typing.ml

(********************************************************************)
(*                                                                  *)
(*  The Why3 Verification Platform   /   The Why3 Development Team  *)
(*  Copyright 2010-2015   --   INRIA - CNRS - Paris-Sud University  *)
(*                                                                  *)
(*  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 Ptree
open Ty
open Term
open Decl
open Theory
open Dterm
open Env

(** debug flags *)

let debug_parse_only = Debug.register_flag "parse_only"
  ~desc:"Stop@ after@ parsing."

let debug_type_only  = Debug.register_flag "type_only"
  ~desc:"Stop@ after@ type-checking."

(** errors *)

exception UnboundTypeVar of string
exception DuplicateTypeVar of string
exception ClashTheory of string

(** lazy declaration of tuples *)

let add_decl_with_tuples uc d =
  if Debug.test_flag Glob.flag then Sid.iter Glob.def d.d_news;
  add_decl_with_tuples uc d

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)

(** symbol lookup *)

let rec qloc = function
  | Qdot (p, id) -> Loc.join (qloc p) id.id_loc
  | Qident id    -> id.id_loc

let qloc_last = function
  | Qdot (_, id) | Qident id -> id.id_loc

let rec print_qualid fmt = function
  | Qdot (p, id) -> Format.fprintf fmt "%a.%s" print_qualid p id.id_str
  | Qident id    -> Format.fprintf fmt "%s" id.id_str

let string_list_of_qualid q =
  let rec sloq acc = function
    | Qdot (p, id) -> sloq (id.id_str :: acc) p
    | Qident id -> id.id_str :: acc in
  sloq [] q

exception UnboundSymbol of qualid

let find_qualid get_id find ns q =
  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_last q) (get_id r);
  r

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

let find_fsymbol_ns ns q =
  let ls = find_lsymbol_ns ns q in
  if ls.ls_value <> None then ls else
    Loc.error ~loc:(qloc q) (FunctionSymbolExpected ls)

let find_psymbol_ns ns q =
  let ls = find_lsymbol_ns ns q in
  if ls.ls_value = None then ls else
    Loc.error ~loc:(qloc q) (PredicateSymbolExpected ls)

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

let find_namespace_ns ns q =
  find_qualid (fun _ -> Glob.dummy_id) ns_find_ns ns q

(** Parsing types *)

let ty_of_pty ?(noop=true) uc pty =
  let rec get_ty = function
    | PTtyvar ({id_loc = loc}, true) when noop ->
        Loc.errorm ~loc "Opaqueness@ annotations@ are@ only@ \
          allowed@ in@ function@ and@ predicate@ prototypes"
    | PTtyvar ({id_str = x}, _) ->
        ty_var (tv_of_string x)
    | PTtyapp (q, tyl) ->
        let ts = find_tysymbol uc q in
        let tyl = List.map get_ty tyl in
        Loc.try2 ~loc:(qloc q) ty_app ts tyl
    | PTtuple tyl ->
        let ts = ts_tuple (List.length tyl) in
        ty_app ts (List.map get_ty tyl)
    | PTarrow (ty1, ty2) ->
        ty_func (get_ty ty1) (get_ty ty2)
    | PTparen ty ->
        get_ty ty
  in
  get_ty pty

let opaque_tvs args =
  let rec opaque_tvs acc = function
    | PTtyvar (id, true) -> Stv.add (tv_of_string id.id_str) acc
    | PTtyvar (_, false) -> acc
    | PTtyapp (_, pl)
    | PTtuple pl -> List.fold_left opaque_tvs acc pl
    | PTarrow (ty1, ty2) -> opaque_tvs (opaque_tvs acc ty1) ty2
    | PTparen ty -> opaque_tvs acc ty in
  List.fold_left (fun acc (_,_,_,ty) -> opaque_tvs acc ty) Stv.empty args

