On the Geometry of Intuitionistic S4 Proofs

@inproceedings{Goubault2003OnTG,
  title={On the Geometry of Intuitionistic S4 Proofs},
  author={{\'E}ric Goubault},
  year={2003}
}
The Curry-Howard correspondence between formulas and types, proofs and programs, proof simplification and program execution, also holds for intuitionistic modal logic S4. It turns out that the S4 modalities translate as a monoidal comonad on the space of proofs, giving rise to a canonical augmented simplicial structure. We study the geometry of these augmented simplicial sets, showing that each type gives rise to an augmented simplicial set which is a disjoint sum of nerves of finite lattices… CONTINUE READING
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