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Higher Inductive Type Eliminators Without Paths
2020
Types for Proofs and Programs
Cubical Agda has support for higher inductive types. Paths are integral to the working of this feature. However, there are other notions of equality. For instance, Cubical Agda comes with an identity type family for which the J rule computes in the usual way when applied to the canonical proof of reflexivity, whereas typical implementations of the J rule for paths do not. This text shows how one can use some of the higher inductive types definable in Cubical Agda with arbitrary notions of
doi:10.4230/lipics.types.2019.10
dblp:conf/types/Danielsson19
fatcat:pgeov2ojdfez7d3ndx5hvppow4