An Analytical Approach to Programs as Data Objects

Danvy, Olivier

doi:10.7146/aul.214.152

Cited by 29 publications

(53 citation statements)

References 296 publications

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“…Programmatically, the J operator has been superseded by control operators that capture the current continuation (i.e., both C and D) instead of the continuation of the caller (i.e., D), even though it is simple to simulate escape and call/cc in terms of J. Yet as we have shown here, both the SECD machine and the J operator fit in the functional correspondence [3,4,6,7,13,16,30,31] as well as in the syntactic correspondence [12,14,15,29,31,40], which made it possible for us to mechanically characterize them in new and precise ways. 7 In turn it was Landin who, through the J operator, invented what we know today as first-class continuations [49].…”

Section: Discussionmentioning

confidence: 99%

“…The path we are taking seems reasonably pedagogical-in particular, the departure from threading a data stack and managing the environment in a callee-save way. Each step is reversible: one can CPS-transform and defunctionalize an evaluator and (re)construct an abstract machine [3,4,6,7,13,16,30,31]. …”

Section: Run : S * E * C * D -> Valuementioning

confidence: 99%

“…Symmetrically to the functional correspondence between evaluation functions and abstract machines that was sparked by the first rational deconstruction of the SECD machine [3,4,6,7,13,16,30,31], a syntactic correspondence exists between calculi and abstract machines, as investigated by Biernacka, Danvy, and Nielsen [12,14,15,29,31,40]. This syntactic correspondence is also derivational, and hinges not on defunctionalization but on a 'refocusing' transformation that mechanically connects an evaluation function defined as the iteration of one-step reduction, and an abstract machine.…”

Section: A Syntactic Theory Of Applicative Expressions With the J Opementioning

confidence: 99%

“…Our angle here is derivational; it follows the 'rational deconstruction' of the SECD machine into a compositional evaluation function presented by Danvy at IFL'04 [30]. This deconstruction laid the ground for a functional correspondence between evaluators and abstract machines [3,4,6,7,13,16,30,31]. Our goal here is to show that this functional correspondence also applies to the SECD machine with the J operator, which too can be deconstructed into a compositional evaluation function.…”

Section: Introductionmentioning

confidence: 99%

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A Rational Deconstruction of Landin's J Operator

Danvy¹,

Millikin²

2006

BRICS

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Landin's J operator was the first control operator for functional languages. It was specified with an extension of the SECD machine, which was the first abstract machine for functional languages. We present a family of compositional evaluation functions corresponding to this extension of the SECD machine, using a series of elementary transformations (transformation into continuation-passing style (CPS) and defunctionalization, chiefly) and their left inverses (transformation into direct style and refunctionalization). To this end, we modernize the SECD machine into a bisimilar one that operates in lock step with the original one but that (1) does not use a data stack and (2) uses the caller-save rather than the callee-save convention for environments. We then characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy. As a byproduct, we also present a reduction semantics for applicative expressions with the J operator, based on Curien's original calculus of explicit substitutions. This reduction semantics mechanically corresponds to the modernized version of the SECD machine and to the best of our knowledge, it provides the first syntactic theory of applicative expressions with the J operator.The present work is concluded by a motivated wish to see Landin's name added to the list of co-discoverers of continuations. Methodologically, however, it mainly illustrates the value of Reynolds's defunctionalization and of refunctionalization as well as the expressive power of the CPS hierarchy (a) to account for the first control operator and the first abstract machine for functional languages and (b) to connect them to their successors.(A preliminary version appears in the proceedings of IFL 2005 [38].)

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Section: Discussionmentioning

confidence: 99%

Section: Run : S * E * C * D -> Valuementioning

confidence: 99%

Section: A Syntactic Theory Of Applicative Expressions With the J Opementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Rational Deconstruction of Landin's J Operator

Danvy¹,

Millikin²

2006

BRICS

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“…Abstract machines (Landin, 1964), and the paths from semantics to machines (Reynolds, 1972;Danvy, 2006;Felleisen et al, 2009) have a long history in the research on programming languages. From canonical abstract machines such as the CEK machine or Krivine's machine, which represent the idealized core of realistic run-time systems, we perform a series of basic machine refactorings to obtain a nondeterministic state-transition system with a finite state space.…”

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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Refunctionalization at Work

Danvy

2006

Lecture Notes in Computer Science

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We present the left inverse of Reynolds's defunctionalization and we show its relevance to programming and to programming languages. We propose two methods to transform a program that is almost in defunctionalized form into one that is actually in defunctionalized form, and we illustrate them with a recognizer for Dyck words and with Dijkstra's shunting-yard algorithm.Revised version of BRICS RS-07-7. * This tutorial documents an invited talk at MPC '06 [26]. † IT-parken,

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An Analytical Approach to Programs as Data Objects

Cited by 29 publications

References 296 publications

A Rational Deconstruction of Landin's J Operator

A Rational Deconstruction of Landin's J Operator

Systematic abstraction of abstract machines

Refunctionalization at Work

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