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Re: [Coq-Club] A question concerning certain variant of the Prod rule


chronological Thread 
  • From: Frederic Blanqui <frederic.blanqui AT inria.fr>
  • To: Edsko de Vries <Edsko.de.Vries AT cs.tcd.ie>
  • Cc: Matej Kosik <kosik AT fiit.stuba.sk>, coq-club AT pauillac.inria.fr
  • Subject: Re: [Coq-Club] A question concerning certain variant of the Prod rule
  • Date: Thu, 16 Apr 2009 16:43:32 +0800
  • List-archive: <http://pauillac.inria.fr/pipermail/coq-club/>


Edsko de Vries a écrit :
or perhaps the special case were
`a' does not occur free in `B':

       E,Γ |- A:Prop      E,Γ |- B:Set
       ----------------------------------
           E,Γ |- A->B:Set

Is it possible to give some meaningful examples of terms that can be
constructed this way?

Such functions are valid only in special cases; in particular, it is possible to use a proof as argument to a function that returns an argument in Set if the proof is used *only* to guard termination of the function, but cannot otherwise influence the value returned. If you are working through Coq'Art, you'll get to such functions eventually: Sections 14.2.3 and 15.2.

Could someone give bibliographic references about this limitation?





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