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(********************************************************************)
(*                                                                  *)
(*  The Why3 Verification Platform   /   The Why3 Development Team  *)
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(*  Copyright 2010-2013   --   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.                           *)
(*                                                                  *)
(********************************************************************)
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open Stdlib
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open Ident
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open Ptree
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open Ty
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open Term
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open Decl
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open Theory
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open Dterm
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open Env
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(** debug flags *)
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let debug_parse_only = Debug.register_flag "parse_only"
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  ~desc:"Stop@ after@ parsing."
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let debug_type_only  = Debug.register_flag "type_only"
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  ~desc:"Stop@ after@ type-checking."
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(** errors *)
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exception UnboundTypeVar of string
exception DuplicateTypeVar of string
exception ClashTheory of string
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(** lazy declaration of tuples *)
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let add_ty_decl uc ts      = add_decl_with_tuples uc (create_ty_decl ts)
let add_data_decl uc dl    = add_decl_with_tuples uc (create_data_decl dl)
let add_param_decl uc ls   = add_decl_with_tuples uc (create_param_decl ls)
let add_logic_decl uc dl   = add_decl_with_tuples uc (create_logic_decl dl)
let add_ind_decl uc s dl   = add_decl_with_tuples uc (create_ind_decl s dl)
let add_prop_decl uc k p f = add_decl_with_tuples uc (create_prop_decl k p f)
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(** symbol lookup *)
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let rec qloc = function
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  | Qdot (p, id) -> Loc.join (qloc p) id.id_loc
  | Qident id    -> id.id_loc

let rec print_qualid fmt = function
  | Qdot (p, id) -> Format.fprintf fmt "%a.%s" print_qualid p id.id
  | Qident id    -> Format.fprintf fmt "%s" id.id
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let string_list_of_qualid q =
  let rec sloq acc = function
    | Qdot (p, id) -> sloq (id.id :: acc) p
    | Qident id -> id.id :: acc in
  sloq [] q
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exception UnboundSymbol of qualid
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let find_qualid get_id find ns q =
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  let sl = string_list_of_qualid q in
  let r = try find ns sl with Not_found ->
    Loc.error ~loc:(qloc q) (UnboundSymbol q) in
  if Debug.test_flag Glob.flag then Glob.use (qloc q) (get_id r);
  r
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let find_prop_ns     ns q = find_qualid (fun pr -> pr.pr_name) ns_find_pr ns q
let find_tysymbol_ns ns q = find_qualid (fun ts -> ts.ts_name) ns_find_ts ns q
let find_lsymbol_ns  ns q = find_qualid (fun ls -> ls.ls_name) ns_find_ls ns q
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let find_fsymbol_ns ns q =
  let ls = find_lsymbol_ns ns q in
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  if ls.ls_value <> None then ls else
    Loc.error ~loc:(qloc q) (FunctionSymbolExpected ls)
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let find_psymbol_ns ns q =
  let ls = find_lsymbol_ns ns q in
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  if ls.ls_value = None then ls else
    Loc.error ~loc:(qloc q) (PredicateSymbolExpected ls)
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let find_prop     uc q = find_prop_ns     (get_namespace uc) q
let find_tysymbol uc q = find_tysymbol_ns (get_namespace uc) q
let find_lsymbol  uc q = find_lsymbol_ns  (get_namespace uc) q
let find_fsymbol  uc q = find_fsymbol_ns  (get_namespace uc) q
let find_psymbol  uc q = find_psymbol_ns  (get_namespace uc) q
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let find_namespace_ns ns q =
  find_qualid (fun _ -> Glob.dummy_id) ns_find_ns ns q
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(** Parsing types *)

let create_user_tv =
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  let hs = Hstr.create 17 in fun s ->
  try Hstr.find hs s with Not_found ->
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  let tv = create_tvsymbol (id_fresh s) in
  Hstr.add hs s tv;
  tv
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let ty_of_pty_top ~noop uc pty =
  let rec get_ty = function
    | PPTtyvar ({id_loc = loc}, true) when noop ->
        Loc.errorm ~loc "Opaqueness@ annotations@ are@ only@ \
          allowed@ in@ function@ and@ predicate@ prototypes"
    | PPTtyvar ({id = x}, _) ->
        ty_var (create_user_tv x)
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    | PPTtyapp (q, tyl) ->
        let ts = find_tysymbol uc q in
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        let tyl = List.map get_ty tyl in
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        Loc.try2 ~loc:(qloc q) ty_app ts tyl
