The RedPRL Proof Assistant


RedPRL is an experimental proof assistant based on cubical computational type theory, which extends the Nuprl semantics by higher-dimensional features inspired by homotopy type theory. RedPRL is created and maintained by the RedPRL Development Team.

RedPRL is written in Standard ML, and is available for download on GitHub.


  • computational canonicity and extraction
  • univalence as a theorem
  • strict (exact) equality types
  • coequalizer and pushout types
  • functional extensionality
  • equality reflection
  • proof tactics

Papers & Talks

RedPRL User Guide


This research was sponsored by the Air Force Office of Scientific Research under grant number FA9550-15-1-0053 and the National Science Foundation under grant number DMS-1638352. We also thank the Isaac Newton Institute for Mathematical Sciences for its support and hospitality during the program “Big Proof” when part of this work was undertaken; the program was supported by the Engineering and Physical Sciences Research Council under grant number EP/K032208/1. The views and conclusions contained here are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, government or any other entity.