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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 Ident
open Ty
open Term
open Decl
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open Theory

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let debug = Debug.register_info_flag "encoding"
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  ~desc:"Print@ debugging@ messages@ about@ polymorphism@ encoding."
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(* meta to tag the protected types *)
let meta_kept = register_meta "encoding : kept" [MTty]
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  ~desc:"Specify@ a@ type@ to@ keep@ during@ polymorphism@ encoding."
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(* sort symbol of the "universal" type *)
let ts_base = create_tysymbol (id_fresh "uni") [] None

(* "universal" sort *)
let ty_base = ty_app ts_base []

(* ts_base declaration *)
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let d_ts_base = create_ty_decl ts_base
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(* sort symbol of (polymorphic) types *)
let ts_type = create_tysymbol (id_fresh "ty") [] None

(* sort of (polymorphic) types *)
let ty_type = ty_app ts_type []

(* ts_type declaration *)
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let d_ts_type = create_ty_decl ts_type
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(* function symbol mapping ty_type^n to ty_type *)
let ls_of_ts = Wts.memoize 63 (fun ts ->
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  let args = List.map (Util.const ty_type) ts.ts_args in
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  create_fsymbol (id_clone ts.ts_name) args ty_type)

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(* function symbol selecting ty_type from ty_type^n *)
let ls_selects_of_ts = Wts.memoize 63 (fun ts ->
  let create_select _ =
    let preid = id_fresh ("select_"^ts.ts_name.id_string) in
    create_fsymbol preid [ty_type] ty_type in
  List.rev_map create_select ts.ts_args)

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let ls_int_of_ty = create_fsymbol (id_fresh "int_of_ty") [ty_type] ty_int

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(** definition of the previous selecting functions *)
let ls_selects_def_of_ts acc ts =
  let ls = ls_of_ts ts in
  let vars = List.rev_map
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    (fun _ -> create_vsymbol (id_fresh "x") ty_type) ts.ts_args
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  in
  let tvars = List.map t_var vars in
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  (** type to int *)
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  let id = id_hash ts.ts_name in
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  let acc =
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    let t = fs_app ls tvars ty_type in
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    let f = t_equ (fs_app ls_int_of_ty [t] ty_int) (t_nat_const id) in
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    let f = t_forall_close vars [[t]] f in
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    let prsymbol = create_prsymbol (id_clone ts.ts_name) in
    create_prop_decl Paxiom prsymbol f :: acc
  in
  (** select *)
  let ls_selects = ls_selects_of_ts ts in
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  let fmlas = List.rev_map2
    (fun ls_select value ->
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      let t = fs_app ls tvars ty_type in
      let t = fs_app ls_select [t] ty_type in
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      let f = t_equ t value in
      let f = t_forall_close vars [[t]] f in
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      f)
    ls_selects tvars in
  let create_props ls_select fmla =
    let prsymbol = create_prsymbol (id_clone ls_select.ls_name) in
    create_prop_decl Paxiom prsymbol fmla in
  let props =
    List.fold_left2 (fun acc x y -> create_props x y::acc)
      acc ls_selects fmlas in
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  let add acc fs = create_param_decl fs :: acc in
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  List.fold_left add props ls_selects

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(* convert a type to a term of type ty_type *)
let rec term_of_ty tvmap ty = match ty.ty_node with
  | Tyvar tv ->
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      Mtv.find tv tvmap
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  | Tyapp (ts,tl) ->
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      fs_app (ls_of_ts ts) (List.map (term_of_ty tvmap) tl) ty_type
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(* rewrite a closed formula modulo its free typevars *)
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let type_close tvs fn f =
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  let get_vs tv = create_vsymbol (id_clone tv.tv_name) ty_type in
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  let tvm = Mtv.mapi (fun v () -> get_vs v) tvs in
  let vl = Mtv.values tvm in
  let tvm = Mtv.map t_var tvm in
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  t_forall_close_simp vl [] (fn tvm f)
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let t_type_close fn f =
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  let tvs = t_ty_freevars Stv.empty f in
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  type_close tvs fn f

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(* convert a type declaration to a list of lsymbol declarations *)
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let lsdecl_of_ts ts = create_param_decl (ls_of_ts ts)
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(* convert a type declaration to a list of lsymbol declarations *)
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let lsdecl_of_ts_select ts =
  let defs = ls_selects_def_of_ts [] ts in
  create_param_decl (ls_of_ts ts) :: defs
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(* convert a constant to a functional symbol of type ty_base *)
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let ls_of_const =
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  let ht = Hterm.create 63 in
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  fun t -> match t.t_node with
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    | Tconst _ ->
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        let t = t_label Slab.empty t in
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        begin try Hterm.find ht t with Not_found ->
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          let s = "const_" ^ Pp.string_of_wnl Pretty.print_term t in
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          let ls = create_fsymbol (id_fresh s) [] ty_base in
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          Hterm.add ht t ls;
          ls
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        end
    | _ -> assert false

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(* unprotected and unprotecting idents *)

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let unprotected_label = Ident.create_label "encoding : unprotected"
let unprotecting_label = Ident.create_label "encoding : unprotecting"
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let id_unprotected n = id_fresh ~label:(Slab.singleton unprotected_label) n
let id_unprotecting n = id_fresh ~label:(Slab.singleton unprotecting_label) n
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let is_protected_id id = not (Slab.mem unprotected_label id.id_label)
let is_protecting_id id = not (Slab.mem unprotecting_label id.id_label)
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let is_protected_vs kept vs =
  is_protected_id vs.vs_name && Sty.mem vs.vs_ty kept

let is_protected_ls kept ls =
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  is_protected_id ls.ls_name && Sty.mem (Opt.get ls.ls_value) kept
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(* monomorphise modulo the set of kept types * and an lsymbol map *)

