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(********************************************************************)
(*                                                                  *)
(*  The Why3 Verification Platform   /   The Why3 Development Team  *)
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(*  Copyright 2010-2017   --   INRIA - CNRS - Paris-Sud University  *)
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(*                                                                  *)
(*  This software is distributed under the terms of the GNU Lesser  *)
(*  General Public License version 2.1, with the special exception  *)
(*  on linking described in file LICENSE.                           *)
(*                                                                  *)
(********************************************************************)

open Stdlib
open Ident
open Ty
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open Term
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open Decl
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open Theory
open Ity
open Expr
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open Pdecl
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(** *)

type prog_symbol =
  | PV of pvsymbol
  | RS of rsymbol

type namespace = {
  ns_ts : itysymbol   Mstr.t;  (* type symbols *)
  ns_ps : prog_symbol Mstr.t;  (* program symbols *)
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  ns_xs : xsymbol     Mstr.t;  (* exception symbols *)
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  ns_ns : namespace   Mstr.t;  (* inner namespaces *)
}

let empty_ns = {
  ns_ts = Mstr.empty;
  ns_ps = Mstr.empty;
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  ns_xs = Mstr.empty;
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  ns_ns = Mstr.empty;
}

let ns_replace eq chk x vo vn =
  if not chk then vn else
  if eq vo vn then vn else
  raise (ClashSymbol x)

let psym_equal p1 p2 = match p1,p2 with
  | PV p1, PV p2 -> pv_equal p1 p2
  | RS p1, RS p2 -> rs_equal p1 p2
  | _, _ -> false

let rec merge_ns chk ns1 ns2 =
  if ns1 == ns2 then ns1 else
  let join eq x n o = Some (ns_replace eq chk x o n) in
  let ns_union eq m1 m2 =
    if m1 == m2 then m1 else Mstr.union (join eq) m1 m2 in
  let fusion _ ns1 ns2 = Some (merge_ns chk ns1 ns2) in
  { ns_ts = ns_union its_equal ns1.ns_ts ns2.ns_ts;
    ns_ps = ns_union psym_equal ns1.ns_ps ns2.ns_ps;
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    ns_xs = ns_union xs_equal ns1.ns_xs ns2.ns_xs;
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    ns_ns = Mstr.union fusion ns1.ns_ns ns2.ns_ns; }

let add_ns chk x ns m = Mstr.change (function
  | Some os -> Some (merge_ns chk ns os)
  | None    -> Some ns) x m

let ns_add eq chk x vn m = Mstr.change (function
  | Some vo -> Some (ns_replace eq chk x vo vn)
  | None    -> Some vn) x m

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let add_xs chk x xs ns = { ns with ns_xs = ns_add xs_equal   chk x xs ns.ns_xs }
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let add_ts chk x ts ns = { ns with ns_ts = ns_add its_equal  chk x ts ns.ns_ts }
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let add_ps chk x ps ns = { ns with ns_ps = ns_add psym_equal chk x ps ns.ns_ps }
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let add_ns chk x nn ns = { ns with ns_ns = add_ns            chk x nn ns.ns_ns }

let rec ns_find get_map ns = function
  | []   -> assert false
  | [a]  -> Mstr.find a (get_map ns)
  | a::l -> ns_find get_map (Mstr.find a ns.ns_ns) l

let ns_find_prog_symbol = ns_find (fun ns -> ns.ns_ps)
let ns_find_ns          = ns_find (fun ns -> ns.ns_ns)
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let ns_find_xs          = ns_find (fun ns -> ns.ns_xs)
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let ns_find_its         = ns_find (fun ns -> ns.ns_ts)

let ns_find_pv ns s = match ns_find_prog_symbol ns s with
  | PV pv -> pv | _ -> raise Not_found

let ns_find_rs ns s = match ns_find_prog_symbol ns s with
  | RS rs -> rs | _ -> raise Not_found

(** {2 Module} *)

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type pmodule = {
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  mod_theory : theory;        (* pure theory *)
  mod_units  : mod_unit list; (* module declarations *)
  mod_export : namespace;     (* exported namespace *)
  mod_known  : known_map;     (* known identifiers *)
  mod_local  : Sid.t;         (* locally declared idents *)
  mod_used   : Sid.t;         (* used modules *)
}

and mod_unit =
  | Udecl  of pdecl
  | Uuse   of pmodule
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  | Uclone of mod_inst
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  | Umeta  of meta * meta_arg list
  | Uscope of string * bool * mod_unit list

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and mod_inst = {
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  mi_mod : pmodule;
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  mi_ty  : ity Mts.t;
  mi_ts  : itysymbol Mts.t;
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  mi_ls  : lsymbol Mls.t;
  mi_pr  : prsymbol Mpr.t;
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  mi_pk  : prop_kind Mpr.t;
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  mi_pv  : pvsymbol Mvs.t;
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  mi_rs  : rsymbol Mrs.t;
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  mi_xs  : xsymbol Mxs.t;
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}

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let empty_mod_inst m = {
  mi_mod = m;
  mi_ty  = Mts.empty;
  mi_ts  = Mts.empty;
  mi_ls  = Mls.empty;
  mi_pr  = Mpr.empty;
  mi_pk  = Mpr.empty;
  mi_pv  = Mvs.empty;
  mi_rs  = Mrs.empty;
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  mi_xs  = Mxs.empty;
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}