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    | PPTtuple tyl ->
        let ts = ts_tuple (List.length tyl) in
        ty_app ts (List.map get_ty tyl)
    | PPTarrow (ty1, ty2) ->
        ty_func (get_ty ty1) (get_ty ty2)
    | PPTparen ty ->
        get_ty ty
  in
  get_ty pty

let ty_of_pty uc pty = ty_of_pty_top ~noop:true uc pty
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let opaque_tvs args =
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  let rec opaque_tvs acc = function
    | PPTtyvar (id, true) -> Stv.add (create_user_tv id.id) acc
    | PPTtyvar (_, false) -> acc
    | PPTtyapp (_, pl)
    | PPTtuple pl -> List.fold_left opaque_tvs acc pl
    | PPTarrow (ty1, ty2) -> opaque_tvs (opaque_tvs acc ty1) ty2
    | PPTparen ty -> opaque_tvs acc ty in
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  List.fold_left (fun acc (_,_,_,ty) -> opaque_tvs acc ty) Stv.empty args
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(** typing using destructive type variables
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    parsed trees        intermediate trees       typed trees
      (Ptree)                (Dterm)               (Term)
   -----------------------------------------------------------
     ppure_type  ---dty--->   dty       ---ty--->    ty
      lexpr      --dterm-->   dterm     --term-->    term
*)
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(** Typing patterns, terms, and formulas *)

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let create_user_id {id = n; id_lab = label; id_loc = loc} =
  let get_labels (label, loc) = function
    | Lstr lab -> Slab.add lab label, loc | Lpos loc -> label, loc in
  let label,loc = List.fold_left get_labels (Slab.empty,loc) label in
  id_user ~label n loc
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let parse_record ~loc uc get_val fl =
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  let fl = List.map (fun (q,e) -> find_lsymbol uc q, e) fl in
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  let cs,pjl,flm = Loc.try2 ~loc parse_record (get_known uc) fl in
  let get_val pj = get_val cs pj (Mls.find_opt pj flm) in
  cs, List.map get_val pjl

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let rec dpattern uc { pat_desc = desc; pat_loc = loc } =
  Dterm.dpattern ~loc (match desc with
    | PPpwild -> DPwild
    | PPpvar x -> DPvar (create_user_id x)
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    | PPpapp (q,pl) ->
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        let pl = List.map (dpattern uc) pl in
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        DPapp (find_lsymbol uc q, pl)
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    | PPptuple pl ->
        let pl = List.map (dpattern uc) pl in
        DPapp (fs_tuple (List.length pl), pl)
    | PPprec fl ->
        let get_val _ _ = function
          | Some p -> dpattern uc p
          | None -> Dterm.dpattern DPwild in
        let cs,fl = parse_record ~loc uc get_val fl in
        DPapp (cs,fl)
    | PPpas (p, x) -> DPas (dpattern uc p, create_user_id x)
    | PPpor (p, q) -> DPor (dpattern uc p, dpattern uc q))
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let quant_var uc (x,ty) =
  create_user_id x, match ty with
    | Some ty -> dty_of_ty (ty_of_pty uc ty)
    | None -> dty_fresh ()

let chainable_op uc op =
  (* non-bool -> non-bool -> bool *)
  op.id = "infix =" || op.id = "infix <>" ||
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  match find_lsymbol uc (Qident op) with
  | {ls_args = [ty1;ty2]; ls_value = ty} ->
      Opt.fold (fun _ ty -> ty_equal ty ty_bool) true ty
      && not (ty_equal ty1 ty_bool)
      && not (ty_equal ty2 ty_bool)
  | _ -> false
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type global_vs = Ptree.qualid -> vsymbol option

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let rec dterm uc gvars denv {pp_desc = desc; pp_loc = loc} =
  let func_app loc e el =
    let app (loc, e) e1 = Loc.join loc e1.pp_loc,
      DTfapp (Dterm.dterm ~loc e, dterm uc gvars denv e1) in
    snd (List.fold_left app (loc, e) el)
  in
  let rec take loc al l el = match l, el with
    | (_::l), (e::el) ->
        take (Loc.join loc e.pp_loc) (dterm uc gvars denv e :: al) l el
    | _, _ -> loc, List.rev al, el
  in
  let qualid_app loc q el = match gvars q with
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    | Some vs ->
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        func_app loc (DTgvar vs) el
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    | None ->
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        let ls = find_lsymbol uc q in
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        let loc, al, el = take loc [] ls.ls_args el in
        func_app loc (DTapp (ls,al)) el
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  in
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  let qualid_app loc q el = match q with
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    | Qident {id = n} ->
        (match denv_get_opt denv n with
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        | Some d -> func_app loc d el
        | None -> qualid_app loc q el)
    | _ -> qualid_app loc q el
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  in
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  Dterm.dterm ~loc (match desc with
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  | PPident q ->
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      qualid_app loc q []
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  | PPidapp (q, tl) ->
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      qualid_app (qloc q) q tl
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  | PPapply (e1, e2) ->
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      DTfapp (dterm uc gvars denv e1, dterm uc gvars denv e2)
