ast_util.ml

(**************************************************************************)
(*     Sail                                                               *)
(*                                                                        *)
(*  Copyright (c) 2013-2017                                               *)
(*    Kathyrn Gray                                                        *)
(*    Shaked Flur                                                         *)
(*    Stephen Kell                                                        *)
(*    Gabriel Kerneis                                                     *)
(*    Robert Norton-Wright                                                *)
(*    Christopher Pulte                                                   *)
(*    Peter Sewell                                                        *)
(*    Alasdair Armstrong                                                  *)
(*    Brian Campbell                                                      *)
(*    Thomas Bauereiss                                                    *)
(*    Anthony Fox                                                         *)
(*    Jon French                                                          *)
(*    Dominic Mulligan                                                    *)
(*    Stephen Kell                                                        *)
(*    Mark Wassell                                                        *)
(*                                                                        *)
(*  All rights reserved.                                                  *)
(*                                                                        *)
(*  This software was developed by the University of Cambridge Computer   *)
(*  Laboratory as part of the Rigorous Engineering of Mainstream Systems  *)
(*  (REMS) project, funded by EPSRC grant EP/K008528/1.                   *)
(*                                                                        *)
(*  Redistribution and use in source and binary forms, with or without    *)
(*  modification, are permitted provided that the following conditions    *)
(*  are met:                                                              *)
(*  1. Redistributions of source code must retain the above copyright     *)
(*     notice, this list of conditions and the following disclaimer.      *)
(*  2. Redistributions in binary form must reproduce the above copyright  *)
(*     notice, this list of conditions and the following disclaimer in    *)
(*     the documentation and/or other materials provided with the         *)
(*     distribution.                                                      *)
(*                                                                        *)
(*  THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS''    *)
(*  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED     *)
(*  TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A       *)
(*  PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR   *)
(*  CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,          *)
(*  SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT      *)
(*  LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF      *)
(*  USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND   *)
(*  ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,    *)
(*  OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT    *)
(*  OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF    *)
(*  SUCH DAMAGE.                                                          *)
(**************************************************************************)

open Ast
open Util
module Big_int = Nat_big_num

type mut = Immutable | Mutable

type 'a lvar = Register of effect * effect * 'a | Enum of 'a | Local of mut * 'a | Unbound

let lvar_typ = function
  | Local (_, typ) -> typ
  | Register (_, _, typ) -> typ
  | Enum typ -> typ
  | Unbound -> failwith "No type for unbound variable"

let no_annot = (Parse_ast.Unknown, ())

let gen_loc l = Parse_ast.Generated l

let inc_ord = Ord_aux (Ord_inc, Parse_ast.Unknown)
let dec_ord = Ord_aux (Ord_dec, Parse_ast.Unknown)

let mk_id str = Id_aux (Id str, Parse_ast.Unknown)

let mk_nc nc_aux = NC_aux (nc_aux, Parse_ast.Unknown)

let mk_nexp nexp_aux = Nexp_aux (nexp_aux, Parse_ast.Unknown)

let mk_exp ?loc:(l=Parse_ast.Unknown) exp_aux = E_aux (exp_aux, (l, ()))
let unaux_exp (E_aux (exp_aux, _)) = exp_aux
let uncast_exp = function
  | E_aux (E_internal_return (E_aux (E_cast (typ, exp), _)), a) ->
     E_aux (E_internal_return exp, a), Some typ
  | E_aux (E_cast (typ, exp), _) -> exp, Some typ
  | exp -> exp, None

let mk_pat pat_aux = P_aux (pat_aux, no_annot)
let unaux_pat (P_aux (pat_aux, _)) = pat_aux
let untyp_pat = function
  | P_aux (P_typ (typ, pat), _) -> pat, Some typ
  | pat -> pat, None

let mk_pexp pexp_aux = Pat_aux (pexp_aux, no_annot)

let mk_mpat mpat_aux = MP_aux (mpat_aux, no_annot)
let mk_mpexp mpexp_aux = MPat_aux (mpexp_aux, no_annot)

let mk_lexp lexp_aux = LEXP_aux (lexp_aux, no_annot)

let mk_typ_pat tpat_aux = TP_aux (tpat_aux, Parse_ast.Unknown)

let mk_lit lit_aux = L_aux (lit_aux, Parse_ast.Unknown)

let mk_lit_exp lit_aux = mk_exp (E_lit (mk_lit lit_aux))

let mk_funcl id pat body = FCL_aux (FCL_Funcl (id, Pat_aux (Pat_exp (pat, body),no_annot)), no_annot)

let mk_qi_nc nc = QI_aux (QI_constraint nc, Parse_ast.Unknown)

let mk_qi_id k kid =
  let kopt =
    KOpt_aux (KOpt_kind (K_aux (k, Parse_ast.Unknown), kid), Parse_ast.Unknown)
  in
  QI_aux (QI_id kopt, Parse_ast.Unknown)

let mk_qi_kopt kopt = QI_aux (QI_id kopt, Parse_ast.Unknown)

let mk_fundef funcls =
  let tannot_opt = Typ_annot_opt_aux (Typ_annot_opt_none, Parse_ast.Unknown) in
  let effect_opt = Effect_opt_aux (Effect_opt_none, Parse_ast.Unknown) in
  let rec_opt = Rec_aux (Rec_nonrec, Parse_ast.Unknown) in
  DEF_fundef
   (FD_aux (FD_function (rec_opt, tannot_opt, effect_opt, funcls), no_annot))

