ocaml/typing/ctype.ml

(***********************************************************************)
(*                                                                     *)
(*                           Objective Caml                            *)
(*                                                                     *)
(* Xavier Leroy and Jerome Vouillon, projet Cristal, INRIA Rocquencourt*)
(*                                                                     *)
(*  Copyright 1996 Institut National de Recherche en Informatique et   *)
(*  en Automatique.  All rights reserved.  This file is distributed    *)
(*  under the terms of the Q Public License version 1.0.               *)
(*                                                                     *)
(***********************************************************************)

(* $Id$ *)

(* Operations on core types *)

open Misc
open Asttypes
open Types
open Btype

(*
   Type manipulation after type inference
   ======================================
   If one wants to manipulate a type after type inference (for
   instance, during code generation or in the debugger), one must
   first make sure that the type levels are correct, using the
   function [correct_levels]. Then, this type can be correctely
   manipulated by [apply], [expand_head] and [moregeneral].
*)

(*
   General notes
   =============
   - As much sharing as possible should be kept : it makes types
     smaller and better abbreviated.
     When necessary, some sharing can be lost. Types will still be
     printed correctly (+++ TO DO...), and abbreviations defined by a
     class do not depend on sharing thanks to constrained
     abbreviations. (Of course, even if some sharing is lost, typing
     will still be correct.)
   - All nodes of a type have a level : that way, one know whether a
     node need to be duplicated or not when instantiating a type.
   - Levels of a type are decreasing (generic level being considered
     as greatest).
   - The level of a type constructor is superior to the binding
     time of its path.
   - Recursive types without limitation should be handled (even if
     there is still an occur check). This avoid treating specially the
     case for objects, for instance. Furthermore, the occur check
     policy can then be easily changed.
*)

(*
   A faire
   =======
   - Revoir affichage des types.
   - Etendre la portee d'un alias [... as 'a] a tout le type englobant.
   - #-type implementes comme de vraies abreviations.
   - Niveaux plus fins pour les identificateurs :
       Champ [global] renomme en [level];
       Niveau -1 : global
               0 : module toplevel
               1 : module contenu dans module toplevel
              ...
     En fait, incrementer le niveau a chaque fois que l'on rentre dans
     un module.

       3   4 6
        \ / /
       1 2 5
        \|/
         0

     [Subst] doit ecreter les niveaux (pour qu'un variable non
     generalisable dans un module de niveau 2 ne se retrouve pas
     generalisable lorsque l'on l'utilise au niveau 0).

   - Traitement de la trace de l'unification separe de la fonction
     [unify].
*)

(**** Errors ****)

exception Unify of (type_expr * type_expr) list

exception Tags of label * label

exception Subtype of
        (type_expr * type_expr) list * (type_expr * type_expr) list

exception Cannot_expand

exception Cannot_apply

exception Recursive_abbrev

(**** Type level management ****)

let current_level = ref 0
let nongen_level = ref 0
let global_level = ref 1
let saved_level = ref []
let saved_global_level = ref []

let init_def level = current_level := level; nongen_level := level
let begin_def () =
  saved_level := (!current_level, !nongen_level) :: !saved_level;
  incr current_level; nongen_level := !current_level
let begin_class_def () =
  saved_level := (!current_level, !nongen_level) :: !saved_level;
  incr current_level
let raise_nongen_level () =
  saved_level := (!current_level, !nongen_level) :: !saved_level;
  nongen_level := !current_level
let end_def () =
  let (cl, nl) = List.hd !saved_level in
  saved_level := List.tl !saved_level;
  current_level := cl; nongen_level := nl

let reset_global_level () =
  global_level := !current_level + 1;
  saved_global_level := []
let increase_global_level () =
  let gl = !global_level in
  global_level := !current_level;
  gl
let restore_global_level gl =
  global_level := gl

(* Abbreviations without parameters *)
(* Shall reset after generalizing *)
let simple_abbrevs = ref Mnil
let proper_abbrevs path tl abbrev =
  if !Clflags.principal || tl <> [] then abbrev else
  let name = match path with Path.Pident id -> Ident.name id
                           | Path.Pdot(_, s,_) -> s
                           | Path.Papply _ -> assert false in
  if name.[0] <> '#' then simple_abbrevs else abbrev

(**** Some type creators ****)

(* Re-export generic type creators *)

let newty2             = Btype.newty2
let newty desc         = newty2 !current_level desc
let new_global_ty desc = newty2 !global_level desc

let newvar ()          = newty2 !current_level Tvar
let newvar2 level      = newty2 level Tvar
let new_global_var ()  = newty2 !global_level Tvar

let newobj fields      = newty (Tobject (fields, ref None))

let newconstr path tyl = newty (Tconstr (path, tyl, ref Mnil))

let none = newty (Ttuple [])                (* Clearly ill-formed type *)

(**** Representative of a type ****)

(* Re-export repr *)
let repr = repr

(**** Type maps ****)

module TypePairs =
  Hashtbl.Make (struct
    type t = type_expr * type_expr
    let equal (t1, t1') (t2, t2') = (t1 == t2) && (t1' == t2')
    let hash (t, t') = t.id + 93 * t'.id
 end)

                  (**********************************************)
                  (*  Miscellaneous operations on object types  *)
                  (**********************************************)


(**** Object field manipulation. ****)

let dummy_method = "*dummy method*"

let object_fields ty =
  match (repr ty).desc with
    Tobject (fields, _) -> fields
  | _                   -> assert false

let flatten_fields ty =
  let rec flatten l ty =
    let ty = repr ty in
    match ty.desc with
      Tfield(s, k, ty1, ty2) ->
        flatten ((s, k, ty1)::l) ty2
    | _ ->
        (l, ty)
  in
    let (l, r) = flatten [] ty in
    (Sort.list (fun (n, _, _) (n', _, _) -> n < n') l, r)

let build_fields level =
  List.fold_right
    (fun (s, k, ty1) ty2 -> newty2 level (Tfield(s, k, ty1, ty2)))

let associate_fields fields1 fields2 =
  let rec associate p s s' =
    function
      (l, []) ->
        (List.rev p, (List.rev s) @ l, List.rev s')
    | ([], l') ->
        (List.rev p, List.rev s, (List.rev s') @ l')
    | ((n, k, t)::r, (n', k', t')::r') when n = n' ->
        associate ((n, k, t, k', t')::p) s s' (r, r')
    | ((n, k, t)::r, ((n', k', t')::_ as l')) when n < n' ->
        associate p ((n, k, t)::s) s' (r, l')
    | (((n, k, t)::r as l), (n', k', t')::r') (* when n > n' *) ->
        associate p s ((n', k', t')::s') (l, r')
  in
  associate [] [] [] (fields1, fields2)

(**** Check whether an object is open ****)

(* +++ Il faudra penser a eventuellement expanser l'abreviation *)
let rec object_row ty =
  let ty = repr ty in
  match ty.desc with
    Tobject (t, _)     -> object_row t
  | Tfield(_, _, _, t) -> object_row t
  | _ -> ty

let opened_object ty =
  match (object_row ty).desc with
  | Tvar               -> true
  | Tunivar            -> true
  | Tconstr _          -> true
  | _                  -> false

(**** Close an object ****)

let close_object ty =
  let rec close ty =
    let ty = repr ty in
    match ty.desc with
      Tvar ->
        link_type ty (newty2 ty.level Tnil)
    | Tfield(_, _, _, ty') -> close ty'
    | _                    -> assert false
  in
  match (repr ty).desc with
    Tobject (ty, _)   -> close ty
  | _                 -> assert false

(**** Row variable of an object type ****)

let row_variable ty =
  let rec find ty =
    let ty = repr ty in
    match ty.desc with
      Tfield (_, _, _, ty) -> find ty
    | Tvar                 -> ty
    | _                    -> assert false
  in
  match (repr ty).desc with
    Tobject (fi, _) -> find fi
  | _               -> assert false

(**** Object name manipulation ****)
(* +++ Bientot obsolete *)

let set_object_name id rv params ty =
  match (repr ty).desc with
    Tobject (fi, nm) ->
      set_name nm (Some (Path.Pident id, rv::params))
  | _ ->
      assert false

let remove_object_name ty =
  match (repr ty).desc with
    Tobject (_, nm)   -> set_name nm None
  | Tconstr (_, _, _) -> ()
  | _                 -> fatal_error "Ctype.remove_object_name"

(**** Hiding of private methods ****)

let hide_private_methods ty =
  match (repr ty).desc with
    Tobject (fi, nm) ->
      nm := None;
      let (fl, _) = flatten_fields fi in
      List.iter
        (function (_, k, _) ->
          match field_kind_repr k with
            Fvar r -> set_kind r Fabsent
          | _      -> ())
        fl
  | _ ->
      assert false


                              (*******************************)
                              (*  Operations on class types  *)
                              (*******************************)


let rec signature_of_class_type =
  function
    Tcty_constr (_, _, cty) -> signature_of_class_type cty
  | Tcty_signature sign     -> sign
  | Tcty_fun (_, ty, cty)   -> signature_of_class_type cty

let self_type cty =
  repr (signature_of_class_type cty).cty_self

let rec class_type_arity =
  function
    Tcty_constr (_, _, cty) ->  class_type_arity cty
  | Tcty_signature _        ->  0
  | Tcty_fun (_, _, cty)    ->  1 + class_type_arity cty


                  (*******************************************)
                  (*  Miscellaneous operations on row types  *)
                  (*******************************************)

let sort_row_fields = Sort.list (fun (p,_) (q,_) -> p < q)

let merge_row_fields fi1 fi2 =
  let rec merge r1 r2 pairs fi1 fi2 =
    match fi1, fi2 with
      (l1,f1 as p1)::fi1', (l2,f2 as p2)::fi2' ->
        if l1 = l2 then merge r1 r2 ((l1,f1,f2)::pairs) fi1' fi2' else
        if l1 < l2 then merge (p1::r1) r2 pairs fi1' fi2 else
        merge r1 (p2::r2) pairs fi1 fi2'
    | [], _ -> (List.rev r1, List.rev_append r2 fi2, pairs)
    | _, [] -> (List.rev_append r1 fi1, List.rev r2, pairs)
  in
  merge [] [] [] (sort_row_fields fi1) (sort_row_fields fi2)

let rec filter_row_fields erase = function
    [] -> []
  | (l,f as p)::fi ->
      let fi = filter_row_fields erase fi in
      match row_field_repr f with
        Rabsent -> fi
      | Reither(_,_,false,e) when erase -> set_row_field e Rabsent; fi
      | _ -> p :: fi

                    (**************************************)
                    (*  Check genericity of type schemes  *)
                    (**************************************)


exception Non_closed

let rec closed_schema_rec ty =
  let ty = repr ty in
  if ty.level >= lowest_level then begin
    let level = ty.level in
    ty.level <- pivot_level - level;
    match ty.desc with
      Tvar when level <> generic_level ->
        raise Non_closed
    | Tfield(_, kind, t1, t2) ->
        if field_kind_repr kind = Fpresent then
          closed_schema_rec t1;
        closed_schema_rec t2
    | Tvariant row ->
        let row = row_repr row in
        iter_row closed_schema_rec {row with row_bound = []};
        if not (static_row row) then closed_schema_rec row.row_more
    | _ ->
        iter_type_expr closed_schema_rec ty
  end

(* Return whether all variables of type [ty] are generic. *)
let closed_schema ty =
  try
    closed_schema_rec ty;
    unmark_type ty;
    true
  with Non_closed ->
    unmark_type ty;
    false

exception Non_closed of type_expr * bool

let free_variables = ref []

let rec free_vars_rec real ty =
  let ty = repr ty in
  if ty.level >= lowest_level then begin
    ty.level <- pivot_level - ty.level;
    begin match ty.desc with
      Tvar ->
        free_variables := (ty, real) :: !free_variables
(* Do not count "virtual" free variables
    | Tobject(ty, {contents = Some (_, p)}) ->
        free_vars_rec false ty; List.iter (free_vars_rec true) p
*)
    | Tobject (ty, _) ->
        free_vars_rec false ty
    | Tfield (_, _, ty1, ty2) ->
        free_vars_rec true ty1; free_vars_rec false ty2
    | Tvariant row ->
        let row = row_repr row in
        iter_row (free_vars_rec true) {row with row_bound = []};
        if not (static_row row) then free_vars_rec false row.row_more
    | _    ->
        iter_type_expr (free_vars_rec true) ty
    end;
  end

let free_vars ty =
  free_variables := [];
  free_vars_rec true ty;
  let res = !free_variables in
  free_variables := [];
  res

let free_variables ty =
  let tl = List.map fst (free_vars ty) in
  unmark_type ty;
  tl

let rec closed_type ty =
  match free_vars ty with
      []           -> ()
  | (v, real) :: _ -> raise (Non_closed (v, real))

let closed_parameterized_type params ty =
  List.iter mark_type params;
  try
    closed_type ty;
    List.iter unmark_type params;
    unmark_type ty;
    true
  with Non_closed _ ->
    List.iter unmark_type params;
    unmark_type ty;
    false

let closed_type_decl decl =
  try
    List.iter mark_type decl.type_params;
    begin match decl.type_kind with
      Type_abstract ->
        ()
    | Type_variant(v, priv) ->
        List.iter (fun (_, tyl) -> List.iter closed_type tyl) v
    | Type_record(r, rep, priv) ->
        List.iter (fun (_, _, ty) -> closed_type ty) r
    end;
    begin match decl.type_manifest with
      None    -> ()
    | Some ty -> closed_type ty
    end;
    unmark_type_decl decl;
    None
  with Non_closed (ty, _) ->
    unmark_type_decl decl;
    Some ty

type closed_class_failure =
    CC_Method of type_expr * bool * string * type_expr
  | CC_Value of type_expr * bool * string * type_expr

exception Failure of closed_class_failure

let closed_class params sign =
  let ty = object_fields (repr sign.cty_self) in
  let (fields, rest) = flatten_fields ty in
  List.iter mark_type params;
  mark_type rest;
  List.iter
    (fun (lab, _, ty) -> if lab = dummy_method then mark_type ty)
    fields;
  try
    mark_type_node (repr sign.cty_self);
    List.iter
      (fun (lab, kind, ty) ->
        if field_kind_repr kind = Fpresent then
        try closed_type ty with Non_closed (ty0, real) ->
          raise (Failure (CC_Method (ty0, real, lab, ty))))
      fields;
    mark_type_params (repr sign.cty_self);
    List.iter unmark_type params;
    unmark_class_signature sign;
    None
  with Failure reason ->
    mark_type_params (repr sign.cty_self);
    List.iter unmark_type params;
    unmark_class_signature sign;
    Some reason


                            (**********************)
                            (*  Type duplication  *)
                            (**********************)


(* Duplicate a type, preserving only type variables *)
let duplicate_type ty =
  Subst.type_expr Subst.identity ty

