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- From: "Terrell, Jeffrey" <jeffrey.terrell AT kcl.ac.uk>
- To: "<coq-club AT inria.fr>" <coq-club AT inria.fr>
- Subject: Re: [Coq-Club] Elimination Rules
- Date: Thu, 7 Aug 2014 05:25:31 +0000
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In some texts, -> is treated in the same way as any other connective; and given that e.g. /\ has an elimination rule, i.e. and_rect, I was wondering whether -> has an elimination rule too. The same applies to forall x : A, P.
It's
clear that there's something fundamental about type P -> Q, because attempting to define it in the normal way is problematic.
Inductive imply (P Q : Prop) : Prop :=
imp : (P -> Q) -> imply P Q.
Regarding forall x : A, P, I'm aware that you can build a proof f a of P[a/x], but what is it that says you can?
Regards,
Jeff.On 6 Aug 2014, at 22:09, Maxime Dénès wrote:
Well, given a proof a of A and a proof f of forall x : A, P, you can build the proof f a of P[a/x].
Not sure if this answer your question, though.
Are you familiar with the Curry-Howard isomorphism? If not, I would advise to read about it.
Best,
Maxime.
On 08/06/2014 04:59 PM, Terrell, Jeffrey wrote:
From a proof of A and a proof of A -> B, we can infer B. This is the -> elimination rule.
Similarly, from a proof a of A and a proof of forall x : A, P, we can infer P[a/x]. This is the forall elimination rule.
How are these elimination rules manifest in Coq?
Regards,
Jeff.
- [Coq-Club] Elimination Rules, Terrell, Jeffrey, 08/06/2014
- Re: [Coq-Club] Elimination Rules, Maxime Dénès, 08/06/2014
- Re: [Coq-Club] Elimination Rules, Terrell, Jeffrey, 08/07/2014
- Re: [Coq-Club] Elimination Rules, Arnaud Spiwack, 08/07/2014
- Re: [Coq-Club] Elimination Rules, Terrell, Jeffrey, 08/08/2014
- Re: [Coq-Club] Elimination Rules, Abhishek Anand, 08/08/2014
- Re: [Coq-Club] Elimination Rules, Vladimir Voevodsky, 08/09/2014
- Message not available
- Re: [Coq-Club] Elimination Rules, Abhishek Anand, 08/10/2014
- Re: [Coq-Club] Elimination Rules, Andrej Bauer, 08/11/2014
- Re: [Coq-Club] Elimination Rules, Andrej Bauer, 08/11/2014
- Re: [Coq-Club] Elimination Rules, Abhishek Anand, 08/11/2014
- Re: [Coq-Club] Elimination Rules, Neel Krishnaswami, 08/12/2014
- Re: [Coq-Club] Elimination Rules, Andrej Bauer, 08/12/2014
- Re: [Coq-Club] Elimination Rules, Vladimir Voevodsky, 08/09/2014
- Re: [Coq-Club] Elimination Rules, Abhishek Anand, 08/08/2014
- Re: [Coq-Club] Elimination Rules, Terrell, Jeffrey, 08/08/2014
- Re: [Coq-Club] Elimination Rules, Arnaud Spiwack, 08/07/2014
- Re: [Coq-Club] Elimination Rules, Terrell, Jeffrey, 08/07/2014
- Re: [Coq-Club] Elimination Rules, Maxime Dénès, 08/06/2014
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