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  | PPtuple tl ->
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      let tl = List.map (dterm uc gvars denv) tl in
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      DTapp (fs_tuple (List.length tl), tl)
  | PPinfix (e12, op2, e3)
  | PPinnfix (e12, op2, e3) ->
      let make_app de1 op de2 = if op.id = "infix <>" then
        let op = { op with id = "infix =" } in
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        let ls = find_lsymbol uc (Qident op) in
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        DTnot (Dterm.dterm ~loc (DTapp (ls, [de1;de2])))
      else
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        DTapp (find_lsymbol uc (Qident op), [de1;de2])
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      in
      let rec make_chain de1 = function
        | [op,de2] ->
            make_app de1 op de2
        | (op,de2) :: ch ->
            let de12 = Dterm.dterm ~loc (make_app de1 op de2) in
            let de23 = Dterm.dterm ~loc (make_chain de2 ch) in
            DTbinop (Tand, de12, de23)
        | [] -> assert false in
      let rec get_chain e12 acc = match e12.pp_desc with
        | PPinfix (e1, op1, e2) when chainable_op uc op1 ->
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            get_chain e1 ((op1, dterm uc gvars denv e2) :: acc)
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        | _ -> e12, acc in
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      let ch = [op2, dterm uc gvars denv e3] in
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      let e1, ch = if chainable_op uc op2
        then get_chain e12 ch else e12, ch in
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      make_chain (dterm uc gvars denv e1) ch
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  | PPconst c ->
      DTconst c
  | PPlet (x, e1, e2) ->
      let id = create_user_id x in
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      let e1 = dterm uc gvars denv e1 in
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      let denv = denv_add_let denv e1 id in
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      let e2 = dterm uc gvars denv e2 in
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      DTlet (e1, id, e2)
  | PPmatch (e1, bl) ->
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      let e1 = dterm uc gvars denv e1 in
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      let branch (p, e) =
        let p = dpattern uc p in
        let denv = denv_add_pat denv p in
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        p, dterm uc gvars denv e in
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      DTcase (e1, List.map branch bl)
  | PPif (e1, e2, e3) ->
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      let e1 = dterm uc gvars denv e1 in
      let e2 = dterm uc gvars denv e2 in
      let e3 = dterm uc gvars denv e3 in
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      DTif (e1, e2, e3)
  | PPtrue ->
      DTtrue
  | PPfalse ->
      DTfalse
  | PPunop (PPnot, e1) ->
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      DTnot (dterm uc gvars denv e1)
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  | PPbinop (e1, op, e2) ->
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      let e1 = dterm uc gvars denv e1 in
      let e2 = dterm uc gvars denv e2 in
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      let op = match op with
        | PPand -> Tand
        | PPor -> Tor
        | PPimplies -> Timplies
        | PPiff -> Tiff in
      DTbinop (op, e1, e2)
  | PPquant (q, uqu, trl, e1) ->
      let qvl = List.map (quant_var uc) uqu in
      let denv = denv_add_quant denv qvl in
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      let dterm e = dterm uc gvars denv e in
      let trl = List.map (List.map dterm) trl in
      let e1 = dterm e1 in
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      begin match q with
        | PPforall -> DTquant (Tforall, qvl, trl, e1)
        | PPexists -> DTquant (Texists, qvl, trl, e1)
        | PPlambda ->
            let id = id_user "fc" loc and dty = dty_fresh () in
            let add acc ({id = x}, _) =
              let arg = Dterm.dterm ~loc (denv_get denv x) in
              DTapp (fs_func_app, [Dterm.dterm ~loc acc; arg]) in
            let app = List.fold_left add (DTvar ("fc",dty)) uqu in
            let f = DTapp (ps_equ, [Dterm.dterm ~loc app; e1]) in
            let f = DTquant (Tforall, qvl, trl, Dterm.dterm ~loc f) in
            DTeps (id, dty, Dterm.dterm ~loc f)
      end
  | PPrecord fl ->
      let get_val cs pj = function
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        | Some e -> dterm uc gvars denv e
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        | None -> Loc.error ~loc (RecordFieldMissing (cs,pj)) in
      let cs, fl = parse_record ~loc uc get_val fl in
      DTapp (cs, fl)
  | PPupdate (e1, fl) ->
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      let e1 = dterm uc gvars denv e1 in
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      let get_val _ pj = function
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        | Some e -> dterm uc gvars denv e
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        | None -> Dterm.dterm ~loc (DTapp (pj,[e1])) in
      let cs, fl = parse_record ~loc uc get_val fl in
      DTapp (cs, fl)
  | PPnamed (Lpos uloc, e1) ->
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      DTuloc (dterm uc gvars denv e1, uloc)
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  | PPnamed (Lstr lab, e1) ->
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      DTlabel (dterm uc gvars denv e1, Slab.singleton lab)