(* Same, for class types *)
let duplicate_class_type ty =
  Subst.class_type Subst.identity ty


                         (*****************************)
                         (*  Type level manipulation  *)
                         (*****************************)

(*
   It would be a bit more efficient to remove abbreviation expansions
   rather than generalizing them: these expansions will usually not be
   used anymore. However, this is not possible in the general case, as
   [expand_abbrev] (via [subst]) requires these expansions to be
   preserved. Does it worth duplicating this code ?
*)
let rec iter_generalize tyl ty =
  let ty = repr ty in
  if (ty.level > !current_level) && (ty.level <> generic_level) then begin
    set_level ty generic_level;
    begin match ty.desc with
      Tconstr (_, _, abbrev) ->
        iter_abbrev (iter_generalize tyl) !abbrev
    | _ -> ()
    end;
    iter_type_expr (iter_generalize tyl) ty
  end else
    tyl := ty :: !tyl

let iter_generalize tyl ty =
  simple_abbrevs := Mnil;
  iter_generalize tyl ty

let generalize ty =
  iter_generalize (ref []) ty

(* Efficient repeated generalisation of the same type *)
let iterative_generalization min_level tyl =
  let tyl' = ref [] in
  List.iter (iter_generalize tyl') tyl;
  List.fold_right (fun ty l -> if ty.level <= min_level then l else ty::l)
    !tyl' []

(* Generalize the structure and lower the variables *)

let rec generalize_structure var_level ty =
  let ty = repr ty in
  if ty.level <> generic_level then begin
    if ty.desc = Tvar && ty.level > var_level then
      set_level ty var_level
    else if ty.level > !current_level then begin
      set_level ty generic_level;
      begin match ty.desc with
        Tconstr (_, _, abbrev) -> abbrev := Mnil
      | _ -> ()
      end;
      iter_type_expr (generalize_structure var_level) ty
    end
  end

let generalize_structure var_level ty =
  simple_abbrevs := Mnil;
  generalize_structure var_level ty

(* let generalize_expansive ty = generalize_structure !nongen_level ty *)
let generalize_global ty = generalize_structure !global_level ty
let generalize_structure ty = generalize_structure !current_level ty

(* Generalize the spine of a function, if the level >= !current_level *)

let rec generalize_spine ty =
  let ty = repr ty in
  if ty.level < !current_level || ty.level = generic_level then () else
  match ty.desc with
    Tarrow (_, _, ty', _) | Tpoly (ty', _) ->
      set_level ty generic_level;
      generalize_spine ty'
  | _ -> ()

let try_expand_once' = (* Forward declaration *)
  ref (fun env ty -> raise Cannot_expand)

(*
   Lower the levels of a type (assume [level] is not
   [generic_level]).
*)
(*
    The level of a type constructor must be greater than its binding
    time. That way, a type constructor cannot escape the scope of its
    definition, as would be the case in
      let x = ref []
      module M = struct type t let _ = (x : t list ref) end
    (without this constraint, the type system would actually be unsound.)
*)
let rec update_level env level ty =
  let ty = repr ty in
  if ty.level > level then begin
    begin match ty.desc with
      Tconstr(p, tl, abbrev)  when level < Path.binding_time p ->
        (* Try first to replace an abbreviation by its expansion. *)
        begin try
          link_type ty (!try_expand_once' env ty);
          update_level env level ty
        with Cannot_expand ->
          (* +++ Levels should be restored... *)
          raise (Unify [(ty, newvar2 level)])
        end
    | Tobject(_, ({contents=Some(p, tl)} as nm))
      when level < Path.binding_time p ->
        set_name nm None;
        update_level env level ty
    | Tvariant row ->
        let row = row_repr row in
        begin match row.row_name with
        | Some (p, tl) when level < Path.binding_time p ->
            log_type ty;
            ty.desc <- Tvariant {row with row_name = None}
        | _ -> ()
        end;
        set_level ty level;
        iter_type_expr (update_level env level) ty
    | Tfield(lab, _, _, _) when lab = dummy_method ->
        raise (Unify [(ty, newvar2 level)])
    | _ ->
        set_level ty level;
        (* XXX what about abbreviations in Tconstr ? *)
        iter_type_expr (update_level env level) ty
    end
  end

(* Generalize and lower levels of contravariant branches simultaneously *)

let rec generalize_expansive env var_level ty =
  let ty = repr ty in
  if ty.level <> generic_level then begin
    if ty.level > var_level then begin
      set_level ty generic_level;
      match ty.desc with
        Tconstr (path, tyl, abbrev) ->
          let variance =
            try (Env.find_type path env).type_variance
            with Not_found -> List.map (fun _ -> (true,true,true)) tyl in
          abbrev := Mnil;
          List.iter2
            (fun (co,cn,ct) t ->
              if ct then update_level env var_level t
              else generalize_expansive env var_level t)
            variance tyl
      | Tarrow (_, t1, t2, _) ->
          update_level env var_level t1;
          generalize_expansive env var_level t2
      | _ ->
          iter_type_expr (generalize_expansive env var_level) ty
    end
  end

let generalize_expansive env ty =
  simple_abbrevs := Mnil;
  try
    generalize_expansive env !nongen_level ty
  with Unify [_, ty'] ->
    raise (Unify [ty, ty'])

(* Correct the levels of type [ty]. *)
let correct_levels ty =
  duplicate_type ty

(* Only generalize the type ty0 in ty *)
let limited_generalize ty0 ty =
  let ty0 = repr ty0 in

  let graph = Hashtbl.create 17 in
  let idx = ref lowest_level in
  let roots = ref [] in

  let rec inverse pty ty =
    let ty = repr ty in
    if (ty.level > !current_level) || (ty.level = generic_level) then begin
      decr idx;
      Hashtbl.add graph !idx (ty, ref pty);
      if (ty.level = generic_level) || (ty == ty0) then
        roots := ty :: !roots;
      set_level ty !idx;
      iter_type_expr (inverse [ty]) ty
    end else if ty.level < lowest_level then begin
      let (_, parents) = Hashtbl.find graph ty.level in
      parents := pty @ !parents
    end

  and generalize_parents ty =
    let idx = ty.level in
    if idx <> generic_level then begin
      set_level ty generic_level;
      List.iter generalize_parents !(snd (Hashtbl.find graph idx));
      (* Special case for rows: must generalize the row variable *)
      match ty.desc with
        Tvariant row ->
          let more = row_more row in
          let lv = more.level in
          if (lv < lowest_level || lv > !current_level)
          && lv <> generic_level then set_level more generic_level
      | _ -> ()
    end
  in

  inverse [] ty;
  if ty0.level < lowest_level then
    iter_type_expr (inverse []) ty0;
  List.iter generalize_parents !roots;
  Hashtbl.iter
    (fun _ (ty, _) ->
       if ty.level <> generic_level then set_level ty !current_level)
    graph


                              (*******************)
                              (*  Instantiation  *)
                              (*******************)


let rec find_repr p1 =
  function
    Mnil ->
      None
  | Mcons (p2, ty, _, _) when Path.same p1 p2 ->
      Some ty
  | Mcons (_, _, _, rem) ->
      find_repr p1 rem
  | Mlink {contents = rem} ->
      find_repr p1 rem

(*
   Generic nodes are duplicated, while non-generic nodes are left
   as-is.
   During instantiation, the description of a generic node is first
   replaced by a link to a stub ([Tsubst (newvar ())]). Once the
   copy is made, it replaces the stub.
   After instantiation, the description of generic node, which was
   stored by [save_desc], must be put back, using [cleanup_types].
*)

let abbreviations = ref (ref Mnil)
  (* Abbreviation memorized. *)

let rec copy ty =
  let ty = repr ty in
  match ty.desc with
    Tsubst ty -> ty
  | _ ->
    if ty.level <> generic_level then ty else
    let desc = ty.desc in
    save_desc ty desc;
    let t = newvar() in          (* Stub *)
    ty.desc <- Tsubst t;
    t.desc <-
      begin match desc with
      | Tconstr (p, tl, _) ->
          let abbrevs = proper_abbrevs p tl !abbreviations in
          begin match find_repr p !abbrevs with
            Some ty when repr ty != t -> (* XXX Commentaire... *)
              Tlink ty
          | _ ->
          (*
             One must allocate a new reference, so that abbrevia-
             tions belonging to different branches of a type are
             independent.
             Moreover, a reference containing a [Mcons] must be
             shared, so that the memorized expansion of an abbrevi-
             ation can be released by changing the content of just
             one reference.
          *)
              Tconstr (p, List.map copy tl,
                       ref (match !(!abbreviations) with
                              Mcons _ -> Mlink !abbreviations
                            | abbrev  -> abbrev))
          end
      | Tvariant row0 ->
          let row = row_repr row0 in
          let more = repr row.row_more in
          (* We must substitute in a subtle way *)
          (* Tsubst takes a tuple containing the row var and the variant *)
          begin match more.desc with
            Tsubst {desc = Ttuple [_;ty2]} ->
              (* This variant type has been already copied *)
              ty.desc <- Tsubst ty2; (* avoid Tlink in the new type *)
              Tlink ty2
          | _ ->
              (* If the row variable is not generic, we must keep it *)
              let keep = more.level <> generic_level in
              let more' =
                match more.desc with
                  Tsubst ty -> ty
                | Tconstr _ ->
                    if keep then save_desc more more.desc;
                    copy more
                | Tvar | Tunivar ->
                    save_desc more more.desc;
                    if keep then more else newty more.desc
                |  _ -> assert false
              in
              (* Register new type first for recursion *)
              more.desc <- Tsubst(newgenty(Ttuple[more';t]));
              (* Return a new copy *)
              Tvariant (copy_row copy true row keep more')
          end
      | Tfield (p, k, ty1, ty2) ->
          begin match field_kind_repr k with
            Fabsent  -> Tlink (copy ty2)
          | Fpresent -> copy_type_desc copy desc
          | Fvar r ->
              dup_kind r;
              copy_type_desc copy desc
          end
      | _ -> copy_type_desc copy desc
      end;
    t

(**** Variants of instantiations ****)

let instance sch =
  let ty = copy sch in
  cleanup_types ();
  ty

let instance_list schl =
  let tyl = List.map copy schl in
  cleanup_types ();
  tyl

let instance_constructor cstr =
  let ty_res = copy cstr.cstr_res in
  let ty_args = List.map copy cstr.cstr_args in
  cleanup_types ();
  (ty_args, ty_res)

let instance_parameterized_type sch_args sch =
  let ty_args = List.map copy sch_args in
  let ty = copy sch in
  cleanup_types ();
  (ty_args, ty)

let instance_parameterized_type_2 sch_args sch_lst sch =
  let ty_args = List.map copy sch_args in
  let ty_lst = List.map copy sch_lst in
  let ty = copy sch in
  cleanup_types ();
  (ty_args, ty_lst, ty)

let instance_class params cty =
  let rec copy_class_type =
    function
      Tcty_constr (path, tyl, cty) ->
        Tcty_constr (path, List.map copy tyl, copy_class_type cty)
    | Tcty_signature sign ->
        Tcty_signature
          {cty_self = copy sign.cty_self;
           cty_vars =
             Vars.map (function (m, v, ty) -> (m, v, copy ty)) sign.cty_vars;
           cty_concr = sign.cty_concr;
           cty_inher =
             List.map (fun (p,tl) -> (p, List.map copy tl)) sign.cty_inher}
    | Tcty_fun (l, ty, cty) ->
        Tcty_fun (l, copy ty, copy_class_type cty)
  in
  let params' = List.map copy params in
  let cty' = copy_class_type cty in
  cleanup_types ();
  (params', cty')

(**** Instanciation for types with free universal variables ****)

module TypeHash = Hashtbl.Make(TypeOps)
module TypeSet = Set.Make(TypeOps)

type inv_type_expr =
    { inv_type : type_expr;
      mutable inv_parents : inv_type_expr list }

let rec inv_type hash pty ty =
  let ty = repr ty in
  try
    let inv = TypeHash.find hash ty in
    inv.inv_parents <- pty @ inv.inv_parents
  with Not_found ->
    let inv = { inv_type = ty; inv_parents = pty } in
    TypeHash.add hash ty inv;
    iter_type_expr (inv_type hash [inv]) ty

let compute_univars ty =
  let inverted = TypeHash.create 17 in
  inv_type inverted [] ty;
  let node_univars = TypeHash.create 17 in
  let rec add_univar univ inv =
    match inv.inv_type.desc with
      Tpoly (ty, tl) when List.memq univ (List.map repr tl) -> ()
    | _ ->
        try
          let univs = TypeHash.find node_univars inv.inv_type in
          if not (TypeSet.mem univ !univs) then begin
            univs := TypeSet.add univ !univs;
            List.iter (add_univar univ) inv.inv_parents
          end
        with Not_found ->
          TypeHash.add node_univars inv.inv_type (ref(TypeSet.singleton univ));
          List.iter (add_univar univ) inv.inv_parents
  in
  TypeHash.iter (fun ty inv -> if ty.desc = Tunivar then add_univar ty inv)
    inverted;
  fun ty ->
    try !(TypeHash.find node_univars ty) with Not_found -> TypeSet.empty

let rec diff_list l1 l2 =
  if l1 == l2 then [] else
  match l1 with [] -> invalid_arg "Ctype.diff_list"
  | a :: l1 -> a :: diff_list l1 l2

let conflicts free bound =
  let bound = List.map repr bound in
  TypeSet.exists (fun t -> List.memq (repr t) bound) free

let delayed_copy = ref []
    (* copying to do later *)

(* Copy without sharing until there are no free univars left *)
(* all free univars must be included in [visited]            *)
let rec copy_sep fixed free bound visited ty =
  let ty = repr ty in
  let univars = free ty in
  if TypeSet.is_empty univars then
    if ty.level <> generic_level then ty else
    let t = newvar () in
    delayed_copy :=
      lazy (t.desc <- Tlink (copy ty))
      :: !delayed_copy;
    t
  else try
    let t, bound_t = List.assq ty visited in
    let dl = if ty.desc = Tunivar then [] else diff_list bound bound_t in
    if dl <> [] && conflicts univars dl then raise Not_found;
    t
  with Not_found -> begin
    let t = newvar() in          (* Stub *)
    let visited =
      match ty.desc with
        Tarrow _ | Ttuple _ | Tvariant _ | Tconstr _ | Tobject _ ->
          (ty,(t,bound)) :: visited
      | _ -> visited in
    let copy_rec = copy_sep fixed free bound visited in
    t.desc <-
      begin match ty.desc with
      | Tvariant row0 ->
          let row = row_repr row0 in
          let more = repr row.row_more in
          (* We shall really check the level on the row variable *)
          let keep = more.desc = Tvar && more.level <> generic_level in
          let more' = copy_rec more in
          let fixed' = fixed && (repr more').desc = Tvar in
          let row = copy_row copy_rec fixed' row keep more' in
          Tvariant row
      | Tpoly (t1, tl) ->
          let tl = List.map repr tl in
          let tl' = List.map (fun t -> newty Tunivar) tl in
          let bound = tl @ bound in
          let visited =
            List.map2 (fun ty t -> ty,(t,bound)) tl tl' @ visited in
          Tpoly (copy_sep fixed free bound visited t1, tl')
      | _ -> copy_type_desc copy_rec ty.desc
      end;
    t
  end

let instance_poly fixed univars sch =
  let vars = List.map (fun _ -> newvar ()) univars in
  let pairs = List.map2 (fun u v -> repr u, (v, [])) univars vars in
  delayed_copy := [];
  let ty = copy_sep fixed (compute_univars sch) [] pairs sch in
  List.iter Lazy.force !delayed_copy;
  delayed_copy := [];
  cleanup_types ();
  vars, ty

let instance_label fixed lbl =
  let ty_res = copy lbl.lbl_res in
  let vars, ty_arg =
    match repr lbl.lbl_arg with
      {desc = Tpoly (ty, tl)} ->
        instance_poly fixed tl ty
    | ty ->
        [], copy lbl.lbl_arg
  in
  cleanup_types ();
  (vars, ty_arg, ty_res)

