From 35fba70509d9fb219b2a88f8e7bd246b2671b39b Mon Sep 17 00:00:00 2001
From: Gaëtan Gilbert
Date: Thu, 9 Nov 2017 17:27:58 +0100
Subject: Simplification: cumulativity information is variance information.

Since cumulativity of an inductive type is the universe constraints
which make a term convertible with its universe-renamed copy, the only
constraints we can get are between a universe and its copy.

As such we do not need to be able to represent arbitrary constraints
between universes and copied universes in a double-sized ucontext,
instead we can just keep around an array describing whether a bound
universe is covariant, invariant or irrelevant (CIC has no
contravariant conversion rule).

Printing is fairly obtuse and should be improved: when we print the
CumulativityInfo we add marks to the universes of the instance: = for
invariant, + for covariant and * for irrelevant. ie

         Record Foo@{i j k} := { foo : Type@{i} -> Type@{j} }.
         Print Foo.

gives

        Cumulative Record Foo : Type@{max(i+1, j+1)} := Build_Foo
          { foo : Type@{i} -> Type@{j} }
          (* =i +j *k |=  *)
---
 test-suite/success/cumulativity.v | 10 ++++++++++
 1 file changed, 10 insertions(+)

(limited to 'test-suite')

diff --git a/test-suite/success/cumulativity.v b/test-suite/success/cumulativity.v
index 0ee85712e2..303cd7146e 100644
--- a/test-suite/success/cumulativity.v
+++ b/test-suite/success/cumulativity.v
@@ -98,3 +98,13 @@ Section down.
     intros H f g Hfg. exact (H f g Hfg).
   Defined.
 End down.
+
+Record Arrow@{i j} := { arrow : Type@{i} -> Type@{j} }.
+
+Fail Definition arrow_lift@{i i' j j' | i' < i, j < j'}
+  : Arrow@{i j} -> Arrow@{i' j'}
+  := fun x => x.
+
+Definition arrow_lift@{i i' j j' | i' = i, j < j'}
+  : Arrow@{i j} -> Arrow@{i' j'}
+  := fun x => x.
-- 
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