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let vs_monomorph kept vs =
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  if is_protected_vs kept vs then vs else
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  create_vsymbol (id_clone vs.vs_name) ty_base
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let rec t_monomorph kept lsmap consts vmap t =
  let t_mono = t_monomorph kept lsmap consts in
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  t_label_copy t (match t.t_node with
    | Tvar v ->
        Mvs.find v vmap
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    | Tconst _ when Sty.mem (t_type t) kept ->
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        t
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    | Tconst _ ->
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        let ls = ls_of_const t in
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        consts := Sls.add ls !consts;
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        fs_app ls [] ty_base
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    | Tapp (ps,[t1;t2]) when ls_equal ps ps_equ ->
        t_equ (t_mono vmap t1) (t_mono vmap t2)
    | Tapp (ls,tl) ->
        let ls = lsmap ls in
        t_app ls (List.map (t_mono vmap) tl) ls.ls_value
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    | Tif (f,t1,t2) ->
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        t_if (t_mono vmap f) (t_mono vmap t1) (t_mono vmap t2)
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    | Tlet (t1,b) ->
        let u,t2,close = t_open_bound_cb b in
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        let v = vs_monomorph kept u in
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        let t2 = t_mono (Mvs.add u (t_var v) vmap) t2 in
        t_let (t_mono vmap t1) (close v t2)
    | Tcase _ ->
        Printer.unsupportedTerm t "no match expressions at this point"
    | Teps b ->
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        let u,f,close = t_open_bound_cb b in
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        let v = vs_monomorph kept u in
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        let f = t_mono (Mvs.add u (t_var v) vmap) f in
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        t_eps (close v f)
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    | Tquant (q,b) ->
        let ul,tl,f1,close = t_open_quant_cb b in
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        let vl = List.map (vs_monomorph kept) ul in
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        let add acc u v = Mvs.add u (t_var v) acc in
        let vmap = List.fold_left2 add vmap ul vl in
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        let tl = tr_map (t_mono vmap) tl in
        t_quant q (close vl tl (t_mono vmap f1))
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    | Tbinop (op,f1,f2) ->
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        t_binary op (t_mono vmap f1) (t_mono vmap f2)
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    | Tnot f1 ->
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        t_not (t_mono vmap f1)
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    | Ttrue | Tfalse ->
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        t)
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let d_monomorph kept lsmap d =
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  let consts = ref Sls.empty in
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  let kept = Sty.add ty_base kept in
  let t_mono = t_monomorph kept lsmap consts in
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  let dl = match d.d_node with
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    | Dtype { ts_def = Some _ } -> []
    | Dtype ts when not (Sty.exists (ty_s_any (ts_equal ts)) kept) -> []
    | Dtype ts ->
        [create_ty_decl ts]
    | Ddata _ ->
        Printer.unsupportedDecl d "no algebraic types at this point"
    | Dparam ls ->
        let ls = if ls_equal ls ps_equ then ls else lsmap ls in
        [create_param_decl ls]
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    | Dlogic ldl ->
        let conv (ls,ld) =
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          let ls = if ls_equal ls ps_equ then ls else lsmap ls in
          let ul,e,close = open_ls_defn_cb ld in
          let vl = List.map (vs_monomorph kept) ul in
          let add acc u v = Mvs.add u (t_var v) acc in
          let vmap = List.fold_left2 add Mvs.empty ul vl in
          close ls vl (t_mono vmap e)
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        in
        [create_logic_decl (List.map conv ldl)]
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    | Dind (s, idl) ->
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        let iconv (pr,f) = pr, t_mono Mvs.empty f in
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        let conv (ls,il) = lsmap ls, List.map iconv il in
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        [create_ind_decl s (List.map conv idl)]
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    | Dprop (k,pr,f) ->
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        [create_prop_decl k pr (t_mono Mvs.empty f)]
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  in
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  let add ls acc = create_param_decl ls :: acc in
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  Sls.fold add !consts dl
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(* replace type variables in a goal with fresh type constants *)
let monomorphise_goal = Trans.goal (fun pr f ->
  let stv = t_ty_freevars Stv.empty f in
  if Stv.is_empty stv then [create_prop_decl Pgoal pr f] else
  let mty,ltv = Stv.fold (fun tv (mty,ltv) ->
    let ts = create_tysymbol (id_clone tv.tv_name) [] None in
    Mtv.add tv (ty_app ts []) mty, ts::ltv) stv (Mtv.empty,[]) in
  let f = t_ty_subst mty Mvs.empty f in
  List.fold_left
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    (fun acc ts -> create_ty_decl ts :: acc)
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    [create_prop_decl Pgoal pr f] ltv)

(* close by subtype the set of types tagged by meta_kept *)
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let close_kept =
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  Trans.on_tagged_ty meta_kept (fun kept ->
    let rec add acc ty = ty_fold add (Sty.add ty acc) ty in
    let kept' = Sty.fold (Util.flip add) kept kept in
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    if kept == kept' then Trans.identity
    else
      let kept' = Sty.diff kept' kept in
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      let fold ty acc = create_meta meta_kept [MAty ty] :: acc in
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      Trans.add_tdecls (Sty.fold fold kept' []))
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(* reconstruct a definition of an lsymbol or make a defining axiom *)
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let defn_or_axiom ls f =
  match Decl.ls_defn_of_axiom f with
    | Some ld -> [create_logic_decl [ld]]
    | None ->
        let nm = ls.ls_name.id_string ^ "_def" in
        let pr = create_prsymbol (id_derive nm ls.ls_name) in
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        [create_param_decl ls; create_prop_decl Paxiom pr f]