MARK P. JONES
Pacific Software Research Center
Department of Computer Science and Engineering
Oregon Graduate Institute of Science and Technology
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I think I’ve figured out most parts of the cubical type theory papers; I’m going to take a shot to explain it informally in the format of Q&As. I prefer using syntax or terminologies that fit better rather than the more standard ones.
Q: What is cubical type theory?
A: It’s a type theory giving homotopy type theory its computational meaning.
Q: What is homotopy type theory then?
A: It’s traditional type theory (which refers to Martin-Löf type theory in this Q&A) augmented with higher inductive types and the univalence axiom.