Explicit Substitutions and Programming Languages

Lévy, Jean-Jacques; Maranget, Luc

doi:10.1007/3-540-46691-6_14

Cited by 19 publications

(27 citation statements)

References 24 publications

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“…One easily shows that the weak λ-calculus is not confluent. In [18], an extension of the weak λ-calculus was introduced. It is strongly inspired from the one of Ç agman and Hindley [6] for Combinatory Logic.…”

Section: Introductionmentioning

confidence: 99%

“…meaning that the ξ-rule is valid when the bound variable x is not free in the redex R contracted between M and N (This rule will be presented in section 2 in a form slightly different from -but equivalent to -the σ-rule used in [18]). The resulting new weak λ-calculus is confluent as shown in [18].…”

Section: Introductionmentioning

confidence: 99%

“…The resulting new weak λ-calculus is confluent as shown in [18]. The theory of optimal reductions in the λ-calculus [5] has been extensively studied by Abadi, Asperti, Coppola, Gonthier, Guerrini, Lamping, Lawall, Lévy, Mairson, Martini et al [3,4,9,13,15,17].…”

Section: Introductionmentioning

confidence: 99%

“…It uses de Bruijn indices and is not confluent for open terms: Klop's counterexample [11] for surjective pairing can be adapted to the calculus of explicit substitutions [1]. However, confluence (on open terms) can be recovered at the price of either considering a much more complex calculus of explicit substitutions [7], or a theory of weak explicit substitutions as in [8,18]. In the latter case, a theory of sharing was sketched, through the definition of a weak labeled calculus of explicit substitutions.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 2, we recall the definitions and basic properties of the weak λ-calculus introduced in [18]. In Section 3, we consider the weak labeled λ-calculus and prove its confluence.…”

Section: Introductionmentioning

confidence: 99%

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Sharing in the Weak Lambda-Calculus

Blanc

Lévy

Maranget

2005

Processes, Terms and Cycles: Steps on the Road to Infinity

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Abstract. Despite decades of research in the λ-calculus, the syntactic properties of the weak λ-calculus did not receive great attention. However, this theory is more relevant for the implementation of programming languages than the usual theory of the strong λ-calculus. In fact, the frameworks of weak explicit substitutions, or computational monads, or λ-calculus with a let statement, or super-combinators, were developed for adhoc purposes related to programming language implementation. In this paper, we concentrate on sharing of subterms in a confluent variant of the weak λ-calculus. We introduce a labeling of this calculus that expresses a confluent theory of reductions with sharing, independent of the reduction strategy. We finally state that Wadsworth's evaluation technique with sharing of subterms corresponds to our formal setting.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In Section 2, we recall the definitions and basic properties of the weak λ-calculus introduced in [18]. In Section 3, we consider the weak labeled λ-calculus and prove its confluence.…”

Section: Introductionmentioning

confidence: 99%

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