results to obtain the analysis of the whole program [32]. Let us finally mention that O Omega is strongly related to abduction [44] If Omega is the set of abducible predicates, the abductive consequences of any goal G can be found by executing G in O Omega (P ) 5 Other observables 5.1 Finite failures There exist other useful observables for ....

....and a semantics at least as detailed as the one in section 3 has to be chosen. ffl If we want to perform analysis of program components in a modular way, we need a semantics compositional w.r.t. program union. As a matter of fact the framework in [13] has been extended to handle modularity [32], by replacing the s semantics with its compositional version (the Omega Gammahe 42 tics of section 4) which has clauses as semantic objects. This extension requires a notion of abstract program and a uniform treatment of concrete and abstract objects (i.e. programs and interpretations) The ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

....and Lafave [11] so that static analysis (especially abstract interpretation [4, 5, 16, 24] and model checking [2, 6, 9] can be conducted on top of the resulting graph. ffl We desire a foolproof methodology for incremental static analysis, along the lines of Codish, Debray, and Giacobazzi [3], where incomplete or modular programs can be analyzed as best as possible, and the residuals of the partially analyzed programs can be combined and further analyzed at link time stages. Only the combination of a program point based operational semantics and an on line partial evaluation based ....

M. Codish, S. Debray, and R. Giacobazzi. Compositional analysis of modular logic programs. In Proc. 20th ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

....of the elements from 1 to i and (observability condition, on the left hand side of the c separator) whether the list is not longer than i or it is longer than i but no element following the i th one is the minimum of the elements from 1 to i. Consider now the call min( 5; 1; 4; 3] x) Since [5,1,4,3] is formed by four elements only, jC 0 i j 2 with i 5 is false. Thus it cannot contribute to any computed answer. Moreover, jC 0 4 j 2 is false because it is not true that 3 is the minimum element among [5,1,4,3] Similarly, jC 0 3 j 2 is false. jC 0 1 j 2 , on the contrary, is ....

....of the elements from 1 to i. Consider now the call min( 5; 1; 4; 3] x) Since [5,1,4,3] is formed by four elements only, jC 0 i j 2 with i 5 is false. Thus it cannot contribute to any computed answer. Moreover, jC 0 4 j 2 is false because it is not true that 3 is the minimum element among [5,1,4,3]. Similarly, jC 0 3 j 2 is false. jC 0 1 j 2 , on the contrary, is satisfiable, since [5,1,4,3] is formed by at the least one element and 5 is the minimum element of [5] However, the observability constraint jC 0 1 j 1 is false since it requires that if [5,1,4,3] is formed by more than one ....

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M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

....on the contrary, can widely be developed in constraint and analysis independent way. It is worth noting that problems of sequences approximation were found in areas which are apparently loosely related to the problem of approximating the control. This is the case of the compositional analysis [25, 10, 23] and of the analysis of concurrent logic programs [13, 14] As we will show in Section 5.3, in several cases the approximation of the simple constraints together with the elimination of multiple constraint occurrences in the sequence, guarantees that the fixpoint is obtained in a finite number ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

....analysis based on abstract interpretation. Such an analysis requires a suitable (compositional) semantic basis which is often very expensive to compute. Therefore, in order to obtain practical tools, further abstractions (e.g. widening) are needed which make the modular analysis rather imprecise [8, 17]. Several extensions of layered modes are possible. Firstly, the idea of associating a timing to atoms positions can be easily applied also to types, thus providing a layered extension of the existing type systems for logic programs. This could be useful to extend to logic programs with dynamic ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

....as the semantic base for modular program analysis. Modularity helps in reducing the complexity of analysis and in proving correctness of programs, since it allows an incremental and structured specification and verification of the software. A first use of our semantics for modular analysis is in [8]. ii) Suitable abstractions of F Omega (P ) can be used to model non standard observables useful for program analysis. The case of partial answers and call patterns is considered in [18] and in [17] Moreover, a modification of F Omega (P ) allows to take into account also the selection rule ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc.Twentieth Annual ACM Symp. on Principles of Programming Languages, 1993.

