Created
July 14, 2015 11:01
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This is an example of Coq collapsing any universe level i to Set when we have a constraint of the form Set <= i.
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Set Universe Polymorphism. | |
Set Printing Universes. | |
Record X : Type := | |
{ | |
A : Type; | |
x : A | |
}. | |
Definition untt := {|A := unit; x := tt|}. | |
Print untt. | |
(* | |
untt = {| A := unit; x := tt |} | |
: X@{Set} | |
untt is universe polymorphic | |
*) | |
Definition UNTT := {|A := unit : Type; x := tt|}. | |
Print UNTT. | |
(* | |
UNTT = | |
{| A := unit:Type@{Top.8}; x := tt |} | |
: X@{Top.8} | |
(* Top.8 |= Set <= Top.8 | |
*) | |
UNTT is universe polymorphic | |
*) | |
Definition W := UNTT. | |
Print W. | |
(* | |
W = UNTT@{Set} | |
: X@{Set} | |
W is universe polymorphic | |
*) | |
Definition W' := UNTT@{i}. | |
Print W'. | |
(* | |
W' = UNTT@{Top.7} | |
: X@{Top.7} | |
(* Top.7 |= Set <= Top.7 | |
*) | |
W' is universe polymorphic | |
*) |
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