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Code and LaTeX sources for Constructing Inductive-Inductive types in Cubical Type Theory.

Conference version of the paper is in paper/current.tex. There is an unpolished draft containing a proof sketch that the contruction generalizes to a large class of inductive-inductive types in paper/longversion.tex.

Code can be found in the code directory. The files UIP_from_Forsberg_II.{v,agda} formalize the argument that Nordvall Forsberg's construction essentially requires UIP in Coq and Agda. We also formalize the construction in cubical type theory of a number of inductive-inductive types:

  • RunningExample.agda: The example used in the paper
  • ConTy.agda: The example with contexts and types from the introduction
  • InfinitaryII.agda: An example with infinitary constructors
  • EvilII.agda : This example has infinitary constructors and indices, and constructors in other constructors and sorts

This code has been checked using Coq 8.8.0 and Agda 2.6.0.1.

The tag FoSSaCS2019-camera-ready refers to the code for FoSSaCS 2019 after revision based on reviewer feedback.

The tag FoSSaCS2019 refers to the code at the time of submission to FoSSaCS 2019.

Check README.md in each of the tags for applicable versions of Coq and Agda.