....to apply on the basis of the current context. To this purpose, we need a finer analysis that is able to distinguish between different clauses defining the same predicate, and therefore associates minimal contexts to each clause. The analysis of modular logic languages has also been considered in [8] where the authors develop a compositional abstract interpretation for [2] i.e. modular programs consisting of only. Thus, no linguistic extension is introduced. Our approach is different in two respects. First, we consider a richer class of languages, also encompassing dynamic module ....

M. Codish, S.K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In , pages 451--464. ACM Press, 1993.

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M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

....12] The second one is a finite description of sequences of atoms. Indeed, even if the set of abstract substitutions is finite, the abstract version of the compositional fixpoint semantics may introduce arbitrary large clauses in the abstract semantics, so that the analysis may not terminate. In [9] this problem has been tackled by introducing an additional layer of abstraction which is obtained by applying fixpont acceleration techniques such as the so called abstraction. This is applied to provide finitary descriptions for arbitrary large clauses, thus introducing a further approximation ....

....fq(a)g, the least Herbrand model M (P [ Q) fp(a) q(a) r(a)g of the union cannot be obtained from M (P) fr(a)g and M (Q) fq(a)g. This kind of compositionality is a desirable property since it allows an incremental and modular definition of programs and of their semantics, and, as shown in [9], it provides a semantic base for modular program analysis. In the case of logic languages, a typical partially defined program could be a program where the intensional definitions are completely known while extensional definitions are only partially known and can be further specified by adding ....

[Article contains additional citation context not shown here]

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

....(clauses) to initial states (goals) with the inference of a result. In logic programming, this deductive approach to program analysis is usually based on abstract unfolding (i.e. replacement abstract unification) and it is shared by most of the frameworks proposed in the literature (e.g. see [3, 6, 7, 8, 14, 29]) A similar deductive method is also applied by Codish et al. 8] in compositional analysis in presence of modules. Compositional abstract interpretation is essential for large program development so that altering one module does not require re analysis of the entire program. A logic program is ....

.... this deductive approach to program analysis is usually based on abstract unfolding (i.e. replacement abstract unification) and it is shared by most of the frameworks proposed in the literature (e.g. see [3, 6, 7, 8, 14, 29] A similar deductive method is also applied by Codish et al. [8] in compositional analysis in presence of modules. Compositional abstract interpretation is essential for large program development so that altering one module does not require re analysis of the entire program. A logic program is viewed as consisting of a set of modules, each module defining a ....

[Article contains additional citation context not shown here]

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. Principles of Programming Languages, POPL '93, pages 451--464. ACM Press, 1993.

....necessitates a second (and orthogonal) abstraction to deal with unbounded clause bodies in the abstract semantics. Observe, for example, that the abstract unfoldings of the module P sp in Figure 1 introduce arbitrarily long abstract clauses. 7 This problem can be addressed in several ways. In [7], a notion of star abstraction adopted from [9] is applied to limit the length of clause bodies using a domain termed Dep for ground dependency analysis. The basic idea is to collapse the occurrences of calls to a predicate p in a clause body to one canonical call p . While this approach ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

....56 disj 59 170 276 38 58 cs 93 1394 294 56 92 kalah 109 1118 238 78 122 press 146 458 317 14 135 read 97 581 272 32 116 peep 105 380 229 34 63 Table 3: Space efficiency and accuracy of the analyses. which are defined in terms of abstract interpretation by applying the approach described in [7]. We focus on groundness analysis; however, the same approach applies directly for other types of analyses involving program properties which can be expressed as propositional formulae on variables. An additional example, is the polymorphic type analysis, recently described in [9] We believe ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional analysis of modular logic programs. In Proceedings of the Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451-- 464. ACM Press, 1993.

....(clauses) to initial states (goals) with the inference of a result. In logic programming, this deductive approach to program analysis is usually based on abstract unfolding (i.e. replacement abstract unification) and it is shared by most of the frameworks proposed in the literature (e.g. see [3, 6, 7, 8, 13, 28]) A similar deductive method is also applied by Codish et al. 8] in compositional analysis in presence of modules. Compositional abstract interpretation is essential for large program development so that altering one module does not require re analysis of the entire program. A logic program is ....

