Hi Robin,

I just saw Thorsten answered your e-mail. I'd better finish what I started though.

I'm not an expert on OTT, but here are a few thoughts.

The "real" rule for coercion is the one on page 3. It doesn't require the types to be definitionally equal. Section 5 mainly speculates on adding two extensions:

* Definitional proof irrelevance

* Definitionally defining all coherence proofs to be refl and coercions within the same type to be the identity.

Like Thorsten says, this is a bit tricky and makes evaluation and equality mutually recursive - which is a bit odd. If you're looking to understand OTT, I wouldn't get too worked up about this rule - it's a bit technical and the really important stuff is in the first few sections.

I'm not sure if it helps, but here's a bit of Agda code "implementing" OTT:

www.cs.nott.ac.uk/~wss/Misc/ott.agda

I certainly understood much more of the paper after writing the Agda. I'm not sure if reading it will have quite the same effect, but it might be worth a shot.

All the best,

  Wouter

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