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[Benedikt Ahrens <benedikt.ahrens AT irit.fr>]

Indeed, [Identity Coercion foo : UU >-> Sortclass.] works.

Thanks a lot,
Benedikt

On 06/02/2014 11:14 AM, Jason Gross wrote:
> The coercion mechanism does not do delta/unfolding.  It sees ": C", looks
> for a coercion to "Sortclass", finds none, and errors.  It does not look
> for the hnf of every coercion it has, seeing if one of them is [Type].  You
> may be able to get around this by declaring an [Identity Coercion] between
> UU and Sortclass, or else declaring an identity function as a coercion from
> UU to Sortclass.  Alternatively, you can do [c : (C : UU)] instead of [c :
> C], or you can make some hacky notation like saying that [x `: y] means [x
> : (y : UU)] or something, and use that.
>
> -Jason
> On Jun 2, 2014 9:45 AM, "Benedikt Ahrens" 
> <benedikt.ahrens AT irit.fr>
>  wrote:
>
> > Hello,
> >
> > of the two pieces of code below, the first one is accepted whereas the
> > second one does not typecheck; the line "Check..." fails (in Coq8.4pl3).
> >
> > Could someone explain why? Is this a necessary restriction of the coercion
> > mechanism?
> >
> > Thanks a lot in advance.
> > Benedikt
> >
> > === 1 ===
> > Definition UU := Type.
> > Definition PointedUU := sigT (fun A : UU => A).
> > Definition carrier (C : PointedUU) : Type := @projT1 _ _ C.
> > Coercion carrier : PointedUU >-> Sortclass.
> > Check (fun C : PointedUU => fun c : C => c).
> > =========
> >
> > === 2 ===
> > Definition UU := Type.
> > Definition PointedUU := sigT (fun A : UU => A).
> > Definition carrier (C : PointedUU) := @projT1 _ _ C.
> > Coercion carrier : PointedUU >-> UU.
> > Check (fun C : PointedUU => fun c : C => c). (* fails *)
> > =========