
A constructive proof of dependent choice in classical arithmetic via memoization
In a recent paper, Herbelin developed dPA^ω, a calculus in which constru...
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Realizability Interpretation and Normalization of Typed CallbyNeed λcalculus With Control
We define a variant of realizability where realizers are pairs of a term...
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Revisiting the duality of computation: an algebraic analysis of classical realizability models
In an impressive series of papers, Krivine showed at the edge of the las...
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A Simple Soundness Proof for Dependent Object Types
Dependent Object Types (DOT) is intended to be a core calculus for model...
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A Path To DOT: Formalizing FullyPathDependent Types
The Dependent Object Types (DOT) calculus aims to formalize the Scala pr...
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IndexStratified Types (Extended Version)
We present Tores, a core language for encoding metatheoretic proofs. The...
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Normalization by Evaluation for CallbyPushValue and Polarized LambdaCalculus
We observe that normalization by evaluation for simplytyped lambdacalc...
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A sequent calculus with dependent types for classical arithmetic
In a recent paper, Herbelin developed dPA^ω, a calculus in which constructive proofs for the axioms of countable and dependent choices could be derived via the encoding of a proof of countable universal quantification as a stream of it components. However, the property of normalization (and therefore the one of soundness) was only conjectured. The difficulty for the proof of normalization is due to the simultaneous presence of dependent types (for the constructive part of the choice), of control operators (for classical logic), of coinductive objects (to encode functions of type N→ A into streams (a_0,a_1,...)) and of lazy evaluation with sharing (for these coinductive objects). Elaborating on previous works, we introduce in this paper a variant of dPA^ω presented as a sequent calculus. On the one hand, we take advantage of a variant of Krivine classical realizability that we developed to prove the normalization of classical callbyneed. On the other hand, we benefit from dL_t̂p̂, a classical sequent calculus with dependent types in which type safety is ensured by using delimited continuations together with a syntactic restriction. By combining the techniques developed in these papers, we manage to define a realizability interpretation à la Krivine of our calculus that allows us to prove normalization and soundness.
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