A Functional Correspondence between Call-by-Need Evaluators and Lazy Abstract Machines

Ager, Mads Sig; Danvy, Olivier; Midtgaard, Jan

doi:10.7146/brics.v11i3.21828

Cited by 4 publications

(11 citation statements)

References 20 publications

(28 reference statements)

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“…We have also calculated abstract machines for lambda calculi with call-by-name and call-by-need semantics, which correspond to the Krivine machine [9] and a lazy variant of the Krivine machine derived by Ager et. al [3], respectively. The calculations can be found in the associated Coq proofs [7].…”

Section: Calculationmentioning

confidence: 99%

Cutting Out Continuations

Hutton

Bahr

2016

A List of Successes That Can Change the World

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Abstract. In the field of program transformation, one often transforms programs into continuation-passing style to make their flow of control explicit, and then immediately removes the resulting continuations using defunctionalisation to make the programs first-order. In this article, we show how these two transformations can be fused together into a single transformation step that cuts out the need to first introduce and then eliminate continuations. Our approach is calculational, uses standard equational reasoning techniques, and is widely applicable.

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Section: Calculationmentioning

confidence: 99%

Cutting Out Continuations

Hutton

Bahr

2016

A List of Successes That Can Change the World

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“…The programmatic transformation of formal semantics dates to work by Reynolds [15]. More recent work by Danvy et al has shown that formal semantics are highly amenable to program transformations and that it is possible to automatically convert denotational semantics into operational semantics and vice versa [2,3,1,[6][7][8]. These techniques, combined with ours, should permit the mechanizable construction of static analyzers for a wider variety of formal semantics paradigms.…”

Section: Related Workmentioning

confidence: 99%

“…3 The observant reader might wonder why we omit dependence edges between syntax nodes, e.g., from Lam to Call and vice versa. In fact, we could add them.…”

Section: Continuation-passing-style λ-Calculusmentioning

confidence: 99%

“…For example, in CPS, we add edges from the node Σ to the node Call and to the node Env , because the definition of the set Σ 2 refers to both Call and Env ; for the same reason, we add edges from the node Clo to the node Lam and to the node Env . 3 Once in dependence-graph form, we must choose a set of edges to "snip" in order to eliminate cycles from the graph.…”

Section: Continuation-passing-style λ-Calculusmentioning

confidence: 99%

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Abstract Interpreters for Free

Might

2010

Static Analysis

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Abstract. In small-step abstract interpretations, the concrete and abstract semantics bear an uncanny resemblance. In this work, we present an analysis-design methodology that both explains and exploits that resemblance. Specifically, we present a two-step method to convert a smallstep concrete semantics into a family of sound, computable abstract interpretations. The first step re-factors the concrete state-space to eliminate recursive structure; this refactoring of the state-space simultaneously determines a store-passing-style transformation on the underlying concrete semantics. The second step uses inference rules to generate an abstract state-space and a Galois connection simultaneously. The Galois connection allows the calculation of the "optimal" abstract interpretation. The two-step process is unambiguous, but nondeterministic: at each step, analysis designers face choices. Some of these choices ultimately influence properties such as flow-, field-and context-sensitivity. Thus, under the method, we can give the emergence of these properties a graphtheoretic characterization. To illustrate the method, we systematically abstract the continuation-passing style lambda calculus to arrive at two distinct families of analyses. The first is the well-known k-CFA family of analyses. The second consists of novel "environment-centric" abstract interpretations, none of which appear in the literature on static analysis of higher-order programs.

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“…• a call-by-value λ-calculus with state and control based on the CESK machine of Felleisen & Friedman (1987), • a call-by-need λ-calculus based on a tail-recursive, lazy variant of Krivine's machine (Krivine, 1985(Krivine, , 2007 derived by Ager et al (2004), and • a call-by-value λ-calculus with stack inspection based on the CM machine of Clements & Felleisen (2004);…”

Section: Introductionmentioning

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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A Functional Correspondence between Call-by-Need Evaluators and Lazy Abstract Machines

Cited by 4 publications

References 20 publications

Cutting Out Continuations

Cutting Out Continuations

Abstract Interpreters for Free

Systematic abstraction of abstract machines

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