(**** Instantiation with parameter substitution ****)

let unify' = (* Forward declaration *)
  ref (fun env ty1 ty2 -> raise (Unify []))

let rec subst env level abbrev ty params args body =
  if List.length params <> List.length args then raise (Unify []);
  let old_level = !current_level in
  current_level := level;
  try
    let body0 = newvar () in          (* Stub *)
    begin match ty with
      None      -> ()
    | Some ({desc = Tconstr (path, tl, _)} as ty) ->
        let abbrev = proper_abbrevs path tl abbrev in
        memorize_abbrev abbrev path ty body0
    | _ ->
        assert false
    end;
    abbreviations := abbrev;
    let (params', body') = instance_parameterized_type params body in
    abbreviations := ref Mnil;
    !unify' env body0 body';
    List.iter2 (!unify' env) params' args;
    current_level := old_level;
    body'
  with Unify _ as exn ->
    current_level := old_level;
    raise exn

(*
   Only the shape of the type matters, not whether is is generic or
   not. [generic_level] might be somewhat slower, but it ensures
   invariants on types are enforced (decreasing levels.), and we don't
   care about efficiency here.
*)
let apply env params body args =
  try
    subst env generic_level (ref Mnil) None params args body
  with
    Unify _ -> raise Cannot_apply


                              (****************************)
                              (*  Abbreviation expansion  *)
                              (****************************)

(*
   If the environnement has changed, memorized expansions might not
   be correct anymore, and so we flush the cache. This is safe but
   quite pessimistic: it would be enough to flush the cache when a
   type or module definition is overriden in the environnement.
*)
let previous_env = ref Env.empty
let check_abbrev_env env =
  if env != !previous_env then begin
    cleanup_abbrev ();
    previous_env := env
  end

(* Expand an abbreviation. The expansion is memorized. *)
(*
   Assume the level is greater than the path binding time of the
   expanded abbreviation.
*)
(*
   An abbreviation expansion will fail in either of these cases:
   1. The type constructor does not correspond to a manifest type.
   2. The type constructor is defined in an external file, and this
      file is not in the path (missing -I options).
   3. The type constructor is not in the "local" environment. This can
      happens when a non-generic type variable has been instantiated
      afterwards to the not yet defined type constructor. (Actually,
      this cannot happen at the moment due to the strong constraints
      between type levels and constructor binding time.)
   4. The expansion requires the expansion of another abbreviation,
      and this other expansion fails.
*)
let expand_abbrev env ty =
  check_abbrev_env env;
  match ty with
    {desc = Tconstr (path, args, abbrev); level = level} ->
      let lookup_abbrev = proper_abbrevs path args abbrev in
      begin match find_expans path !lookup_abbrev with
        Some ty ->
          if level <> generic_level then
            begin try
              update_level env level ty
            with Unify _ ->
              (* XXX This should not happen.
                 However, levels are not correctly restored after a
                 typing error *)
              ()
            end;
          ty
      | None ->
          let (params, body) =
            try Env.find_type_expansion path env with Not_found ->
              raise Cannot_expand
          in
          let ty' = subst env level abbrev (Some ty) params args body in
          (* Hack to name the variant type *)
          begin match repr ty' with
            {desc=Tvariant row} as ty when static_row row ->
              ty.desc <- Tvariant { row with row_name = Some (path, args) }
          | _ -> ()
          end;
          ty'
      end
  | _ ->
      assert false

let safe_abbrev env ty =
  let snap = Btype.snapshot () in
  try ignore (expand_abbrev env ty); true
  with Cannot_expand | Unify _ ->
    Btype.backtrack snap;
    false

let try_expand_once env ty =
  let ty = repr ty in
  match ty.desc with
    Tconstr _ -> repr (expand_abbrev env ty)
  | _ -> raise Cannot_expand

let _ = try_expand_once' := try_expand_once

(* Fully expand the head of a type.
   Raise Cannot_expand if the type cannot be expanded.
   May raise Unify, if a recursion was hidden in the type. *)
let rec try_expand_head env ty =
  let ty' = try_expand_once env ty in
  begin try
    try_expand_head env ty'
  with Cannot_expand ->
    ty'
  end

(* Expand once the head of a type *)
let expand_head_once env ty =
  try expand_abbrev env (repr ty) with Cannot_expand -> assert false

(* Fully expand the head of a type. *)
let expand_head_unif env ty =
  try try_expand_head env ty with Cannot_expand -> repr ty

let expand_head env ty =
  let snap = Btype.snapshot () in
  try try_expand_head env ty
  with Cannot_expand | Unify _ -> (* expand_head shall never fail *)
    Btype.backtrack snap;
    repr ty

(* Make sure that the type parameters of the type constructor [ty]
   respect the type constraints *)
let enforce_constraints env ty =
  match ty with
    {desc = Tconstr (path, args, abbrev); level = level} ->
      let decl = Env.find_type path env in
      ignore
        (subst env level (ref Mnil) None decl.type_params args (newvar2 level))
  | _ ->
      assert false

(* Recursively expand the head of a type.
   Also expand #-types. *)
let rec full_expand env ty =
  let ty = repr (expand_head env ty) in
  match ty.desc with
    Tobject (fi, {contents = Some (_, v::_)}) when (repr v).desc = Tvar ->
      newty2 ty.level (Tobject (fi, ref None))
  | _ ->
      ty

(*
   Check whether the abbreviation expands to a well-defined type.
   During the typing of a class, abbreviations for correspondings
   types expand to non-generic types.
*)
let generic_abbrev env path =
  try
    let (_, body) = Env.find_type_expansion path env in
    (repr body).level = generic_level
  with
    Not_found ->
      false


                              (*****************)
                              (*  Occur check  *)
                              (*****************)


exception Occur

(* The marks are already used by [expand_abbrev]... *)
let visited = ref []

let rec non_recursive_abbrev env ty0 ty =
  let ty = repr ty in
  if ty == repr ty0 then raise Recursive_abbrev;
  if not (List.memq ty !visited) then begin
    visited := ty :: !visited;
    match ty.desc with
      Tconstr(p, args, abbrev) ->
        begin try
          non_recursive_abbrev env ty0 (try_expand_head env ty)
        with Cannot_expand ->
          if !Clflags.recursive_types then () else
          iter_type_expr (non_recursive_abbrev env ty0) ty
        end
    | Tobject _ | Tvariant _ ->
        ()
    | _ ->
        if !Clflags.recursive_types then () else
        iter_type_expr (non_recursive_abbrev env ty0) ty
  end

let correct_abbrev env path params ty =
  check_abbrev_env env;
  let ty0 = newgenvar () in
  visited := [];
  let abbrev = Mcons (path, ty0, ty0, Mnil) in
  simple_abbrevs := abbrev;
  try
    non_recursive_abbrev env ty0
      (subst env generic_level (ref abbrev) None [] [] ty);
    simple_abbrevs := Mnil;
    visited := []
  with exn ->
    simple_abbrevs := Mnil;
    visited := [];
    raise exn

let rec occur_rec env visited ty0 ty =
  if ty == ty0  then raise Occur;
  match ty.desc with
    Tconstr(p, tl, abbrev) ->
      begin try
        if List.memq ty visited || !Clflags.recursive_types then raise Occur;
        iter_type_expr (occur_rec env (ty::visited) ty0) ty
      with Occur -> try
        let ty' = try_expand_head env ty in
        (* Maybe we could simply make a recursive call here,
           but it seems it could make the occur check loop
           (see change in rev. 1.58) *)
        if ty' == ty0 || List.memq ty' visited then raise Occur;
        match ty'.desc with
          Tobject _ | Tvariant _ -> ()
        | _ ->
            if not !Clflags.recursive_types then
              iter_type_expr (occur_rec env (ty'::visited) ty0) ty'
      with Cannot_expand ->
        if not !Clflags.recursive_types then raise Occur
      end
  | Tobject _ | Tvariant _ ->
      ()
  | _ ->
      if not !Clflags.recursive_types then
        iter_type_expr (occur_rec env visited ty0) ty

let type_changed = ref false (* trace possible changes to the studied type *)

let merge r b = if b then r := true

let occur env ty0 ty =
  let old = !type_changed in
  try
    while type_changed := false; occur_rec env [] ty0 ty; !type_changed
    do () (* prerr_endline "changed" *) done;
    merge type_changed old
  with exn ->
    merge type_changed old;
    raise (match exn with Occur -> Unify [] | _ -> exn)


                   (*****************************)
                   (*  Polymorphic Unification  *)
                   (*****************************)

(* Since we cannot duplicate universal variables, unification must
   be done at meta-level, using bindings in univar_pairs *)
let rec unify_univar t1 t2 = function
    (cl1, cl2) :: rem ->
      let find_univ t cl =
        try
          let (_, r) = List.find (fun (t',_) -> t == repr t') cl in
          Some r
        with Not_found -> None
      in
      begin match find_univ t1 cl1, find_univ t2 cl2 with
        Some {contents=Some t'2}, Some _ when t2 == repr t'2 ->
          ()
      | Some({contents=None} as r1), Some({contents=None} as r2) ->
          set_univar r1 t2; set_univar r2 t1
      | None, None ->
          unify_univar t1 t2 rem
      | _ ->
          raise (Unify [])
      end
  | [] -> raise (Unify [])

module TypeMap = Map.Make (TypeOps)

(* Test the occurence of free univars in a type *)
(* that's way too expansive. Must do some kind of cacheing *)
let occur_univar env ty =
  let visited = ref TypeMap.empty in
  let rec occur_rec bound ty =
    let ty = repr ty in
    if ty.level >= lowest_level &&
      if TypeSet.is_empty bound then
        (ty.level <- pivot_level - ty.level; true)
      else try
        let bound' = TypeMap.find ty !visited in
        if TypeSet.exists (fun x -> not (TypeSet.mem x bound)) bound' then
          (visited := TypeMap.add ty (TypeSet.inter bound bound') !visited;
           true)
        else false
      with Not_found ->
        visited := TypeMap.add ty bound !visited;
        true
    then
      match ty.desc with
        Tunivar ->
          if not (TypeSet.mem ty bound) then raise (Unify [ty, newgenvar()])
      | Tpoly (ty, tyl) ->
          let bound = List.fold_right TypeSet.add (List.map repr tyl) bound in
          occur_rec bound  ty
      | Tconstr (_, [], _) -> ()
      | Tconstr (p, tl, _) ->
          begin try
            let td = Env.find_type p env in
            List.iter2
              (fun t (pos,neg,_) -> if pos || neg then occur_rec bound t)
              tl td.type_variance
          with Not_found ->
            List.iter (occur_rec bound) tl
          end
      | _ -> iter_type_expr (occur_rec bound) ty
  in
  try
    occur_rec TypeSet.empty ty; unmark_type ty
  with exn ->
    unmark_type ty; raise exn

(* Grouping univars by families according to their binders *)
let add_univars =
  List.fold_left (fun s (t,_) -> TypeSet.add (repr t) s)

let get_univar_family univar_pairs univars =
  if univars = [] then TypeSet.empty else
  let rec insert s = function
      cl1, (_::_ as cl2) ->
        if List.exists (fun (t1,_) -> TypeSet.mem (repr t1) s) cl1 then
          add_univars s cl2
        else s
    | _ -> s
  in
  let s = List.fold_right TypeSet.add univars TypeSet.empty in
  List.fold_left insert s univar_pairs

(* Whether a family of univars escapes from a type *)
let univars_escape env univar_pairs vl ty =
  let family = get_univar_family univar_pairs vl in
  let visited = ref TypeSet.empty in
  let rec occur t =
    let t = repr t in
    if TypeSet.mem t !visited then () else begin
      visited := TypeSet.add t !visited;
      match t.desc with
        Tpoly (t, tl) ->
          if List.exists (fun t -> TypeSet.mem (repr t) family) tl then ()
          else occur t
      | Tunivar ->
          if TypeSet.mem t family then raise Occur
      | Tconstr (_, [], _) -> ()
      | Tconstr (p, tl, _) ->
          begin try
            let td = Env.find_type p env in
            List.iter2 (fun t (pos,neg,_) -> if pos || neg then occur t)
              tl td.type_variance
          with Not_found ->
            List.iter occur tl
          end
      | _ ->
          iter_type_expr occur t
    end
  in
  try occur ty; false with Occur -> true

(* Wrapper checking that no variable escapes and updating univar_pairs *)
let enter_poly env univar_pairs t1 tl1 t2 tl2 f =
  let old_univars = !univar_pairs in
  let known_univars =
    List.fold_left (fun s (cl,_) -> add_univars s cl)
      TypeSet.empty old_univars
  in
  let tl1 = List.map repr tl1 and tl2 = List.map repr tl2 in
  if List.exists (fun t -> TypeSet.mem t known_univars) tl1 &&
    univars_escape env old_univars tl1 (newty(Tpoly(t2,tl2)))
  || List.exists (fun t -> TypeSet.mem t known_univars) tl2 &&
    univars_escape env old_univars tl2 (newty(Tpoly(t1,tl1)))
  then raise (Unify []);
  let cl1 = List.map (fun t -> t, ref None) tl1
  and cl2 = List.map (fun t -> t, ref None) tl2 in
  univar_pairs := (cl1,cl2) :: (cl2,cl1) :: old_univars;
  try let res = f t1 t2 in univar_pairs := old_univars; res
  with exn -> univar_pairs := old_univars; raise exn

let univar_pairs = ref []


                              (*****************)
                              (*  Unification  *)
                              (*****************)



let rec has_cached_expansion p abbrev =
  match abbrev with
    Mnil                   -> false
  | Mcons(p', _, _, rem)   -> Path.same p p' || has_cached_expansion p rem
  | Mlink rem              -> has_cached_expansion p !rem

