11 research outputs found
Realizability Interpretation and Normalization of Typed Call-by-Need -calculus With Control
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 \lambda$-$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 \lambda-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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The hosts of Nemeritis canescens a problem in the host specificity of insect parasitoids
Realizability Interpretation and Normalization of Typed Call-by-Need λ-calculus With Control
International audienceWe 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