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  | PPcast (e1, ty) ->
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      DTcast (dterm uc gvars denv e1, ty_of_pty uc ty))
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(** Export for program parsing *)
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let type_term uc gvars t =
  let t = dterm uc gvars denv_empty t in
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  Dterm.term ~strict:true ~keep_loc:true t
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let type_fmla uc gvars f =
  let f = dterm uc gvars denv_empty f in
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  Dterm.fmla ~strict:true ~keep_loc:true f
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(** Typing declarations *)
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let tyl_of_params ~noop uc pl =
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  let ty_of_param (loc,_,gh,ty) =
    if gh then Loc.errorm ~loc
      "ghost parameters are not allowed in pure declarations";
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    ty_of_pty_top ~noop uc ty in
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  List.map ty_of_param pl

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let add_types dl th =
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  let def = List.fold_left
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    (fun def d ->
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      let id = d.td_ident.id in
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      Mstr.add_new (Loc.Located (d.td_loc, ClashSymbol id)) id d def)
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    Mstr.empty dl
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  in
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  let tysymbols = Hstr.create 17 in
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  let rec visit x =
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    let d = Mstr.find x def in
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    try
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      match Hstr.find tysymbols x with
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        | None -> Loc.errorm ~loc:d.td_loc "Cyclic type definition"
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        | Some ts -> ts
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    with Not_found ->
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      Hstr.add tysymbols x None;
      let vars = Hstr.create 17 in
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      let vl = List.map (fun id ->
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        if Hstr.mem vars id.id then
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          Loc.error ~loc:id.id_loc (DuplicateTypeVar id.id);
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        let i = create_user_tv id.id in
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        Hstr.add vars id.id i;
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        i) d.td_params
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      in
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      let id = create_user_id d.td_ident in
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      let ts = match d.td_def with
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        | TDalias ty ->
            let rec apply = function
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              | PPTtyvar (v, _) ->
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                  begin
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                    try ty_var (Hstr.find vars v.id) with Not_found ->
                      Loc.error ~loc:v.id_loc (UnboundTypeVar v.id)
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                  end
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              | PPTtyapp (q, tyl) ->
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                  let ts = match q with
                    | Qident x when Mstr.mem x.id def ->
                        visit x.id
                    | Qident _ | Qdot _ ->
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                        find_tysymbol th q
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                  in
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                  Loc.try2 ~loc:(qloc q) ty_app ts (List.map apply tyl)
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              | PPTtuple tyl ->
                  let ts = ts_tuple (List.length tyl) in
                  ty_app ts (List.map apply tyl)
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              | PPTarrow (ty1, ty2) ->
                  ty_func (apply ty1) (apply ty2)
              | PPTparen ty ->
                  apply ty
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            in
            create_tysymbol id vl (Some (apply ty))
        | TDabstract | TDalgebraic _ ->
            create_tysymbol id vl None
        | TDrecord _ ->
            assert false
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      in
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      Hstr.add tysymbols x (Some ts);
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      ts
  in
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  let th' =
    let add_ts (abstr,alias) d =
      let ts = visit d.td_ident.id in
      if ts.ts_def = None then ts::abstr, alias else abstr, ts::alias in
    let abstr,alias = List.fold_left add_ts ([],[]) dl in
    try
      let th = List.fold_left add_ty_decl th abstr in
      let th = List.fold_left add_ty_decl th alias in
      th
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    with ClashSymbol s ->
      Loc.error ~loc:(Mstr.find s def).td_loc (ClashSymbol s)