(**** Transform error trace ****)
(* +++ Move it to some other place ? *)

let expand_trace env trace =
  List.fold_right
    (fun (t1, t2) rem ->
       (repr t1, full_expand env t1)::(repr t2, full_expand env t2)::rem)
    trace []

(* build a dummy variant type *)
let mkvariant fields closed =
  newgenty
    (Tvariant
       {row_fields = fields; row_closed = closed; row_more = newvar();
        row_bound = []; row_fixed = false; row_name = None })

(**** Unification ****)

(* Return whether [t0] occurs in [ty]. Objects are also traversed. *)
let deep_occur t0 ty =
  let rec occur_rec ty =
    let ty = repr ty in
    if ty.level >= lowest_level then begin
      if ty == t0 then raise Occur;
      ty.level <- pivot_level - ty.level;
      iter_type_expr occur_rec ty
    end
  in
  try
    occur_rec ty; unmark_type ty; false
  with Occur ->
    unmark_type ty; true

(*
   1. When unifying two non-abbreviated types, one type is made a link
      to the other. When unifying an abbreviated type with a
      non-abbreviated type, the non-abbreviated type is made a link to
      the other one. When unifying to abbreviated types, these two
      types are kept distincts, but they are made to (temporally)
      expand to the same type.
   2. Abbreviations with at least one parameter are systematically
      expanded. The overhead does not seem to high, and that way
      abbreviations where some parameters does not appear in the
      expansion, such as ['a t = int], are correctly handled. In
      particular, for this example, unifying ['a t] with ['b t] keeps
      ['a] and ['b] distincts. (Is it really important ?)
   3. Unifying an abbreviation ['a t = 'a] with ['a] should not yield
      ['a t as 'a]. Indeed, the type variable would otherwise be lost.
      This problem occurs for abbreviations expanding to a type
      variable, but also to many other constrained abbreviations (for
      instance, [(< x : 'a > -> unit) t = <x : 'a>]). The solution is
      that, if an abbreviation is unified with some subpart of its
      parameters, then the parameter actually does not get
      abbreviated.  It would be possible to check whether some
      information is indeed lost, but it probably does not worth it.
*)
let rec unify env t1 t2 =
  (* First step: special cases (optimizations) *)
  if t1 == t2 then () else
  let t1 = repr t1 in
  let t2 = repr t2 in
  if t1 == t2 then () else

  try
    type_changed := true;
    match (t1.desc, t2.desc) with
      (Tvar, Tconstr _) when deep_occur t1 t2 ->
        unify2 env t1 t2
    | (Tconstr _, Tvar) when deep_occur t2 t1 ->
        unify2 env t1 t2
    | (Tvar, _) ->
        occur env t1 t2; occur_univar env t2;
        update_level env t1.level t2;
        link_type t1 t2
    | (_, Tvar) ->
        occur env t2 t1; occur_univar env t1;
        update_level env t2.level t1;
        link_type t2 t1
    | (Tunivar, Tunivar) ->
        unify_univar t1 t2 !univar_pairs;
        update_level env t1.level t2;
        link_type t1 t2
    | (Tconstr (p1, [], a1), Tconstr (p2, [], a2))
          when Path.same p1 p2
            (* This optimization assumes that t1 does not expand to t2
               (and conversely), so we fall back to the general case
               when any of the types has a cached expansion. *)
            && not (has_cached_expansion p1 !a1
                 || has_cached_expansion p2 !a2) ->
        update_level env t1.level t2;
        link_type t1 t2
    | _ ->
        unify2 env t1 t2
  with Unify trace ->
    raise (Unify ((t1, t2)::trace))

and unify2 env t1 t2 =
  (* Second step: expansion of abbreviations *)
  let rec expand_both t1'' t2'' =
    let t1' = expand_head_unif env t1 in
    let t2' = expand_head_unif env t2 in
    (* Expansion may have changed the representative of the types... *)
    if t1' == t1'' && t2' == t2'' then (t1',t2') else
    expand_both t1' t2'
  in
  let t1', t2' = expand_both t1 t2 in
  if t1' == t2' then () else

  let t1 = repr t1 and t2 = repr t2 in
  if (t1 == t1') || (t2 != t2') then
    unify3 env t1 t1' t2 t2'
  else
    try unify3 env t2 t2' t1 t1' with Unify trace ->
      raise (Unify (List.map (fun (x, y) -> (y, x)) trace))

and unify3 env t1 t1' t2 t2' =
  (* Third step: truly unification *)
  (* Assumes either [t1 == t1'] or [t2 != t2'] *)
  let d1 = t1'.desc and d2 = t2'.desc in

  let create_recursion = (t2 != t2') && (deep_occur t1' t2) in
  occur env t1' t2;
  update_level env t1'.level t2;
  link_type t1' t2;

  try
    begin match (d1, d2) with
      (Tvar, _) ->
        occur_univar env t2
    | (_, Tvar) ->
        let td1 = newgenty d1 in
        occur env t2' td1;
        occur_univar env td1;
        if t1 == t1' then begin
          (* The variable must be instantiated... *)
          let ty = newty2 t1'.level d1 in
          update_level env t2'.level ty;
          link_type t2' ty
        end else begin
          log_type t1';
          t1'.desc <- d1;
          update_level env t2'.level t1;
          link_type t2' t1
        end
    | (Tarrow (l1, t1, u1, c1), Tarrow (l2, t2, u2, c2)) when l1 = l2
      || !Clflags.classic && not (is_optional l1 || is_optional l2) ->
        unify env t1 t2; unify env u1 u2;
        begin match commu_repr c1, commu_repr c2 with
          Clink r, c2 -> set_commu r c2
        | c1, Clink r -> set_commu r c1
        | _ -> ()
        end
    | (Ttuple tl1, Ttuple tl2) ->
        unify_list env tl1 tl2
    | (Tconstr (p1, tl1, _), Tconstr (p2, tl2, _)) when Path.same p1 p2 ->
        unify_list env tl1 tl2
    | (Tobject (fi1, nm1), Tobject (fi2, _)) ->
        unify_fields env fi1 fi2;
        (* Type [t2'] may have been instantiated by [unify_fields] *)
        (* XXX One should do some kind of unification... *)
        begin match (repr t2').desc with
          Tobject (_, {contents = Some (_, va::_)})
          when let va = repr va in List.mem va.desc [Tvar; Tunivar; Tnil] ->
            ()
        | Tobject (_, nm2) ->
            set_name nm2 !nm1
        | _ ->
            ()
        end
    | (Tvariant row1, Tvariant row2) ->
        unify_row env row1 row2
    | (Tfield _, Tfield _) ->           (* Actually unused *)
        unify_fields env t1' t2'
    | (Tfield(f,kind,_,rem), Tnil) | (Tnil, Tfield(f,kind,_,rem)) ->
        begin match field_kind_repr kind with
          Fvar r when f <> dummy_method -> set_kind r Fabsent
        | _      -> raise (Unify [])
        end
    | (Tnil, Tnil) ->
        ()
    | (Tpoly (t1, []), Tpoly (t2, [])) ->
        unify env t1 t2
    | (Tpoly (t1, tl1), Tpoly (t2, tl2)) ->
        enter_poly env univar_pairs t1 tl1 t2 tl2 (unify env)
    | (_, _) ->
        raise (Unify [])
    end;

(* XXX Commentaires + changer "create_recursion" *)
    if create_recursion then begin
      match t2.desc with
        Tconstr (p, tl, abbrev) ->
          forget_abbrev abbrev p;
          let t2'' = expand_head_unif env t2 in
          if not (closed_parameterized_type tl t2'') then
            link_type (repr t2) (repr t2')
      | _ ->
          () (* t2 has already been expanded by update_level *)
    end

(*
    (*
       Can only be done afterwards, once the row variable has
       (possibly) been instantiated.
    *)
    if t1 != t1' (* && t2 != t2' *) then begin
      match (t1.desc, t2.desc) with
        (Tconstr (p, ty::_, _), _)
            when ((repr ty).desc <> Tvar)
              && weak_abbrev p
              && not (deep_occur t1 t2) ->
          update_level env t1.level t2;
          link_type t1 t2
      | (_, Tconstr (p, ty::_, _))
            when ((repr ty).desc <> Tvar)
              && weak_abbrev p
              && not (deep_occur t2 t1) ->
          update_level env t2.level t1;
          link_type t2 t1;
          link_type t1' t2'
      | _ ->
          ()
    end
*)
  with Unify trace ->
    t1'.desc <- d1;
    raise (Unify trace)

and unify_list env tl1 tl2 =
  if List.length tl1 <> List.length tl2 then
    raise (Unify []);
  List.iter2 (unify env) tl1 tl2

and unify_fields env ty1 ty2 =          (* Optimization *)
  let (fields1, rest1) = flatten_fields ty1
  and (fields2, rest2) = flatten_fields ty2 in
  let (pairs, miss1, miss2) = associate_fields fields1 fields2 in
  let l1 = (repr ty1).level and l2 = (repr ty2).level in
  let va =
    if miss1 = [] then rest2
    else if miss2 = [] then rest1
    else newty2 (min l1 l2) Tvar
  in
  let d1 = rest1.desc and d2 = rest2.desc in
  try
    unify env (build_fields l1 miss1 va) rest2;
    unify env rest1 (build_fields l2 miss2 va);
    List.iter
      (fun (n, k1, t1, k2, t2) ->
        unify_kind k1 k2;
        try unify env t1 t2 with Unify trace ->
          raise (Unify ((newty (Tfield(n, k1, t1, va)),
                         newty (Tfield(n, k2, t2, va)))::trace)))
      pairs
  with exn ->
    log_type rest1; rest1.desc <- d1;
    log_type rest2; rest2.desc <- d2;
    raise exn

and unify_kind k1 k2 =
  let k1 = field_kind_repr k1 in
  let k2 = field_kind_repr k2 in
  if k1 == k2 then () else
  match k1, k2 with
    (Fvar r, (Fvar _ | Fpresent)) -> set_kind r k2
  | (Fpresent, Fvar r)            -> set_kind r k1
  | (Fpresent, Fpresent)          -> ()
  | _                             -> assert false

and unify_pairs env tpl =
  List.iter (fun (t1, t2) -> unify env t1 t2) tpl

and unify_row env row1 row2 =
  let row1 = row_repr row1 and row2 = row_repr row2 in
  let rm1 = row_more row1 and rm2 = row_more row2 in
  if rm1 == rm2 then () else
  let r1, r2, pairs = merge_row_fields row1.row_fields row2.row_fields in
  if r1 <> [] && r2 <> [] then begin
    let ht = Hashtbl.create (List.length r1) in
    List.iter (fun (l,_) -> Hashtbl.add ht (hash_variant l) l) r1;
    List.iter
      (fun (l,_) ->
        try raise (Tags(l, Hashtbl.find ht (hash_variant l)))
        with Not_found -> ())
      r2
  end;
  let more =
    if row1.row_fixed then rm1 else
    if row2.row_fixed then rm2 else
    newgenvar ()
  in update_level env (min rm1.level rm2.level) more;
  let fixed = row1.row_fixed || row2.row_fixed
  and closed = row1.row_closed || row2.row_closed in
  let keep switch =
    List.for_all
      (fun (_,f1,f2) ->
        let f1, f2 = switch f1 f2 in
        row_field_repr f1 = Rabsent || row_field_repr f2 <> Rabsent)
      pairs
  in
  let empty fields =
    List.for_all (fun (_,f) -> row_field_repr f = Rabsent) fields in
  (* Check whether we are going to build an empty type *)
  if closed && (empty r1 || row2.row_closed) && (empty r2 || row1.row_closed)
  && List.for_all
      (fun (_,f1,f2) ->
        row_field_repr f1 = Rabsent || row_field_repr f2 = Rabsent)
      pairs
  then raise (Unify [mkvariant [] true, mkvariant [] true]);
  let name =
    if row1.row_name <> None && (row1.row_closed || empty r2) &&
      (not row2.row_closed || keep (fun f1 f2 -> f1, f2) && empty r1)
    then row1.row_name
    else if row2.row_name <> None && (row2.row_closed || empty r1) &&
      (not row1.row_closed || keep (fun f1 f2 -> f2, f1) && empty r2)
    then row2.row_name
    else None
  in
  let bound = row1.row_bound @ row2.row_bound in
  let row0 = {row_fields = []; row_more = more; row_bound = bound;
              row_closed = closed; row_fixed = fixed; row_name = name} in
  let set_more row rest =
    let rest =
      if closed then
        filter_row_fields row.row_closed rest
      else rest in
    if rest <> [] && (row.row_closed || row.row_fixed)
    || closed && row.row_fixed && not row.row_closed then begin
      let t1 = mkvariant [] true and t2 = mkvariant rest false in
      raise (Unify [if row == row1 then (t1,t2) else (t2,t1)])
    end;
    let rm = row_more row in
    if row.row_fixed then
      if row0.row_more == rm then () else
      if rm.desc = Tvar then link_type rm row0.row_more else
      unify env rm row0.row_more
    else
      let ty = newty2 generic_level (Tvariant {row0 with row_fields = rest}) in
      update_level env rm.level ty;
      link_type rm ty
  in
  let md1 = rm1.desc and md2 = rm2.desc in
  begin try
    set_more row2 r1;
    set_more row1 r2;
    List.iter
      (fun (l,f1,f2) ->
        try unify_row_field env row1.row_fixed row2.row_fixed l f1 f2
        with Unify trace ->
          raise (Unify ((mkvariant [l,f1] true,
                         mkvariant [l,f2] true) :: trace)))
      pairs;
  with exn ->
    log_type rm1; rm1.desc <- md1; log_type rm2; rm2.desc <- md2; raise exn
  end

and unify_row_field env fixed1 fixed2 l f1 f2 =
  let f1 = row_field_repr f1 and f2 = row_field_repr f2 in
  if f1 == f2 then () else
  match f1, f2 with
    Rpresent(Some t1), Rpresent(Some t2) -> unify env t1 t2
  | Rpresent None, Rpresent None -> ()
  | Reither(c1, tl1, m1, e1), Reither(c2, tl2, m2, e2) ->
      if e1 == e2 then () else
      let redo =
        (m1 || m2) &&
        begin match tl1 @ tl2 with [] -> false
        | t1 :: tl ->
            if c1 || c2 then raise (Unify []);
            List.iter (unify env t1) tl;
            !e1 <> None || !e2 <> None
        end in
      if redo then unify_row_field env fixed1 fixed2 l f1 f2 else
      let tl1 = List.map repr tl1 and tl2 = List.map repr tl2 in
      let rec remq tl = function [] -> []
        | ty :: tl' ->
            if List.memq ty tl then remq tl tl' else ty :: remq tl tl'
      in
      let tl2' = remq tl2 tl1 and tl1' = remq tl1 tl2 in
      let e = ref None in
      let f1' = Reither(c1 || c2, tl1', m1 || m2, e)
      and f2' = Reither(c1 || c2, tl2', m1 || m2, e) in
      set_row_field e1 f1'; set_row_field e2 f2';
  | Reither(_, _, false, e1), Rabsent -> set_row_field e1 f2
  | Rabsent, Reither(_, _, false, e2) -> set_row_field e2 f1
  | Rabsent, Rabsent -> ()
  | Reither(false, tl, _, e1), Rpresent(Some t2) when not fixed1 ->
      set_row_field e1 f2;
      (try List.iter (fun t1 -> unify env t1 t2) tl
      with exn -> e1 := None; raise exn)
  | Rpresent(Some t1), Reither(false, tl, _, e2) when not fixed2 ->
      set_row_field e2 f1;
      (try List.iter (unify env t1) tl
      with exn -> e2 := None; raise exn)
  | Reither(true, [], _, e1), Rpresent None when not fixed1 ->
      set_row_field e1 f2
  | Rpresent None, Reither(true, [], _, e2) when not fixed2 ->
      set_row_field e2 f1
  | _ -> raise (Unify [])


let unify env ty1 ty2 =
  try
    unify env ty1 ty2
  with Unify trace ->
    raise (Unify (expand_trace env trace))

let unify_var env t1 t2 =
  let t1 = repr t1 and t2 = repr t2 in
  if t1 == t2 then () else
  match t1.desc with
    Tvar ->
      begin try
        occur env t1 t2;
        update_level env t1.level t2;
        link_type t1 t2
      with Unify trace ->
        raise (Unify (expand_trace env ((t1,t2)::trace)))
      end
  | _ ->
      unify env t1 t2

let _ = unify' := unify_var

let unify_pairs env ty1 ty2 pairs =
  univar_pairs := pairs;
  unify env ty1 ty2

let unify env ty1 ty2 =
  univar_pairs := [];
  unify env ty1 ty2


(**** Special cases of unification ****)

