Canonicity of Weak ω-groupoid Laws Using Parametricity Theory

Marc Lasson 1, 2
2 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, Inria Paris-Rocquencourt, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique : UMR7126
Abstract : We show that terms witnessing a groupoid law from the ω-groupoid structure of types are all propositionally equal. Our proof reduce this problem to the unicity of the canonical point in the n-th loop space and conclude using Bernardy's parametricity theory for dependent types.
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Marc Lasson. Canonicity of Weak ω-groupoid Laws Using Parametricity Theory. MFPS 2014, Jun 2014, Ithaca, United States. pp.229 - 244, ⟨10.1016/j.entcs.2014.10.013⟩. ⟨hal-01105252⟩

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