Merge PR #7384: Split Universes

1 files changed, 68 insertions, 2 deletions

diff --git a/vernac/comInductive.ml b/vernac/comInductive.ml
index b2532485a..629fcce5a 100644
--- a/vernac/comInductive.ml
+++ b/vernac/comInductive.ml
@@ -177,6 +177,72 @@ let is_flexible_sort evd u =
   | Some l -> Evd.is_flexible_level evd l
   | None -> false
 
+(**********************************************************************)
+(* Tools for template polymorphic inductive types                         *)
+
+(* Miscellaneous functions to remove or test local univ assumed to
+   occur only in the le constraints *)
+
+(*
+   Solve a system of universe constraint of the form
+
+   u_s11, ..., u_s1p1, w1 <= u1
+   ...
+   u_sn1, ..., u_snpn, wn <= un
+
+where
+
+  - the ui (1 <= i <= n) are universe variables,
+  - the sjk select subsets of the ui for each equations,
+  - the wi are arbitrary complex universes that do not mention the ui.
+*)
+
+let is_direct_sort_constraint s v = match s with
+  | Some u -> Univ.univ_level_mem u v
+  | None -> false
+
+let solve_constraints_system levels level_bounds =
+  let open Univ in
+  let levels =
+    Array.mapi (fun i o ->
+      match o with
+      | Some u ->
+        (match Universe.level u with
+        | Some u -> Some u
+        | _ -> level_bounds.(i) <- Universe.sup level_bounds.(i) u; None)
+      | None -> None)
+      levels in
+  let v = Array.copy level_bounds in
+  let nind = Array.length v in
+  let clos = Array.map (fun _ -> Int.Set.empty) levels in
+  (* First compute the transitive closure of the levels dependencies *)
+  for i=0 to nind-1 do
+    for j=0 to nind-1 do
+      if not (Int.equal i j) && is_direct_sort_constraint levels.(j) v.(i) then
+        clos.(i) <- Int.Set.add j clos.(i);
+    done;
+  done;
+  let rec closure () =
+    let continue = ref false in
+      Array.iteri (fun i deps ->
+        let deps' =
+          Int.Set.fold (fun j acc -> Int.Set.union acc clos.(j)) deps deps
+        in
+          if Int.Set.equal deps deps' then ()
+          else (clos.(i) <- deps'; continue := true))
+        clos;
+      if !continue then closure ()
+      else ()
+  in
+  closure ();
+  for i=0 to nind-1 do
+    for j=0 to nind-1 do
+      if not (Int.equal i j) && Int.Set.mem j clos.(i) then
+        (v.(i) <- Universe.sup v.(i) level_bounds.(j));
+    done;
+  done;
+  v
+
 let inductive_levels env evd poly arities inds =
   let destarities = List.map (fun x -> x, Reduction.dest_arity env x) arities in
   let levels = List.map (fun (x,(ctx,a)) ->
@@ -205,8 +271,8 @@ let inductive_levels env evd poly arities inds =
   in
   (* Take the transitive closure of the system of constructors *)
   (* level constraints and remove the recursive dependencies *)
-  let levels' = Universes.solve_constraints_system (Array.of_list levels)
-    (Array.of_list cstrs_levels) (Array.of_list min_levels)
+  let levels' = solve_constraints_system (Array.of_list levels)
+    (Array.of_list cstrs_levels)
   in
   let evd, arities =
     CList.fold_left3 (fun (evd, arities) cu (arity,(ctx,du)) len ->