Deriving the full-reducing Krivine machine from the small-step operational semantics of normal order

García-Pérez, Álvaro; Nogueira, Pablo; Moreno-Navarro, Juan José

doi:10.1145/2505879.2505887

Cited by 11 publications

(18 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The semantic artefacts in this paper are qualitatively different from those in [12] and [16]. The semantics ⇓ here is single-stage (there is only one pass of the big-step definitional interpreter) but its implementation is 2-levelled.…”

Section: Conclusion and Related Workmentioning

confidence: 81%

“…The machine relies on a hybrid, or layered, reduction strategy with two separated stages for eval and readback. We have independently investigated in [16] a different approach for single-stage (as opposed to eval-readback) hybrid artefacts, showcasing the derivation of the full-reducing Krivine machine [3] from the operational semantics of normal order. In [12] the subsidiary strategy is modular, but this introduces a conceptual overhead in the 2CPS transformations.…”

Section: Conclusion and Related Workmentioning

confidence: 99%

“…In [12] the subsidiary strategy is modular, but this introduces a conceptual overhead in the 2CPS transformations. In [16] we show how to use plain CPS when the target strategy is single-staged, but this requires reasoning on the shape of the continuation stack. Both approaches differ in their weaknesses and strengths, as well as in their range of applicability.…”

Section: Conclusion and Related Workmentioning

confidence: 99%

“…We think two important ingredients in this regard are hybrid or layered calculi [16,17], and two-level continuation-passing style [12]. On the one hand hybrid or layered calculi depend on subsidiary sub-calculi, which ought to be turned into a parameter.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Deriving interpretations of the gradually-typed lambda calculus

García-Pérez

Nogueira

Sergey

2014

Proceedings of the ACM SIGPLAN 2014 Workshop on Partial Evaluation and Program Manipulation

Self Cite

View full text Add to dashboard Cite

Siek and Garcia (2012) have explored the dynamic semantics of the gradually-typed lambda calculus by means of definitional interpreters and abstract machines. The correspondence between the calculus's mathematically described small-step reduction semantics and the implemented big-step definitional interpreters was left as a conjecture. We prove and generalise Siek and Garcia's conjectures using program transformation. We establish the correspondence between the definitional interpreters and the reduction semantics of a closure-converted gradually-typed lambda calculus that unifies and amends various versions of the calculus. We use a layered approach and two-level continuation-passing style so that the correspondence is parametric on the subsidiary coercion calculus. We have implemented the whole derivation for the eager errordetection policy and the downcast blame-tracking strategy. The correspondence can be established for other choices of error-detection policies and blame-tracking strategies, by plugging in the appropriate artefacts for the particular subsidiary coercion calculus.

show abstract

Section: Conclusion and Related Workmentioning

confidence: 81%

Section: Conclusion and Related Workmentioning

confidence: 99%

Section: Conclusion and Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Deriving interpretations of the gradually-typed lambda calculus

García-Pérez

Nogueira

Sergey

2014

Proceedings of the ACM SIGPLAN 2014 Workshop on Partial Evaluation and Program Manipulation

Self Cite

View full text Add to dashboard Cite

show abstract

“…Both Danvy, Millikin and Munk [48,84,89], and García-Pérez and Nogueira [59][60][61] overcome this problem by disregarding redexes of the form (λx.t){e} on the lefthand side of applications. This means that the set of reduction rules changes depending on the reduction context that the redex appears in, and hence so does the grammar of redexes.…”

Section: Unique Decomposition For Outermost Reductionmentioning

confidence: 99%

On Computational Small Steps and Big Steps: Refocusing for Outermost Reduction

Johannsen

View full text Add to dashboard Cite

We study the relationship between small-step semantics, big-step semantics and abstract machines, for programming languages that employ an outermost reduction strategy, i.e., languages where reductions near the root of the abstract syntax tree are performed before reductions near the leaves. In particular, we investigate how Biernacka and Danvy's syntactic correspondence and Reynolds's functional correspondence can be applied to inter-derive semantic specifications for such languages.The main contribution of this dissertation is three-fold: First, we identify that backward overlapping reduction rules in the small-step semantics cause the refocusing step of the syntactic correspondence to be inapplicable. Second, we propose two solutions to overcome this in-applicability: backtracking and rule generalization. Third, we show how these solutions affect the other transformations of the two correspondences.Other contributions include the application of the syntactic and functional correspondences to Boolean normalization. In particular, we show how to systematically derive a spectrum of normalization functions for negational and conjunctive normalization. ResuméVi studerer sammenhaengen mellem small-step semantikker, big-step semantikker og abstrakte maskiner, for programmeringssprog, der bruger yderste reduktionsstrategier, dvs. sprog, hvor reduktioner taet på roden af det abstrakte syntaks-trae bliver udført før reduktioner naer bladene. Specielt undersøger vi, hvordan Biernacka og Danvys syntaktiske korrespondence og Reynolds' funktionelle korrespondence kan anvendes til at udlede semantiske specifikationer fra hinanden for sådanne sprog.Det primaere resultat i denne afhandling består af tre dele: Først observerer vi, at reduktionsregler med bagudrettede overlap i small-step semantikker gør, at refokuserings-skridtet i den syntaktiske korrespondence ikke kan anvendes. Derefter fremsaetter vi to løsninger til at overvinde denne manglende anvendelighed: tilbagevenden og regel-generalisering. Til sidst viser vi, hvordan disse løsninger påvirker de øvrige transformationer i de to korrespondencer.De øvrige resultater inkluderer anvendelsen af de syntaktiske og funktionelle korrespondencer til Boolesk normalisering. Specielt viser vi, hvordan man systematisk kan udlede et spektrum af normaliseringsfunktioner for negationel og konjunktiv normalisering.iii

show abstract

A Strong Distillery

Accattoli

Barenbaum

Mazza

2015

Programming Languages and Systems

View full text Add to dashboard Cite

International audienceAbstract machines for the strong evaluation of λ-terms (that is, under abstractions) are a mostly neglected topic, despite their use in the implementation of proof assistants and higher-order logic programming languages. This paper introduces a machine for the simplest form of strong evaluation, leftmost-outermost (call-by-name) evaluation to normal form, proving it correct, complete, and bounding its overhead. Such a machine, deemed Strong Milner Abstract Machine, is a variant of the KAM computing normal forms and using just one global environment. Its properties are studied via a special form of decoding, called a distillation, into the Linear Substitution Calculus, neatly reformulating the machine as a standard micro-step strategy for explicit substitutions, namely linear leftmost-outermost reduction, i.e. the extension to normal form of linear head reduction. Additionally, the overhead of the machine is shown to be linear both in the number of steps and in the size of the initial term, validating its design. The study highlights two distinguished features of strong machines, namely backtracking phases and their interactions with abstractions and environments

show abstract

Deriving the full-reducing Krivine machine from the small-step operational semantics of normal order

Cited by 11 publications

References 26 publications

Deriving interpretations of the gradually-typed lambda calculus

Deriving interpretations of the gradually-typed lambda calculus

On Computational Small Steps and Big Steps: Refocusing for Outermost Reduction

A Strong Distillery

Contact Info

Product

Resources

About