(** typing using destructive type variables

    parsed trees        intermediate trees       typed trees
      (Ptree)                (Dterm)               (Term)
   -----------------------------------------------------------
     ppure_type  ---dty--->   dty       ---ty--->    ty
      lexpr      --dterm-->   dterm     --term-->    term
*)

(** Typing patterns, terms, and formulas *)

let create_user_id {id_str = 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

let parse_record ~loc uc get_val fl =
  let fl = List.map (fun (q,e) -> find_lsymbol uc q, e) fl in
  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

let rec dpattern uc { pat_desc = desc; pat_loc = loc } =
  Dterm.dpattern ~loc (match desc with
    | Ptree.Pwild -> DPwild
    | Ptree.Pvar x -> DPvar (create_user_id x)
    | Ptree.Papp (q,pl) ->
        let pl = List.map (dpattern uc) pl in
        DPapp (find_lsymbol uc q, pl)
    | Ptree.Ptuple pl ->
        let pl = List.map (dpattern uc) pl in
        DPapp (fs_tuple (List.length pl), pl)
    | Ptree.Prec 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)
    | Ptree.Pas (p, x) -> DPas (dpattern uc p, create_user_id x)
    | Ptree.Por (p, q) -> DPor (dpattern uc p, dpattern uc q)
    | Ptree.Pcast (p, ty) -> DPcast (dpattern uc p, ty_of_pty uc ty))

let quant_var uc (loc, id, gh, ty) =
  assert (not gh);
  let ty = match ty with
    | Some ty -> dty_of_ty (ty_of_pty uc ty)
    | None    -> dty_fresh () in
  Opt.map create_user_id id, ty, Some loc

let is_reusable dt = match dt.dt_node with
  | DTvar _ | DTgvar _ | DTconst _ | DTtrue | DTfalse -> true
  | DTapp (_,[]) -> true
  | _ -> false

let mk_var n dt =
  let dty = match dt.dt_dty with
    | None -> dty_of_ty ty_bool
    | Some dty -> dty in
  Dterm.dterm ?loc:dt.dt_loc (DTvar (n, dty))

let mk_let ~loc n dt node =
  DTlet (dt, id_user n loc, Dterm.dterm ~loc node)

let chainable_op uc op =
  (* non-bool -> non-bool -> bool *)
  op.id_str = "infix =" || op.id_str = "infix <>" ||
  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

type global_vs = Ptree.qualid -> vsymbol option

let mk_closure loc ls =
  let mk dt = Dterm.dterm ~loc dt in
  let mk_v i _ =
    Some (id_user ("y" ^ string_of_int i) loc), dty_fresh (), None in
  let mk_t (id, dty, _) = mk (DTvar ((Opt.get id).pre_name, dty)) in
  let vl = Lists.mapi mk_v ls.ls_args in
  DTquant (DTlambda, vl, [], mk (DTapp (ls, List.map mk_t vl)))

