Realizability interpretation and normalization of typed call-by-need λ-calculus with control - Inria - Institut national de recherche en sciences et technologies du numérique
Preprints, Working Papers, ... Year : 2017

Realizability interpretation and normalization of typed call-by-need λ-calculus with control

Abstract

We define a variant of realizability where realizers are pairs of a term and a substitution. This variant allows us to prove the normalization of a simply-typed call-by-need λ-calculus with control due to Ariola et al. Indeed, in such call-by-need calculus, substitutions have to be delayed until knowing if an argument is really needed. In a second step, we extend the proof to a call-by-need λ-calculus equipped with a type system equivalent to classical second-order predicate logic, representing one step towards proving the normalization of the call-by-need classical second-order arithmetic introduced by the second author to provide a proof-as-program interpretation of the axiom of dependent choice.
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Dates and versions

hal-01624839 , version 1 (26-10-2017)
hal-01624839 , version 2 (02-03-2018)

Identifiers

  • HAL Id : hal-01624839 , version 1

Cite

Étienne Miquey, Hugo Herbelin. Realizability interpretation and normalization of typed call-by-need λ-calculus with control. 2017. ⟨hal-01624839v1⟩
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