.... this deductive approach to program analysis is usually based on abstract unfolding (i.e. replacement abstract unification) and it is shared by most of the frameworks proposed in the literature (e.g. see [3, 6, 7, 8, 13, 28] A similar deductive method is also applied by Codish et al. [8] in compositional analysis in presence of modules. Compositional abstract interpretation is essential for large program development so that altering one module does not require re analysis of the entire program. A logic program is viewed as consisting of a set of modules, each module defining a ....

[Article contains additional citation context not shown here]

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. Principles of Programming Languages, POPL '93, pages 451--464. ACM Press, 1993.

....bodies. The standard meaning of the program is obtained by further unfolding these clauses with the clauses defining the open predicates. The problem with this approach is that termination is not guaranteed even over a finite domain as the clauses in an interpretation may become arbitrarily long [8]. In [16] the authors illustrate how this problem can be solved in the general case by unfolding clauses in an interpretation only if there is no observable difference with respect to program composition. This solution is based on the observation that since the domain is finite, there are only ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional analysis of modular logic programs. In Proc' of POPL'93, pages 451--464. ACM Press, 1993.

....by applying rules (clauses) to initial states (goals) with the inference of a result. This deductive approach to logic program analysis is usually based on abstract unfolding (i.e. replacement abstract unification) and is shared by several of the frameworks proposed in the literature (e.g. see [2, 4, 5, 6, 10, 20]) In [6] this approach has been applied to modular logic programs providing a compositional analysis in presence of modules. Compositional abstract interpretation is essential for large program development so that altering one module does not require re analysis of the entire program. A logic ....

....to initial states (goals) with the inference of a result. This deductive approach to logic program analysis is usually based on abstract unfolding (i.e. replacement abstract unification) and is shared by several of the frameworks proposed in the literature (e.g. see [2, 4, 5, 6, 10, 20] In [6] this approach has been applied to modular logic programs providing a compositional analysis in presence of modules. Compositional abstract interpretation is essential for large program development so that altering one module does not require re analysis of the entire program. A logic program is ....

[Article contains additional citation context not shown here]

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

....bodies. The standard meaning of the program is obtained by further unfolding these clauses with the clauses defining the open predicates. The problem with this approach is that termination is not guaranteed even over a finite domain as the clauses in an interpretation may become arbitrarily long [8]. In [16] the authors illustrate how this problem can be solved in the general case by unfolding clauses in an interpretation only if there is no observable difference with respect to program composition. This solution is based on the observation that since the domain is finite, there are only ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional analysis of modular logic programs. In Proc' of POPL'93, pages 451--464. ACM Press, 1993.

.... P (SLD) Clause) is such that ff (X ) fh b j h c Gamma b 2 X g. This abstraction induces a semantics which is equivalent to the compositional semantics for partial answers in [5, 17] This semantics has been used for compositional analysis of modular logic programs in [9]. The semantics for call patterns in [17] can also be derived by further approximating partial answers. Recall that an atom a 2 Atom is a call pattern for a goal G in a program P if G c Gamma a j b 2 TP (SLD) The corresponding abstraction maps traces into binary clauses in BClause: ....

M. Codish, S. Debray, and R. Giacobazzi. Compositional analysis of modular logic programs. In ACM POPL '93 , pp. 451-464, 1993.

....presence of separately compiled code; and second, generating code to ensure that values can be communicated correctly between the caller and callee, which reside in separately compiled modules. The first problem can be handled using techniques for compositional and or incremental program analysis [8, 12]. There are two alternatives for handling the second problem. If the different modules of a program are compiled and loaded in sequence, so that the code generated for one module is available while code is being generated for another module, then incremental optimization [8] using multiple entry ....

M. Codish, S. K. Debray, and R. Giacobazzi, "Compositional Analysis of Modular Logic Programs", Proc. Twentieth ACM Symposium on Principles of Programming Languages, Charlotte, SC, Jan. 1993, pp. 451--464. 24

....12] The second one is a finite description of sequences of atoms. Indeed, even if the set of abstract substitutions is finite, the abstract version of the compositional fixpoint semantics may introduce arbitrary large clauses in the abstract semantics, so that the analysis may not terminate. In [9] this problem has been tackled by introducing an additional layer of abstraction which is obtained by applying fixpont acceleration techniques such as the so called abstraction. This is applied to provide finitary descriptions for arbitrary large clauses, thus introducing a further approximation ....