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(** {2 Module under construction} *)

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type pmodule_uc = {
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  muc_theory : theory_uc;
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  muc_units  : mod_unit list;
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  muc_import : namespace list;
  muc_export : namespace list;
  muc_known  : known_map;
  muc_local  : Sid.t;
  muc_used   : Sid.t;
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  muc_env    : Env.env;
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}

let empty_module env n p = {
  muc_theory = create_theory ~path:p n;
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  muc_units  = [];
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  muc_import = [empty_ns];
  muc_export = [empty_ns];
  muc_known  = Mid.empty;
  muc_local  = Sid.empty;
  muc_used   = Sid.empty;
  muc_env    = env;
}

let close_module, restore_module =
  let h = Hid.create 17 in
  (fun uc ->
     let th = close_theory uc.muc_theory in (* catches errors *)
     let m = { mod_theory = th;
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               mod_units  = List.rev uc.muc_units;
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               mod_export = List.hd uc.muc_export;
               mod_known  = uc.muc_known;
               mod_local  = uc.muc_local;
               mod_used   = uc.muc_used; } in
     Hid.add h th.th_name m;
     m),
  (fun th -> Hid.find h th.th_name)

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let open_scope uc s = match uc.muc_import with
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  | ns :: _ -> { uc with
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      muc_theory = Theory.open_scope uc.muc_theory s;
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      muc_units  = [Uscope (s, false, uc.muc_units)];
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      muc_import =       ns :: uc.muc_import;
      muc_export = empty_ns :: uc.muc_export; }
  | [] -> assert false

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let close_scope uc ~import =
  let th = Theory.close_scope uc.muc_theory ~import in
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  match List.rev uc.muc_units, uc.muc_import, uc.muc_export with
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  | [Uscope (_,_,ul1)], _ :: sti, _ :: ste -> (* empty scope *)
      { uc with muc_theory = th;  muc_units  = ul1;
                muc_import = sti; muc_export = ste; }
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  | Uscope (s,_,ul1) :: ul0, _ :: i1 :: sti, e0 :: e1 :: ste ->
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      let i1 = if import then merge_ns false e0 i1 else i1 in
      let i1 = add_ns false s e0 i1 in
      let e1 = add_ns true  s e0 e1 in
      { uc with
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          muc_theory = th;
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          muc_units  = Uscope (s, import, ul0) :: ul1;
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          muc_import = i1 :: sti;
          muc_export = e1 :: ste; }
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  | _ -> assert false
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let use_export uc ({mod_theory = mth} as m) =
  let th = Theory.use_export uc.muc_theory mth in
  let uc = if Sid.mem mth.th_name uc.muc_used then uc
    else { uc with
      muc_known = merge_known uc.muc_known m.mod_known;
      muc_used  = Sid.add mth.th_name uc.muc_used } in
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  match uc.muc_import, uc.muc_export with
  | i0 :: sti, e0 :: ste -> { uc with
      muc_theory = th;
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      muc_units  = Uuse m :: uc.muc_units;
      muc_import = merge_ns false m.mod_export i0 :: sti;
      muc_export = merge_ns true  m.mod_export e0 :: ste; }
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  | _ -> assert false

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let add_meta uc m al = { uc with
  muc_theory = Theory.add_meta uc.muc_theory m al;
  muc_units  = Umeta (m,al) :: uc.muc_units; }
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let store_path, store_module, restore_path =
  let id_to_path = Wid.create 17 in
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  let store_path {muc_theory = uc} path id =
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    (* this symbol already belongs to some theory *)
    if Wid.mem id_to_path id then () else
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    let prefix = List.rev (id.id_string :: path @ uc.uc_prefix) in
    Wid.set id_to_path id (uc.uc_path, uc.uc_name.id_string, prefix) in
  let store_module {mod_theory = {th_name = id} as th} =
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    (* this symbol is already a module *)
    if Wid.mem id_to_path id then () else
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    Wid.set id_to_path id (th.th_path, id.id_string, []) in
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  let restore_path id = Wid.find id_to_path id in
  store_path, store_module, restore_path

let close_module uc =
  let m = close_module uc in
  store_module m;
  m

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(*
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let count_regions {muc_known = kn} {pv_ity = ity} mr =
  let add_reg r mr = Mreg.change (fun n -> Some (n <> None)) r mr in
  let meet mr1 mr2 = Mreg.union (fun _ x y -> Some (x || y)) mr1 mr2 in
  let join mr1 mr2 = Mreg.union (fun _ _ _ -> Some true) mr1 mr2 in
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  let rec down mr ity = if ity.ity_imm then mr else
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    match ity.ity_node with
    | Ityreg r -> fields (add_reg r mr) r.reg_its r.reg_args r.reg_regs
    | Ityapp (s,tl,rl) -> fields mr s tl rl
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    | Ityvar _ -> assert false
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  and fields mr s tl rl =
    if s.its_private && rl = [] then mr else
    let isb = its_match_regs s tl rl in
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    let add_ity mr ity = down mr (ity_full_inst isb ity) in
    let add_proj mr f = add_ity mr f.rs_cty.cty_result in
    let add_field mr v = add_ity mr v.pv_ity in
    let d = find_its_defn kn s in
    if d.itd_constructors = [] then
      List.fold_left add_proj mr d.itd_fields
    else
      join mr (List.fold_left (fun mr c ->
        meet mr (List.fold_left add_field Mreg.empty c.rs_cty.cty_args))
        Mreg.empty d.itd_constructors) in
  down mr ity
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*)
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let add_symbol add id v uc =
  store_path uc [] id;
  match uc.muc_import, uc.muc_export with
  | i0 :: sti, e0 :: ste -> { uc with
      muc_import = add false id.id_string v i0 :: sti;
      muc_export = add true  id.id_string v e0 :: ste }
  | _ -> assert false