let mk_letbind pat exp = LB_aux (LB_val (pat, exp), no_annot)

let mk_val_spec vs_aux =
  DEF_spec (VS_aux (vs_aux, no_annot))

let kopt_kid (KOpt_aux (KOpt_kind (_, kid), _)) = kid
let kopt_kind (KOpt_aux (KOpt_kind (k, _), _)) = k

let is_int_kopt = function
  | KOpt_aux (KOpt_kind (K_aux (K_int, _), _), _) -> true
  | _ -> false

let is_order_kopt = function
  | KOpt_aux (KOpt_kind (K_aux (K_order, _), _), _) -> true
  | _ -> false

let is_typ_kopt = function
  | KOpt_aux (KOpt_kind (K_aux (K_type, _), _), _) -> true
  | _ -> false

let is_bool_kopt = function
  | KOpt_aux (KOpt_kind (K_aux (K_bool, _), _), _) -> true
  | _ -> false

let string_of_kid = function
  | Kid_aux (Var v, _) -> v

module Kid = struct
  type t = kid
  let compare kid1 kid2 = String.compare (string_of_kid kid1) (string_of_kid kid2)
end

module Kind = struct
  type t = kind
  let compare (K_aux (aux1, _)) (K_aux (aux2, _)) =
    match aux1, aux2 with
    | K_int, K_int -> 0
    | K_type, K_type -> 0
    | K_order, K_order -> 0
    | K_bool, K_bool -> 0
    | K_int, _ -> 1 | _, K_int -> -1
    | K_type, _ -> 1 | _, K_type -> -1
    | K_order, _ -> 1 | _, K_order -> -1
end

module KOpt = struct
  type t = kinded_id
  let compare kopt1 kopt2 =
    let lex_ord c1 c2 = if c1 = 0 then c2 else c1 in
    lex_ord (Kid.compare (kopt_kid kopt1) (kopt_kid kopt2))
            (Kind.compare (kopt_kind kopt1) (kopt_kind kopt2))
end

module Id = struct
  type t = id
  let compare id1 id2 =
    match (id1, id2) with
    | Id_aux (Id x, _), Id_aux (Id y, _) -> String.compare x y
    | Id_aux (Operator x, _), Id_aux (Operator y, _) -> String.compare x y
    | Id_aux (Id _, _), Id_aux (Operator _, _) -> -1
    | Id_aux (Operator _, _), Id_aux (Id _, _) -> 1
end

module Nexp = struct
  type t = nexp
  let rec compare (Nexp_aux (nexp1, _)) (Nexp_aux (nexp2, _)) =
    let lex_ord (c1, c2) = if c1 = 0 then c2 else c1 in
    match nexp1, nexp2 with
    | Nexp_id v1, Nexp_id v2 -> Id.compare v1 v2
    | Nexp_var kid1, Nexp_var kid2 -> Kid.compare kid1 kid2
    | Nexp_constant c1, Nexp_constant c2 -> Big_int.compare c1 c2
    | Nexp_app (op1, args1), Nexp_app (op2, args2) ->
       let lex1 = Id.compare op1 op2 in
       let lex2 = List.length args1 - List.length args2 in
       let lex3 =
         if lex2 = 0 then
           List.fold_left2 (fun l n1 n2 -> if compare n1 n2 = 0 then 0 else compare n1 n2) 0 args1 args2
         else 0
       in
       lex_ord (lex1, lex_ord (lex2, lex3))
    | Nexp_times (n1a, n1b), Nexp_times (n2a, n2b)
    | Nexp_sum (n1a, n1b), Nexp_sum (n2a, n2b)
    | Nexp_minus (n1a, n1b), Nexp_minus (n2a, n2b) ->
      lex_ord (compare n1a n2a, compare n1b n2b)
    | Nexp_exp n1, Nexp_exp n2 -> compare n1 n2
    | Nexp_neg n1, Nexp_neg n2 -> compare n1 n2
    | Nexp_constant _, _ -> -1 | _, Nexp_constant _ -> 1
    | Nexp_id _, _ -> -1 | _, Nexp_id _ -> 1
    | Nexp_var _, _ -> -1 | _, Nexp_var _ -> 1
    | Nexp_neg _, _ -> -1 | _, Nexp_neg _ -> 1
    | Nexp_exp _, _ -> -1 | _, Nexp_exp _ -> 1
    | Nexp_minus _, _ -> -1 | _, Nexp_minus _ -> 1
    | Nexp_sum _, _ -> -1 | _, Nexp_sum _ -> 1
    | Nexp_times _, _ -> -1 | _, Nexp_times _ -> 1
end

module Bindings = Map.Make(Id)
module IdSet = Set.Make(Id)
module KBindings = Map.Make(Kid)
module KidSet = Set.Make(Kid)
module KOptSet = Set.Make(KOpt)
module KOptMap = Map.Make(KOpt)
module NexpSet = Set.Make(Nexp)
module NexpMap = Map.Make(Nexp)

let rec nexp_identical nexp1 nexp2 = (Nexp.compare nexp1 nexp2 = 0)

let rec is_nexp_constant (Nexp_aux (nexp, _)) = match nexp with
  | Nexp_id _ | Nexp_var _ -> false
  | Nexp_constant _ -> true
  | Nexp_times (n1, n2) | Nexp_sum (n1, n2) | Nexp_minus (n1, n2) ->
    is_nexp_constant n1 && is_nexp_constant n2
  | Nexp_exp n | Nexp_neg n -> is_nexp_constant n
  | Nexp_app (_, nexps) -> List.for_all is_nexp_constant nexps

