Realizability Interpretation and Normalization of Typed Call-by-Need λ-calculus With Control
Résumé
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.
Domaines
Logique en informatique [cs.LO]
Fichier principal
cbncps.pdf (257.27 Ko)
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cbncps.aux (5.94 Ko)
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cbncps.blg (1001 B)
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cbncps.dvi (115.99 Ko)
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figures/typing_rules_lbvtstar.log (39.17 Ko)
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