(*
   Unify [t] and [l:'a -> 'b]. Return ['a] and ['b].
   In label mode, label mismatch is accepted when
   (1) the requested label is ""
   (2) the original label is not optional
*)
let rec filter_arrow env t l =
  let t = expand_head_unif env t in
  match t.desc with
    Tvar ->
      let t1 = newvar () and t2 = newvar () in
      let t' = newty (Tarrow (l, t1, t2, Cok)) in
      update_level env t.level t';
      link_type t t';
      (t1, t2)
  | Tarrow(l', t1, t2, _)
    when l = l' || !Clflags.classic && l = "" && not (is_optional l') ->
      (t1, t2)
  | _ ->
      raise (Unify [])

(* Used by [filter_method]. *)
let rec filter_method_field env name priv ty =
  let ty = repr ty in
  match ty.desc with
    Tvar ->
      let level = ty.level in
      let ty1 = newvar2 level and ty2 = newvar2 level in
      let ty' = newty2 level (Tfield (name,
                                      begin match priv with
                                        Private -> Fvar (ref None)
                                      | Public  -> Fpresent
                                      end,
                                      ty1, ty2))
      in
      link_type ty ty';
      ty1
  | Tfield(n, kind, ty1, ty2) ->
      let kind = field_kind_repr kind in
      if (n = name) && (kind <> Fabsent) then begin
        if priv = Public then
          unify_kind kind Fpresent;
        ty1
      end else
        filter_method_field env name priv ty2
  | _ ->
      raise (Unify [])

(* Unify [ty] and [< name : 'a; .. >]. Return ['a]. *)
let rec filter_method env name priv ty =
  let ty = expand_head_unif env ty in
  match ty.desc with
    Tvar ->
      let ty1 = newvar () in
      let ty' = newobj ty1 in
      update_level env ty.level ty';
      link_type ty ty';
      filter_method_field env name priv ty1
  | Tobject(f, _) ->
      filter_method_field env name priv f
  | _ ->
      raise (Unify [])

let check_filter_method env name priv ty =
  ignore(filter_method env name priv ty)

let filter_self_method env lab priv meths ty =
  let ty' = filter_method env lab priv ty in
  try
    Meths.find lab !meths
  with Not_found ->
    let pair = (Ident.create lab, ty') in
    meths := Meths.add lab pair !meths;
    pair


                        (***********************************)
                        (*  Matching between type schemes  *)
                        (***********************************)

(*
   Update the level of [ty]. First check that the levels of generic
   variables from the subject are not lowered.
*)
let moregen_occur env level ty =
  let rec occur ty =
    let ty = repr ty in
    if ty.level > level then begin
      if ty.desc = Tvar && ty.level >= generic_level - 1 then raise Occur;
      ty.level <- pivot_level - ty.level;
      match ty.desc with
        Tvariant row when static_row row ->
          iter_row occur row
      | _ ->
          iter_type_expr occur ty
    end
  in
  begin try
    occur ty; unmark_type ty
  with Occur ->
    unmark_type ty; raise (Unify [])
  end;
  (* also check for free univars *)
  occur_univar env ty;
  update_level env level ty

let rec moregen inst_nongen type_pairs env t1 t2 =
  if t1 == t2 then () else
  let t1 = repr t1 in
  let t2 = repr t2 in
  if t1 == t2 then () else

  try
    match (t1.desc, t2.desc) with
      (Tunivar, Tunivar) ->
        unify_univar t1 t2 !univar_pairs
    | (Tvar, _) when if inst_nongen then t1.level <> generic_level - 1
                                    else t1.level =  generic_level ->
        moregen_occur env t1.level t2;
        occur env t1 t2;
        link_type t1 t2
    | (Tconstr (p1, [], _), Tconstr (p2, [], _)) when Path.same p1 p2 ->
        ()
    | _ ->
        let t1' = expand_head_unif env t1 in
        let t2' = expand_head_unif env t2 in
        (* Expansion may have changed the representative of the types... *)
        let t1' = repr t1' and t2' = repr t2' in
        if t1' == t2' then () else
        begin try
          TypePairs.find type_pairs (t1', t2')
        with Not_found ->
          TypePairs.add type_pairs (t1', t2') ();
          match (t1'.desc, t2'.desc) with
            (Tvar, _) when if inst_nongen then t1'.level <> generic_level - 1
                                          else t1'.level =  generic_level ->
              moregen_occur env t1'.level t2;
              link_type t1' t2
          | (Tarrow (l1, t1, u1, _), Tarrow (l2, t2, u2, _)) when l1 = l2
            || !Clflags.classic && not (is_optional l1 || is_optional l2) ->
              moregen inst_nongen type_pairs env t1 t2;
              moregen inst_nongen type_pairs env u1 u2
          | (Ttuple tl1, Ttuple tl2) ->
              moregen_list inst_nongen type_pairs env tl1 tl2
          | (Tconstr (p1, tl1, _), Tconstr (p2, tl2, _))
                when Path.same p1 p2 ->
              moregen_list inst_nongen type_pairs env tl1 tl2
          | (Tvariant row1, Tvariant row2) ->
              moregen_row inst_nongen type_pairs env row1 row2
          | (Tobject (fi1, nm1), Tobject (fi2, nm2)) ->
              moregen_fields inst_nongen type_pairs env fi1 fi2
          | (Tfield _, Tfield _) ->           (* Actually unused *)
              moregen_fields inst_nongen type_pairs env t1' t2'
          | (Tnil, Tnil) ->
              ()
          | (Tpoly (t1, []), Tpoly (t2, [])) ->
              moregen inst_nongen type_pairs env t1 t2
          | (Tpoly (t1, tl1), Tpoly (t2, tl2)) ->
              enter_poly env univar_pairs t1 tl1 t2 tl2
                (moregen inst_nongen type_pairs env)
          | (_, _) ->
              raise (Unify [])
        end
  with Unify trace ->
    raise (Unify ((t1, t2)::trace))

and moregen_list inst_nongen type_pairs env tl1 tl2 =
  if List.length tl1 <> List.length tl2 then
    raise (Unify []);
  List.iter2 (moregen inst_nongen type_pairs env) tl1 tl2

and moregen_fields inst_nongen type_pairs env ty1 ty2 =
  let (fields1, rest1) = flatten_fields ty1
  and (fields2, rest2) = flatten_fields ty2 in
  let (pairs, miss1, miss2) = associate_fields fields1 fields2 in
  if miss1 <> [] then raise (Unify []);
  moregen inst_nongen type_pairs env rest1
    (build_fields (repr ty2).level miss2 rest2);
  List.iter
    (fun (n, k1, t1, k2, t2) ->
       moregen_kind k1 k2;
       try moregen inst_nongen type_pairs env t1 t2 with Unify trace ->
         raise (Unify ((newty (Tfield(n, k1, t1, rest2)),
                        newty (Tfield(n, k2, t2, rest2)))::trace)))
    pairs

and moregen_kind k1 k2 =
  let k1 = field_kind_repr k1 in
  let k2 = field_kind_repr k2 in
  if k1 == k2 then () else
  match k1, k2 with
    (Fvar r, (Fvar _ | Fpresent))  -> set_kind r k2
  | (Fpresent, Fpresent)           -> ()
  | _                              -> raise (Unify [])

and moregen_row inst_nongen type_pairs env row1 row2 =
  let row1 = row_repr row1 and row2 = row_repr row2 in
  let r1, r2, pairs = merge_row_fields row1.row_fields row2.row_fields in
  let r1, r2 =
    if row2.row_closed then
      filter_row_fields true r1, filter_row_fields false r2
    else r1, r2
  in
  if r1 <> [] || row1.row_closed && (not row2.row_closed || r2 <> [])
  then raise (Unify []);
  let rm1 = repr row1.row_more and rm2 = repr row2.row_more in
  let univ =
    match rm1.desc, rm2.desc with
      Tunivar, Tunivar ->
        unify_univar rm1 rm2 !univar_pairs;
        true
    | Tunivar, _ | _, Tunivar ->
        raise (Unify [])
    | _ ->
        if not (static_row row2) then moregen_occur env rm1.level rm2;
        let ext =
          if r2 = [] then rm2 else
          let row_ext = {row2 with row_fields = r2} in
          iter_row (moregen_occur env rm1.level) row_ext;
          newty2 rm1.level (Tvariant row_ext)
        in
        if ext != rm1 then link_type rm1 ext;
        false
  in
  List.iter
    (fun (l,f1,f2) ->
      let f1 = row_field_repr f1 and f2 = row_field_repr f2 in
      if f1 == f2 then () else
      match f1, f2 with
        Rpresent(Some t1), Rpresent(Some t2) ->
          moregen inst_nongen type_pairs env t1 t2
      | Rpresent None, Rpresent None -> ()
      | Reither(false, tl1, _, e1), Rpresent(Some t2) when not univ ->
          set_row_field e1 f2;
          List.iter (fun t1 -> moregen inst_nongen type_pairs env t1 t2) tl1
      | Reither(c1, tl1, _, e1), Reither(c2, tl2, m2, e2) ->
          if e1 != e2 then begin
            if c1 && not c2 then raise(Unify []);
            set_row_field e1 (Reither (c2, [], m2, e2));
            if List.length tl1 = List.length tl2 then
              List.iter2 (moregen inst_nongen type_pairs env) tl1 tl2
            else match tl2 with
              t2 :: _ ->
                List.iter (fun t1 -> moregen inst_nongen type_pairs env t1 t2)
                  tl1
            | [] ->
                if tl1 <> [] then raise (Unify [])
          end
      | Reither(true, [], _, e1), Rpresent None when not univ ->
          set_row_field e1 f2
      | Reither(_, _, _, e1), Rabsent when not univ ->
          set_row_field e1 f2
      | Rabsent, Rabsent -> ()
      | _ -> raise (Unify []))
    pairs

(* Must empty univar_pairs first *)
let moregen inst_nongen type_pairs env patt subj =
  univar_pairs := [];
  moregen inst_nongen type_pairs env patt subj

(*
   Non-generic variable can be instanciated only if [inst_nongen] is
   true. So, [inst_nongen] should be set to false if the subject might
   contain non-generic variables (and we do not want them to be
   instanciated).
   Usually, the subject is given by the user, and the pattern
   is unimportant.  So, no need to propagate abbreviations.
*)
let moregeneral env inst_nongen pat_sch subj_sch =
  let old_level = !current_level in
  current_level := generic_level - 1;
  (*
     Generic variables are first duplicated with [instance].  So,
     their levels are lowered to [generic_level - 1].  The subject is
     then copied with [duplicate_type].  That way, its levels won't be
     changed.
  *)
  let subj = duplicate_type (instance subj_sch) in
  current_level := generic_level;
  (* Duplicate generic variables *)
  let patt = instance pat_sch in
  let res =
    try moregen inst_nongen (TypePairs.create 13) env patt subj; true with
      Unify _ -> false
  in
  current_level := old_level;
  res


(* Alternative approach: "rigidify" a type scheme,
   and check validity after unification *)
(* Simpler, no? *)

let rec rigidify_rec vars ty =
  let ty = repr ty in
  if ty.level >= lowest_level then begin
    ty.level <- pivot_level - ty.level;
    match ty.desc with
    | Tvar ->
        if not (List.memq ty !vars) then vars := ty :: !vars
    | Tvariant row ->
        let row = row_repr row in
        let more = repr row.row_more in
        if more.desc = Tvar && not row.row_fixed then begin
          let more' = newty2 more.level Tvar in
          let row' = {row with row_fixed=true; row_fields=[]; row_more=more'}
          in link_type more (newty2 ty.level (Tvariant row'))
        end;
        iter_row (rigidify_rec vars) row;
        (* only consider the row variable if the variant is not static *)
        if not (static_row row) then rigidify_rec vars (row_more row)
    | _ ->
        iter_type_expr (rigidify_rec vars) ty
  end

let rigidify ty =
  let vars = ref [] in
  rigidify_rec vars ty;
  unmark_type ty;
  !vars

let all_distinct_vars env vars =
  let tyl = ref [] in
  List.for_all
    (fun ty ->
      let ty = expand_head env ty in
      if List.memq ty !tyl then false else
      (tyl := ty :: !tyl; ty.desc = Tvar))
    vars

let matches env ty ty' =
  let snap = snapshot () in
  let vars = rigidify ty in
  cleanup_abbrev ();
  let ok =
    try unify env ty ty'; all_distinct_vars env vars
    with Unify _ -> false
  in
  backtrack snap;
  ok


