The Coq mailing list

[Thorsten Altenkirch <Thorsten.Altenkirch AT nottingham.ac.uk>]

Not long ago Maxime Denes reported a problem with Coq which lead to it being incompatible with univalence. Also it meant that there are programs definable by structural recursion which are not derivable using eliminators. This was also applicable to Agda even with the without-K flag turned on. One version of the bug in Agda (by Conor) is below.

My question is: is this bug fixed in the current versions of Agda and Coq?

Next question: how can we make sure that there are no other issues of this kind?

Thorsten

{-# OPTIONS --without-K #-}

module BadWithoutK where

data Zero : Set where

data WOne : Set where

  wrap : (Zero -> WOne) -> WOne

data _<->_ (X : Set) : Set -> Set where

  Refl : X <-> X

postulate

  myIso : WOne <-> (Zero -> WOne)

moo : WOne -> Zero

noo : (X : Set) -> (WOne <-> X) -> X -> Zero

moo (wrap f) = noo (Zero -> WOne) myIso f

noo .WOne Refl x = moo x

bad : Zero

bad = moo (wrap \ ())

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