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  in
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  let csymbols = Hstr.create 17 in
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  let decl d (abstr,algeb,alias) =
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    let ts = match Hstr.find tysymbols d.td_ident.id with
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      | None ->
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          assert false
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      | Some ts ->
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          ts
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    in
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    match d.td_def with
      | TDabstract -> ts::abstr, algeb, alias
      | TDalias _ -> abstr, algeb, ts::alias
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      | TDalgebraic cl ->
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          let ht = Hstr.create 17 in
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          let constr = List.length cl in
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          let opaque = Stv.of_list ts.ts_args in
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          let ty = ty_app ts (List.map ty_var ts.ts_args) in
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          let projection (_,id,_,_) fty = match id with
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            | None -> None
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            | Some ({ id = x; id_loc = loc } as id) ->
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                try
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                  let pj = Hstr.find ht x in
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                  let ty = Opt.get pj.ls_value in
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                  ignore (Loc.try2 ~loc ty_equal_check ty fty);
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                  Some pj
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                with Not_found ->
                  let fn = create_user_id id in
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                  let pj = create_fsymbol ~opaque fn [ty] fty in
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                  Hstr.replace csymbols x loc;
                  Hstr.replace ht x pj;
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                  Some pj
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          in
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          let constructor (loc, id, pl) =
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            let tyl = tyl_of_params ~noop:true th' pl in
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            let pjl = List.map2 projection pl tyl in
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            Hstr.replace csymbols id.id loc;
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            create_fsymbol ~opaque ~constr (create_user_id id) tyl ty, pjl
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          in
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          abstr, (ts, List.map constructor cl) :: algeb, alias
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      | TDrecord _ ->
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          assert false
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  in
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  let abstr,algeb,alias = List.fold_right decl dl ([],[],[]) in
  try
    let th = List.fold_left add_ty_decl th abstr in
    let th = if algeb = [] then th else add_data_decl th algeb in
    let th = List.fold_left add_ty_decl th alias in
    th
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  with
    | ClashSymbol s ->
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        Loc.error ~loc:(Hstr.find csymbols s) (ClashSymbol s)
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    | RecordFieldMissing ({ ls_name = { id_string = s }} as cs,ls) ->
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        Loc.error ~loc:(Hstr.find csymbols s) (RecordFieldMissing (cs,ls))
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    | DuplicateRecordField ({ ls_name = { id_string = s }} as cs,ls) ->
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        Loc.error ~loc:(Hstr.find csymbols s) (DuplicateRecordField (cs,ls))
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let prepare_typedef td =
  if td.td_model then
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    Loc.errorm ~loc:td.td_loc "model types are not allowed in pure theories";
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  if td.td_vis <> Public then
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    Loc.errorm ~loc:td.td_loc "pure types cannot be abstract or private";
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  if td.td_inv <> [] then
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    Loc.errorm ~loc:td.td_loc "pure types cannot have invariants";
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  match td.td_def with
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  | TDabstract | TDalgebraic _ | TDalias _ ->
      td
  | TDrecord fl ->
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      let field { f_loc = loc; f_ident = id; f_pty = ty;
                  f_mutable = mut; f_ghost = gh } =
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        if mut then Loc.errorm ~loc "a logic record field cannot be mutable";
        if gh then Loc.errorm ~loc "a logic record field cannot be ghost";
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        loc, Some id, false, ty
