<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>Hi Nisse,</div><div><br></div><div>I noticed that a weak version of K is provable even though the without-K flag is set:</div><div><br></div><div><div>{-# OPTIONS --without-K #-}</div><div>module K-bug where</div><div><br></div><div>open import Relation.Binary.PropositionalEquality</div><div><br></div><div><div>weakK : {A : Set}{a b : A}(p q : a $B"a(B b)($B&A(B $B&B(B : p $B"a(B q) $B"*(B $B&A(B $B"a(B $B&B(B</div><div>weakK refl .refl refl refl = refl</div></div></div><div><br></div><div>This would imply that all types have dimension of at most 3. I don't think it is provable with J.</div><div><br></div><div>A simpler term which is provable but shouldn't was found by my student Nicolai:</div><div><br></div><div><div>weak2 : {A : Set} {a : A} ($B&A(B : refl {x = a} $B"a(B refl) $B"*(B $B&A(B $B"a(B refl</div><div>weak2 refl = refl</div></div><div><br></div><div>It seems to me that these patterns satisfy the specification of without-K (I.e. the condition is too weak).</div><div><br></div><div>Do you see a fix?</div><div><br></div><div>Cheers,</div><div>Thorsten</div><br/>
<p>
This message and any attachment are intended solely for the addressee and may
contain confidential information. If you have received this message in error,
please send it back to me, and immediately delete it. Please do not use,
copy or disclose the information contained in this message or in any attachment.
Any views or opinions expressed by the author of this email do not necessarily
reflect the views of the University of Nottingham.
</p>
<p>
This message has been checked for viruses but the contents of an attachment
may still contain software viruses which could damage your computer system:
you are advised to perform your own checks. Email communications with the
University of Nottingham may be monitored as permitted by UK legislation.
</p></body></html>