let int_of_nexp_opt nexp =
  match nexp with
  | Nexp_aux(Nexp_constant i,_) -> Some i
  | _ -> None

let rec nexp_simp (Nexp_aux (nexp, l)) = Nexp_aux (nexp_simp_aux nexp, l)
and nexp_simp_aux = function
  (* (n - (n - m)) often appears in foreach loops *)
  | Nexp_minus (nexp1, Nexp_aux (Nexp_minus (nexp2, Nexp_aux (n3,_)),_))
      when nexp_identical nexp1 nexp2 ->
     nexp_simp_aux n3
  | Nexp_minus (Nexp_aux (Nexp_sum (Nexp_aux (n1, _), nexp2), _), nexp3)
    when nexp_identical nexp2 nexp3 ->
     nexp_simp_aux n1
  | Nexp_sum (Nexp_aux (Nexp_minus (Nexp_aux (n1, _), nexp2), _), nexp3)
    when nexp_identical nexp2 nexp3 ->
     nexp_simp_aux n1
  | Nexp_sum (n1, n2) ->
     begin
       let (Nexp_aux (n1_simp, _) as n1) = nexp_simp n1 in
       let (Nexp_aux (n2_simp, _) as n2) = nexp_simp n2 in
       match n1_simp, n2_simp with
       | Nexp_constant c1, Nexp_constant c2 -> Nexp_constant (Big_int.add c1 c2)
       | _, Nexp_neg n2 -> Nexp_minus (n1, n2)
       | _, _ -> Nexp_sum (n1, n2)
     end
  | Nexp_times (n1, n2) ->
     begin
       let (Nexp_aux (n1_simp, _) as n1) = nexp_simp n1 in
       let (Nexp_aux (n2_simp, _) as n2) = nexp_simp n2 in
       match n1_simp, n2_simp with
       | Nexp_constant c, _ when Big_int.equal c (Big_int.of_int 1) -> n2_simp
       | _, Nexp_constant c when Big_int.equal c (Big_int.of_int 1) -> n1_simp
       | Nexp_constant c1, Nexp_constant c2 -> Nexp_constant (Big_int.mul c1 c2)
       | _, _ -> Nexp_times (n1, n2)
     end
  | Nexp_minus (n1, n2) ->
     begin
       let (Nexp_aux (n1_simp, _) as n1) = nexp_simp n1 in
       let (Nexp_aux (n2_simp, _) as n2) = nexp_simp n2 in
       match n1_simp, n2_simp with
       | Nexp_constant c1, Nexp_constant c2 -> Nexp_constant (Big_int.sub c1 c2)
       (* A vector range x['n-1 .. 0] can result in the size "('n-1) - -1" *)
       | Nexp_minus (Nexp_aux (n,_), Nexp_aux (Nexp_constant c1,_)), Nexp_constant c2
         when Big_int.equal c1 (Big_int.negate c2) -> n
       | _, _ -> Nexp_minus (n1, n2)
     end
  | Nexp_neg n ->
     begin
       let (Nexp_aux (n_simp, _) as n) = nexp_simp n in
       match n_simp with
       | Nexp_constant c -> Nexp_constant (Big_int.negate c)
       | _ -> Nexp_neg n
     end
  | Nexp_app (Id_aux (Id "div",_) as id,[n1;n2]) ->
     begin
       let (Nexp_aux (n1_simp, _) as n1) = nexp_simp n1 in
       let (Nexp_aux (n2_simp, _) as n2) = nexp_simp n2 in
       match n1_simp, n2_simp with
       | Nexp_constant c1, Nexp_constant c2 -> Nexp_constant (Big_int.div c1 c2)
       | _, _ -> Nexp_app (id,[n1;n2])
     end
  | nexp -> nexp

let rec constraint_simp (NC_aux (nc_aux, l)) =
  let nc_aux = match nc_aux with
    | NC_equal (nexp1, nexp2) ->
       let nexp1, nexp2 = nexp_simp nexp1, nexp_simp nexp2 in
       if nexp_identical nexp1 nexp2 then
         NC_true
       else
         NC_equal (nexp1, nexp2)

    | NC_and (nc1, nc2) ->
       let nc1, nc2 = constraint_simp nc1, constraint_simp nc2 in
       begin match nc1, nc2 with
       | NC_aux (NC_true, _), NC_aux (nc, _) -> nc
       | NC_aux (nc, _), NC_aux (NC_true, _) -> nc
       | _, _ -> NC_and (nc1, nc2)
       end

    | NC_or (nc1, nc2) ->
       let nc1, nc2 = constraint_simp nc1, constraint_simp nc2 in
       begin match nc1, nc2 with
       | NC_aux (NC_false, _), NC_aux (nc, _) -> nc
       | NC_aux (nc, _), NC_aux (NC_false, _) -> nc
       | NC_aux (NC_true, _), NC_aux (nc, _) -> NC_true
       | NC_aux (nc, _), NC_aux (NC_true, _) -> NC_true
       | _, _ -> NC_or (nc1, nc2)
       end

