An abstract machine for Lambda-terms normalization

Crégut, Pierre

doi:10.1145/91556.91681

Cited by 60 publications

(77 citation statements)

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“…It is also equivalent to the evaluator of Section 2.2, since it was derived using meaning-preserving transformations that make the evaluation steps explicit without changing the call-by-need nature of evaluation. We recognize it as a lazy and properly tail-recursive variant of Krivine's machine [9,26]: (the locations of) arguments are pushed on the stack and functions are directly entered and find (the locations of) their arguments on the stack. In particular, C 1 acts as the update marker of the Three Instructions Machine [15].…”

Section: • Storable Values: W ::= D(t E) | C(v)mentioning

confidence: 99%

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

Ager¹,

Danvy²,

Midtgaard³

2004

BRICS

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We bridge the gap between compositional evaluators and abstract machines for the lambda-calculus, using closure conversion, transformation into continuation-passing style, and defunctionalization of continuations. This article is a followup of our article at PPDP 2003, where we consider call by name and call by value. Here, however, we consider call by need.We derive a lazy abstract machine from an ordinary call-by-need evaluator that threads a heap of updatable cells. In this resulting abstract machine, the continuation fragment for updating a heap cell naturally appears as an 'update marker', an implementation technique that was invented for the Three Instruction Machine and subsequently used to construct lazy variants of Krivine's abstract machine. Tuning the evaluator leads to other implementation techniques such as unboxed values. The correctness of the resulting abstract machines is a corollary of the correctness of the original evaluators and of the program transformations used in the derivation.

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Section: • Storable Values: W ::= D(t E) | C(v)mentioning

confidence: 99%

“…On the one hand, few abstract machines are actually derived with meaningpreserving steps, and on the other hand, few abstract machines are invented from scratch. Instead, most abstract machines are inspired by one formal system or another and they are subsequently proved to correctly implement a given evaluation strategy [8,9,20,21,26].…”

Section: Related Workmentioning

confidence: 99%

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

Ager¹,

Danvy²,

Midtgaard³

2004

BRICS

View full text Add to dashboard Cite

show abstract

“…The key to the correctness of λχ is a translation from the first to the second. This translation relies on two operators σ j and τ j i introduced for describing β reduction in DB-terms [4]. The grammar of χ-terms is described by a set of inference rules, which we call the level system.…”

Section: χ-Terms Rules and Examplesmentioning

confidence: 99%

“…As we have seen in the previous examples, β reduction is described by a For this, we connect it with a definition known to be correct, namely a definition given in terms of De Bruijn indices [4,5] and based on the two basic functions σ n and τ n i .…”

Section: Translation and Correctnessmentioning

confidence: 99%

“…Second the association between variables and their values, the so-called environment, keeps changing whenever one leaves or enters an abstraction. To our knowledge "levels" were only mentioned twice in the literature, first by de Bruijn [8] and later by Crégut [4], but never in the framework of explicit substitutions. Both authors suggest a canonical indexing of the variables;…”

Section: Introductionmentioning

confidence: 99%

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