User:Chalst/Classical Curry Howard
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Classically typed dependent type theories
- A Constructive Proof of Dependent Choice, Compatible with Classical Logic (Hugo Herbelin 2012), formalises dPA^omega.
- Classical realizability and side-effects (Phd theses, Etienne Miquey, 2017), considers theories similar to Herbelin's dPA^omega in order to get better properties, and looks at algebras for classical realizability drawing on Alexandre Miquel's implicative algebras.[1]
- ^ Implicative Algebras: A new foundation for realizability and forcing, 2018, https://arxiv.org/abs/1802.00528