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[Jesper Cockx <Jesper AT sikanda.be>]

From the patch notes:

* (Since Agda 2.4.2:) Termination checking --without-K restricts
  structural descent to arguments ending in data types or `Size`.
  Likewise, guardedness is only tracked when result type is data or
  record type.

    mutual
      data WOne : Set where wrap : FOne → WOne
      FOne = ⊥ → WOne

    noo : (X : Set) → (WOne ≡ X) → X → ⊥
    noo .WOne refl (wrap f) = noo FOne iso f

  `noo` is rejected since at type `X` the structural descent
  `f < wrap f` is discounted --without-K.

    data Pandora : Set where
      C : ∞ ⊥ → Pandora

    loop : (A : Set) → A ≡ Pandora → A
    loop .Pandora refl = C (♯ (loop ⊥ foo))

  `loop` is rejected since guardedness is not tracked at type `A`
  --without-K.

  See issues 1023, 1264, 1292.

Regarding the second question, please take a look at our ICFP paper from this year: http://dl.acm.org/authorize?N87775.

Cheers,

Jesper

On Thu, Nov 27, 2014 at 11:03 AM, Thorsten Altenkirch <Thorsten.Altenkirch AT nottingham.ac.uk> wrote:

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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