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- From: Maxime Dénès <mail AT maximedenes.fr>
- To: coq-club AT inria.fr
- Subject: Re: [Coq-Club] Reduction rule for fixpoints
- Date: Mon, 14 Nov 2016 13:46:25 +0100
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Hi Randy,
If I read correctly, this restriction is needed even without axioms as
soon as you have strong reduction (i.e. under lambdas, match):
Fixpoint my_identity (n : nat) :=
match n with
| O => O
| S p => S (my_identity p)
end.
Consider the normal form of my_identity. You don't want to infinitely
expand the recursive call.
Maxime.
On 11/14/16 13:35, Randy Pollack wrote:
> Page 134 of the reference manual (8.5pl2) describes the reduction rule
> for a fixpoint application:
>
> ================================
> The reduction for fixpoints is:
> [...]
> when aki starts with a constructor. This last restriction is needed in
> order to keep strong normalization.
> ==================================
>
> Is is known if this last restriction is needed when the context in
> which the fixpoint application is well typed doesn't contain any
> axioms? (References or examples?)
>
> What about for specific axioms, such as functional extensionality, axiom K,
> ...?
>
> Thanks,
> --Randy
>
- [Coq-Club] Reduction rule for fixpoints, Randy Pollack, 11/14/2016
- Re: [Coq-Club] Reduction rule for fixpoints, Maxime Dénès, 11/14/2016
- Re: [Coq-Club] Reduction rule for fixpoints, Maxime Dénès, 11/14/2016
- Re: [Coq-Club] Reduction rule for fixpoints, Pierre Courtieu, 11/14/2016
- Re: [Coq-Club] Reduction rule for fixpoints, Randy Pollack, 11/14/2016
- [Coq-Club] Mysterious type of sig for predicates on identity types, Dominique Larchey-Wendling, 11/16/2016
- Re: [Coq-Club] Mysterious type of sig for predicates on identity types, Jason Gross, 11/16/2016
- Re: [Coq-Club] Mysterious type of sig for predicates on identity types, Dominique Larchey-Wendling, 11/16/2016
- Re: [Coq-Club] Mysterious type of sig for predicates on identity types, Jason Gross, 11/16/2016
- Re: [Coq-Club] Reduction rule for fixpoints, Maxime Dénès, 11/14/2016
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