    | NC_bounded_ge (nexp1, nexp2) ->
       let nexp1, nexp2 = nexp_simp nexp1, nexp_simp nexp2 in
       begin match nexp1, nexp2 with
       | Nexp_aux (Nexp_constant c1, _), Nexp_aux (Nexp_constant c2, _) ->
          if Big_int.greater_equal c1 c2 then NC_true else NC_false
       | _, _ -> NC_bounded_ge (nexp1, nexp2)
       end

    | NC_bounded_le (nexp1, nexp2) ->
       let nexp1, nexp2 = nexp_simp nexp1, nexp_simp nexp2 in
       begin match nexp1, nexp2 with
       | Nexp_aux (Nexp_constant c1, _), Nexp_aux (Nexp_constant c2, _) ->
          if Big_int.less_equal c1 c2 then NC_true else NC_false
       | _, _ -> NC_bounded_le (nexp1, nexp2)
       end

    | _ -> nc_aux
  in
  NC_aux (nc_aux, l)

let rec constraint_conj (NC_aux (nc_aux, l) as nc) =
  match nc_aux with
  | NC_and (nc1, nc2) -> constraint_conj nc1 @ constraint_conj nc2
  | _ -> [nc]

let rec constraint_disj (NC_aux (nc_aux, l) as nc) =
  match nc_aux with
  | NC_or (nc1, nc2) -> constraint_disj nc1 @ constraint_disj nc2
  | _ -> [nc]

let mk_typ typ = Typ_aux (typ, Parse_ast.Unknown)
let mk_typ_arg arg = A_aux (arg, Parse_ast.Unknown)
let mk_kid str = Kid_aux (Var ("'" ^ str), Parse_ast.Unknown)
let mk_infix_id str = Id_aux (Operator str, Parse_ast.Unknown)

let mk_id_typ id = Typ_aux (Typ_id id, Parse_ast.Unknown)

let mk_kopt kind_aux id =
  KOpt_aux (KOpt_kind (K_aux (kind_aux, Parse_ast.Unknown), id), Parse_ast.Unknown)

let mk_ord ord_aux = Ord_aux (ord_aux, Parse_ast.Unknown)

let unknown_typ = mk_typ Typ_internal_unknown
let int_typ = mk_id_typ (mk_id "int")
let nat_typ = mk_id_typ (mk_id "nat")
let unit_typ = mk_id_typ (mk_id "unit")
let bit_typ = mk_id_typ (mk_id "bit")
let real_typ = mk_id_typ (mk_id "real")
let app_typ id args = mk_typ (Typ_app (id, args))
let register_typ typ = mk_typ (Typ_app (mk_id "register", [mk_typ_arg (A_typ typ)]))
let atom_typ nexp =
  mk_typ (Typ_app (mk_id "atom", [mk_typ_arg (A_nexp (nexp_simp nexp))]))
let implicit_typ nexp =
  mk_typ (Typ_app (mk_id "implicit", [mk_typ_arg (A_nexp (nexp_simp nexp))]))
let range_typ nexp1 nexp2 =
  mk_typ (Typ_app (mk_id "range", [mk_typ_arg (A_nexp (nexp_simp nexp1));
                                   mk_typ_arg (A_nexp (nexp_simp nexp2))]))
let bool_typ = mk_id_typ (mk_id "bool")
let atom_bool_typ nc = mk_typ (Typ_app (mk_id "atom_bool", [mk_typ_arg (A_bool nc)]))
let string_typ = mk_id_typ (mk_id "string")
let list_typ typ = mk_typ (Typ_app (mk_id "list", [mk_typ_arg (A_typ typ)]))
let tuple_typ typs = mk_typ (Typ_tup typs)
let function_typ arg_typs ret_typ eff = mk_typ (Typ_fn (arg_typs, ret_typ, eff))

let vector_typ n ord typ =
  mk_typ (Typ_app (mk_id "vector",
                   [mk_typ_arg (A_nexp (nexp_simp n));
                    mk_typ_arg (A_order ord);
                    mk_typ_arg (A_typ typ)]))

let exc_typ = mk_id_typ (mk_id "exception")

let nconstant c = Nexp_aux (Nexp_constant c, Parse_ast.Unknown)
let nint i = nconstant (Big_int.of_int i)
let nminus n1 n2 = Nexp_aux (Nexp_minus (n1, n2), Parse_ast.Unknown)
let nsum n1 n2 = Nexp_aux (Nexp_sum (n1, n2), Parse_ast.Unknown)
let ntimes n1 n2 = Nexp_aux (Nexp_times (n1, n2), Parse_ast.Unknown)
let npow2 n = Nexp_aux (Nexp_exp n, Parse_ast.Unknown)
let nvar kid = Nexp_aux (Nexp_var kid, Parse_ast.Unknown)
let nid id = Nexp_aux (Nexp_id id, Parse_ast.Unknown)
let napp id args = Nexp_aux (Nexp_app (id, args), Parse_ast.Unknown)

let nc_set kid nums = mk_nc (NC_set (kid, nums))
let nc_int_set kid ints = mk_nc (NC_set (kid, List.map Big_int.of_int ints))
let nc_eq n1 n2 = mk_nc (NC_equal (n1, n2))
let nc_neq n1 n2 = mk_nc (NC_not_equal (n1, n2))
let nc_lteq n1 n2 = NC_aux (NC_bounded_le (n1, n2), Parse_ast.Unknown)
let nc_gteq n1 n2 = NC_aux (NC_bounded_ge (n1, n2), Parse_ast.Unknown)
let nc_lt n1 n2 = nc_lteq (nsum n1 (nint 1)) n2
let nc_gt n1 n2 = nc_gteq n1 (nsum n2 (nint 1))
let nc_var kid = mk_nc (NC_var kid)
let nc_true = mk_nc NC_true
let nc_false = mk_nc NC_false

