Jens Palsberg. Global program analysis in constraint form. In Sophie Tison, editor, Proceedings CAAP'94, volume 787 of Lecture Notes in Computer Science, pages 276-290. Springer-Verlag, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... a seminal contribution to the eld of control ow analysis; this eld was further developed by a number of the members of Neil s TOPPS group at the University of Copenhagen (notably [Ses91,Mos97a,Mos97b] Moreover, the work has inspired a great deal of work on this topic in other research groups [Shi91,Deu92,Pal94,HM97b,NN97,MH98b] (which represents a very small sample ) Imperial College of Science, Technology and Medicine, London SW7 2BZ. University of Warwick, Coventry CV4 7AL. Teamphone.com, London W1D 7EQ. Most approaches in the literature specify control ow analysis as the solution to a set of (in)equations ....

....type of the proof net. The actual term is mainly used to compute the type assignment , and its inverse , which are required for the read back of the analysis. Computing the 1 relation e ectively performs the same task as the closing rules of [Mos97a] and the conditional constraints of [Pal94], but 0CFA performs the computation on the type structure (intensional type) rather than on the term (proof net) In general, the procedure given above is not sucient to compute 0 CFA. Given a variable x, of higher type, 1 ( x) a is a node in the intensional type. In general, the sub term ....

[Article contains additional citation context not shown here]

Jens Palsberg. Global program analysis in constraint form. In Sophie Tison, editor, Proceedings CAAP'94, volume 787 of Lecture Notes in Computer Science, pages 276-290. Springer-Verlag, 1994.

.... collecting semantics are the table generated from solving a set of data flow equations (see the next section) the cache generated from solving a set of denotational semantics equations [28, 10] and the solution of a constraints set generated for type inference [4, 5, 67] or control flow analysis [27, 52]. Because of the emphasis placed upon the collecting semantics, it is all too easy to confuse an a.i. with the collecting semantics extracted from it. As a result, precision can be inadvertantly lost when an algorithm for calculating directly the collecting semantics is formulated before the ....

J. Palsberg. Global program analysis in constraint form. In M. P. Fourman, P. T. Johnstone, and A. M. Pitts, editors, Proc. CAAP`94, Lecture Notes in Computer Science, pages 258--269.

....at a given application) Values are abstracted by a label of the occurrence of the value i.e. the label of rst order values uniquely identi es the occurrence of the value, while data structures and closures are abstracted by the label of the constructor resp. lambda. Thus, closure analysis [26,24] and control ow analysis [27] are special cases focusing on closures. Flow information is directly useful for program transformations such as constant propagation or rsti cation, and, by interpreting the value ow in an appropriate domain, for many other program analyses. Furthermore, ....

....and that all normal forms are typable. 12.2 Flow Analysis Flow analysis as discussed in this paper is described by Sestoft [26] who coined his analysis closure analysis) and Shivers [27] who coined his family of analyses kCFA) Palsberg gave a constraint formulation of closure analysis [24]. It is shown in [21] that, in contrast to popular belief, 0CFA di ers from closure analysis: Shivers family of analyses is evaluation order dependent 2 . Palsberg and O Keefe showed that the type information derived using closure analysis corresponds to Amadio Cardelli typing [25] ....

J. Palsberg. Global program analysis in constraint form. In 19th International Colloquium on Trees in Algebra and Programming (CAAP'94), volume 787 of LNCS, pages 276-290, 1994.

....control ow in rst order languages is almost trivial. It is a much more dicult problem for higher order languages where functions may be passed as parameters and invoked from anywhere in the program. Over recent years there has been intense activity in designing CFAs for higherorder languages [4, 5, 12, 16 18, 20, 22, 23, 26, 27]. There has been convergence on the de nition of the fundamental notion of CFA which has been dubbed standard CFA by [14] A number of algorithms have been proposed for standard CFA. The best algorithms are cubic; recent work by Heintze and McAllester suggests that this situation cannot be ....

....Shivers [27] and Jagannathan and Weeks [16] abstract from an operational semantics. Constraint based: A number of authors have used intensional semantics (usually operational semantics) to generate constraints that describe control ow. Heintze [12] Nielson and Nielson [22] and Palsberg [23] are examples of this approach. Type based: Recently, a number of authors have proposed the use of annotated types to capture control ow information. Mossin [20] and Banerjee [4] are good examples of this approach. Our approach is essentially based on abstract semantics and is related also with ....

Palsberg J. Global program analysis in constraint form. In Proc. CAAP'94, LNCS 787, pp 276-290, Springer-Verlag, 1994.