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let add_pdecl_no_logic uc d =
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  let uc = { uc with
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    muc_units = Udecl d :: uc.muc_units;
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    muc_known = known_add_decl uc.muc_known d;
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    muc_local = Sid.union uc.muc_local d.pd_news } in
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  let add_rs uc s = add_symbol add_ps s.rs_name (RS s) uc in
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  let add_rd uc d = add_rs uc d.rec_sym in
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  match d.pd_node with
  | PDtype tdl ->
      let add uc d =
        let uc = List.fold_left add_rs uc d.itd_fields in
        let uc = List.fold_left add_rs uc d.itd_constructors in
        add_symbol add_ts d.itd_its.its_ts.ts_name d.itd_its uc in
      List.fold_left add uc tdl
  | PDlet (LDvar (v,_)) -> add_symbol add_ps v.pv_vs.vs_name (PV v) uc
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  | PDlet (LDsym (s,_)) -> add_rs uc s
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  | PDlet (LDrec l) -> List.fold_left add_rd uc l
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  | PDexn xs -> add_symbol add_xs xs.xs_name xs uc
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  | PDpure -> uc
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let add_pdecl_raw ?(warn=true) uc d =
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  let uc = add_pdecl_no_logic uc d in
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  let th = List.fold_left (add_decl ~warn) uc.muc_theory d.pd_pure in
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  let add_meta th (m,l) = Theory.add_meta th m l in
  let th = List.fold_left add_meta th d.pd_meta in
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  { uc with muc_theory = th }

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(** {2 Builtin symbols} *)

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let dummy_env = Env.create_env []

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let builtin_module =
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  let uc = empty_module dummy_env (id_fresh "BuiltIn") ["why3";"BuiltIn"] in
  let uc = add_pdecl_no_logic uc pd_int in
  let uc = add_pdecl_no_logic uc pd_real in
  let uc = add_pdecl_no_logic uc pd_equ in
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  let m = close_module uc in
  { m with mod_theory = builtin_theory }
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let bool_module =
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  let uc = empty_module dummy_env (id_fresh "Bool") ["why3";"Bool"] in
  let uc = add_pdecl_no_logic uc pd_bool in
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  let m = close_module uc in
  { m with mod_theory = bool_theory }
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let highord_module =
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  let uc = empty_module dummy_env (id_fresh "HighOrd") ["why3";"HighOrd"] in
  let uc = add_pdecl_no_logic uc pd_func in
  let uc = add_pdecl_no_logic uc pd_func_app in
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  let m = close_module uc in
  { m with mod_theory = highord_theory }
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let tuple_module = Hint.memo 17 (fun n ->
  let nm = "Tuple" ^ string_of_int n in
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  let uc = empty_module dummy_env (id_fresh nm) ["why3";nm] in
  let uc = add_pdecl_no_logic uc (pd_tuple n) in
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  let m = close_module uc in
  { m with mod_theory = tuple_theory n })
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let unit_module =
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  let uc = empty_module dummy_env (id_fresh "Unit") ["why3";"Unit"] in
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  let uc = use_export uc (tuple_module 0) in
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  let add uc d = add_pdecl_raw ~warn:false uc d in
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  let td = create_alias_decl (id_fresh "unit") [] ity_unit in
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  close_module (List.fold_left add uc (create_type_decl [td]))
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let create_module env ?(path=[]) n =
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  let m = empty_module env n path in
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  let m = use_export m builtin_module in
  let m = use_export m bool_module in
  let m = use_export m unit_module in
  m

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let add_use uc d = Sid.fold (fun id uc ->
  if id_equal id ts_func.ts_name then
    use_export uc highord_module
  else match is_ts_tuple_id id with
  | Some n -> use_export uc (tuple_module n)
  | None -> uc) (Mid.set_diff d.pd_syms uc.muc_known) uc

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let add_pdecl ?(warn=true) ~vc uc d =
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  let uc = add_use uc d in
  let dl = if vc then Vc.vc uc.muc_env uc.muc_known d else [] in
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  (* verification conditions must not add additional dependencies
     on built-in theories like TupleN or HighOrd. Also, we expect
     int.Int or any other library theory to be in the context:
     importing them automatically seems to be too invasive. *)
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  add_pdecl_raw ~warn (List.fold_left (add_pdecl_raw ~warn) uc dl) d
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(** {2 Cloning} *)

type clones = {
  cl_local : Sid.t;
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  mutable ty_table : ity Mts.t;
  mutable ts_table : itysymbol Mts.t;
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  mutable ls_table : lsymbol Mls.t;
  mutable pr_table : prsymbol Mpr.t;
  mutable rn_table : region Mreg.t;
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  mutable fd_table : pvsymbol Mpv.t;
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  mutable pv_table : pvsymbol Mvs.t;
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  mutable rs_table : rsymbol Mrs.t;
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  mutable xs_table : xsymbol Mxs.t;
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}