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      in
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      (* constructor for type t is "mk t" (and not String.capitalize t) *)
      let id = { td.td_ident with id = "mk " ^ td.td_ident.id } in
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      { td with td_def = TDalgebraic [td.td_loc, id, List.map field fl] }

let add_types dl th =
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  add_types (List.map prepare_typedef dl) th
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let add_logics dl th =
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  let lsymbols = Hstr.create 17 in
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  (* 1. create all symbols and make an environment with these symbols *)
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  let create_symbol th d =
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    let id = d.ld_ident.id in
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    let v = create_user_id d.ld_ident in
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    let pl = tyl_of_params ~noop:false th d.ld_params in
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    let ty = Opt.map (ty_of_pty th) d.ld_type in
    let opaque = opaque_tvs d.ld_params in
    (* for abstract lsymbols fresh tyvars are opaque *)
    let opaque = if d.ld_def = None && ty <> None then
      let atvs = List.fold_left ty_freevars Stv.empty pl in
      let vtvs = oty_freevars Stv.empty ty in
      Stv.union opaque (Stv.diff vtvs atvs)
    else opaque in
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    let ls = create_lsymbol ~opaque v pl ty in
    Hstr.add lsymbols id ls;
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    Loc.try2 ~loc:d.ld_loc add_param_decl th ls
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  in
  let th' = List.fold_left create_symbol th dl in
  (* 2. then type-check all definitions *)
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  let type_decl d (abst,defn) =
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    let id = d.ld_ident.id in
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    let ls = Hstr.find lsymbols id in
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    let create_var (loc,x,_,_) ty =
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      let id = match x with
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        | Some id -> create_user_id id
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        | None -> id_user "_" loc in
      create_vsymbol id ty in
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    let vl = List.map2 create_var d.ld_params ls.ls_args in
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    let add_var mvs (_,x,_,_) vs = match x with
      | Some {id = id} -> Mstr.add_new (DuplicateVar id) id (DTgvar vs) mvs
      | None -> mvs in
    let denv = List.fold_left2 add_var denv_empty d.ld_params vl in
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    match d.ld_def, d.ld_type with
    | None, _ -> ls :: abst, defn
    | Some e, None -> (* predicate *)
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        let f = dterm th' (fun _ -> None) denv e in
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        let f = fmla ~strict:true ~keep_loc:true f in
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        abst, (ls, vl, f) :: defn
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    | Some e, Some ty -> (* function *)
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        let e = { e with pp_desc = PPcast (e, ty) } in
        let t = dterm th' (fun _ -> None) denv e in
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        let t = term ~strict:true ~keep_loc:true t in
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        abst, (ls, vl, t) :: defn
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  in
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  let abst,defn = List.fold_right type_decl dl ([],[]) in
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  (* 3. detect opacity *)
  let ldefns defn =
    let ht = Hls.create 3 in
    let add_ls (ls,_,_) =
      let tvs = oty_freevars Stv.empty ls.ls_value in
      let tvs = List.fold_left ty_freevars tvs ls.ls_args in
      Hls.replace ht ls tvs in
    List.iter add_ls defn;
    let compared s ls args value =
      let sbs = oty_match Mtv.empty ls.ls_value value in
      let sbs = List.fold_left2 ty_match sbs ls.ls_args args in
      let opq = try Hls.find ht ls with Not_found -> ls.ls_opaque in
      Mtv.fold (fun _ ty s -> ty_freevars s ty) (Mtv.set_diff sbs opq) s in
    let check_ld fixp (ls,_,t) =
      let opq = Hls.find ht ls in
      let npq = Stv.diff opq (t_app_fold compared Stv.empty t) in
      Hls.replace ht ls npq;
      fixp && Stv.equal opq npq in
    let rec fixp () =
      if not (List.fold_left check_ld true defn) then fixp () in
    fixp ();
    let mk_sbs sbs ({ls_name = id} as ls,_,_) =
      let opaque = Stv.union ls.ls_opaque (Hls.find ht ls) in
      if Stv.equal ls.ls_opaque opaque then sbs else
      let nls = create_lsymbol ~opaque (id_clone id) ls.ls_args ls.ls_value in
      Mls.add ls nls sbs in
    let sbs = List.fold_left mk_sbs Mls.empty defn in
    let mk_ld (ls,vl,t) =
      let get_ls ls = Mls.find_def ls ls sbs in
      make_ls_defn (get_ls ls) vl (t_s_map (fun ty -> ty) get_ls t) in
    List.map mk_ld defn
  in
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  let th = List.fold_left add_param_decl th abst in
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  let th = if defn = [] then th else add_logic_decl th (ldefns defn) in
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  th
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let add_prop k loc s f th =