let nc_or nc1 nc2 =
  match nc1, nc2 with
  | _, NC_aux (NC_false, _) -> nc1
  | NC_aux (NC_false, _), _ -> nc2
  | _, _ -> mk_nc (NC_or (nc1, nc2))

let nc_and nc1 nc2 =
  match nc1, nc2 with
  | _, NC_aux (NC_true, _) -> nc1
  | NC_aux (NC_true, _), _ -> nc2
  | _, _ -> mk_nc (NC_and (nc1, nc2))

let arg_nexp ?loc:(l=Parse_ast.Unknown) n = A_aux (A_nexp n, l)
let arg_order ?loc:(l=Parse_ast.Unknown) ord = A_aux (A_order ord, l)
let arg_typ ?loc:(l=Parse_ast.Unknown) typ = A_aux (A_typ typ, l)
let arg_bool ?loc:(l=Parse_ast.Unknown) nc = A_aux (A_bool nc, l)

let arg_kopt (KOpt_aux (KOpt_kind (K_aux (k, _), v), l)) =
  match k with
  | K_int -> arg_nexp (nvar v)
  | K_order -> arg_order (Ord_aux (Ord_var v, l))
  | K_bool -> arg_bool (nc_var v)
  | K_type -> arg_typ (mk_typ (Typ_var v))

let nc_not nc = mk_nc (NC_app (mk_id "not", [arg_bool nc]))

let mk_typschm typq typ = TypSchm_aux (TypSchm_ts (typq, typ), Parse_ast.Unknown)

let mk_typquant qis = TypQ_aux (TypQ_tq qis, Parse_ast.Unknown)

let mk_fexp id exp = FE_aux (FE_Fexp (id, exp), no_annot)

let mk_effect effs =
  Effect_aux (Effect_set (List.map (fun be_aux -> BE_aux (be_aux, Parse_ast.Unknown)) effs), Parse_ast.Unknown)

let no_effect = mk_effect []

let quant_add qi typq =
  match qi, typq with
  | QI_aux (QI_constraint (NC_aux (NC_true, _)), _), _ -> typq
  | QI_aux (QI_id _, _), TypQ_aux (TypQ_tq qis, l) -> TypQ_aux (TypQ_tq (qi :: qis), l)
  | QI_aux (QI_constant _, _), TypQ_aux (TypQ_tq qis, l) -> TypQ_aux (TypQ_tq (qis @ [qi]), l)
  | QI_aux (QI_constraint nc, _), TypQ_aux (TypQ_tq qis, l) -> TypQ_aux (TypQ_tq (qis @ [qi]), l)
  | _, TypQ_aux (TypQ_no_forall, l) -> TypQ_aux (TypQ_tq [qi], l)

let quant_items : typquant -> quant_item list = function
  | TypQ_aux (TypQ_tq qis, _) -> qis
  | TypQ_aux (TypQ_no_forall, _) -> []

let quant_kopts typq =
  let qi_kopt = function
    | QI_aux (QI_id kopt, _) -> [kopt]
    | QI_aux _ -> []
  in
  quant_items typq |> List.map qi_kopt |> List.concat

let quant_split typq =
  let qi_kopt = function
    | QI_aux (QI_id kopt, _) -> [kopt]
    | _ -> []
  in
  let qi_nc = function
    | QI_aux (QI_constraint nc, _) -> [nc]
    | _ -> []
  in
  let qis = quant_items typq in
  List.concat (List.map qi_kopt qis), List.concat (List.map qi_nc qis)

let quant_map_items f = function
  | TypQ_aux (TypQ_no_forall, l) -> TypQ_aux (TypQ_no_forall, l)
  | TypQ_aux (TypQ_tq qis, l) -> TypQ_aux (TypQ_tq (List.map f qis), l)

let is_quant_kopt = function
  | QI_aux (QI_id _, _) -> true
  | _ -> false

let is_quant_constraint = function
  | QI_aux (QI_constraint _, _) -> true
  | _ -> false

let unaux_nexp (Nexp_aux (nexp, _)) = nexp
let unaux_order (Ord_aux (ord, _)) = ord
let unaux_typ (Typ_aux (typ, _)) = typ
let unaux_kind (K_aux (k, _)) = k
let unaux_constraint (NC_aux (nc, _)) = nc

