<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; color: rgb(0, 0, 0); font-size: 14px; font-family: Calibri, sans-serif;"><div>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.</div><div><br></div><div>My question is: is this bug fixed in the current versions of Agda and Coq?</div><div><br></div><div>Next question: how can we make sure that there are no other issues of this kind?</div><div><br></div><div>Thorsten</div><div><br></div><div><br></div><div><div style="font-family: Consolas; font-size: medium;">{-# OPTIONS --without-K #-}</div><div style="font-family: Consolas; font-size: medium;"><br></div><div style="font-family: Consolas; font-size: medium;">module BadWithoutK where</div><div style="font-family: Consolas; font-size: medium;"><br></div><div style="font-family: Consolas; font-size: medium;">data Zero : Set where</div><div style="font-family: Consolas; font-size: medium;"><br></div><div style="font-family: Consolas; font-size: medium;">data WOne : Set where</div><div style="font-family: Consolas; font-size: medium;"> wrap : (Zero -> WOne) -> WOne</div><div style="font-family: Consolas; font-size: medium;"><br></div><div style="font-family: Consolas; font-size: medium;">data _<->_ (X : Set) : Set -> Set where</div><div style="font-family: Consolas; font-size: medium;"> Refl : X <-> X</div><div style="font-family: Consolas; font-size: medium;"><br></div><div style="font-family: Consolas; font-size: medium;">postulate</div><div style="font-family: Consolas; font-size: medium;"> myIso : WOne <-> (Zero -> WOne)</div><div style="font-family: Consolas; font-size: medium;"><br></div><div style="font-family: Consolas; font-size: medium;">moo : WOne -> Zero</div><div style="font-family: Consolas; font-size: medium;">noo : (X : Set) -> (WOne <-> X) -> X -> Zero</div><div style="font-family: Consolas; font-size: medium;"><br></div><div style="font-family: Consolas; font-size: medium;">moo (wrap f) = noo (Zero -> WOne) myIso f</div><div style="font-family: Consolas; font-size: medium;">noo .WOne Refl x = moo x</div><div style="font-family: Consolas; font-size: medium;"><br></div><div style="font-family: Consolas; font-size: medium;">bad : Zero</div><div style="font-family: Consolas; font-size: medium;">bad = moo (wrap \ ())</div></div><div><br></div><br>
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