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  let pr = create_prsymbol (create_user_id s) in
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  let f = type_fmla th (fun _ -> None) f in
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  Loc.try4 ~loc add_prop_decl th k pr f
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let loc_of_id id = Opt.get id.Ident.id_loc
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let add_inductives s dl th =
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  (* 1. create all symbols and make an environment with these symbols *)
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  let psymbols = Hstr.create 17 in
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  let create_symbol th d =
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    let id = d.in_ident.id in
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    let v = create_user_id d.in_ident in
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    let pl = tyl_of_params ~noop:false th d.in_params in
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    let opaque = opaque_tvs d.in_params in
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    let ps = create_psymbol ~opaque v pl in
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    Hstr.add psymbols id ps;
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    Loc.try2 ~loc:d.in_loc add_param_decl th ps
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  in
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  let th' = List.fold_left create_symbol th dl in
  (* 2. then type-check all definitions *)
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  let propsyms = Hstr.create 17 in
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  let type_decl d =
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    let id = d.in_ident.id in
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    let ps = Hstr.find psymbols id in
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    let clause (loc, id, f) =
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      Hstr.replace propsyms id.id loc;
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      let f = type_fmla th' (fun _ -> None) f in
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      create_prsymbol (create_user_id id), f
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    in
    ps, List.map clause d.in_def
  in
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  try add_ind_decl th s (List.map type_decl dl)
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  with
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  | ClashSymbol s ->
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      Loc.error ~loc:(Hstr.find propsyms s) (ClashSymbol s)
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  | InvalidIndDecl (ls,pr) ->
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      Loc.error ~loc:(loc_of_id pr.pr_name) (InvalidIndDecl (ls,pr))
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  | NonPositiveIndDecl (ls,pr,s) ->
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      Loc.error ~loc:(loc_of_id pr.pr_name) (NonPositiveIndDecl (ls,pr,s))
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(* parse declarations *)
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let prop_kind = function
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  | Kaxiom -> Paxiom
  | Kgoal -> Pgoal
  | Klemma -> Plemma
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let find_theory env lenv q = match q with
  | Qident { id = id } -> (* local theory *)
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      begin try Mstr.find id lenv
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      with Not_found -> read_lib_theory env [] id end
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  | Qdot (p, { id = id }) -> (* theory in file f *)
      read_lib_theory env (string_list_of_qualid p) id
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let rec clone_ns kn sl path ns2 ns1 s =
  let qualid fmt path = Pp.print_list
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    (fun fmt () -> Format.pp_print_char fmt '.')
    Format.pp_print_string fmt (List.rev path) in
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  let s = Mstr.fold (fun nm ns1 acc ->
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    let ns2 = Mstr.find_def empty_ns nm ns2.ns_ns in
    clone_ns kn sl (nm::path) ns2 ns1 acc) ns1.ns_ns s
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  in
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  let inst_ts = Mstr.fold (fun nm ts1 acc ->
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    match Mstr.find_opt nm ns2.ns_ts with
    | Some ts2 when ts_equal ts1 ts2 -> acc
    | Some _ when not (Sid.mem ts1.ts_name sl) ->
        raise (NonLocal ts1.ts_name)
    | Some _ when ts1.ts_def <> None ->
        raise (CannotInstantiate ts1.ts_name)
    | Some ts2 ->
        begin match (Mid.find ts1.ts_name kn).d_node with
          | Decl.Dtype _ -> Mts.add_new (ClashSymbol nm) ts1 ts2 acc
          | _ -> raise (CannotInstantiate ts1.ts_name)
        end
    | None when not (Sid.mem ts1.ts_name sl) -> acc
    | None when ts1.ts_def <> None -> acc
    | None ->
        begin match (Mid.find ts1.ts_name kn).d_node with
          | Decl.Dtype _ -> Loc.errorm
              "type symbol %a not found in the target theory"
              qualid (nm::path)
          | _ -> acc
        end)
    ns1.ns_ts s.inst_ts
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  in
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  let inst_ls = Mstr.fold (fun nm ls1 acc ->
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    match Mstr.find_opt nm ns2.ns_ls with
    | Some ls2 when ls_equal ls1 ls2 -> acc
