Fast abstract interpretation using sequential algorithms

Ferguson, Alex; Hughes, John

doi:10.1007/3-540-57264-3_28

Cited by 7 publications

(6 citation statements)

References 12 publications

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“…For the last example, a good alternative to a complete analysis was presented in [23], that gives results in a few seconds. However, this analysis only answers one question and so is not usable for separate compilation.…”

Section: Practical Resultsmentioning

confidence: 99%

Abstract interpretation using typed decision graphs

Mauborgne¹

1998

Science of Computer Programming

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This article presents a way of implementing abstract interpretations that can be very efficient. The improvement lies in the use of a symbolic representation of boolean functions called Typed Decision Graphs (TDGs), a refinement of Binary Decision Diagrams. A general procedure for using this representation in abstract interpretation is given; we examine in particular the possibility of encoding higher order functions into TDGs. Moreover, this representation is used to design a widening operator based on the size of the objects represented, so that abstract interpretations will not fail due to insufficient memory. This approach is illustrated on strictness analysis of higher-order functions, showing a great increase in efficiency.

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Section: Practical Resultsmentioning

confidence: 99%

Abstract interpretation using typed decision graphs

Mauborgne¹

1998

Science of Computer Programming

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“…The problem of designing efficient algorithms for strictness analysis has received much attention recently and one current trend seems to revert from the usual "extensional" approach to more "intensional" or syntactic techniques [20,21,18,6,10,24]. The key observation underlying these works is that the choice of representing abstract functions by functions can be disastrous in terms of efficiency and is not always justified in terms of accuracy.…”

Section: Discussionmentioning

confidence: 99%

“…Some of these proposals trade a cheaper implementation against a loss of accuracy [20,21]. In contrast, [10,24] use extensional representations of functions to build very efficient algorithms without sacrificing accuracy. The analysis of [10] uses concrete data structures; these are special kinds of Scott domains whose elements can be seen as syntax trees.…”

Section: Discussionmentioning

confidence: 99%

“…In contrast, [10,24] use extensional representations of functions to build very efficient algorithms without sacrificing accuracy. The analysis of [10] uses concrete data structures; these are special kinds of Scott domains whose elements can be seen as syntax trees. In [24] the analysis is expressed as a form of reduction of abstract graphs.…”

Section: Discussionmentioning

confidence: 99%

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Lazy type inference for the strictness analysis of lists

Hankin

Métayer

1994

Programming Languages and Systems — ESOP '94

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We present a type inference system for the strictness analysis of fists and we show that it can be used as the basis for an efficient algorithm. The algorithm is as accurate as the usual abstract interpretation technique. One distinctive advantage of this approach is that it is not necessary to impose an abstract domain of a particular depth prior to the analysis: the lazy type algorithm will instead explore the part of a potentially infinite domain required to prove the strictness property.

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“…Recent progresses in the development of abstract interpretation, not all of them based on least fixed point finding, abound as well in the literature. See, for example, Ferguson and Hughes (1993), Hankin and Hunt (1992), Hankin and Le Métayer (1994), Nocker (1993) and Seward (1993). We will briefly describe their work, and compare our approach to theirs, in section 6.…”

Section: Motivation and Introductionmentioning

confidence: 99%

A syntactic method for finding least fixed points of higher-order functions over finite domains

Chuang

Goldberg

1997

J. Funct. Prog.

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This paper describes a method for finding the least fixed points of higher-order functions over finite domains using symbolic manipulation. Fixed point finding is an essential component in the calculation of abstract semantics of functional programs, providing the foundation for program analyses based on abstract interpretation. Previous methods for fixed point finding have primarily used semantic approaches, which often must traverse large portions of the semantic domain even for simple programs. This paper provides the theoretical framework for a syntax-based analysis that is potentially very fast. The proposed syntactic method is based on an augmented simply typed lambda calculus where the symbolic representation of each function produced in the fixed point iteration is transformed to a syntactic normal form. Normal forms resulting from successive iterations are then compared syntactically to determine their ordering in the semantic domain, and to decide whether a fixed point has been reached. We show the method to be sound, complete and compositional. Examples are presented to show how this method can be used to perform strictness analysis for higher-order functions over non-flat domains. Our method is compositional in the sense that the strictness property of an expression can be easily calculated from those of its sub-expressions. This is contrary to most strictness analysers, where the strictness property of an expression has to be computed anew whenever one of its subexpressions changes. We also compare our approach with recent developments in strictness analysis.

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Fast abstract interpretation using sequential algorithms

Cited by 7 publications

References 12 publications

Abstract interpretation using typed decision graphs

Abstract interpretation using typed decision graphs

Lazy type inference for the strictness analysis of lists

A syntactic method for finding least fixed points of higher-order functions over finite domains

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