A Survey of Polyvariance in Abstract Interpretations

Gilray, Thomas; Might, Matthew

doi:10.1007/978-3-642-45340-3_9

Cited by 6 publications

(5 citation statements)

References 24 publications

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“…The issue of context-sensitivity (sometimes called polyvariance) is well-studied in the field of abstract interpretation (e.g., [28,34,41,50,51], see [25] for a recent survey). Polyvariance has also been used in type systems to assign different behaviors to the same function depending on its call site [3,6,63].…”

Section: Related Workmentioning

confidence: 99%

ConSORT: Context- and Flow-Sensitive Ownership Refinement Types for Imperative Programs

Toman

Siqi

Suenaga

et al. 2020

Programming Languages and Systems

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We present ConSORT, a type system for safety verification in the presence of mutability and aliasing. Mutability requires strong updates to model changing invariants during program execution, but aliasing between pointers makes it difficult to determine which invariants must be updated in response to mutation. Our type system addresses this difficulty with a novel combination of refinement types and fractional ownership types. Fractional ownership types provide flow-sensitive and precise aliasing information for reference variables. ConSORT interprets this ownership information to soundly handle strong updates of potentially aliased references. We have proved ConSORT sound and implemented a prototype, fully automated inference tool. We evaluated our tool and found it verifies non-trivial programs including data structure implementations.

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Section: Related Workmentioning

confidence: 99%

ConSORT: Context- and Flow-Sensitive Ownership Refinement Types for Imperative Programs

Toman

Siqi

Suenaga

et al. 2020

Programming Languages and Systems

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“…In a sense, syntactic lambdas are at least as specific as a type (their type signature, whatever type system is used) whether or not that type is known a priori by an analysis [14].…”

Section: Argument Sensitivitymentioning

confidence: 99%

“…A wide gamut of polyvariant techniques has been discussed in the literature [1, 2, 4, 6, 14-16, 19, 20, 22, 26, 29-33, 41-44, 51-53, 59, 60], comprised of both subtle variations and completely disparate strategies from methods and applications like type systems, abstract interpretations, and constraint-based analyses. While many of these designs and presentations share elements in common, each was designed and implemented separately with rather little work focused on unifying or connecting distinct implementations and strategies [2,14,53].…”

Section: Introductionmentioning

confidence: 99%

Allocation characterizes polyvariance: a unified methodology for polyvariant control-flow analysis

2016

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The polyvariance of a static analysis is the degree to which it structurally differentiates approximations of program values. Polyvariant techniques come in a number of different flavors that represent alternative heuristics for managing the trade-off an analysis strikes between precision and complexity. For example, call sensitivity supposes that values will tend to correlate with recent call sites, object sensitivity supposes that values will correlate with the allocation points of related objects, the Cartesian product algorithm supposes correlations between the values of arguments to the same function, and so forth. In this paper, we describe a unified methodology for implementing and understanding polyvariance in a higher-order setting (i.e., for control-flow analyses). We do this by extending the method of abstracting abstract machines (AAM), a systematic approach to producing an abstract interpretation of abstract-machine semantics. AAM eliminates recursion within a language's semantics by passing around an explicit store, and thus places importance on the strategy an analysis uses for allocating abstract addresses within the abstract heap or store. We build on AAM by showing that the design space of possible abstract allocators exactly and uniquely corresponds to the design space of polyvariant strategies. This allows us to both unify and generalize polyvariance as tunings of a single function. Changes to the behavior of this function easily recapitulate classic styles of analysis and produce novel variations, combinations of techniques, and fundamentally new techniques.

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“…A wide gamut of polyvariant techniques has been discussed in the literature (Agesen, 1995;Amtoft & Turbak, 2000;Banerjee, 1997;Bravenboer & Smaragdakis, 2009;Gilray & Might, 2013Gilray et al, 2016b;Harrison, 1989;Holdermans & Hage, 2010;Jagannathan et al, 1997;Jones & Muchnick, 1982;Koot & Hage, 2015;Lhoták, 2006;Lhoták & Hendren, 2006Liang et al, 2005;Milanova et al, 2005;Naik et al, 2006;Oxhøj et al, 1992;Palsberg & Pavlopoulou, 2001;Sharir & Pnueli, 1981;Shivers, 1991;Smaragdakis et al, 2011;Verstoep & Hage, 2015;Wright & Jagannathan, 1998). These include both subtle variations and disparate strategies.…”

Section: Introductionmentioning

confidence: 99%

“…A wide gamut of polyvariant techniques has been discussed in the literature (Sharir & Pnueli 1981;Jones & Muchnick 1982;Harrison 1989;Shivers 1991;Oxhøj et al 1992;Agesen 1995;Banerjee 1997;Jagannathan et al 1997;Wright & Jagannathan 1998;Amtoft & Turbak 2000;Palsberg & Pavlopoulou 2001;Liang et al 2005;Milanova et al 2005;Naik et al 2006;Lhoták 2006;Lhoták & Hendren 2006;Bravenboer & Smaragdakis 2009;Holdermans & Hage 2010;Smaragdakis et al 2011;Gilray & Might 2013;Koot & Hage 2015;Verstoep & Hage 2015;Gilray et al 2016b). These include both subtle variations and disparate strategies.…”

Section: Introductionmentioning

confidence: 99%

Abstract allocation as a unified approach to polyvariance in control-flow analyses

2018

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In higher order settings, control-flow analysis aims to model the propagation of both data and control by finitely approximating program behaviors across all possible executions. The polyvariance of an analysis describes the number of distinct abstract representations, or variants, for each syntactic entity (e.g., functions, variables, or intermediate expressions). Monovariance, one of the most basic forms of polyvariance, maintains only a single abstract representation for each variable or expression. Other polyvariant strategies allow a greater number of distinct abstractions and increase analysis complexity with the aim of increasing analysis precision. For example, k-call sensitivity distinguishes flows by the most recent k call sites, k-object sensitivity by a history of allocation points, and argument sensitivity by a tuple of dynamic argument types. From this perspective, even a concrete operational semantics may be thought of as an unboundedly polyvariant analysis. In this paper, we develop a unified methodology that fully captures this design space. It is easily tunable and guarantees soundness regardless of how tuned. We accomplish this by extending the method of abstracting abstract machines, a systematic approach to abstract interpretation of operational abstract-machine semantics. Our approach permits arbitrary instrumentation of the underlying analysis and arbitrary tuning of an abstract-allocation function. We show that the design space of abstract allocators both unifies and generalizes existing notions of polyvariance. Simple changes to the behavior of this function recapitulate classic styles of analysis and yield novel combinations and variants.

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A Survey of Polyvariance in Abstract Interpretations

Cited by 6 publications

References 24 publications

ConSORT: Context- and Flow-Sensitive Ownership Refinement Types for Imperative Programs

ConSORT: Context- and Flow-Sensitive Ownership Refinement Types for Imperative Programs

Allocation characterizes polyvariance: a unified methodology for polyvariant control-flow analysis

Abstract allocation as a unified approach to polyvariance in control-flow analyses

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