let rec map_exp_annot f (E_aux (exp, annot)) = E_aux (map_exp_annot_aux f exp, f annot)
and map_exp_annot_aux f = function
  | E_block xs -> E_block (List.map (map_exp_annot f) xs)
  | E_nondet xs -> E_nondet (List.map (map_exp_annot f) xs)
  | E_id id -> E_id id
  | E_ref id -> E_ref id
  | E_lit lit -> E_lit lit
  | E_cast (typ, exp) -> E_cast (typ, map_exp_annot f exp)
  | E_app (id, xs) -> E_app (id, List.map (map_exp_annot f) xs)
  | E_app_infix (x, op, y) -> E_app_infix (map_exp_annot f x, op, map_exp_annot f y)
  | E_tuple xs -> E_tuple (List.map (map_exp_annot f) xs)
  | E_if (cond, t, e) -> E_if (map_exp_annot f cond, map_exp_annot f t, map_exp_annot f e)
  | E_for (v, e1, e2, e3, o, e4) -> E_for (v, map_exp_annot f e1, map_exp_annot f e2, map_exp_annot f e3, o, map_exp_annot f e4)
  | E_loop (loop_type, measure, e1, e2) -> E_loop (loop_type, map_measure_annot f measure, map_exp_annot f e1, map_exp_annot f e2)
  | E_vector exps -> E_vector (List.map (map_exp_annot f) exps)
  | E_vector_access (exp1, exp2) -> E_vector_access (map_exp_annot f exp1, map_exp_annot f exp2)
  | E_vector_subrange (exp1, exp2, exp3) -> E_vector_subrange (map_exp_annot f exp1, map_exp_annot f exp2, map_exp_annot f exp3)
  | E_vector_update (exp1, exp2, exp3) -> E_vector_update (map_exp_annot f exp1, map_exp_annot f exp2, map_exp_annot f exp3)
  | E_vector_update_subrange (exp1, exp2, exp3, exp4) ->
     E_vector_update_subrange (map_exp_annot f exp1, map_exp_annot f exp2, map_exp_annot f exp3, map_exp_annot f exp4)
  | E_vector_append (exp1, exp2) -> E_vector_append (map_exp_annot f exp1, map_exp_annot f exp2)
  | E_list xs -> E_list (List.map (map_exp_annot f) xs)
  | E_cons (exp1, exp2) -> E_cons (map_exp_annot f exp1, map_exp_annot f exp2)
  | E_record fexps -> E_record (List.map (map_fexp_annot f) fexps)
  | E_record_update (exp, fexps) -> E_record_update (map_exp_annot f exp, List.map (map_fexp_annot f) fexps)
  | E_field (exp, id) -> E_field (map_exp_annot f exp, id)
  | E_case (exp, cases) -> E_case (map_exp_annot f exp, List.map (map_pexp_annot f) cases)
  | E_try (exp, cases) -> E_try (map_exp_annot f exp, List.map (map_pexp_annot f) cases)
  | E_let (letbind, exp) -> E_let (map_letbind_annot f letbind, map_exp_annot f exp)
  | E_assign (lexp, exp) -> E_assign (map_lexp_annot f lexp, map_exp_annot f exp)
  | E_sizeof nexp -> E_sizeof nexp
  | E_constraint nc -> E_constraint nc
  | E_exit exp -> E_exit (map_exp_annot f exp)
  | E_throw exp -> E_throw (map_exp_annot f exp)
  | E_return exp -> E_return (map_exp_annot f exp)
  | E_assert (test, msg) -> E_assert (map_exp_annot f test, map_exp_annot f msg)
  | E_internal_value v -> E_internal_value v
  | E_var (lexp, exp1, exp2) -> E_var (map_lexp_annot f lexp, map_exp_annot f exp1, map_exp_annot f exp2)
  | E_internal_plet (pat, exp1, exp2) -> E_internal_plet (map_pat_annot f pat, map_exp_annot f exp1, map_exp_annot f exp2)
  | E_internal_return exp -> E_internal_return (map_exp_annot f exp)
and map_measure_annot f (Measure_aux (m, l)) = Measure_aux (map_measure_annot_aux f m, l)
and map_measure_annot_aux f = function
  | Measure_none -> Measure_none
  | Measure_some exp -> Measure_some (map_exp_annot f exp)
and map_opt_default_annot f (Def_val_aux (df, annot)) = Def_val_aux (map_opt_default_annot_aux f df, f annot)
and map_opt_default_annot_aux f = function
  | Def_val_empty -> Def_val_empty
  | Def_val_dec exp -> Def_val_dec (map_exp_annot f exp)
and map_fexp_annot f (FE_aux (FE_Fexp (id, exp), annot)) = FE_aux (FE_Fexp (id, map_exp_annot f exp), f annot)
and map_pexp_annot f (Pat_aux (pexp, annot)) = Pat_aux (map_pexp_annot_aux f pexp, f annot)
and map_pexp_annot_aux f = function
  | Pat_exp (pat, exp) -> Pat_exp (map_pat_annot f pat, map_exp_annot f exp)
  | Pat_when (pat, guard, exp) -> Pat_when (map_pat_annot f pat, map_exp_annot f guard, map_exp_annot f exp)
and map_pat_annot f (P_aux (pat, annot)) = P_aux (map_pat_annot_aux f pat, f annot)
and map_pat_annot_aux f = function
  | P_lit lit -> P_lit lit
  | P_wild -> P_wild
  | P_or (pat1, pat2) -> P_or  (map_pat_annot f pat1, map_pat_annot f pat2)
  | P_not pat         -> P_not (map_pat_annot f pat)
  | P_as (pat, id) -> P_as (map_pat_annot f pat, id)
  | P_typ (typ, pat) -> P_typ (typ, map_pat_annot f pat)
  | P_id id -> P_id id
  | P_var (pat, tpat) -> P_var (map_pat_annot f pat, tpat)
  | P_app (id, pats) -> P_app (id, List.map (map_pat_annot f) pats)
  | P_record (fpats, b) -> P_record (List.map (map_fpat_annot f) fpats, b)
  | P_tup pats -> P_tup (List.map (map_pat_annot f) pats)
  | P_list pats -> P_list (List.map (map_pat_annot f) pats)
  | P_vector_concat pats -> P_vector_concat (List.map (map_pat_annot f) pats)
  | P_vector pats -> P_vector (List.map (map_pat_annot f) pats)
  | P_cons (pat1, pat2) -> P_cons (map_pat_annot f pat1, map_pat_annot f pat2)
  | P_string_append pats -> P_string_append (List.map (map_pat_annot f) pats)