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let empty_clones m = {
  cl_local = m.mod_local;
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  ty_table = Mts.empty;
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  ts_table = Mts.empty;
  ls_table = Mls.empty;
  pr_table = Mpr.empty;
  rn_table = Mreg.empty;
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  fd_table = Mpv.empty;
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  pv_table = Mvs.empty;
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  rs_table = Mrs.empty;
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  xs_table = Mxs.empty;
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}

(* populate the clone structure *)

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let rec sm_trans_ty tym tsm ty = match ty.ty_node with
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  | Tyapp (s, tl) ->
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      let tl = List.map (sm_trans_ty tym tsm) tl in
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      begin match Mts.find_opt s tsm with
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      | Some its -> ty_app its.its_ts tl
      | None -> begin match Mts.find_opt s tym with
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      | Some ity -> ty_inst (ts_match_args s tl) (ty_of_ity ity)
      | None -> ty_app s tl
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      end end
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  | Tyvar _ -> ty

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let clone_ty cl ty = sm_trans_ty cl.ty_table cl.ts_table ty
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let cl_find_its cl its =
  if not (Sid.mem its.its_ts.ts_name cl.cl_local) then its
  else Mts.find its.its_ts cl.ts_table
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let cl_find_ts cl ts =
  if not (Sid.mem ts.ts_name cl.cl_local) then ts
  else (Mts.find ts cl.ts_table).its_ts
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let rec clone_ity cl ity = match ity.ity_node with
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  | Ityreg r ->
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      ity_reg (clone_reg cl r)
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  | Ityapp (s, tl, rl) ->
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      let tl = List.map (clone_ity cl) tl in
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      let rl = List.map (clone_ity cl) rl in
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      begin match Mts.find_opt s.its_ts cl.ts_table with
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      | Some its -> ity_app_pure its tl rl
      | None -> (* creative indentation *)
      begin match Mts.find_opt s.its_ts cl.ty_table with
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      | Some ity -> ity_full_inst (its_match_regs s tl rl) ity
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      | None -> ity_app_pure s tl rl
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      end end
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  | Ityvar _ -> ity

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and clone_reg cl reg =
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  (* FIXME: what about top-level non-instantiated regions?
     We cannot check in cl.cl_local to see if they are there.
     Instead, we should prefill cl.pv_table and cl.rn_table
     with all top-level pvsymbols (local or external) before
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     descending into a let_defn.
     TODO: add to module/uc a list of locally-defined toplevel
     variables, as well as a set of imported toplevel variables. *)
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  try Mreg.find reg cl.rn_table with Not_found ->
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  let tl = List.map (clone_ity cl) reg.reg_args in
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  let rl = List.map (clone_ity cl) reg.reg_regs in
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  let r = match Mts.find_opt reg.reg_its.its_ts cl.ts_table with
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    | Some its ->
        create_region (id_clone reg.reg_name) its tl rl
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    | None -> (* creative indentation *)
    begin match Mts.find_opt reg.reg_its.its_ts cl.ty_table with
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    | Some {ity_node = Ityreg r} ->
        let sbs = its_match_regs reg.reg_its tl rl in
        let tl = List.map (ity_full_inst sbs) r.reg_args in
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        let rl = List.map (ity_full_inst sbs) r.reg_regs in
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        create_region (id_clone reg.reg_name) r.reg_its tl rl
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    | Some _ -> assert false
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    | None ->
        create_region (id_clone reg.reg_name) reg.reg_its tl rl
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    end in
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  cl.rn_table <- Mreg.add reg r cl.rn_table;
  r
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let cl_find_ls cl ls =
  if not (Sid.mem ls.ls_name cl.cl_local) then ls
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  else Mls.find ls cl.ls_table
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let clone_term cl mv t = t_gen_map (clone_ty cl) (cl_find_ls cl) mv t
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let clone_fmla cl f = clone_term cl Mvs.empty f (* for closed terms *)
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let cl_find_pr cl pr =
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  if not (Sid.mem pr.pr_name cl.cl_local) then pr
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  else Mpr.find pr cl.pr_table
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let cl_find_pv cl pv =
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  if not (Sid.mem pv.pv_vs.vs_name cl.cl_local) then pv
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  else Mvs.find pv.pv_vs cl.pv_table
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let cl_find_rs cl rs =
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  if not (Sid.mem rs.rs_name cl.cl_local) then rs
  else Mrs.find rs cl.rs_table

