On the syntactic and functional correspondence between hybrid (or layered) normalisers and abstract machines

García-Pérez, Álvaro; Nogueira, Pablo

doi:10.1016/j.scico.2014.05.011

Cited by 8 publications

(8 citation statements)

References 13 publications

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“…Our operational semantics are 'single-stage' [17,18], i.e., they define a single but hybrid normal order strategy that relies on a subsidiary call-byname strategy (Section 3). Consequently, we can use single-layer CPS without control delimiters, as opposed to a two-layer CPS or a single-layer CPS with control delimiters, as found in other works (Section 10).…”

Section: Contributionsmentioning

confidence: 99%

“…Third, we introduce a non-standard but straightforward 'preponing' step and show that it is equivalence-preserving (Section 8). Last, we construct the grammar of continuation stacks as in [18]. In that work we showed that the stack is easily obtained from the grammar of the reduction semantics, but we only used the stack grammar to recover shallow inspection whereas in this paper we also use it to remove explicit control.…”

Section: Contributionsmentioning

confidence: 99%

“…Using the correlation between explicit control and the continuation stack [17,18], we finally obtain the open-terms version of KN by applying further standard derivation steps.…”

Section: Contributionsmentioning

confidence: 99%

“…The unique decomposition of C" 0 [ ] is proven by induction on terms [17,18]. The Ap calculus of Biernacka and Danvy [5] extends the pure lambda calculus with definitions for closures C and environments p. This calculus is itself an extension of Curien's calculus of closures X p .…”

Section: Normal Order In All Substitution-based Stylesmentioning

confidence: 99%

“…In a recent work [17,18] we have refined the current interderivation techniques to inter-derive semantic artefacts for fullreducing strategies, and have showcased the inter-derivation of 'We prefer 'full-reducing' to 'strong-' or 'strongly-reducing', as used by some authors, because the latter can be confused with 'stronglynormalising' which means something different. Strong normalisation is a property of a calculus.…”

Section: Introductionmentioning

confidence: 99%

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

García-Pérez

Nogueira

Moreno-Navarro

2013

Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming

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We derive by program transformation Pierre Cregut's full-reducing Krivine machine KN from the structural operational semantics of the normal order reduction strategy in a closure-converted pure lambda calculus. We thus establish the correspondence between the strategy and the machine, and showcase our technique for deriving full-reducing abstract machines. Actually, the machine we obtain is a slightly optimised version that can work with open terms and may be used in implementations of proof assistants.

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Section: Contributionsmentioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

“…Using the correlation between explicit control and the continuation stack [17,18], we finally obtain the open-terms version of KN by applying further standard derivation steps.…”

Section: Contributionsmentioning

confidence: 99%

Section: Normal Order In All Substitution-based Stylesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

García-Pérez

Nogueira

Moreno-Navarro

2013

Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming

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An Abstract Machine for Strong Call by Value

Biernacka

Biernacki

Charatonik

et al. 2020

Programming Languages and Systems

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The full-reducing Krivine abstract machine KN simulates pure normal-order reduction in lockstep: A proof via corresponding calculus

García-Pérez

Nogueira²

2019

J. Funct. Prog.

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We exploit the idea of proving properties of an abstract machine by using a corresponding semantic artefact better suited to their proof. The abstract machine is an improved version of Pierre Crégut’s full-reducing Krivine machine KN. The original version works with closed terms of the pure lambda calculus with de Bruijn indices. The improved version reduces in similar fashion but works on closures where terms may be open. The corresponding semantic artefact is a structural operational semantics of a calculus of closures whose reduction relation is purposely a reduction strategy. As shown in previous work, improved KN and the structural operational semantics ‘correspond’, i.e. both artefacts realise the same reduction strategy. In this paper, we prove in the calculus of closures that the reduction strategy simulates in lockstep (at every reduction step) the complete and standard normal-order strategy (i.e. leftmost reduction to normal form) of the pure lambda calculus. The simulation is witnessed by a substitution function from closures of the closure calculus to pure terms of the pure lambda calculus. Thus, KN also simulates normal-order in lockstep by the correspondence. This result is stronger than the known proof that KN is complete, for in the pure lambda calculus there are complete but non-standard strategies. The lockstep simulation proof consists of straightforward structural inductions, thanks to three properties of the closure calculus we call ‘index alignment’, ‘parameters-as-levels’ and ‘balanced derivations’. The first two come from KN. Thanks to these properties, a proof in a calculus of closures involving de Bruijn indices and de Bruijn levels is unproblematic. There is no lexical adjustment at binding lookup, on-the-fly alpha-conversion or recursive traversals of the term to deal with bound and free variables as in other calculi. This paper contributes to the framework for environment machines of Biernacka and Danvy a full-reducing open-terms closure calculus, its corresponding abstract machine, and a lockstep simulation proof via a substitution function.

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On the syntactic and functional correspondence between hybrid (or layered) normalisers and abstract machines

Cited by 8 publications

References 13 publications

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

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

An Abstract Machine for Strong Call by Value

The full-reducing Krivine abstract machine KN simulates pure normal-order reduction in lockstep: A proof via corresponding calculus

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