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FUIN
2008
73views more  FUIN 2008»
13 years 9 months ago
On Krivine's Realizability Interpretation of Classical Second-Order Arithmetic
This article investigates Krivine's realizability interpretation of classical second-order arithmetic and its recent extension handling countable choice. We will start by pre...
Paulo Oliva, Thomas Streicher
CORR
2011
Springer
137views Education» more  CORR 2011»
13 years 4 months ago
Existential witness extraction in classical realizability and via a negative translation
Abstract. We show how to extract existential witnesses from classical proofs using Krivine’s classical realizability—where classical proofs are interpreted as λ-terms with the...
Alexandre Miquel
CSL
2007
Springer
14 years 3 months ago
Classical Program Extraction in the Calculus of Constructions
We show how to extract classical programs expressed in Krivine λc-calculus from proof-terms built in a proof-irrelevant and classical version of the calculus of constructions with...
Alexandre Miquel
CSL
2000
Springer
14 years 1 months ago
Disjunctive Tautologies as Synchronisation Schemes
In the ambient logic of classical second order propositional calculus, we solve the specification problem for a family of excluded middle like tautologies. These are shown to be r...
Vincent Danos, Jean-Louis Krivine
APAL
2010
114views more  APAL 2010»
13 years 9 months ago
Classical predicative logic-enriched type theories
A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTT0 and LTT 0, which we...
Robin Adams, Zhaohui Luo