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let cl_find_xs cl xs =
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  if not (Sid.mem xs.xs_name cl.cl_local) then xs
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  else Mxs.find xs cl.xs_table
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let cl_init m inst =
  let cl = empty_clones m in
  let non_local id =
    if not (Sid.mem id cl.cl_local) then raise (NonLocal id) in
  Mts.iter (fun ts _ -> non_local ts.ts_name) inst.mi_ts;
  Mts.iter (fun ts _ -> non_local ts.ts_name) inst.mi_ty;
  let check_ls ls _ =
    non_local ls.ls_name;
    try  ignore (restore_rs ls); raise (BadInstance ls.ls_name)
    with Not_found -> () in
  Mls.iter check_ls inst.mi_ls;
  let check_rs rs _ =
    non_local rs.rs_name;
    match (Mid.find rs.rs_name m.mod_known).pd_node with
    | PDtype _ -> raise (BadInstance rs.rs_name)
    | PDlet  _ | PDexn  _ | PDpure -> () in
  Mrs.iter check_rs inst.mi_rs;
  Mvs.iter (fun vs _ -> non_local vs.vs_name) inst.mi_pv;
  Mxs.iter (fun xs _ -> non_local xs.xs_name) inst.mi_xs;
  let check_pk pr _ =
    non_local pr.pr_name;
    match (Mid.find pr.pr_name m.mod_known).pd_node with
    | PDtype _ | PDlet  _ | PDexn  _ -> raise (BadInstance pr.pr_name)
    | PDpure -> () in
  Mpr.iter check_pk inst.mi_pk;
  Mpr.iter (fun pr _ -> raise (BadInstance pr.pr_name)) inst.mi_pr;
  cl

(* clone declarations *)

let clone_ls cl ls =
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  let constr = ls.ls_constr in
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  let id = id_clone ls.ls_name in
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  let at = List.map (clone_ty cl) ls.ls_args in
  let vt = Opt.map (clone_ty cl) ls.ls_value in
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  let ls' = create_lsymbol ~constr id at vt in
  cl.ls_table <- Mls.add ls ls' cl.ls_table;
  ls'

let clone_decl inst cl uc d = match d.d_node with
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  | Dtype _ | Ddata _ -> assert false (* impossible *)
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  | Dparam ({ls_name = id} as ls) when Mls.mem ls inst.mi_ls ->
      let ls' = Mls.find ls inst.mi_ls in
      let mtch sb ty ty' = try ty_match sb ty' (clone_ty cl ty)
        with TypeMismatch _ -> raise (BadInstance id) in
      let sbs = match ls.ls_value,ls'.ls_value with
        | Some ty, Some ty' -> mtch Mtv.empty ty ty'
        | None, None -> Mtv.empty
        | _ -> raise (BadInstance id) in
      ignore (try List.fold_left2 mtch sbs ls.ls_args ls'.ls_args
        with Invalid_argument _ -> raise (BadInstance id));
      cl.ls_table <- Mls.add ls ls' cl.ls_table;
      uc
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  | Dparam ls ->
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      let d = create_param_decl (clone_ls cl ls) in
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      add_pdecl ~warn:false ~vc:false uc (create_pure_decl d)
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  | Dlogic ldl ->
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      List.iter (fun (ls,_) ->
        if Mls.mem ls inst.mi_ls then raise (CannotInstantiate ls.ls_name);
        ignore (clone_ls cl ls)) ldl;
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      let get_logic (_,ld) =
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        Opt.get (ls_defn_of_axiom (clone_fmla cl (ls_defn_axiom ld))) in
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      let d = create_logic_decl (List.map get_logic ldl) in
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      add_pdecl ~warn:false ~vc:false uc (create_pure_decl d)
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  | Dind (s, idl) ->
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      let lls = List.map (fun (ls,_) ->
        if Mls.mem ls inst.mi_ls then raise (CannotInstantiate ls.ls_name);
        clone_ls cl ls) idl in
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      let get_case (pr,f) =
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        if Mpr.mem pr inst.mi_pk then raise (CannotInstantiate pr.pr_name);
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        let pr' = create_prsymbol (id_clone pr.pr_name) in
        cl.pr_table <- Mpr.add pr pr' cl.pr_table;
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        pr', clone_fmla cl f in
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      let get_ind ls (_,la) = ls, List.map get_case la in
      let d = create_ind_decl s (List.map2 get_ind lls idl) in
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      add_pdecl ~warn:false ~vc:false uc (create_pure_decl d)
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  | Dprop (k,pr,f) ->
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      let skip, k' = match k, Mpr.find_opt pr inst.mi_pk with
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        | Pgoal, _ -> true, Pgoal
        | Plemma, Some Pgoal -> true, Pgoal
        | Plemma, _ -> false, Plemma
        | Paxiom, Some k -> false, k
        | Paxiom, None -> false, Paxiom (* TODO: Plemma *) in
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      if skip then uc else
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      let pr' = create_prsymbol (id_clone pr.pr_name) in
      cl.pr_table <- Mpr.add pr pr' cl.pr_table;
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      let d = create_prop_decl k' pr' (clone_fmla cl f) in
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      add_pdecl ~warn:false ~vc:false uc (create_pure_decl d)
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let cl_save_ls cl s s' =
  cl.ls_table <- Mls.add_new (CannotInstantiate s.ls_name) s s' cl.ls_table

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let cl_save_rs cl s s' =
  cl.rs_table <- Mrs.add s s' cl.rs_table;
  begin match s.rs_field, s'.rs_field with
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  | Some v, Some v' -> cl.fd_table <- Mpv.add v v' cl.fd_table
  | None, _ -> () (* can instantiate a non-field with a field *)
  | _ -> assert false (* but not vice versa *)
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  end;
  match s.rs_logic, s'.rs_logic with
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  | RLls s, RLls s' -> cl_save_ls cl s s'
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  | RLlemma, RLlemma -> () (* TODO: update cl.pr_table? *)
  | RLnone, RLnone -> ()
  | _ -> assert false