let rec dterm uc gvars denv {term_desc = desc; term_loc = loc} =
  let func_app e el =
    List.fold_left (fun e1 (loc, e2) ->
      DTfapp (Dterm.dterm ~loc e1, e2)) e el
  in
  let rec apply_ls loc ls al l el = match l, el with
    | (_::l), (e::el) -> apply_ls loc ls (e::al) l el
    | [], _ -> func_app (DTapp (ls, List.rev_map snd al)) el
    | _, [] -> func_app (mk_closure loc ls) (List.rev_append al el)
  in
  let qualid_app q el = match gvars q with
    | Some vs -> func_app (DTgvar vs) el
    | None ->
        let ls = find_lsymbol uc q in
        apply_ls (qloc q) ls [] ls.ls_args el
  in
  let qualid_app q el = match q with
    | Qident {id_str = n} ->
        (match denv_get_opt denv n with
        | Some d -> func_app d el
        | None -> qualid_app q el)
    | _ -> qualid_app q el
  in
  let rec unfold_app e1 e2 el = match e1.term_desc with
    | Tapply (e11,e12) ->
        let e12 = dterm uc gvars denv e12 in
        unfold_app e11 e12 ((e1.term_loc, e2)::el)
    | Tident q ->
        qualid_app q ((e1.term_loc, e2)::el)
    | _ ->
        func_app (DTfapp (dterm uc gvars denv e1, e2)) el
  in
  Dterm.dterm ~loc (match desc with
  | Ptree.Tident q ->
      qualid_app q []
  | Ptree.Tidapp (q, tl) ->
      let tl = List.map (dterm uc gvars denv) tl in
      DTapp (find_lsymbol uc q, tl)
  | Ptree.Tapply (e1, e2) ->
      unfold_app e1 (dterm uc gvars denv e2) []
  | Ptree.Ttuple tl ->
      let tl = List.map (dterm uc gvars denv) tl in
      DTapp (fs_tuple (List.length tl), tl)
  | Ptree.Tinfix (e12, op2, e3)
  | Ptree.Tinnfix (e12, op2, e3) ->
      let make_app de1 op de2 = if op.id_str = "infix <>" then
        let op = { op with id_str = "infix =" } in
        let ls = find_lsymbol uc (Qident op) in
        DTnot (Dterm.dterm ~loc (DTapp (ls, [de1;de2])))
      else
        DTapp (find_lsymbol uc (Qident op), [de1;de2])
      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 (DTand, de12, de23)
        | [] -> assert false in
      let rec get_chain e12 acc = match e12.term_desc with
        | Tinfix (e1, op1, e2) when chainable_op uc op1 ->
            get_chain e1 ((op1, dterm uc gvars denv e2) :: acc)
        | _ -> e12, acc in
      let ch = [op2, dterm uc gvars denv e3] in
      let e1, ch = if chainable_op uc op2
        then get_chain e12 ch else e12, ch in
      make_chain (dterm uc gvars denv e1) ch
  | Ptree.Tconst c ->
      DTconst c
  | Ptree.Tlet (x, e1, e2) ->