....Science, London SW7 2BZ; Telephone: 44 (020) 8868 4557, Fax: 44 (020) 8723 6769, e mail: p.sampath doc.ic.ac.uk flow analysis of lambda expressions [17] which used the framework of abstract machines to formulate the analysis. Subsequent work has explored various aspects of controlflow analysis [41, 15, 36, 32, 34]. Most approaches in the literature specify control flow analysis as the solution to a set of (in)equations derived from the syntax of the program. Soundness of the analysis is then demonstrated with respect to an operational semantics; i.e. the derived set of (in)equations describes, for each ....

....the judgement of the proof net. The actual term is mainly used to compute the type assignment , and its inverse 1 , which are required for the read back of the analysis. Computing the 1 relation effectively performs the same task as the closing rules of [32] and the conditional constraints of [36], but 0CFA performs the computation on the type structure (judgement) rather than on the term (proof net) In general, the procedure given above is not sufficient to compute 0 CFA. Given a variable x, of higher type, 1 ( x) a is a node in the judgement. In general, the sub term given by ....

[Article contains additional citation context not shown here]

J. Palsberg. Global program analysis in constraint form. In Tison [43], pages 276--290.

.... problems can be answered in linear time and all sources all uses can be answered in quadratic time (in the size of the flow graph, which is equivalent to the size of the explicitly typed program) On simply typed programs, the precision of the resulting analysis is equivalent to closure analysis [10,11,8]. In practice, it is a reasonable assumption that typed programs are only bigger than their untyped equivalent by a constant factor, hence this is an asymptotic improvement over previous algorithms. We extend the analysis to handle polymorphism, sum types and recursive types. As a consequence, the ....

....can be performed on this graph by standard reachability algorithms in linear time and, similarly, full flow information can be obtained in quadratic time. On simply typed programs our analysis is equivalent in strength to closure analysis [10,11] and the constraint based analysis of Palsberg [8]. Since explicitly typed programs are typically only a constant bigger than the underlying untyped program, this gives (under the assumption that all types are bounded by a constant) an asymptotic improvement over previously published algorithms. Independently of this work, Heintze and McAllester ....

[Article contains additional citation context not shown here]

J. Palsberg. Global program analysis in constraint form. In S. Tison, editor, 19th International Colloquium on Trees in Algebra and Programming (CAAP), volume 787 of LNCS, pages 276--290. Springer-Verlag, 1994.

....and where all function exits are linked to all return sites. Often this is accomplished by means of contours [25] a la call strings [23] or tokens [12] so as to improve the precision of the information obtained. One way to specify the analysis is to show how to generate a set of constraints [8, 9, 18, 19] whose least solution is then computed using graph based ideas. However, the majority of papers on Control Flow Analysis (e.g. 24, 25, 11, 16] do not consider side e ects a notable exception being [10] Data Flow Analysis. The intraprocedural fragment of Data Flow Analysis ignores procedure ....

.... of program analyses is likely to span a spectrum from abstract speci cations (like [16] in the case of Control Flow Analysis) over syntax directed speci cations (as in the present paper) to actual implementations in the form of constraints being generated and subsequently solved (as in [8, 9, 18, 19, 6]) The main advantage of this approach is that semantic issues can be ignored in later stages once they have been dealt with in earlier stages. The rst stage, often called the collecting semantics, is intended to cover a superset of the semantic considerations that are deemed of potential ....

J. Palsberg. Global program analysis in constraint form. In Proc. CAAP '94, volume 787 of Lecture Notes in Computer Science, pages 255-265. Springer, 1994.

....types in a more powerful type language that should yield more a precise analysis than Soft Scheme s type system, but no implementation is available for a realistic programming language. Besides type inference and abstract interpretation, there has been recent work on using constraint systems [7, 15] to analyze high level programs. These systems are based on an operational semantics that ignores all inter variable dependencies. Consequently, while efficient implementations of these analyses can be built, it is unclear whether they provide the necessary precision to perform useful run time ....

Jens Palsberg. Global Program Analysis in Constraint Form. In Proceedings of the 1994 Colloquium on Trees in Algebra and Programming, pages 276--290. SpringerVerlag, 1994. Appears as LNCS 787.

.... problems can be answered in linear time and all sources all uses can be answered in quadratic time (in the size of the flow graph, which is equivalent to the size of the explicitly typed program) On simply typed programs, the precision of the resulting analysis is equivalent to closure analysis [10,11,8]. In practice, it is a reasonable assumption that typed programs are only bigger than their untyped equivalent by a constant factor, hence this is an asymptotic improvement over previous algorithms. We extend the analysis to handle polymorphism, sum types and recursive types. As a consequence, the ....

....can be performed on this graph by standard reachability algorithms in linear time and, similarly, full flow information can be obtained in quadratic time. On simply typed programs our analysis is equivalent in strength to closure analysis [10,11] and the constraint based analysis of Palsberg [8]. Since explicitly typed programs are typically only a constant bigger than the underlying untyped program, this gives (under the assumption that all types are bounded by a constant) an asymptotic improvement over previously published algorithms. Independently of this work, Heintze and McAllester ....

