Call-by-Value  -calculus and LJQ

Dyckhoff, Roy; Lengrand, Stéphane

doi:10.1093/logcom/exm037

Cited by 23 publications

(25 citation statements)

References 21 publications

(44 reference statements)

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“…There are many proposals of alternative CBV λ-calculi (see [9,10,11,12,5]) extending Plotkin's one by using explicit substitutions (constructors of the form let...in). In particular, Accattoli and Paolini [5] introduced recently the λ vsubcalculus where the reduction rule acts at a distance by extending the notion of β v -redex (with explicit substitutions).…”

Section: Introductionmentioning

confidence: 99%

A Semantical and Operational Account of Call-by-Value Solvability

Carraro

Guerrieri

2014

Lecture Notes in Computer Science

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Abstract. In Plotkin's call-by-value lambda-calculus, solvable terms are characterized syntactically by means of call-by-name reductions and there is no neat semantical characterization of such terms. Preserving confluence, we extend Plotkin's original reduction without adding extra syntactical constructors, and we get a call-by-value operational characterization of solvable terms. Moreover, we give a semantical characterization of solvable terms in a relational model, based on Linear Logic, satisfying the Taylor expansion formula. As a technical tool, we also use a resource-sensitive calculus (with tests) in which the elements of the model are definable.

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Section: Introductionmentioning

confidence: 99%

A Semantical and Operational Account of Call-by-Value Solvability

Carraro

Guerrieri

2014

Lecture Notes in Computer Science

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“…Dyckhoff and Lengrand [4] prove an equational correspondence [23] between LJQ (the Q subsystem of intuitionistic sequent calculus) and Moggi's computational λ-calculus [14]. An isomorphism is to be expected between LJQ and the intuitionistic, Q subsystem of λµlet.…”

Section: Final Remarksmentioning

confidence: 99%

“…The execution itself, by σ or π, is in one go, by calling meta-operations. 4 Hole expressions are indeed expressions that go into the hole of contexts: see below.…”

Section: The Natural Deduction System λµLetmentioning

confidence: 99%

Towards a Canonical Classical Natural Deduction System

Santo

2010

Computer Science Logic

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This paper studies a new classical natural deduction system, presented as a typed calculus named λµlet. It is designed to be isomorphic to Curien-Herbelin's λµμ-calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and substitution (resp. elimination) in natural deduction. It is a combination of Parigot's λµ-calculus with the idea of "coercion calculus" due to Cervesato-Pfenning, accommodating let-expressions in a surprising way: they expand Parigot's syntactic class of named terms. This calculus aims to be the simultaneous answer to three problems. The first problem is the lack of a canonical natural deduction system for classical logic. λµlet is not yet another classical calculus, but rather a canonical reflection in natural deduction of the impeccable treatment of classical logic by sequent calculus. The second problem is the lack of a formalization of the usual semantics of λµμ-calculus, that explains co-terms and cuts as, respectively, contexts and hole-filling instructions. The mentioned isomorphism is the required formalization, based on the precise notions of context and hole-expression offered by λµlet. The third problem is the lack of a robust process of "read-back" into natural deduction syntax of calculi in the sequent calculus format, that affects mainly the recent proof-theoretic efforts of derivation of λ-calculi for call-byvalue. An isomorphic counterpart to the Q-subsystem of λµμ-calculus is derived, obtaining a new λ-calculus for call-by-value, combining control and let-expressions. stitution). To avoid confusion, we refer to any meta-operation of substitution as "meta-substitution".

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“…The weakness of β v -reduction is a fact widely recognized and accepted, indeed there have been many proposals of alternative CBV calculi [11,12,17,24,9]. The value-substitution λ vsub -calculus.…”

Section: λ-Theories a Term T Is Solvable If There Exists A Head Contmentioning

confidence: 99%

Call-by-Value Solvability, Revisited

Accattoli

Paolini

2012

Functional and Logic Programming

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Abstract. In the call-by-value lambda-calculus solvable terms have been characterised by means of call-by-name reductions, which is disappointing and requires complex reasonings. We introduce the valuesubstitution lambda-calculus, a simple calculus borrowing ideas from Herbelin and Zimmerman's call-by-value λCBV calculus and from Accattoli and Kesner's substitution calculus λsub. In this new setting, we characterise solvable terms as those terms having normal form with respect to a suitable restriction of the rewriting relation.

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Call-by-Value -calculus and LJQ

Cited by 23 publications

References 21 publications

A Semantical and Operational Account of Call-by-Value Solvability

A Semantical and Operational Account of Call-by-Value Solvability

Towards a Canonical Classical Natural Deduction System

Call-by-Value Solvability, Revisited

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