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Re: [Coq-Club] Propositional extensionality is inconsistent in Coq


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  • From: Pierre Boutillier <pierre.boutillier AT pps.univ-paris-diderot.fr>
  • To: coq-club AT inria.fr
  • Subject: Re: [Coq-Club] Propositional extensionality is inconsistent in Coq
  • Date: Fri, 13 Dec 2013 11:18:19 +0100

Le vendredi 13 décembre 2013 à 11:04 +0100, Viktor Vafeiadis a écrit :
> On 13 Dec 2013, at 08:21, Christine Paulin wrote:
>
> > The principle is the recursive call in the definition of f x should be of
> > the form
> > f t
> > with t a strict recursive subterm of x
> >
> > there is a rule to accept a term t of the form (match u with t1 .. tn end)
> > whenever all ti are recursive subterms of x
> > in particular when u has type False (match u with end) is accepted
> [...]
> > So some check needs to be added. A simple idea would be that a recursive
> > subterm could never be an abstraction, or to add some finer analysis in
> > which context u should be typable.
>
> An even simpler fix would be to just drop the rule that accepts (match u
> with t1 .. tn end) as a subterm.
>
> I wonder whether there are any actual proofs that rely on recursive
> definitions of such form.
Require Import NPeano.

Print gcd.

>
>
> Viktor





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