                 (*********************************************)
                 (*  Equivalence between parameterized types  *)
                 (*********************************************)

let normalize_subst subst =
  if List.exists
      (function {desc=Tlink _}, _ | _, {desc=Tlink _} -> true | _ -> false)
      !subst
  then subst := List.map (fun (t1,t2) -> repr t1, repr t2) !subst

let rec eqtype rename type_pairs subst env t1 t2 =
  if t1 == t2 then () else
  let t1 = repr t1 in
  let t2 = repr t2 in
  if t1 == t2 then () else

  try
    match (t1.desc, t2.desc) with
      (Tvar, Tvar) when rename ->
        begin try
          normalize_subst subst;
          if List.assq t1 !subst != t2 then raise (Unify [])
        with Not_found ->
          subst := (t1, t2) :: !subst
        end
    | (Tconstr (p1, [], _), Tconstr (p2, [], _)) when Path.same p1 p2 ->
        ()
    | _ ->
        let t1' = expand_head_unif env t1 in
        let t2' = expand_head_unif env t2 in
        (* Expansion may have changed the representative of the types... *)
        let t1' = repr t1' and t2' = repr t2' in
        if t1' == t2' then () else
        begin try
          TypePairs.find type_pairs (t1', t2')
        with Not_found ->
          TypePairs.add type_pairs (t1', t2') ();
          match (t1'.desc, t2'.desc) with
            (Tvar, Tvar) when rename ->
              begin try
                normalize_subst subst;
                if List.assq t1' !subst != t2' then raise (Unify [])
              with Not_found ->
                subst := (t1', t2') :: !subst
              end
          | (Tarrow (l1, t1, u1, _), Tarrow (l2, t2, u2, _)) when l1 = l2
            || !Clflags.classic && not (is_optional l1 || is_optional l2) ->
              eqtype rename type_pairs subst env t1 t2;
              eqtype rename type_pairs subst env u1 u2;
          | (Ttuple tl1, Ttuple tl2) ->
              eqtype_list rename type_pairs subst env tl1 tl2
          | (Tconstr (p1, tl1, _), Tconstr (p2, tl2, _))
                when Path.same p1 p2 ->
              eqtype_list rename type_pairs subst env tl1 tl2
          | (Tvariant row1, Tvariant row2) ->
              eqtype_row rename type_pairs subst env row1 row2
          | (Tobject (fi1, nm1), Tobject (fi2, nm2)) ->
              eqtype_fields rename type_pairs subst env fi1 fi2
          | (Tfield _, Tfield _) ->       (* Actually unused *)
              eqtype_fields rename type_pairs subst env t1' t2'
          | (Tnil, Tnil) ->
              ()
          | (Tpoly (t1, []), Tpoly (t2, [])) ->
              eqtype rename type_pairs subst env t1 t2
          | (Tpoly (t1, tl1), Tpoly (t2, tl2)) ->
              enter_poly env univar_pairs t1 tl1 t2 tl2
                (eqtype rename type_pairs subst env)
          | (Tunivar, Tunivar) ->
              unify_univar t1 t2 !univar_pairs
          | (_, _) ->
              raise (Unify [])
        end
  with Unify trace ->
    raise (Unify ((t1, t2)::trace))

and eqtype_list rename type_pairs subst env tl1 tl2 =
  if List.length tl1 <> List.length tl2 then
    raise (Unify []);
  List.iter2 (eqtype rename type_pairs subst env) tl1 tl2

and eqtype_fields rename type_pairs subst env ty1 ty2 =
  let (fields2, rest2) = flatten_fields ty2 in
  (* Try expansion, needed when called from Includecore.type_manifest *)
  try match try_expand_head env rest2 with
    {desc=Tobject(ty2,_)} -> eqtype_fields rename type_pairs subst env ty1 ty2
  | _ -> raise Cannot_expand
  with Cannot_expand ->
  let (fields1, rest1) = flatten_fields ty1 in
  let (pairs, miss1, miss2) = associate_fields fields1 fields2 in
  eqtype rename type_pairs subst env rest1 rest2;
  if (miss1 <> []) || (miss2 <> []) then raise (Unify []);
  List.iter
    (function (n, k1, t1, k2, t2) ->
       eqtype_kind k1 k2;
       try eqtype rename type_pairs subst env t1 t2 with Unify trace ->
         raise (Unify ((newty (Tfield(n, k1, t1, rest2)),
                        newty (Tfield(n, k2, t2, rest2)))::trace)))
    pairs

and eqtype_kind k1 k2 =
  let k1 = field_kind_repr k1 in
  let k2 = field_kind_repr k2 in
  match k1, k2 with
    (Fvar _, Fvar _)
  | (Fpresent, Fpresent) -> ()
  | _                    -> raise (Unify [])

and eqtype_row rename type_pairs subst env row1 row2 =
  (* Try expansion, needed when called from Includecore.type_manifest *)
  try match try_expand_head env (row_more row2) with
    {desc=Tvariant row2} -> eqtype_row rename type_pairs subst env row1 row2
  | _ -> raise Cannot_expand
  with Cannot_expand ->
  let row1 = row_repr row1 and row2 = row_repr row2 in
  let r1, r2, pairs = merge_row_fields row1.row_fields row2.row_fields in
  if row1.row_closed <> row2.row_closed
  || not row1.row_closed && (r1 <> [] || r2 <> [])
  || filter_row_fields false (r1 @ r2) <> []
  then raise (Unify []);
  if not (static_row row1) then
    eqtype rename type_pairs subst env row1.row_more row2.row_more;
  List.iter
    (fun (_,f1,f2) ->
      match row_field_repr f1, row_field_repr f2 with
        Rpresent(Some t1), Rpresent(Some t2) ->
          eqtype rename type_pairs subst env t1 t2
      | Reither(true, [], _, _), Reither(true, [], _, _) ->
          ()
      | Reither(false, t1::tl1, _, _), Reither(false, t2::tl2, _, _) ->
          eqtype rename type_pairs subst env t1 t2;
          if List.length tl1 = List.length tl2 then
            (* if same length allow different types (meaning?) *)
            List.iter2 (eqtype rename type_pairs subst env) tl1 tl2
          else begin
            (* otherwise everything must be equal *)
            List.iter (eqtype rename type_pairs subst env t1) tl2;
            List.iter (fun t1 -> eqtype rename type_pairs subst env t1 t2) tl1
          end
      | Rpresent None, Rpresent None -> ()
      | Rabsent, Rabsent -> ()
      | _ -> raise (Unify []))
    pairs

(* Two modes: with or without renaming of variables *)
let equal env rename tyl1 tyl2 =
  try
    univar_pairs := [];
    eqtype_list rename (TypePairs.create 11) (ref []) env tyl1 tyl2; true
  with
    Unify _ -> false

(* Must empty univar_pairs first *)
let eqtype rename type_pairs subst env t1 t2 =
  univar_pairs := [];
  eqtype rename type_pairs subst env t1 t2


                          (*************************)
                          (*  Class type matching  *)
                          (*************************)


type class_match_failure =
    CM_Virtual_class
  | CM_Parameter_arity_mismatch of int * int
  | CM_Type_parameter_mismatch of (type_expr * type_expr) list
  | CM_Class_type_mismatch of class_type * class_type
  | CM_Parameter_mismatch of (type_expr * type_expr) list
  | CM_Val_type_mismatch of string * (type_expr * type_expr) list
  | CM_Meth_type_mismatch of string * (type_expr * type_expr) list
  | CM_Non_mutable_value of string
  | CM_Non_concrete_value of string
  | CM_Missing_value of string
  | CM_Missing_method of string
  | CM_Hide_public of string
  | CM_Hide_virtual of string * string
  | CM_Public_method of string
  | CM_Private_method of string
  | CM_Virtual_method of string

exception Failure of class_match_failure list

let rec moregen_clty trace type_pairs env cty1 cty2 =
  try
    match cty1, cty2 with
      Tcty_constr (_, _, cty1), _ ->
        moregen_clty true type_pairs env cty1 cty2
    | _, Tcty_constr (_, _, cty2) ->
        moregen_clty true type_pairs env cty1 cty2
    | Tcty_fun (l1, ty1, cty1'), Tcty_fun (l2, ty2, cty2') when l1 = l2 ->
        begin try moregen true type_pairs env ty1 ty2 with Unify trace ->
          raise (Failure [CM_Parameter_mismatch (expand_trace env trace)])
        end;
        moregen_clty false type_pairs env cty1' cty2'
    | Tcty_signature sign1, Tcty_signature sign2 ->
        let ty1 = object_fields (repr sign1.cty_self) in
        let ty2 = object_fields (repr sign2.cty_self) in
        let (fields1, rest1) = flatten_fields ty1
        and (fields2, rest2) = flatten_fields ty2 in
        let (pairs, miss1, miss2) = associate_fields fields1 fields2 in
        List.iter
          (fun (lab, k1, t1, k2, t2) ->
            begin try moregen true type_pairs env t1 t2 with Unify trace ->
              raise (Failure [CM_Meth_type_mismatch
                                 (lab, expand_trace env trace)])
           end)
        pairs;
      Vars.iter
        (fun lab (mut, v, ty) ->
           let (mut', v', ty') = Vars.find lab sign1.cty_vars in
           try moregen true type_pairs env ty' ty with Unify trace ->
             raise (Failure [CM_Val_type_mismatch
                                (lab, expand_trace env trace)]))
        sign2.cty_vars
  | _ ->
      raise (Failure [])
  with
    Failure error when trace ->
      raise (Failure (CM_Class_type_mismatch (cty1, cty2)::error))

let match_class_types env pat_sch subj_sch =
  let type_pairs = TypePairs.create 53 in
  let old_level = !current_level in
  current_level := generic_level - 1;
  (*
     Generic variables are first duplicated with [instance].  So,
     their levels are lowered to [generic_level - 1].  The subject is
     then copied with [duplicate_type].  That way, its levels won't be
     changed.
  *)
  let (_, subj_inst) = instance_class [] subj_sch in
  let subj = duplicate_class_type subj_inst in
  current_level := generic_level;
  (* Duplicate generic variables *)
  let (_, patt) = instance_class [] pat_sch in
  let res =
    let sign1 = signature_of_class_type patt in
    let sign2 = signature_of_class_type subj in
    let t1 = repr sign1.cty_self in
    let t2 = repr sign2.cty_self in
    TypePairs.add type_pairs (t1, t2) ();
    let (fields1, rest1) = flatten_fields (object_fields t1)
    and (fields2, rest2) = flatten_fields (object_fields t2) in
    let (pairs, miss1, miss2) = associate_fields fields1 fields2 in
    let error =
      List.fold_right
        (fun (lab, k, _) err ->
           let err =
             let k = field_kind_repr k in
             begin match k with
               Fvar r -> set_kind r Fabsent; err
             | _      -> CM_Hide_public lab::err
             end
           in
           if Concr.mem lab sign1.cty_concr then err
           else CM_Hide_virtual ("method", lab) :: err)
        miss1 []
    in
    let missing_method = List.map (fun (m, _, _) -> m) miss2 in
    let error =
      (List.map (fun m -> CM_Missing_method m) missing_method) @ error
    in
    (* Always succeeds *)
    moregen true type_pairs env rest1 rest2;
    let error =
      List.fold_right
        (fun (lab, k1, t1, k2, t2) err ->
           try moregen_kind k1 k2; err with
             Unify _ -> CM_Public_method lab::err)
        pairs error
    in
    let error =
      Vars.fold
        (fun lab (mut, vr, ty) err ->
          try
            let (mut', vr', ty') = Vars.find lab sign1.cty_vars in
            if mut = Mutable && mut' <> Mutable then
              CM_Non_mutable_value lab::err
            else if vr = Concrete && vr' <> Concrete then
              CM_Non_concrete_value lab::err
            else
              err
          with Not_found ->
            CM_Missing_value lab::err)
        sign2.cty_vars error
    in
    let error =
      Vars.fold
        (fun lab (_,vr,_) err ->
          if vr = Virtual && not (Vars.mem lab sign2.cty_vars) then
            CM_Hide_virtual ("instance variable", lab) :: err
          else err)
        sign1.cty_vars error
    in
    let error =
      List.fold_right
        (fun e l ->
           if List.mem e missing_method then l else CM_Virtual_method e::l)
        (Concr.elements (Concr.diff sign2.cty_concr sign1.cty_concr))
        error
    in
    match error with
      [] ->
        begin try
          moregen_clty true type_pairs env patt subj;
          []
        with
          Failure r -> r
        end
    | error ->
        CM_Class_type_mismatch (patt, subj)::error
  in
  current_level := old_level;
  res

let rec equal_clty trace type_pairs subst env cty1 cty2 =
  try
    match cty1, cty2 with
      Tcty_constr (_, _, cty1), Tcty_constr (_, _, cty2) ->
        equal_clty true type_pairs subst env cty1 cty2
    | Tcty_constr (_, _, cty1), _ ->
        equal_clty true type_pairs subst env cty1 cty2
    | _, Tcty_constr (_, _, cty2) ->
        equal_clty true type_pairs subst env cty1 cty2
    | Tcty_fun (l1, ty1, cty1'), Tcty_fun (l2, ty2, cty2') when l1 = l2 ->
        begin try eqtype true type_pairs subst env ty1 ty2 with Unify trace ->
          raise (Failure [CM_Parameter_mismatch (expand_trace env trace)])
        end;
        equal_clty false type_pairs subst env cty1' cty2'
    | Tcty_signature sign1, Tcty_signature sign2 ->
        let ty1 = object_fields (repr sign1.cty_self) in
        let ty2 = object_fields (repr sign2.cty_self) in
        let (fields1, rest1) = flatten_fields ty1
        and (fields2, rest2) = flatten_fields ty2 in
        let (pairs, miss1, miss2) = associate_fields fields1 fields2 in
        List.iter
          (fun (lab, k1, t1, k2, t2) ->
             begin try eqtype true type_pairs subst env t1 t2 with
               Unify trace ->
                 raise (Failure [CM_Meth_type_mismatch
                                    (lab, expand_trace env trace)])
             end)
          pairs;
        Vars.iter
          (fun lab (_, _, ty) ->
             let (_, _, ty') = Vars.find lab sign1.cty_vars in
             try eqtype true type_pairs subst env ty ty' with Unify trace ->
               raise (Failure [CM_Val_type_mismatch
                                  (lab, expand_trace env trace)]))
          sign2.cty_vars
    | _ ->
        raise
          (Failure (if trace then []
                    else [CM_Class_type_mismatch (cty1, cty2)]))
  with
    Failure error when trace ->
      raise (Failure (CM_Class_type_mismatch (cty1, cty2)::error))