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type smap = {
  sm_vs : vsymbol Mvs.t;
  sm_pv : pvsymbol Mvs.t;
  sm_rs : rsymbol Mrs.t;
}

let sm_of_cl cl = {
  sm_vs = Mvs.map (fun v -> v.pv_vs) cl.pv_table;
  sm_pv = cl.pv_table;
  sm_rs = cl.rs_table }

let sm_save_vs sm v v' = {
  sm_vs = Mvs.add v v'.pv_vs sm.sm_vs;
  sm_pv = Mvs.add v v' sm.sm_pv;
  sm_rs = sm.sm_rs }

let sm_save_pv sm v v' = {
  sm_vs = Mvs.add v.pv_vs v'.pv_vs sm.sm_vs;
  sm_pv = Mvs.add v.pv_vs v' sm.sm_pv;
  sm_rs = sm.sm_rs }

let sm_save_rs cl sm s s' =
  let sm = { sm with sm_rs = Mrs.add s s' sm.sm_rs } in
  match s.rs_logic, s'.rs_logic with
  | RLls s, RLls s' -> cl_save_ls cl s s'; sm
  | RLpv v, RLpv v' -> sm_save_pv sm v v'
  | _ -> sm

let sm_find_pv sm v = Mvs.find_def v v.pv_vs sm.sm_pv
  (* non-instantiated global variables are not in sm *)

let clone_pv cl {pv_vs = vs; pv_ity = ity; pv_ghost = ghost} =
  create_pvsymbol (id_clone vs.vs_name) ~ghost (clone_ity cl ity)