[Article contains additional citation context not shown here]

J. Palsberg. Global program analysis in constraint form. In S. Tison, editor, 19th International Colloquium on Trees in Algebra and Programming (CAAP), volume 787 of LNCS, pages 276--290. Springer-Verlag, 1994.

....and where all function exits are linked to all return sites. Often this is accomplished by means of contours [29] a la call strings [27] or tokens [14] so as to improve the precision of the information obtained. One way to specify the analysis is to show how to generate a set of constraints [10, 11, 22, 23] whose least solution is then computed using graph based ideas. However, the majority of papers on Control Flow Analysis (e.g. 28, 29, 13, 20] do not consider side e ects an exception to this is [12] that considers a functional language with shared variable communication between concurrent ....

.... of program analyses is likely to span a spectrum from abstract speci cations (like [20] in the case of Control Flow Analysis) over syntax directed speci cations 1 (as in the present paper) to actual implementations in the form of constraints being generated and subsequently solved (as in [10, 11, 22, 23, 8]) The main advantage of this approach is that semantic issues can be ignored in later stages once they have been dealt with in earlier stages, and another advantage is that in all stages the set of solutions will be known always to have a least solution that will continue to be a solution also to ....

J. Palsberg. Global program analysis in constraint form. In Proc. CAAP '94, volume 787 of Lecture Notes in Computer Science, pages 255-265. Springer, 1994.

....a more powerful type language that should yield more a precise analysis than the soft type system mentioned above, but no implementation is available for a realistic programming language. Besides type inference and abstract interpretation, there has been recent work on using constraint systems [8, 16] to analyze high level programs. These systems are based on an operational semantics that ignores all inter variable dependencies. Consequently, while efficient implementations of these analyses can be built, it is unclear whether they provide the necessary precision to perform useful run time ....

Jens Palsberg. Global Program Analysis in Constraint Form. In Proceedings of the 1994 Colloquium on Trees in Algebra and Programming, pages 276--290. SpringerVerlag, 1994. Appears as LNCS 787.

....algorithm is shown to be a special case of Shivers . Palsberg has developed a closure analysis for the untyped calculus that is correct with respect to arbitrary fi reductions and uses a constraint system that characterizes the result of the analysis without specifying how it is computed [104]. Goldberg and Park formulate an escape analysis for stackability [54] They consider a call by value calculus, and use an abstract interpretation to track which parameters of a function escape , i.e. outlive the scope of the function s definition. Escaping parameters cannot be put on a ....

Palsberg, J. Global program analysis in constraint form. In Proceedings of Colloquium of Trees in Algebra and Programming (1994), Springer-Verlag, p. ???

.... problems can be answered in linear time and all sources all uses can be answered in quadratic time (in the size of the flow graph, which is equivalent to the size of the explicitly typed program) On simply typed programs, the precision of the resulting analysis is equivalent to closure analysis [10,11,8]. In practice, it is a reasonable assumption that typed programs are only bigger than their untyped equivalent by a constant factor, hence this is an asymptotic improvement over previous algorithms. We extend the analysis to handle polymorphism, sum types and recursive types. As a consequence, the ....

....can be performed on this graph by standard reachability algorithms in linear time and, similarly, full flow information can be obtained in quadratic time. On simply typed programs our analysis is equivalent in strength to closure analysis [10,11] and the constraint based analysis of Palsberg [8]. Since explicitly typed programs are typically only a constant bigger than the underlying untyped program, this gives (under the assumption that all types are bounded by a constant) an asymptotic improvement over previously published algorithms. Independently of this work, Heintze and McAllester ....

[Article contains additional citation context not shown here]

J. Palsberg. Global program analysis in constraint form. In S. Tison, editor, 19th International Colloquium on Trees in Algebra and Programming (CAAP), volume 787 of LNCS, pages 276--290. Springer-Verlag, 1994.

....: T n 2 e n ) T 0 2 X or (fT 1 g e 1 : fT n g e n ) fT 0 g X . Using such simple set theoretic algebraic identities, program analysis methods formulated as a fixpoint resolution problem (10) can be reformulated as the problem of solving a system of constraints (see e.g. [28]) Example Considering the formal language abstractions hff fl ; fl fl i respectively defined by (5) 6) 7) and (8) for programs (1) 2) 3) and (4) we get, in all cases, the same fixpoint equation: X = fcons(0; cons(0; cons(0; nil) g [ fcons(a(x) cons(b(y) cons(c(z) nil) ....

J. Palsberg. Global program analysis in constraint form. Proc. 19 th CAAP'94, LNCS 787, 276--290. Springer-Verlag, 1994.

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