Control-Flow Analysis of Functional Programs

Abstract. Flow analysis is a ubiquitous and much-studied component of compiler technology-and its variations abound. Amongst the most well known is Shivers' 0CFA; however, the best known algorithm for 0CFA requires time cubic in the size of the analyzed program and is unlikely to be improved. Consequently, several analyses have been designed to approximate 0CFA by trading precision for faster computation. Henglein's simple closure analysis, for example, forfeits the notion of directionality in flows and enjoys an "almost linear" time algorithm. But in making trade-offs between precision and complexity, what has been given up and what has been gained? Where do these analyses differ and where do they coincide?We identify a core language-the linear λ-calculus-where 0CFA, simple closure analysis, and many other known approximations or restrictions to 0CFA are rendered identical. Moreover, for this core language, analysis corresponds with (instrumented) evaluation. Because analysis faithfully captures evaluation, and because the linear λ-calculus is complete for ptime, we derive ptime-completeness results for all of these analyses.

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“…4 By similar reasoning to that given for 0CFA, simple closure analysis is clearly computable within polynomial time.…”

Section: Henglein's Simple Closure Analysismentioning

confidence: 98%

“…Flow analysis [1,2,3,4] is concerned with providing sound approximations to the question of "does a given value flow into a given program point during evaluation?" The most approximate analysis will always answer yes, which takes no resources to compute-and is of little use.…”

Section: Introductionmentioning

confidence: 99%

Flow Analysis, Linearity, and PTIME

Horn

Mairson

2008

Static Analysis

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“…In contrast our calculated analysis needs no such ad-hoc modifications. For a further discussion of related work we refer to a recent survey by the first author [21].…”

Section: Related Workmentioning

confidence: 99%

A Calculational Approach to Control-Flow Analysis by Abstract Interpretation

Midtgaard

Jensen

Static Analysis

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Abstract. We present a derivation of a control-flow analysis by abstract interpretation. Our starting point is a transition system semantics defined as an abstract machine for a small functional language in continuation-passing style. We obtain a Galois connection for abstracting the machine states by composing Galois connections, most notable an independent-attribute Galois connection on machine states and a Galois connection induced by a closure operator associated with a constituentparts relation on environments. We calculate abstract transfer functions by applying the state abstraction to the collecting semantics, resulting in a novel characterization of demand-driven 0-CFA.

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“…An old idea in program analysis is that dynamically allocated storage can be represented by the state of the computation at allocation time (Jones and Muchnick, 1982;Midtgaard, to appear, Sec. 1.2.2).…”

Section: Addresses Abstraction and Allocationmentioning

confidence: 99%

Systematic abstraction of abstract machines

Horn¹,

Might²

2012

J. Funct. Prog.

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We describe a derivational approach to abstract interpretation that yields novel and transparently sound static analyses when applied to well-established abstract machines for higherorder and imperative programming languages. To demonstrate the technique and support our claim, we transform the CEK machine of Felleisen and Friedman (Proc. of the 14th ACM SIGACT-SIGPLAN Symp. Prin. Program. Langs, 1987, pp. 314-325), a lazy variant of Krivine's machine (Higher-Order Symb. Comput. Vol 20, 2007, pp. 199-207), and the stackinspecting CM machine of Clements and Felleisen (ACM Trans. Program. Lang. Syst. Vol 26, 2004Vol 26, , pp. 1029Vol 26, -1052 into abstract interpretations of themselves. The resulting analyses bound temporal ordering of program events; predict return-flow and stack-inspection behavior; and approximate the flow and evaluation of by-need parameters. For all of these machines, we find that a series of well-known concrete machine refactorings, plus a technique of store-allocated continuations, leads to machines that abstract into static analyses simply by bounding their stores. These machines are parameterized by allocation functions that tune performance and precision and substantially expand the space of analyses that this framework can represent. We demonstrate that the technique scales up uniformly to allow static analysis of realistic language features, including tail calls, conditionals, mutation, exceptions, first-class continuations, and even garbage collection. In order to close the gap between formalism and implementation, we provide translations of the mathematics as running Haskell code for the initial development of our method.

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Control-Flow Analysis of Functional Programs

Cited by 9 publications

References 29 publications

Flow Analysis, Linearity, and PTIME

Flow Analysis, Linearity, and PTIME

A Calculational Approach to Control-Flow Analysis by Abstract Interpretation

Systematic abstraction of abstract machines

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