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 |=  *)

1 files changed, 32 insertions, 2 deletions

diff --git a/checker/univ.ml b/checker/univ.ml
index 7d01657df..46b3ce680 100644
--- a/checker/univ.ml
+++ b/checker/univ.ml
@@ -1003,12 +1003,42 @@ end
 
 type abstract_universe_context = AUContext.t
 
+module Variance =
+struct
+  (** A universe position in the instance given to a cumulative
+     inductive can be the following. Note there is no Contravariant
+     case because [forall x : A, B <= forall x : A', B'] requires [A =
+     A'] as opposed to [A' <= A]. *)
+  type t = Irrelevant | Covariant | Invariant
+
+  let leq_constraint csts variance u u' =
+    match variance with
+    | Irrelevant -> csts
+    | Covariant -> Constraint.add (u, Le, u') csts
+    | Invariant -> Constraint.add (u, Eq, u') csts
+
+  let eq_constraint csts variance u u' =
+    match variance with
+    | Irrelevant -> csts
+    | Covariant | Invariant -> Constraint.add (u, Eq, u') csts
+
+  let leq_constraints variance u u' csts =
+    let len = Array.length u in
+    assert (len = Array.length u' && len = Array.length variance);
+    Array.fold_left3 leq_constraint csts variance u u'
+
+  let eq_constraints variance u u' csts =
+    let len = Array.length u in
+    assert (len = Array.length u' && len = Array.length variance);
+    Array.fold_left3 eq_constraint csts variance u u'
+end
+
 module CumulativityInfo =
 struct
-  type t = universe_context * universe_context
+  type t = universe_context * Variance.t array
 
   let univ_context (univcst, subtypcst) = univcst
-  let subtyp_context (univcst, subtypcst) = subtypcst
+  let variance (univs, variance) = variance
 
 end