    | Some _ when not (Sid.mem ls1.ls_name sl) ->
       raise (NonLocal ls1.ls_name)
    | Some ls2 ->
        begin match (Mid.find ls1.ls_name kn).d_node with
          | Decl.Dparam _ -> Mls.add_new (ClashSymbol nm) ls1 ls2 acc
          | _ -> raise (CannotInstantiate ls1.ls_name)
        end
    | None when not (Sid.mem ls1.ls_name sl) -> acc
    | None ->
        begin match (Mid.find ls1.ls_name kn).d_node with
          | Decl.Dparam _ -> Loc.errorm
              "%s symbol %a not found in the target theory"
              (if ls1.ls_value <> None then "function" else "predicate")
              qualid (nm::path)
          | _ -> acc
        end)
    ns1.ns_ls s.inst_ls
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  in
  { s with inst_ts = inst_ts; inst_ls = inst_ls }

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let add_decl loc th = function
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  | Ptree.TypeDecl dl ->
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      add_types dl th
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  | Ptree.LogicDecl dl ->
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      add_logics dl th
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  | Ptree.IndDecl (s, dl) ->
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      add_inductives s dl th
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  | Ptree.PropDecl (k, s, f) ->
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      add_prop (prop_kind k) loc s f th
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  | Ptree.Meta (id, al) ->
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      let convert = function
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        | PMAty (PPTtyapp (q,[]))
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                   -> MAts (find_tysymbol th q)
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        | PMAty ty -> MAty (ty_of_pty th ty)
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        | PMAfs q  -> MAls (find_fsymbol th q)
        | PMAps q  -> MAls (find_psymbol th q)
        | PMApr q  -> MApr (find_prop th q)
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        | PMAstr s -> MAstr s
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        | PMAint i -> MAint i
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      in
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      let add s = add_meta th (lookup_meta s) (List.map convert al) in
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      Loc.try1 ~loc add id.id
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let add_decl loc th d =
  if Debug.test_flag debug_parse_only then th else
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  Loc.try3 ~loc add_decl loc th d
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let type_inst th t s =
  let add_inst s = function
    | CSns (loc,p,q) ->
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      let ns1 = Opt.fold find_namespace_ns t.th_export p in
      let ns2 = Opt.fold find_namespace_ns (get_namespace th) q in
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      Loc.try6 ~loc clone_ns t.th_known t.th_local [] ns2 ns1 s
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    | CStsym (loc,p,[],PPTtyapp (q,[])) ->
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      let ts1 = find_tysymbol_ns t.th_export p in
      let ts2 = find_tysymbol th q in
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      if Mts.mem ts1 s.inst_ts
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      then Loc.error ~loc (ClashSymbol ts1.ts_name.id_string);
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      { s with inst_ts = Mts.add ts1 ts2 s.inst_ts }
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    | CStsym (loc,p,tvl,pty) ->
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      let ts1 = find_tysymbol_ns t.th_export p in
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      let id = id_user (ts1.ts_name.id_string ^ "_subst") loc in
      let tvl = List.map (fun id -> create_user_tv id.id) tvl in
      let def = Some (ty_of_pty th pty) in
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      let ts2 = Loc.try3 ~loc create_tysymbol id tvl def in
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      if Mts.mem ts1 s.inst_ts
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      then Loc.error ~loc (ClashSymbol ts1.ts_name.id_string);
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      { s with inst_ts = Mts.add ts1 ts2 s.inst_ts }
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    | CSfsym (loc,p,q) ->
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      let ls1 = find_fsymbol_ns t.th_export p in
      let ls2 = find_fsymbol th q in
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      if Mls.mem ls1 s.inst_ls
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      then Loc.error ~loc (ClashSymbol ls1.ls_name.id_string);
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      { s with inst_ls = Mls.add ls1 ls2 s.inst_ls }
    | CSpsym (loc,p,q) ->
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      let ls1 = find_psymbol_ns t.th_export p in
      let ls2 = find_psymbol th q in
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      if Mls.mem ls1 s.inst_ls
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      then Loc.error ~loc (ClashSymbol ls1.ls_name.id_string);
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      { s with inst_ls = Mls.add ls1 ls2 s.inst_ls }
    | CSlemma (loc,p) ->
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      let pr = find_prop_ns t.th_export p in
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      if Spr.mem pr s.inst_lemma || Spr.mem pr s.inst_goal