let clone_invl cl sm invl =
  List.map (fun t -> clone_term cl sm.sm_vs t) invl

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let clone_type_record cl s d s' d' =
  let id = s.its_ts.ts_name in
  let fields' = Hstr.create 16 in
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  let add_field' rs' = let pj' = fd_of_rs rs' in
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    Hstr.add fields' pj'.pv_vs.vs_name.id_string rs' in
  List.iter add_field' d'.itd_fields;
  (* check if fields from former type are also declared in the new type *)
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  let match_pj rs = let pj = fd_of_rs rs in
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    let pj_str = pj.pv_vs.vs_name.id_string in
    let pj_ity = clone_ity cl pj.pv_ity in
    let pj_ght = pj.pv_ghost in
    let rs' = try Hstr.find fields' pj_str
      with Not_found -> raise (BadInstance id) in
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    let pj' = fd_of_rs rs' in
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    let pj'_ity = pj'.pv_ity in
    let pj'_ght = pj'.pv_ghost in
    if not (ity_equal pj_ity pj'_ity && (pj_ght || not pj'_ght)) then
      raise (BadInstance id);
    let ls, ls' = ls_of_rs rs, ls_of_rs rs' in
    cl.ls_table <- Mls.add ls ls' cl.ls_table;
    cl.rs_table <- Mrs.add rs rs' cl.rs_table;
    cl.fd_table <- Mpv.add pj pj' cl.fd_table in
  List.iter match_pj d.itd_fields;
  cl.ts_table <- Mts.add s.its_ts s' cl.ts_table
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let clone_type_decl inst cl tdl kn =
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  let def =
    List.fold_left (fun m d -> Mits.add d.itd_its d m) Mits.empty tdl in
  let htd = Hits.create 5 in
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  let vcs = ref ([] : (itysymbol * term) list) in
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  let rec visit alg ({its_ts = {ts_name = id} as ts} as s) d =
    if not (Hits.mem htd s) then
    let alg = Sits.add s alg in
    let id' = id_clone id in
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    let cloned = Mts.mem ts inst.mi_ts || Mts.mem ts inst.mi_ty in
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    let conv_pj v = create_pvsymbol
      (id_clone v.pv_vs.vs_name) ~ghost:v.pv_ghost (conv_ity alg v.pv_ity) in
    let save_itd itd =
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      List.iter2 (cl_save_rs cl) d.itd_constructors itd.itd_constructors;
      List.iter2 (cl_save_rs cl) d.itd_fields itd.itd_fields;
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      Hits.add htd s (Some itd) in
    (* alias *)
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    if s.its_def <> NoDef then begin
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      if cloned then raise (CannotInstantiate id);
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      let itd = match s.its_def with
        | Alias ty -> create_alias_decl id' ts.ts_args (conv_ity alg ty)
        | Range ir -> create_range_decl id' ir
        | Float ff -> create_float_decl id' ff
        | NoDef -> assert false (* never *) in
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      cl.ts_table <- Mts.add ts itd.itd_its cl.ts_table;
      save_itd itd
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    end else
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    (* abstract *)
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    if s.its_private && cloned then begin
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      begin match Mts.find_opt ts inst.mi_ts with
      | Some s' ->
          if not (List.length ts.ts_args = List.length s'.its_ts.ts_args) then
            raise (BadInstance id);
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          let pd' = Mid.find s'.its_ts.ts_name kn in
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          let d' = match pd'.pd_node with
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            | PDtype [d'] -> d'
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            (* FIXME: we could refine with mutual types *)
            | PDtype _ -> raise (BadInstance id)
            | PDlet _ | PDexn _ | PDpure -> raise (BadInstance id) in
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          clone_type_record cl s d s' d'; (* clone record fields *)
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          (* generate and add VC for type invariant implication *)
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          if d.itd_invariant <> [] then begin
            let inv = axiom_of_invariant d in
            let invl = clone_invl cl (sm_of_cl cl) [inv] in
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            let add_vc inv = vcs := (d.itd_its, inv) :: !vcs in
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            List.iter add_vc invl end
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      | None -> begin match Mts.find_opt ts inst.mi_ty with
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      | Some ity -> (* creative indentation *)
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          (* TODO: clone_type_record, axiom_of_invariant *)
          (* TODO: should we only allow cloning into ity for
             private types with no fields and no invariant? *)
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          let stv = Stv.of_list ts.ts_args in
          if not (Stv.subset (ity_freevars Stv.empty ity) stv &&
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                  its_pure s && ity_immutable ity) then raise (BadInstance id);
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          cl.ty_table <- Mts.add ts ity cl.ty_table
      | None -> assert false end end;
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      Hits.add htd s None;
      (* TODO: check typing conditions for refined record type *)
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    end else
    (* variant *)
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    if not s.its_mutable && d.itd_constructors <> [] &&
                            d.itd_invariant = [] then begin
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      if cloned then raise (CannotInstantiate id);
      let conv_fd m fd =
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        let v = fd_of_rs fd in Mpv.add v (conv_pj v) m in
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      let fldm = List.fold_left conv_fd Mpv.empty d.itd_fields in
      let conv_pj pj = match Mpv.find_opt pj fldm with
        | Some pj' -> true, pj' | None -> false, conv_pj pj in
      let conv_cs cs =
        id_clone cs.rs_name, List.map conv_pj cs.rs_cty.cty_args in
      let csl = List.map conv_cs d.itd_constructors in
      match Mts.find_opt ts cl.ts_table with
      | Some s' ->
          let itd = create_rec_variant_decl s' csl in
          save_itd itd
      | None ->
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          let itd = create_plain_variant_decl id' ts.ts_args csl in
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          cl.ts_table <- Mts.add ts itd.itd_its cl.ts_table;
          save_itd itd
    end else begin
    (* flat record *)
      if cloned then raise (CannotInstantiate id);
      let mfld = Spv.of_list s.its_mfields in
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      let pjl = List.map fd_of_rs d.itd_fields in
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      let fdl = List.map (fun v -> Spv.mem v mfld, conv_pj v) pjl in
      let inv =
        if d.itd_invariant = [] then [] else
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        let add mv u (_,v) = Mvs.add u.pv_vs v.pv_vs mv in
        let mv = List.fold_left2 add Mvs.empty pjl fdl in
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        List.map (clone_term cl mv) d.itd_invariant in
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      let itd = create_plain_record_decl id' ts.ts_args
        ~priv:s.its_private ~mut:s.its_mutable fdl inv in
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      cl.ts_table <- Mts.add ts itd.itd_its cl.ts_table;
      save_itd itd
    end
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  and conv_ity alg ity =
    let rec down ity = match ity.ity_node with
      | Ityreg {reg_its = s; reg_args = tl}
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      | Ityapp (s,tl,_) ->
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          if Sits.mem s alg then begin
            if not (Mts.mem s.its_ts cl.ts_table) then
            let id = id_clone s.its_ts.ts_name in
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            let s' = create_rec_itysymbol id s.its_ts.ts_args in
            cl.ts_table <- Mts.add s.its_ts s' cl.ts_table
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          end else Opt.iter (visit alg s) (Mits.find_opt s def);
          List.iter down tl
      | Ityvar _ -> () in
    down ity;
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    clone_ity cl ity in
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  Mits.iter (visit Sits.empty) def;
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  Lists.map_filter (fun d -> Hits.find htd d.itd_its) tdl,
  !vcs
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let clone_varl cl sm varl = List.map (fun (t,r) ->
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  clone_term cl sm.sm_vs t, Opt.map (cl_find_ls cl) r) varl
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let clone_cty cl sm ?(drop_decr=false) cty =
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  let res = clone_ity cl cty.cty_result in
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  let args = List.map (clone_pv cl) cty.cty_args in
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  let sm_args = List.fold_left2 sm_save_pv sm cty.cty_args args in
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  let add_old o n (sm, olds) = let o' = clone_pv cl o in
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    sm_save_pv sm o o', Mpv.add o' (sm_find_pv sm_args n) olds in
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  let sm_olds, olds = Mpv.fold add_old cty.cty_oldies (sm_args, Mpv.empty) in
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  let pre = if drop_decr then List.tl cty.cty_pre else cty.cty_pre in
  let pre = clone_invl cl sm_args pre in
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  let post = clone_invl cl sm_olds cty.cty_post in
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  let xpost = Mxs.fold (fun xs fl q ->
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    let xs = cl_find_xs cl xs in
    let fl = clone_invl cl sm_olds fl in
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    Mxs.add xs fl q) cty.cty_xpost Mxs.empty in
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  let add_read v s = Spv.add (sm_find_pv sm_args v) s in
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  let reads = Spv.fold add_read (cty_reads cty) Spv.empty in
  let reads = List.fold_right add_read cty.cty_args reads in
  let reads = Spv.union reads (Mpv.domain olds) in
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  let add_write reg fs m = (* add new mutable fields to functions effect *)
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    let add_fd fd s = Spv.add (Mpv.find_def fd fd cl.fd_table) s in
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    let reg' = clone_reg cl reg in
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    let smf_reg' = Spv.of_list reg'.reg_its.its_mfields in
    let smf_reg = Spv.of_list reg.reg_its.its_mfields in
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    let smf_ref = Spv.fold add_fd smf_reg Spv.empty in
    let smf_new = Spv.diff smf_reg' smf_ref in
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    let fs = Spv.fold add_fd fs Spv.empty in
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    Mreg.add reg' (Spv.union fs smf_new) m in
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  let writes = Mreg.fold add_write cty.cty_effect.eff_writes Mreg.empty in
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  let add_reset reg s = Sreg.add (clone_reg cl reg) s in
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  let resets = Sreg.fold add_reset cty.cty_effect.eff_resets Sreg.empty in
  let eff = eff_reset (eff_write reads writes) resets in
  let add_raise xs eff = eff_raise eff (cl_find_xs cl xs) in
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  let eff = Sxs.fold add_raise cty.cty_effect.eff_raises eff in
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  let eff = if cty.cty_effect.eff_oneway then eff_diverge eff else eff in
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  let cty = create_cty ~mask:cty.cty_mask args pre post xpost olds eff res in
  cty_ghostify (cty_ghost cty) cty
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let sm_save_args sm c c' =
  List.fold_left2 sm_save_pv sm c.cty_args c'.cty_args

