[Agda] without-K problem

Altenkirch Thorsten psztxa at exmail.nottingham.ac.uk
Mon Jun 18 21:00:39 CEST 2012

Hi Nisse,

I noticed that a weak version of K is provable even though the without-K flag is set:

{-# OPTIONS --without-K #-}
module K-bug where

open import Relation.Binary.PropositionalEquality

weakK : {A : Set}{a b : A}(p q : a ≡ b)(α β : p ≡ q) → α ≡ β
weakK refl .refl refl refl = refl

This would imply that all types have dimension of at most 3. I don't think it is provable with J.

A simpler term which is provable but shouldn't was found by my student Nicolai:

weak2 : {A : Set} {a : A} (α : refl {x = a} ≡ refl) → α ≡ refl
weak2 refl = refl

It seems to me that these patterns satisfy the specification of without-K (I.e. the condition is too weak).

Do you see a fix?

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