....fq(a)g, the least Herbrand model M (P [ Q) fp(a) q(a) r(a)g of the union cannot be obtained from M (P) fr(a)g and M (Q) fq(a)g. This kind of compositionality is a desirable property since it allows an incremental and modular definition of programs and of their semantics, and, as shown in [9], it provides a semantic base for modular program analysis. In the case of logic languages, a typical partially defined program could be a program where the intensional definitions are completely known while extensional definitions are only partially known and can be further specified by adding ....

[Article contains additional citation context not shown here]

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

....(clauses) to initial states (goals) with the inference of a result. In logic programming, this deductive approach to program analysis is usually based on abstract unfolding (i.e. replacement abstract unification) and it is shared by most of the frameworks proposed in the literature (e.g. see [3, 6, 7, 8, 14, 29]) A similar deductive method is also applied by Codish et al. 8] in compositional analysis in presence of modules. Compositional abstract interpretation is essential for large program development so that altering one module does not require re analysis of the entire program. A logic program is ....

.... this deductive approach to program analysis is usually based on abstract unfolding (i.e. replacement abstract unification) and it is shared by most of the frameworks proposed in the literature (e.g. see [3, 6, 7, 8, 14, 29] A similar deductive method is also applied by Codish et al. [8] in compositional analysis in presence of modules. Compositional abstract interpretation is essential for large program development so that altering one module does not require re analysis of the entire program. A logic program is viewed as consisting of a set of modules, each module defining a ....

[Article contains additional citation context not shown here]

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. Principles of Programming Languages, POPL '93, pages 451--464. ACM Press, 1993.

....as well as their justification. In addition, we apply a novel technique so that call patterns for arbitrary initial goals are evaluated in an efficient way. This approach is easily generalized for analyses which are defined in terms of abstract interpretation by applying the approach described in [8]. We focus on groundness analysis; however, the same approach applies directly for other types of analyses involving program properties which can be expressed as propositional formulae on variables. An additional example, is the polymorphic type analysis, recently described in [10] We believe ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional analysis of modular logic programs. In Proceedings of the Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

....interpretation. The meaning of I a is specified by the following concretization function fl(I a ) ae c fi fi fi fi hc; i 2 I a 2 fl S ( oe Several abstract objects may represent the same concrete interpretation (i.e. fl may not be injective) A similar problem was solved in [7], where abstract clauses were used to support compositionality in the analysis, by defining an equivalence relation fl on (LC Theta ASub) such that I a 1 fl I a 2 iff fl(I a 1 ) fl(I a 2 ) Notice that the equivalence fl provides variable restriction and equivalence up to ....

....if grounds x then any 0 grounds x too. Thus fl Prop ( Phi 2 Sub fi fi 0 ) asg( 0 ) j= Psi Consider the following program to reverse a list, and the leftmost selection rule: 3 A similar problem was considered in compositional analysis of modular logic programs [7], where an additional layer of abstraction was required. append( L, L) append( H Y] X2, H Z] Gamma append(Y, X2, Z) nrev( nrev( H L] R) Gamma nrev(L, L1) append(L1, H] R) The corresponding abstract clauses (abstract program) is hnrev(x1 ; x2) Gamma true; x1 ....

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. Twentieth Annual ACM Symp. on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

No context found.

M. Codish, S. K. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In Proc. of the ACM Symposium on Principles of Programming Languages, pages 451--464. ACM Press, 1993.

No context found.

M. Codish, S.K. Debray, and R. Giacobazzi. Compositional analysis of modular logic programs. In ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages POPL'93, pages 451-464, Charleston, South Carolina, 1993. ACM.

No context found.

M. Codish, S.K. Debray, and R. Giacobazzi. Compositional analysis of modular logic programs. In Proc. POPL'93, 1993.

No context found.

M. Codish, S. Debray, and R. Giacobazzi. Compositional Analysis of Modular Logic Programs. In ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages POPL'93, pages 451-464, Charleston, South Carolina, 1993. ACM.

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