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[Jason Gross <jasongross9 AT gmail.com>]

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 *)
=========