      let id = create_user_id x in
      let e1 = dterm uc gvars denv e1 in
      let denv = denv_add_let denv e1 id in
      let e2 = dterm uc gvars denv e2 in
      DTlet (e1, id, e2)
  | Ptree.Tmatch (e1, bl) ->
      let e1 = dterm uc gvars denv e1 in
      let branch (p, e) =
        let p = dpattern uc p in
        let denv = denv_add_pat denv p in
        p, dterm uc gvars denv e in
      DTcase (e1, List.map branch bl)
  | Ptree.Tif (e1, e2, e3) ->
      let e1 = dterm uc gvars denv e1 in
      let e2 = dterm uc gvars denv e2 in
      let e3 = dterm uc gvars denv e3 in
      DTif (e1, e2, e3)
  | Ptree.Ttrue ->
      DTtrue
  | Ptree.Tfalse ->
      DTfalse
  | Ptree.Tunop (Ptree.Tnot, e1) ->
      DTnot (dterm uc gvars denv e1)
  | Ptree.Tbinop (e1, op, e2) ->
      let e1 = dterm uc gvars denv e1 in
      let e2 = dterm uc gvars denv e2 in
      let op = match op with
        | Ptree.Tand -> DTand
        | Ptree.Tand_asym -> DTand_asym
        | Ptree.Tor -> DTor
        | Ptree.Tor_asym -> DTor_asym
        | Ptree.Timplies -> DTimplies
        | Ptree.Tiff -> DTiff in
      DTbinop (op, e1, e2)
  | Ptree.Tquant (q, uqu, trl, e1) ->
      let qvl = List.map (quant_var uc) uqu in
      let denv = denv_add_quant denv qvl in
      let dterm e = dterm uc gvars denv e in
      let trl = List.map (List.map dterm) trl in
      let e1 = dterm e1 in
      let q = match q with
        | Ptree.Tforall -> DTforall
        | Ptree.Texists -> DTexists
        | Ptree.Tlambda -> DTlambda in
      DTquant (q, qvl, trl, e1)
  | Ptree.Trecord fl ->
      let get_val cs pj = function
        | Some e -> dterm uc gvars denv e
        | None -> Loc.error ~loc (RecordFieldMissing (cs,pj)) in
      let cs, fl = parse_record ~loc uc get_val fl in
      DTapp (cs, fl)
  | Ptree.Tupdate (e1, fl) ->
      let e1 = dterm uc gvars denv e1 in
      let re = is_reusable e1 in
      let v = if re then e1 else mk_var "_q " e1 in
      let get_val _ pj = function
        | Some e -> dterm uc gvars denv e
        | None -> Dterm.dterm ~loc (DTapp (pj,[v])) in
      let cs, fl = parse_record ~loc uc get_val fl in
      let d = DTapp (cs, fl) in
      if re then d else mk_let ~loc "_q " e1 d
  | Ptree.Tnamed (Lpos uloc, e1) ->
      DTuloc (dterm uc gvars denv e1, uloc)
  | Ptree.Tnamed (Lstr lab, e1) ->
      DTlabel (dterm uc gvars denv e1, Slab.singleton lab)
  | Ptree.Tcast (e1, ty) ->
      DTcast (dterm uc gvars denv e1, ty_of_pty uc ty))