let sm_save_olds sm c c' =
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  let revs = Mpv.fold (fun o n m -> Mpv.add n o m) c'.cty_oldies Mpv.empty in
  let add_old o n sm = sm_save_pv sm o (Mpv.find (sm_find_pv sm n) revs) in
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  Mpv.fold add_old c.cty_oldies sm

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let clone_ppat cl sm pp mask =
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  let rec conv_pat p = match p.pat_node with
    | Term.Pwild -> PPwild
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    | Term.Pvar v -> PPvar (id_clone v.vs_name, (restore_pv v).pv_ghost)
    | Term.Pas (p,v) ->
        PPas (conv_pat p, id_clone v.vs_name, (restore_pv v).pv_ghost)
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    | Term.Por (p1,p2) -> PPor (conv_pat p1, conv_pat p2)
    | Term.Papp (s,pl) ->
        PPapp (restore_rs (cl_find_ls cl s), List.map conv_pat pl) in
  let pre = conv_pat pp.pp_pat in
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  let vm, pp' = create_prog_pattern pre (clone_ity cl pp.pp_ity) mask in
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  let save v sm = sm_save_vs sm v (Mstr.find v.vs_name.id_string vm) in
  Svs.fold save pp.pp_pat.pat_vars sm, pp'

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let rec clone_expr cl sm e = e_label_copy e (match e.e_node with
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  | Evar v -> e_var (sm_find_pv sm v)
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  | Econst c -> e_const c e.e_ity
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  | Eexec (c,_) -> e_exec (clone_cexp cl sm c)
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  | Eassign asl ->
      let conv (r,f,v) =
        e_var (sm_find_pv sm r), cl_find_rs cl f, e_var (sm_find_pv sm v) in
      e_assign (List.map conv asl)
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  | Elet (ld, e) ->
      let sm, ld = clone_let_defn cl sm ld in
      e_let ld (clone_expr cl sm e)
  | Eif (e1, e2, e3) ->
      e_if (clone_expr cl sm e1) (clone_expr cl sm e2) (clone_expr cl sm e3)
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  | Ecase (d, bl) ->
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      let d = clone_expr cl sm d in
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      let conv_br (pp, e) =
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        let sm, pp = clone_ppat cl sm pp d.e_mask in
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        pp, clone_expr cl sm e in
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      e_case d (List.map conv_br bl)
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  | Ewhile (c,invl,varl,e) ->
      e_while (clone_expr cl sm c) (clone_invl cl sm invl)
              (clone_varl cl sm varl) (clone_expr cl sm e)
  | Efor (i, (f,dir,t), invl, e) ->
      let i' = clone_pv cl i in
      let ism = sm_save_pv sm i i' in
      e_for i'
        (e_var (sm_find_pv sm f)) dir (e_var (sm_find_pv sm t))
        (clone_invl cl ism invl) (clone_expr cl ism e)
  | Etry (d, xl) ->
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      let conv_br xs (vl, e) m =
        let vl' = List.map (clone_pv cl) vl in
        let sm = List.fold_left2 sm_save_pv sm vl vl' in
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        Mxs.add (cl_find_xs cl xs) (vl', clone_expr cl sm e) m in
      e_try (clone_expr cl sm d) (Mxs.fold conv_br xl Mxs.empty)
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  | Eraise (xs, e) ->
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      e_raise (cl_find_xs cl xs) (clone_expr cl sm e) (clone_ity cl e.e_ity)
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  | Eassert (k, f) ->
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      e_assert k (clone_term cl sm.sm_vs f)
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  | Eghost e ->
      e_ghostify true (clone_expr cl sm e)
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  | Epure t ->
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      e_pure (clone_term cl sm.sm_vs t)