(* XXX On pourrait autoriser l'instantiation du type des parametres... *)
(* XXX Correct ? (variables de type dans parametres et corps de classe *)
let match_class_declarations env patt_params patt_type subj_params subj_type =
  let type_pairs = TypePairs.create 53 in
  let subst = ref [] in
  let sign1 = signature_of_class_type patt_type in
  let sign2 = signature_of_class_type subj_type in
  let t1 = repr sign1.cty_self in
  let t2 = repr sign2.cty_self in
  TypePairs.add type_pairs (t1, t2) ();
  let (fields1, rest1) = flatten_fields (object_fields t1)
  and (fields2, rest2) = flatten_fields (object_fields t2) in
  let (pairs, miss1, miss2) = associate_fields fields1 fields2 in
  let error =
    List.fold_right
      (fun (lab, k, _) err ->
        let err =
          let k = field_kind_repr k in
          begin match k with
            Fvar r -> err
          | _      -> CM_Hide_public lab::err
          end
        in
        if Concr.mem lab sign1.cty_concr then err
        else CM_Hide_virtual ("method", lab) :: err)
      miss1 []
  in
  let missing_method = List.map (fun (m, _, _) -> m) miss2 in
  let error =
    (List.map (fun m -> CM_Missing_method m) missing_method) @ error
  in
  (* Always succeeds *)
  eqtype true type_pairs subst env rest1 rest2;
  let error =
    List.fold_right
      (fun (lab, k1, t1, k2, t2) err ->
        let k1 = field_kind_repr k1 in
        let k2 = field_kind_repr k2 in
        match k1, k2 with
          (Fvar _, Fvar _)
        | (Fpresent, Fpresent) -> err
        | (Fvar _, Fpresent)   -> CM_Private_method lab::err
        | (Fpresent, Fvar _)  -> CM_Public_method lab::err
        | _                    -> assert false)
      pairs error
  in
  let error =
    Vars.fold
      (fun lab (mut, vr, ty) err ->
         try
           let (mut', vr', ty') = Vars.find lab sign1.cty_vars in
           if mut = Mutable && mut' <> Mutable then
             CM_Non_mutable_value lab::err
           else if vr = Concrete && vr' <> Concrete then
             CM_Non_concrete_value lab::err
           else
             err
         with Not_found ->
           CM_Missing_value lab::err)
      sign2.cty_vars error
  in
  let error =
    Vars.fold
      (fun lab (_,vr,_) err ->
        if vr = Virtual && not (Vars.mem lab sign2.cty_vars) then
          CM_Hide_virtual ("instance variable", lab) :: err
        else err)
      sign1.cty_vars error
  in
  let error =
    List.fold_right
      (fun e l ->
        if List.mem e missing_method then l else CM_Virtual_method e::l)
      (Concr.elements (Concr.diff sign2.cty_concr sign1.cty_concr))
      error
  in
  match error with
    [] ->
      begin try
        let lp = List.length patt_params in
        let ls = List.length subj_params in
        if lp  <> ls then
          raise (Failure [CM_Parameter_arity_mismatch (lp, ls)]);
        List.iter2 (fun p s ->
          try eqtype true type_pairs subst env p s with Unify trace ->
            raise (Failure [CM_Type_parameter_mismatch
                               (expand_trace env trace)]))
          patt_params subj_params;
        equal_clty false type_pairs subst env patt_type subj_type;
        []
      with
        Failure r -> r
      end
  | error ->
      error


                              (***************)
                              (*  Subtyping  *)
                              (***************)


(**** Build a subtype of a given type. ****)

(* build_subtype:
   [visited] traces traversed object and variant types
   [loops] is a mapping from variables to variables, to reproduce
     positive loops in a class type
   [posi] true if the current variance is positive
   [level] number of expansions/enlargement allowed on this branch *)

let warn = ref false  (* whether double coercion might do better *)
let pred_expand n = if n mod 2 = 0 && n > 0 then pred n else n
let pred_enlarge n = if n mod 2 = 1 then pred n else n

type change = Unchanged | Equiv | Changed
let collect l = List.fold_left (fun c1 (_, c2) -> max c1 c2) Unchanged l

let rec filter_visited = function
    [] -> []
  | {desc=Tobject _|Tvariant _} :: _ as l -> l
  | _ :: l -> filter_visited l

let memq_warn t visited =
  if List.memq t visited then (warn := true; true) else false

let rec lid_of_path sharp = function
    Path.Pident id ->
      Longident.Lident (sharp ^ Ident.name id)
  | Path.Pdot (p1, s, _) ->
      Longident.Ldot (lid_of_path "" p1, sharp ^ s)
  | Path.Papply (p1, p2) ->
      Longident.Lapply (lid_of_path sharp p1, lid_of_path "" p2)

let find_cltype_for_path env p =
  let path, cl_abbr = Env.lookup_type (lid_of_path "#" p) env in
  match cl_abbr.type_manifest with
    Some ty ->
      begin match (repr ty).desc with
        Tobject(_,{contents=Some(p',_)}) when Path.same p p' -> cl_abbr, ty
      | _ -> raise Not_found
      end
  | None -> assert false

let has_constr_row' env t =
  has_constr_row (expand_abbrev env t)

let rec build_subtype env visited loops posi level t =
  let t = repr t in
  match t.desc with
    Tvar ->
      if posi then
        try
          let t' = List.assq t loops in
          warn := true;
          (t', Equiv)
        with Not_found ->
          (t, Unchanged)
      else
        (t, Unchanged)
  | Tarrow(l, t1, t2, _) ->
      if memq_warn t visited then (t, Unchanged) else
      let visited = t :: visited in
      let (t1', c1) = build_subtype env visited loops (not posi) level t1 in
      let (t2', c2) = build_subtype env visited loops posi level t2 in
      let c = max c1 c2 in
      if c > Unchanged then (newty (Tarrow(l, t1', t2', Cok)), c)
      else (t, Unchanged)
  | Ttuple tlist ->
      if memq_warn t visited then (t, Unchanged) else
      let visited = t :: visited in
      let tlist' =
        List.map (build_subtype env visited loops posi level) tlist
      in
      let c = collect tlist' in
      if c > Unchanged then (newty (Ttuple (List.map fst tlist')), c)
      else (t, Unchanged)
  | Tconstr(p, tl, abbrev)
    when level > 0 && generic_abbrev env p && safe_abbrev env t
    && not (has_constr_row' env t) ->
      let t' = repr (expand_abbrev env t) in
      let level' = pred_expand level in
      begin try match t'.desc with
        Tobject _ when posi && not (opened_object t') ->
          let cl_abbr, body = find_cltype_for_path env p in
          let ty =
            subst env !current_level abbrev None cl_abbr.type_params tl body in
          let ty = repr ty in
          let ty1, tl1 =
            match ty.desc with
              Tobject(ty1,{contents=Some(p',tl1)}) when Path.same p p' ->
                ty1, tl1
            | _ -> raise Not_found
          in
          ty.desc <- Tvar;
          let t'' = newvar () in
          let loops = (ty, t'') :: loops in
          (* May discard [visited] as level is going down *)
          let (ty1', c) =
            build_subtype env [t'] loops posi (pred_enlarge level') ty1 in
          assert (t''.desc = Tvar);
          let nm =
            if c > Equiv || deep_occur ty ty1' then None else Some(p,tl1) in
          t''.desc <- Tobject (ty1', ref nm);
          (try unify_var env ty t with Unify _ -> assert false);
          (t'', Changed)
      | _ -> raise Not_found
      with Not_found ->
        let (t'',c) = build_subtype env visited loops posi level' t' in
        if c > Unchanged then (t'',c)
        else (t, Unchanged)
      end
  | Tconstr(p, tl, abbrev) ->
      (* Must check recursion on constructors, since we do not always
         expand them *)
      if memq_warn t visited then (t, Unchanged) else
      let visited = t :: visited in
      begin try
        let decl = Env.find_type p env in
        if level = 0 && generic_abbrev env p && safe_abbrev env t
        && not (has_constr_row' env t)
        then warn := true;
        let tl' =
          List.map2
            (fun (co,cn,_) t ->
              if cn then
                if co then (t, Unchanged)
                else build_subtype env visited loops (not posi) level t
              else
                if co then build_subtype env visited loops posi level t
                else (newvar(), Changed))
            decl.type_variance tl
        in
        let c = collect tl' in
        if c > Unchanged then (newconstr p (List.map fst tl'), c)
        else (t, Unchanged)
      with Not_found ->
        (t, Unchanged)
      end
  | Tvariant row ->
      let row = row_repr row in
      if memq_warn t visited || not (static_row row) then (t, Unchanged) else
      let level' = pred_enlarge level in
      let visited =
        t :: if level' < level then [] else filter_visited visited in
      let bound = ref row.row_bound in
      let fields = filter_row_fields false row.row_fields in
      let fields =
        List.map
          (fun (l,f as orig) -> match row_field_repr f with
            Rpresent None ->
              if posi then
                (l, Reither(true, [], false, ref None)), Unchanged
              else
                orig, Unchanged
          | Rpresent(Some t) ->
              let (t', c) = build_subtype env visited loops posi level' t in
              if posi && level > 0 then begin
                bound := t' :: !bound;
                (l, Reither(false, [t'], false, ref None)), c
              end else
                (l, Rpresent(Some t')), c
          | _ -> assert false)
          fields
      in
      let c = collect fields in
      let row =
        { row_fields = List.map fst fields; row_more = newvar();
          row_bound = !bound; row_closed = posi; row_fixed = false;
          row_name = if c > Unchanged then None else row.row_name }
      in
      (newty (Tvariant row), Changed)
  | Tobject (t1, _) ->
      if memq_warn t visited || opened_object t1 then (t, Unchanged) else
      let level' = pred_enlarge level in
      let visited =
        t :: if level' < level then [] else filter_visited visited in
      let (t1', c) = build_subtype env visited loops posi level' t1 in
      if c > Unchanged then (newty (Tobject (t1', ref None)), c)
      else (t, Unchanged)
  | Tfield(s, _, t1, t2) (* Always present *) ->
      let (t1', c1) = build_subtype env visited loops posi level t1 in
      let (t2', c2) = build_subtype env visited loops posi level t2 in
      let c = max c1 c2 in
      if c > Unchanged then (newty (Tfield(s, Fpresent, t1', t2')), c)
      else (t, Unchanged)
  | Tnil ->
      if posi then
        let v = newvar () in
        (v, Changed)
      else begin
        warn := true;
        (t, Unchanged)
      end
  | Tsubst _ | Tlink _ ->
      assert false
  | Tpoly(t1, tl) ->
      let (t1', c) = build_subtype env visited loops posi level t1 in
      if c > Unchanged then (newty (Tpoly(t1', tl)), c)
      else (t, Unchanged)
  | Tunivar ->
      (t, Unchanged)

let enlarge_type env ty =
  warn := false;
  (* [level = 4] allows 2 expansions involving objects/variants *)
  let (ty', _) = build_subtype env [] [] true 4 ty in
  (ty', !warn)

(**** Check whether a type is a subtype of another type. ****)

(*
    During the traversal, a trace of visited types is maintained. It
    is printed in case of error.
    Constraints (pairs of types that must be equals) are accumulated
    rather than being enforced straight. Indeed, the result would
    otherwise depend on the order in which these constraints are
    enforced.
    A function enforcing these constraints is returned. That way, type
    variables can be bound to their actual values before this function
    is called (see Typecore).
    Only well-defined abbreviations are expanded (hence the tests
    [generic_abbrev ...]).
*)

let subtypes = TypePairs.create 17

let subtype_error env trace =
  raise (Subtype (expand_trace env (List.rev trace), []))

let rec subtype_rec env trace t1 t2 cstrs =
  let t1 = repr t1 in
  let t2 = repr t2 in
  if t1 == t2 then cstrs else

  begin try
    TypePairs.find subtypes (t1, t2);
    cstrs
  with Not_found ->
    TypePairs.add subtypes (t1, t2) ();
    match (t1.desc, t2.desc) with
      (Tvar, _) | (_, Tvar) ->
        (trace, t1, t2, !univar_pairs)::cstrs
    | (Tarrow(l1, t1, u1, _), Tarrow(l2, t2, u2, _)) when l1 = l2
      || !Clflags.classic && not (is_optional l1 || is_optional l2) ->
        let cstrs = subtype_rec env ((t2, t1)::trace) t2 t1 cstrs in
        subtype_rec env ((u1, u2)::trace) u1 u2 cstrs
    | (Ttuple tl1, Ttuple tl2) ->
        subtype_list env trace tl1 tl2 cstrs
    | (Tconstr(p1, [], _), Tconstr(p2, [], _)) when Path.same p1 p2 ->
        cstrs
    | (Tconstr(p1, tl1, abbrev1), _)
      when generic_abbrev env p1 && safe_abbrev env t1 ->
        subtype_rec env trace (expand_abbrev env t1) t2 cstrs
    | (_, Tconstr(p2, tl2, abbrev2))
      when generic_abbrev env p2 && safe_abbrev env t2 ->
        subtype_rec env trace t1 (expand_abbrev env t2) cstrs
    | (Tconstr(p1, tl1, _), Tconstr(p2, tl2, _)) when Path.same p1 p2 ->
        begin try
          let decl = Env.find_type p1 env in
          List.fold_left2
            (fun cstrs (co, cn, _) (t1, t2) ->
              if co then
                if cn then
                  (trace, newty2 t1.level (Ttuple[t1]),
                   newty2 t2.level (Ttuple[t2]), !univar_pairs) :: cstrs
                else subtype_rec env ((t1, t2)::trace) t1 t2 cstrs
              else
                if cn then subtype_rec env ((t2, t1)::trace) t2 t1 cstrs
                else cstrs)
            cstrs decl.type_variance (List.combine tl1 tl2)
        with Not_found ->
          (trace, t1, t2, !univar_pairs)::cstrs
        end
    | (Tobject (f1, _), Tobject (f2, _))
      when (object_row f1).desc = Tvar && (object_row f2).desc = Tvar ->
        (* Same row variable implies same object. *)
        (trace, t1, t2, !univar_pairs)::cstrs
    | (Tobject (f1, _), Tobject (f2, _)) ->
        subtype_fields env trace f1 f2 cstrs
    | (Tvariant row1, Tvariant row2) ->
        begin try
          subtype_row env trace row1 row2 cstrs
        with Exit ->
          (trace, t1, t2, !univar_pairs)::cstrs
        end
    | (Tpoly (u1, []), Tpoly (u2, [])) ->
        subtype_rec env trace u1 u2 cstrs
    | (Tpoly (u1, tl1), Tpoly (u2,tl2)) ->
        begin try
          enter_poly env univar_pairs u1 tl1 u2 tl2
            (fun t1 t2 -> subtype_rec env trace t1 t2 cstrs)
        with Unify _ ->
          (trace, t1, t2, !univar_pairs)::cstrs
        end
    | (_, _) ->
        (trace, t1, t2, !univar_pairs)::cstrs
  end

and subtype_list env trace tl1 tl2 cstrs =
  if List.length tl1 <> List.length tl2 then
    subtype_error env trace;
  List.fold_left2
    (fun cstrs t1 t2 -> subtype_rec env ((t1, t2)::trace) t1 t2 cstrs)
    cstrs tl1 tl2