(** Export for program parsing *)

let type_term uc gvars t =
  let t = dterm uc gvars denv_empty t in
  Dterm.term ~strict:true ~keep_loc:true t

let type_fmla uc gvars f =
  let f = dterm uc gvars denv_empty f in
  Dterm.fmla ~strict:true ~keep_loc:true f

(** Typing declarations *)

let tyl_of_params ?(noop=false) uc pl =
  let ty_of_param (loc,_,gh,ty) =
    if gh then Loc.errorm ~loc
      "ghost parameters are not allowed in pure declarations";
    ty_of_pty ~noop uc ty in
  List.map ty_of_param pl

let add_types dl th =
  let def = List.fold_left
    (fun def d ->
      let id = d.td_ident.id_str in
      Mstr.add_new (Loc.Located (d.td_loc, ClashSymbol id)) id d def)
    Mstr.empty dl
  in
  let tysymbols = Hstr.create 17 in
  let rec visit x =
    let d = Mstr.find x def in
    try
      match Hstr.find tysymbols x with
        | None -> Loc.errorm ~loc:d.td_loc "Cyclic type definition"
        | Some ts -> ts
    with Not_found ->
      Hstr.add tysymbols x None;
      let vars = Hstr.create 17 in
      let vl = List.map (fun id ->
        if Hstr.mem vars id.id_str then
          Loc.error ~loc:id.id_loc (DuplicateTypeVar id.id_str);
        let i = tv_of_string id.id_str in
        Hstr.add vars id.id_str i;
        i) d.td_params
      in
      let id = create_user_id d.td_ident in
      let ts = match d.td_def with
        | TDalias ty ->
            let rec apply = function
              | PTtyvar (v, _) ->
                  begin
                    try ty_var (Hstr.find vars v.id_str) with Not_found ->
                      Loc.error ~loc:v.id_loc (UnboundTypeVar v.id_str)
                  end
              | PTtyapp (q, tyl) ->
                  let ts = match q with
                    | Qident x when Mstr.mem x.id_str def ->
                        visit x.id_str
                    | Qident _ | Qdot _ ->
                        find_tysymbol th q
                  in
                  Loc.try2 ~loc:(qloc q) ty_app ts (List.map apply tyl)
              | PTtuple tyl ->
                  let ts = ts_tuple (List.length tyl) in
                  ty_app ts (List.map apply tyl)
              | PTarrow (ty1, ty2) ->
                  ty_func (apply ty1) (apply ty2)
              | PTparen ty ->
                  apply ty
            in
            create_tysymbol id vl (Some (apply ty))
        | TDabstract | TDalgebraic _ ->
            create_tysymbol id vl None
        | TDrecord _ ->
            assert false
      in
      Hstr.add tysymbols x (Some ts);
      ts
  in
  let th' =
    let add_ts (abstr,alias) d =
      let ts = visit d.td_ident.id_str 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
    with ClashSymbol s ->
      Loc.error ~loc:(Mstr.find s def).td_loc (ClashSymbol s)
  in
  let csymbols = Hstr.create 17 in
  let decl d (abstr,algeb,alias) =
    let ts = match Hstr.find tysymbols d.td_ident.id_str with
      | None ->
          assert false
      | Some ts ->
          ts
    in
    match d.td_def with
      | TDabstract -> ts::abstr, algeb, alias
      | TDalias _ -> abstr, algeb, ts::alias
      | TDalgebraic cl ->
          let ht = Hstr.create 17 in
          let constr = List.length cl in
          let opaque = Stv.of_list ts.ts_args in
          let ty = ty_app ts (List.map ty_var ts.ts_args) in
          let projection (_,id,_,_) fty = match id with
            | None -> None
            | Some ({ id_str = x; id_loc = loc } as id) ->
                try
                  let pj = Hstr.find ht x in
                  let ty = Opt.get pj.ls_value in
                  ignore (Loc.try2 ~loc ty_equal_check ty fty);
                  Some pj
                with Not_found ->
                  let fn = create_user_id id in
                  let pj = create_fsymbol ~opaque fn [ty] fty in
                  Hstr.replace csymbols x loc;
                  Hstr.replace ht x pj;
                  Some pj
          in
          let constructor (loc, id, pl) =
            let tyl = tyl_of_params ~noop:true th' pl in
            let pjl = List.map2 projection pl tyl in
            Hstr.replace csymbols id.id_str loc;
            create_fsymbol ~opaque ~constr (create_user_id id) tyl ty, pjl
          in
          abstr, (ts, List.map constructor cl) :: algeb, alias
      | TDrecord _ ->
          assert false
  in
  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
  with
    | ClashSymbol s ->
        Loc.error ~loc:(Hstr.find csymbols s) (ClashSymbol s)
    | RecordFieldMissing ({ ls_name = { id_string = s }} as cs,ls) ->
        Loc.error ~loc:(Hstr.find csymbols s) (RecordFieldMissing (cs,ls))
    | DuplicateRecordField ({ ls_name = { id_string = s }} as cs,ls) ->
        Loc.error ~loc:(Hstr.find csymbols s) (DuplicateRecordField (cs,ls))

let prepare_typedef td =
  if td.td_model then
    Loc.errorm ~loc:td.td_loc "model types are not allowed in pure theories";
  if td.td_vis <> Public then
    Loc.errorm ~loc:td.td_loc "pure types cannot be abstract or private";
  if td.td_inv <> [] then
    Loc.errorm ~loc:td.td_loc "pure types cannot have invariants";
  match td.td_def with
  | TDabstract | TDalgebraic _ | TDalias _ ->
      td
  | TDrecord fl ->
      let field { f_loc = loc; f_ident = id; f_pty = ty;
                  f_mutable = mut; f_ghost = gh } =
        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";
        loc, Some id, false, ty
      in
      (* constructor for type t is "mk t" (and not String.capitalize t) *)
      let id = { td.td_ident with id_str = "mk " ^ td.td_ident.id_str } in
      { td with td_def = TDalgebraic [td.td_loc, id, List.map field fl] }

