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, 0 insertions, 6 deletions

diff --git a/engine/universes.mli b/engine/universes.mli
index 130dcf8bb..cb6e2ba1b 100644
--- a/engine/universes.mli
+++ b/engine/universes.mli
@@ -221,9 +221,3 @@ val pr_universe_opt_subst : universe_opt_subst -> Pp.t
 
 val solve_constraints_system : Universe.t option array -> Universe.t array -> Universe.t array ->
   Universe.t array
-
-(** Operations for universe_info_ind *)
-
-(** Given a universe context representing constraints of an inductive
-    this function produces a UInfoInd.t that with the trivial subtyping relation. *)
-val univ_inf_ind_from_universe_context : UContext.t -> CumulativityInfo.t