and map_mpexp_annot f (MPat_aux (mpexp, annot)) = MPat_aux (map_mpexp_annot_aux f mpexp, f annot)
and map_mpexp_annot_aux f = function
  | MPat_pat mpat -> MPat_pat (map_mpat_annot f mpat)
  | MPat_when (mpat, guard) -> MPat_when (map_mpat_annot f mpat, map_exp_annot f guard)

and map_mapcl_annot f = function
  | (MCL_aux (MCL_bidir (mpexp1, mpexp2), annot)) ->
     MCL_aux (MCL_bidir (map_mpexp_annot f mpexp1, map_mpexp_annot f mpexp2), f annot)
  | (MCL_aux (MCL_forwards (mpexp, exp), annot)) ->
     MCL_aux (MCL_forwards (map_mpexp_annot f mpexp, map_exp_annot f exp), f annot)
  | (MCL_aux (MCL_backwards (mpexp, exp), annot)) ->
     MCL_aux (MCL_backwards (map_mpexp_annot f mpexp, map_exp_annot f exp), f annot)

and map_mpat_annot f (MP_aux (mpat, annot)) = MP_aux (map_mpat_annot_aux f mpat, f annot)
and map_mpat_annot_aux f = function
  | MP_lit lit -> MP_lit lit
  | MP_id id -> MP_id id
  | MP_app (id, mpats) -> MP_app (id, List.map (map_mpat_annot f) mpats)
  | MP_record (fmpats, b) -> MP_record (List.map (map_mfpat_annot f) fmpats, b)
  | MP_tup mpats -> MP_tup (List.map (map_mpat_annot f) mpats)
  | MP_list mpats -> MP_list (List.map (map_mpat_annot f) mpats)
  | MP_vector_concat mpats -> MP_vector_concat (List.map (map_mpat_annot f) mpats)
  | MP_vector mpats -> MP_vector (List.map (map_mpat_annot f) mpats)
  | MP_cons (mpat1, mpat2) -> MP_cons (map_mpat_annot f mpat1, map_mpat_annot f mpat2)
  | MP_string_append mpats -> MP_string_append (List.map (map_mpat_annot f) mpats)
  | MP_typ (mpat, typ) -> MP_typ (map_mpat_annot f mpat, typ)
  | MP_as (mpat, id) -> MP_as (map_mpat_annot f mpat, id)

and map_fpat_annot f (FP_aux (FP_Fpat (id, pat), annot)) = FP_aux (FP_Fpat (id, map_pat_annot f pat), f annot)
and map_mfpat_annot f (MFP_aux (MFP_mpat (id, mpat), annot)) = MFP_aux (MFP_mpat (id, map_mpat_annot f mpat), f annot)
and map_letbind_annot f (LB_aux (lb, annot)) = LB_aux (map_letbind_annot_aux f lb, f annot)
and map_letbind_annot_aux f = function
  | LB_val (pat, exp) -> LB_val (map_pat_annot f pat, map_exp_annot f exp)
and map_lexp_annot f (LEXP_aux (lexp, annot)) = LEXP_aux (map_lexp_annot_aux f lexp, f annot)
and map_lexp_annot_aux f = function
  | LEXP_id id -> LEXP_id id
  | LEXP_deref exp -> LEXP_deref (map_exp_annot f exp)
  | LEXP_memory (id, exps) -> LEXP_memory (id, List.map (map_exp_annot f) exps)
  | LEXP_cast (typ, id) -> LEXP_cast (typ, id)
  | LEXP_tup lexps -> LEXP_tup (List.map (map_lexp_annot f) lexps)
  | LEXP_vector_concat lexps -> LEXP_vector_concat (List.map (map_lexp_annot f) lexps)
  | LEXP_vector (lexp, exp) -> LEXP_vector (map_lexp_annot f lexp, map_exp_annot f exp)
  | LEXP_vector_range (lexp, exp1, exp2) -> LEXP_vector_range (map_lexp_annot f lexp, map_exp_annot f exp1, map_exp_annot f exp2)
  | LEXP_field (lexp, id) -> LEXP_field (map_lexp_annot f lexp, id)

and map_typedef_annot f = function
  | TD_aux (td_aux, annot) -> TD_aux (td_aux, f annot)

and map_fundef_annot f = function
  | FD_aux (fd_aux, annot) -> FD_aux (map_fundef_annot_aux f fd_aux, f annot)
and map_fundef_annot_aux f = function
  | FD_function (rec_opt, tannot_opt, eff_opt, funcls) -> FD_function (map_recopt_annot f rec_opt, tannot_opt, eff_opt,
                                                                       List.map (map_funcl_annot f) funcls)
and map_funcl_annot f = function
  | FCL_aux (fcl, annot) -> FCL_aux (map_funcl_annot_aux f fcl, f annot)
and map_funcl_annot_aux f = function
  | FCL_Funcl (id, pexp) -> FCL_Funcl (id, map_pexp_annot f pexp)
and map_recopt_annot f = function
  | Rec_aux (rec_aux, l) -> Rec_aux (map_recopt_annot_aux f rec_aux, l)
and map_recopt_annot_aux f = function
  | Rec_nonrec -> Rec_nonrec
  | Rec_rec -> Rec_rec
  | Rec_measure (pat, exp) -> Rec_measure (map_pat_annot f pat, map_exp_annot f exp)