let add_types dl th =
  add_types (List.map prepare_typedef dl) th

let add_logics dl th =
  let lsymbols = Hstr.create 17 in
  (* 1. create all symbols and make an environment with these symbols *)
  let create_symbol th d =
    let id = d.ld_ident.id_str in
    let v = create_user_id d.ld_ident in
    let pl = tyl_of_params th d.ld_params in
    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
    let ls = create_lsymbol ~opaque v pl ty in
    Hstr.add lsymbols id ls;
    Loc.try2 ~loc:d.ld_loc add_param_decl th ls
  in
  let th' = List.fold_left create_symbol th dl in
  (* 2. then type-check all definitions *)
  let type_decl d (abst,defn) =
    let id = d.ld_ident.id_str in
    let ls = Hstr.find lsymbols id in
    let create_var (loc,x,_,_) ty =
      let id = match x with
        | Some id -> create_user_id id
        | None -> id_user "_" loc in
      create_vsymbol id ty in
    let vl = List.map2 create_var d.ld_params ls.ls_args in
    let add_var mvs (_,x,_,_) vs = match x with
      | Some {id_str = x} -> Mstr.add_new (DuplicateVar x) x (DTgvar vs) mvs
      | None -> mvs in
    let denv = List.fold_left2 add_var denv_empty d.ld_params vl in
    match d.ld_def, d.ld_type with
    | None, _ -> ls :: abst, defn
    | Some e, None -> (* predicate *)
        let f = dterm th' (fun _ -> None) denv e in
        let f = fmla ~strict:true ~keep_loc:true f in
        abst, (ls, vl, f) :: defn
    | Some e, Some ty -> (* function *)
        let e = { e with term_desc = Tcast (e, ty) } in
        let t = dterm th' (fun _ -> None) denv e in
        let t = term ~strict:true ~keep_loc:true t in
        abst, (ls, vl, t) :: defn
  in
  let abst,defn = List.fold_right type_decl dl ([],[]) in
  (* 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
  let th = List.fold_left add_param_decl th abst in
  let th = if defn = [] then th else add_logic_decl th (ldefns defn) in
  th

let add_prop k loc s f th =
  let pr = create_prsymbol (create_user_id s) in
  let f = type_fmla th (fun _ -> None) f in
  Loc.try4 ~loc add_prop_decl th k pr f

let loc_of_id id = Opt.get id.Ident.id_loc

let add_inductives s dl th =
  (* 1. create all symbols and make an environment with these symbols *)
  let psymbols = Hstr.create 17 in
  let create_symbol th d =
    let id = d.in_ident.id_str in
    let v = create_user_id d.in_ident in
    let pl = tyl_of_params th d.in_params in
    let opaque = opaque_tvs d.in_params in
    let ps = create_psymbol ~opaque v pl in
    Hstr.add psymbols id ps;
    Loc.try2 ~loc:d.in_loc add_param_decl th ps
  in
  let th' = List.fold_left create_symbol th dl in
  (* 2. then type-check all definitions *)
  let propsyms = Hstr.create 17 in
  let type_decl d =
    let id = d.in_ident.id_str in
    let ps = Hstr.find psymbols id in
    let clause (loc, id, f) =
      Hstr.replace propsyms id.id_str loc;
      let f = type_fmla th' (fun _ -> None) f in
      create_prsymbol (create_user_id id), f
    in
    ps, List.map clause d.in_def
  in
  try add_ind_decl th s (List.map type_decl dl)
  with
  | ClashSymbol s ->
      Loc.error ~loc:(Hstr.find propsyms s) (ClashSymbol s)
  | InvalidIndDecl (ls,pr) ->
      Loc.error ~loc:(loc_of_id pr.pr_name) (InvalidIndDecl (ls,pr))
  | NonPositiveIndDecl (ls,pr,s) ->
      Loc.error ~loc:(loc_of_id pr.pr_name) (NonPositiveIndDecl (ls,pr,s))

(* parse declarations *)

let find_theory env lenv q = match q with
  | Qident { id_str = id } -> (* local theory *)
      begin try Mstr.find id lenv
      with Not_found -> read_theory env [] id end
  | Qdot (p, { id_str = id }) -> (* theory in file f *)
      read_theory env (string_list_of_qualid p) id

let rec clone_ns kn sl path ns2 ns1 s =
  let qualid fmt path = Pp.print_list
    (fun fmt () -> Format.pp_print_char fmt '.')
    Format.pp_print_string fmt (List.rev path) in