and subtype_fields env trace ty1 ty2 cstrs =
  (* Assume that either rest1 or rest2 is not Tvar *)
  let (fields1, rest1) = flatten_fields ty1 in
  let (fields2, rest2) = flatten_fields ty2 in
  let (pairs, miss1, miss2) = associate_fields fields1 fields2 in
  let cstrs =
    if rest2.desc = Tnil then cstrs else
    if miss1 = [] then
      subtype_rec env ((rest1, rest2)::trace) rest1 rest2 cstrs
    else
      (trace, build_fields (repr ty1).level miss1 rest1, rest2,
       !univar_pairs) :: cstrs
  in
  let cstrs =
    if miss2 = [] then cstrs else
    (trace, rest1, build_fields (repr ty2).level miss2 (newvar ()),
     !univar_pairs) :: cstrs
  in
  List.fold_left
    (fun cstrs (_, k1, t1, k2, t2) ->
      (* Theses fields are always present *)
      subtype_rec env ((t1, t2)::trace) t1 t2 cstrs)
    cstrs pairs

and subtype_row env trace row1 row2 cstrs =
  let row1 = row_repr row1 and row2 = row_repr row2 in
  let r1, r2, pairs =
    merge_row_fields row1.row_fields row2.row_fields in
  let more1 = repr row1.row_more
  and more2 = repr row2.row_more in
  match more1.desc, more2.desc with
    Tconstr(p1,_,_), Tconstr(p2,_,_) when Path.same p1 p2 ->
      subtype_rec env ((more1,more2)::trace) more1 more2 cstrs
  | (Tvar|Tconstr _), (Tvar|Tconstr _)
    when row1.row_closed && r1 = [] ->
      List.fold_left
        (fun cstrs (_,f1,f2) ->
          match row_field_repr f1, row_field_repr f2 with
            (Rpresent None|Reither(true,_,_,_)), Rpresent None ->
              cstrs
          | Rpresent(Some t1), Rpresent(Some t2) ->
              subtype_rec env ((t1, t2)::trace) t1 t2 cstrs
          | Reither(false, t1::_, _, _), Rpresent(Some t2) ->
              subtype_rec env ((t1, t2)::trace) t1 t2 cstrs
          | Rabsent, _ -> cstrs
          | _ -> raise Exit)
        cstrs pairs
  | Tunivar, Tunivar
    when row1.row_closed = row2.row_closed && r1 = [] && r2 = [] ->
      let cstrs =
        subtype_rec env ((more1,more2)::trace) more1 more2 cstrs in
      List.fold_left
        (fun cstrs (_,f1,f2) ->
          match row_field_repr f1, row_field_repr f2 with
            Rpresent None, Rpresent None
          | Reither(true,[],_,_), Reither(true,[],_,_)
          | Rabsent, Rabsent ->
              cstrs
          | Rpresent(Some t1), Rpresent(Some t2)
          | Reither(false,[t1],_,_), Reither(false,[t2],_,_) ->
              subtype_rec env ((t1, t2)::trace) t1 t2 cstrs
          | _ -> raise Exit)
        cstrs pairs
  | _ ->
      raise Exit

let subtype env ty1 ty2 =
  TypePairs.clear subtypes;
  univar_pairs := [];
  (* Build constraint set. *)
  let cstrs = subtype_rec env [(ty1, ty2)] ty1 ty2 [] in
  TypePairs.clear subtypes;
  (* Enforce constraints. *)
  function () ->
    List.iter
      (function (trace0, t1, t2, pairs) ->
         try unify_pairs env t1 t2 pairs with Unify trace ->
           raise (Subtype (expand_trace env (List.rev trace0),
                           List.tl (List.tl trace))))
      (List.rev cstrs)

                              (*******************)
                              (*  Miscellaneous  *)
                              (*******************)

(* Utility for printing. The resulting type is not used in computation. *)
let rec unalias_object ty =
  let ty = repr ty in
  match ty.desc with
    Tfield (s, k, t1, t2) ->
      newty2 ty.level (Tfield (s, k, t1, unalias_object t2))
  | Tvar | Tnil ->
      newty2 ty.level ty.desc
  | Tunivar ->
      ty
  | Tconstr _ ->
      newty2 ty.level Tvar
  | _ ->
      assert false

let unalias ty =
  let ty = repr ty in
  match ty.desc with
    Tvar | Tunivar ->
      ty
  | Tvariant row ->
      let row = row_repr row in
      let more = row.row_more in
      newty2 ty.level
        (Tvariant {row with row_more = newty2 more.level more.desc})
  | Tobject (ty, nm) ->
      newty2 ty.level (Tobject (unalias_object ty, nm))
  | _ ->
      newty2 ty.level ty.desc

let unroll_abbrev id tl ty =
  let ty = repr ty in
  if (ty.desc = Tvar) || (List.exists (deep_occur ty) tl) then
    ty
  else
    let ty' = newty2 ty.level ty.desc in
    link_type ty (newty2 ty.level (Tconstr (Path.Pident id, tl, ref Mnil)));
    ty'

(* Return the arity (as for curried functions) of the given type. *)
let rec arity ty =
  match (repr ty).desc with
    Tarrow(_, t1, t2, _) -> 1 + arity t2
  | _ -> 0

(* Check whether an abbreviation expands to itself. *)
let cyclic_abbrev env id ty =
  let rec check_cycle seen ty =
    let ty = repr ty in
    match ty.desc with
      Tconstr (p, tl, abbrev) ->
        p = Path.Pident id || List.memq ty seen ||
        begin try
          check_cycle (ty :: seen) (expand_abbrev env ty)
        with
          Cannot_expand -> false
        | Unify _ -> true
        end
    | _ ->
        false
  in check_cycle [] ty

(* Normalize a type before printing, saving... *)
let rec normalize_type_rec env ty =
  let ty = repr ty in
  if ty.level >= lowest_level then begin
    mark_type_node ty;
    begin match ty.desc with
    | Tvariant row ->
      let row = row_repr row in
      let fields = List.map
          (fun (l,f) ->
            let f = row_field_repr f in l,
            match f with Reither(b, ty::(_::_ as tyl), m, e) ->
              let tyl' =
                List.fold_left
                  (fun tyl ty ->
                    if List.exists (fun ty' -> equal env false [ty] [ty']) tyl
                    then tyl else ty::tyl)
                  [ty] tyl
              in
              if List.length tyl' <= List.length tyl then
                let f = Reither(b, List.rev tyl', m, ref None) in
                set_row_field e f;
                f
              else f
            | _ -> f)
          row.row_fields in
      let fields =
        List.sort (fun (p,_) (q,_) -> compare p q)
          (List.filter (fun (_,fi) -> fi <> Rabsent) fields)
      and bound = List.fold_left
          (fun tyl ty -> if List.memq ty tyl then tyl else ty :: tyl)
          [] (List.map repr row.row_bound)
      in
      log_type ty;
      ty.desc <- Tvariant {row with row_fields = fields; row_bound = bound}
    | Tobject (fi, nm) ->
        begin match !nm with
        | None -> ()
        | Some (n, v :: l) ->
            let v' = repr v in
            begin match v'.desc with
            | Tvar|Tunivar ->
                if v' != v then set_name nm (Some (n, v' :: l))
            | Tnil -> log_type ty; ty.desc <- Tconstr (n, l, ref Mnil)
            | _ -> set_name nm None
            end
        | _ ->
            fatal_error "Ctype.normalize_type_rec"
        end;
        let fi = repr fi in
        if fi.level < lowest_level then () else
        let fields, row = flatten_fields fi in
        let fi' = build_fields fi.level fields row in
        log_type ty; fi.desc <- fi'.desc
    | _ -> ()
    end;
    iter_type_expr (normalize_type_rec env) ty
  end

let normalize_type env ty =
  normalize_type_rec env ty;
  unmark_type ty


                              (*************************)
                              (*  Remove dependencies  *)
                              (*************************)


(*
   Variables are left unchanged. Other type nodes are duplicated, with
   levels set to generic level.
   During copying, the description of a (non-variable) node is first
   replaced by a link to a stub ([Tsubst (newgenvar ())]).
   Once the copy is made, it replaces the stub.
   After copying, the description of node, which was stored by
   [save_desc], must be put back, using [cleanup_types].
*)

let rec nondep_type_rec env id ty =
  let ty = repr ty in
  match ty.desc with
    Tvar | Tunivar -> ty
  | Tsubst ty -> ty
  | _ ->
    let desc = ty.desc in
    save_desc ty desc;
    let ty' = newgenvar () in        (* Stub *)
    ty.desc <- Tsubst ty';
    ty'.desc <-
      begin match desc with
      | Tconstr(p, tl, abbrev) ->
          if Path.isfree id p then
            begin try
              Tlink (nondep_type_rec env id
                       (expand_abbrev env (newty2 ty.level desc)))
              (*
                 The [Tlink] is important. The expanded type may be a
                 variable, or may not be completely copied yet
                 (recursive type), so one cannot just take its
                 description.
               *)
            with Cannot_expand ->
              raise Not_found
            end
          else
            Tconstr(p, List.map (nondep_type_rec env id) tl, ref Mnil)
      | Tobject (t1, name) ->
          Tobject (nondep_type_rec env id t1,
                 ref (match !name with
                        None -> None
                      | Some (p, tl) ->
                          if Path.isfree id p then None
                          else Some (p, List.map (nondep_type_rec env id) tl)))
      | Tvariant row ->
          let row = row_repr row in
          let more = repr row.row_more in
          (* We must substitute in a subtle way *)
          (* Tsubst denotes the variant itself, as the row var is unchanged *)
          begin match more.desc with
            Tsubst ty2 ->
              (* This variant type has been already copied *)
              ty.desc <- Tsubst ty2; (* avoid Tlink in the new type *)
              Tlink ty2
          | _ ->
              let static = static_row row in
              (* Register new type first for recursion *)
              save_desc more more.desc;
              more.desc <- ty.desc;
              let more' = if static then newgenvar () else more in
              (* Return a new copy *)
              let row =
                copy_row (nondep_type_rec env id) true row true more' in
              match row.row_name with
                Some (p, tl) when Path.isfree id p ->
                  Tvariant {row with row_name = None}
              | _ -> Tvariant row
          end
      | _ -> copy_type_desc (nondep_type_rec env id) desc
      end;
    ty'

let nondep_type env id ty =
  try
    let ty' = nondep_type_rec env id ty in
    cleanup_types ();
    unmark_type ty';
    ty'
  with Not_found ->
    cleanup_types ();
    raise Not_found

(* Preserve sharing inside type declarations. *)
let nondep_type_decl env mid id is_covariant decl =
  try
    let params = List.map (nondep_type_rec env mid) decl.type_params in
    let decl =
      { type_params = params;
        type_arity = decl.type_arity;
        type_kind =
          begin try
            match decl.type_kind with
              Type_abstract ->
                Type_abstract
            | Type_variant(cstrs, priv) ->
                Type_variant(List.map
                  (fun (c, tl) -> (c, List.map (nondep_type_rec env mid) tl))
                  cstrs, priv)
            | Type_record(lbls, rep, priv) ->
                Type_record(
                  List.map
                    (fun (c, mut, t) -> (c, mut, nondep_type_rec env mid t))
                    lbls,
                  rep, priv)
          with Not_found when is_covariant ->
            Type_abstract
          end;
        type_manifest =
          begin try
            match decl.type_manifest with
              None -> None
            | Some ty ->
                Some (unroll_abbrev id params (nondep_type_rec env mid ty))
          with Not_found when is_covariant ->
            None
          end;
        type_variance = decl.type_variance;
      }
    in
    cleanup_types ();
    List.iter unmark_type decl.type_params;
    begin match decl.type_kind with
      Type_abstract -> ()
    | Type_variant(cstrs, priv) ->
        List.iter (fun (c, tl) -> List.iter unmark_type tl) cstrs
    | Type_record(lbls, rep, priv) ->
        List.iter (fun (c, mut, t) -> unmark_type t) lbls
    end;
    begin match decl.type_manifest with
      None    -> ()
    | Some ty -> unmark_type ty
    end;
    decl
  with Not_found ->
    cleanup_types ();
    raise Not_found

(* Preserve sharing inside class types. *)
let nondep_class_signature env id sign =
  { cty_self = nondep_type_rec env id sign.cty_self;
    cty_vars =
      Vars.map (function (m, v, t) -> (m, v, nondep_type_rec env id t))
        sign.cty_vars;
    cty_concr = sign.cty_concr;
    cty_inher =
      List.map (fun (p,tl) -> (p, List.map (nondep_type_rec env id) tl))
        sign.cty_inher }

let rec nondep_class_type env id =
  function
    Tcty_constr (p, _, cty) when Path.isfree id p ->
      nondep_class_type env id cty
  | Tcty_constr (p, tyl, cty) ->
      Tcty_constr (p, List.map (nondep_type_rec env id) tyl,
                   nondep_class_type env id cty)
  | Tcty_signature sign ->
      Tcty_signature (nondep_class_signature env id sign)
  | Tcty_fun (l, ty, cty) ->
      Tcty_fun (l, nondep_type_rec env id ty, nondep_class_type env id cty)

let nondep_class_declaration env id decl =
  assert (not (Path.isfree id decl.cty_path));
  let decl =
    { cty_params = List.map (nondep_type_rec env id) decl.cty_params;
      cty_variance = decl.cty_variance;
      cty_type = nondep_class_type env id decl.cty_type;
      cty_path = decl.cty_path;
      cty_new =
        begin match decl.cty_new with
          None    -> None
        | Some ty -> Some (nondep_type_rec env id ty)
        end }
  in
  cleanup_types ();
  List.iter unmark_type decl.cty_params;
  unmark_class_type decl.cty_type;
  begin match decl.cty_new with
    None    -> ()
  | Some ty -> unmark_type ty
  end;
  decl

let nondep_cltype_declaration env id decl =
  assert (not (Path.isfree id decl.clty_path));
  let decl =
    { clty_params = List.map (nondep_type_rec env id) decl.clty_params;
      clty_variance = decl.clty_variance;
      clty_type = nondep_class_type env id decl.clty_type;
      clty_path = decl.clty_path }
  in
  cleanup_types ();
  List.iter unmark_type decl.clty_params;
  unmark_class_type decl.clty_type;
  decl

(* collapse conjonctive types in class parameters *)
let rec collapse_conj env visited ty =
  let ty = repr ty in
  if List.memq ty visited then () else
  let visited = ty :: visited in
  match ty.desc with
    Tvariant row ->
      let row = row_repr row in
      List.iter
        (fun (l,fi) ->
          match row_field_repr fi with
            Reither (c, t1::(_::_ as tl), m, e) ->
              List.iter (unify env t1) tl;
              set_row_field e (Reither (c, [t1], m, ref None))
          | _ ->
              ())
        row.row_fields;
      iter_row (collapse_conj env visited) row
  | _ ->
      iter_type_expr (collapse_conj env visited) ty

let collapse_conj_params env params =
  List.iter (collapse_conj env []) params