The People's Refinement Logic

RedPRL is a proof assistant for Computational Cubical Type Theory being developed at Carnegie Mellon University by Jon Sterling under Robert Harper, inspired by Nuprl.

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Papers & Talks



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

History & Philosophy

The first negation of formalism consists in decisively abolishing the old intensional order of truth-as-derivability, and reversing the prior relations between meaning theory and proof theory. The meaning explanation is both concrete and definitive, and proof theory is no longer a classifier of models, but a mere means of implementation.

In a negation of the negation, the standard semantics are generalized to a theory of Kripke logical relations to account for transcendental phenomena, including continuity and higher dimension. The purely formal negative freedom accorded by the toppled edifice is replaced with a living open-endedness, emanating from the free generation of fresh objects.


Jon Sterling, James Wilcox, Danny Gratzer, Darin Morrison, David Christiansen, Eugene Akentyev and Ayberk Tosun contributed to the design and implementation of RedPRL.