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Re: [Coq-Club] Parametric Morphisms


Chronological Thread 
  • From: Durward McDonell <Durward.McDonell AT jhuapl.edu>
  • To: coq-club AT inria.fr
  • Subject: Re: [Coq-Club] Parametric Morphisms
  • Date: Tue, 08 Jul 2014 10:05:38 -0400


That's not a bad idea, but we really want to carry around
(foo e f) and apply it to a state. But given a fixed state,
we want to be able to switch e' and f' in for e and f when
appropriate.

Thanks for the reply.

--
Durward

On 07/08/2014 04:05 AM, Cedric Auger wrote:
> Maybe you could define a notation to change the order the arguments are
> parsed/printed and in fact use the expected order for "Parametric Morphism".
>
>
> 2014-07-07 20:32 GMT+02:00 Durward McDonell
> <Durward.McDonell AT jhuapl.edu
> <mailto:Durward.McDonell AT jhuapl.edu>>:
>
>
> Hello.
>
> Here's what I understand: suppose you have two types, "expr" and
> "state". Also suppose you have
>
> eq_expr : state -> expr -> expr -> Prop
>
> and that you Add (eq_expr st) as a reflexive, symmetric, and
> transitive Parametric Relation for all (st : state). Finally, suppose
> you have
>
> foo : state -> expr -> expr -> Prop
>
> that respects eq_expr on both of its expr arguments. Then you can
> do
>
> Add Parametric Morphism (st : state) :
> (foo st)
> with signature ((eq_expr st) ==> (eq_expr st) ==> impl)
> as foo_mor.
>
> Subsequently, if you have
>
> H : foo st e f
> G : eq_expr st e e'
>
> you can use "rewrite G in H" to get
>
> H : foo st e' f
>
> So far, so good, I hope. My question is what if, for some perverse
> reason, you really, really want foo to be
>
> foo' : expr -> expr -> state -> Prop
>
> that is, you just want to reorder the arguments to foo. What do you do
> about the Parametric Morphism statement? I've tried a couple of things
> that were either unsatisfactory, or simply didn't work. Any suggestion
> would be welcome.
>
> --
> Durward McDonell
>
> durward.mcdonell AT jhuapl.edu
>
> <mailto:durward.mcdonell AT jhuapl.edu>
> 240-228-2690 <tel:240-228-2690> (DC)
> 443-778-2690 <tel:443-778-2690> (Balt.)
>
>
>
>
> --
> .../Sedrikov\...


--
Durward McDonell
durward.mcdonell AT jhuapl.edu
240-228-2690 (DC)
443-778-2690 (Balt.)

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