Explicit substitution on the edge of strong normalization

Bloo, Roel; Geuvers, Herman

doi:10.1016/s0304-3975(97)00183-7

Cited by 36 publications

(31 citation statements)

References 8 publications

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“…(which still gives a terminating substitution calculus), then a variation of Melliès's counterexample reported by [7], summarized in Fig. 2, can be used to demonstrate that the strongly normalizing λ term (λy.…”

Section: Preservation Of Strong Normalizationmentioning

confidence: 92%

On Explicit Substitution with Names

2011

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International audienceThis paper recounts the origins of the λx family of calculi of explicit substitution with proper variable names, including the original result of preservation of strong β-normalization based on the use of synthetic reductions for garbage collection. We then discuss the properties of a variant of the calculus which is also confluent for "open" terms (with meta-variables), and verify that a version with garbage collection preserves strong β-normalization (as is the state of the art), and we summarize the relationship with other efforts on using names and garbage collection rules in explicit substitution

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Section: Preservation Of Strong Normalizationmentioning

confidence: 92%

On Explicit Substitution with Names

2011

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“…Here we work on λµμx, an explicit substitutions version "à la" λx [4] of the λµμ-calculus. Its syntax was introduced in [9] and, in the same paper, there was an attempt to prove strong normalization of the deterministic call-by-name fragment directly by the reducibility technique.…”

Section: The λµμ-Calculus With Explicit Substitutions: λµμXmentioning

confidence: 99%

Strong Normalization of $\overline{\lambda}\mu\widetilde{\mu}$ -Calculus with Explicit Substitutions

Polonovski

2004

Lecture Notes in Computer Science

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Abstract. The λµμ-calculus, defined by Curien and Herbelin [7], is a variant of the λµ-calculus that exhibits symmetries such as term/context and call-by-name/call-by-value. Since it is a symmetric, and hence a non-deterministic calculus, usual proof techniques of normalization needs some adjustments to be made to work in this setting. Here we prove the strong normalization (SN) of simply typed λµμ-calculus with explicit substitutions. For that purpose, we first prove SN of simply typed λµμ-calculus (by a variant of the reducibility technique from Barbanera and Berardi [2]), then we formalize a proof technique of SN via PSN (preservation of strong normalization), and we prove PSN by the perpetuality technique, as formalized by Bonelli [5].

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“…Explicit substitutions calculi without composition typically enjoy the preservation of strong normalization property: a pure term is strongly normalizing in the presence of explicit substitutions if it is so under β-reduction [32,8,11,9,10,38,18]. It follows that the classical intersection type system does characterize strong normalization for pure terms.…”

Section: Example 11 Consider the Termsmentioning

confidence: 99%

“…Composition-free calculi of explicit substitutions have been studied in [31,11,26,10,8], among other works. Here we work in the composition-free calculus λx [11] and a calculus λx gc obtained by adding explicit garbage collection to λx.…”

Section: Introductionmentioning

confidence: 99%

Reductions, intersection types, and explicit substitutions

Dougherty

Lescanne

2003

Math. Struct. in Comp. Science

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We present a new system of intersection types for a composition-free calculus of explicit substitutions with a rule for garbage collection, and show that it characterizes those terms which are strongly normalizing. This system extends previous work on the natural generalization of the classical intersection types system, which characterized head normalization and weak normalization, but was not complete for strong normalization. An important role is played by the notion of available variable in a term, which is a generalization of the classical notion of free variable.

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Explicit substitution on the edge of strong normalization

Cited by 36 publications

References 8 publications

On Explicit Substitution with Names

On Explicit Substitution with Names

Strong Normalization of $\overline{\lambda}\mu\widetilde{\mu}$ -Calculus with Explicit Substitutions

Reductions, intersection types, and explicit substitutions

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