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Galois connection based abstract interpretations for strictness analysis

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Formal Methods in Programming and Their Applications

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 735))

Abstract

The abstract interpretation framework based upon the approximation of a fixpoint collecting semantics using Galois connections and widening/narrowing operators on complete lattices [CC77a, CC79b] has been considered difficult to apply to Mycroft's strictness analysis [Myc80, Myc81] for which denotational semantics was though to be more adequate (because non-termination has to be taken into account), see e.g. [AH87], page 25.

Considering a non-deterministic first-order language, we show, contrary to expectation, and using the classical Galois connection-based framework, that Mycroft strictness analysis algorithm is the abstract interpretation of a relational semantics (a big-steps operational semantics including non-termination which can be defined in G∞SOS either in rule-based or fixpoint style by induction on the syntax of programs [CC92])

An improved version of Johnsson's algorithm [Joh81] is obtained by a subsequent dependence-free abstraction of Mycroft's dependence-sensitive method.

Finally, a compromise between the precision of dependence-sensitive algorithms and the efficiency of dependence-free algorithms is suggested using widening operators.

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Author information

Authors and Affiliations

  1. LIENS, École Normale Supérieure, 45, rue d'Ulm, 75230, Paris cedex 05, France

    Patrick Cousot

  2. LIX, École Polytechnique, 91128, Palaiseau cedex, France

    Radhia Cousot

Authors
  1. Patrick Cousot
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  2. Radhia Cousot
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Editor information

Dines Bjørner Manfred Broy Igor V. Pottosin

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© 1993 Springer-Verlag Berlin Heidelberg

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Cousot, P., Cousot, R. (1993). Galois connection based abstract interpretations for strictness analysis. In: Bjørner, D., Broy, M., Pottosin, I.V. (eds) Formal Methods in Programming and Their Applications. Lecture Notes in Computer Science, vol 735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039703

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  • DOI: https://doi.org/10.1007/BFb0039703

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57316-6

  • Online ISBN: 978-3-540-48056-3

  • eBook Packages: Springer Book Archive

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