and map_mapdef_annot f = function
  | MD_aux (md_aux, annot) -> MD_aux (map_mapdef_annot_aux f md_aux, f annot)
and map_mapdef_annot_aux f = function
  | MD_mapping (id, tannot_opt, mapcls) -> MD_mapping (id, tannot_opt, List.map (map_mapcl_annot f) mapcls)

and map_valspec_annot f = function
  | VS_aux (vs_aux, annot) -> VS_aux (vs_aux, f annot)

and map_scattered_annot f = function
  | SD_aux (sd_aux, annot) -> SD_aux (map_scattered_annot_aux f sd_aux, f annot)
and map_scattered_annot_aux f = function
  | SD_function (rec_opt, tannot_opt, eff_opt, name) -> SD_function (map_recopt_annot f rec_opt, tannot_opt, eff_opt, name)
  | SD_funcl fcl -> SD_funcl (map_funcl_annot f fcl)
  | SD_variant (id, typq) -> SD_variant (id, typq)
  | SD_unioncl (id, tu) -> SD_unioncl (id, tu)
  | SD_mapping (id, tannot_opt) -> SD_mapping (id, tannot_opt)
  | SD_mapcl (id, mcl) -> SD_mapcl (id, map_mapcl_annot f mcl)
  | SD_end id -> SD_end id

and map_decspec_annot f = function
  | DEC_aux (dec_aux, annot) -> DEC_aux (map_decspec_annot_aux f dec_aux, f annot)
and map_decspec_annot_aux f = function
  | DEC_reg (eff1, eff2, typ, id) -> DEC_reg (eff1, eff2, typ, id)
  | DEC_config (id, typ, exp) -> DEC_config (id, typ, map_exp_annot f exp)
  | DEC_alias (id, als) -> DEC_alias (id, map_aliasspec_annot f als)
  | DEC_typ_alias (typ, id, als) -> DEC_typ_alias (typ, id, map_aliasspec_annot f als)
and map_aliasspec_annot f = function
  | AL_aux (al_aux, annot) -> AL_aux (map_aliasspec_annot_aux f al_aux, f annot)
and map_aliasspec_annot_aux f = function
  | AL_subreg (reg_id, id) -> AL_subreg (map_regid_annot f reg_id, id)
  | AL_bit (reg_id, exp) -> AL_bit (map_regid_annot f reg_id, map_exp_annot f exp)
  | AL_slice (reg_id, exp1, exp2) -> AL_slice (map_regid_annot f reg_id, map_exp_annot f exp1, map_exp_annot f exp2)
  | AL_concat (reg_id1, reg_id2) -> AL_concat (map_regid_annot f reg_id1, map_regid_annot f reg_id2)
and map_regid_annot f = function
  | RI_aux (ri_aux, annot) -> RI_aux (map_regid_annot_aux f ri_aux, f annot)
and map_regid_annot_aux f = function
  | RI_id id -> RI_id id

and map_def_annot f = function
  | DEF_type td -> DEF_type (map_typedef_annot f td)
  | DEF_fundef fd -> DEF_fundef (map_fundef_annot f fd)
  | DEF_mapdef md -> DEF_mapdef (map_mapdef_annot f md)
  | DEF_val lb -> DEF_val (map_letbind_annot f lb)
  | DEF_spec vs -> DEF_spec (map_valspec_annot f vs)
  | DEF_fixity (prec, n, id) -> DEF_fixity (prec, n, id)
  | DEF_overload (name, overloads) -> DEF_overload (name, overloads)
  | DEF_default ds -> DEF_default ds
  | DEF_scattered sd -> DEF_scattered (map_scattered_annot f sd)
  | DEF_measure (id, pat, exp) -> DEF_measure (id, map_pat_annot f pat, map_exp_annot f exp)
  | DEF_loop_measures (id, measures) -> DEF_loop_measures (id, List.map (map_loop_measure_annot f) measures)
  | DEF_reg_dec ds -> DEF_reg_dec (map_decspec_annot f ds)
  | DEF_internal_mutrec fds -> DEF_internal_mutrec (List.map (map_fundef_annot f) fds)
  | DEF_pragma (name, arg, l) -> DEF_pragma (name, arg, l)
and map_defs_annot f = function
  | Defs defs -> Defs (List.map (map_def_annot f) defs)

and map_loop_measure_annot f = function
  | Loop (loop, exp) -> Loop (loop, map_exp_annot f exp)

let id_loc = function
  | Id_aux (_, l) -> l

let kid_loc = function
  | Kid_aux (_, l) -> l

let typ_loc = function
  | Typ_aux (_, l) -> l

let pat_loc = function
  | P_aux (_, (l, _)) -> l

let exp_loc = function
  | E_aux (_, (l, _)) -> l

let def_loc = function
  | DEF_type (TD_aux (_, (l, _)))
  | DEF_fundef (FD_aux (_, (l, _)))
  | DEF_mapdef (MD_aux (_, (l, _)))
  | DEF_val (LB_aux (_, (l, _)))
  | DEF_spec (VS_aux (_, (l, _)))
  | DEF_default (DT_aux (_, l))
  | DEF_scattered (SD_aux (_, (l, _)))
  | DEF_reg_dec (DEC_aux (_, (l, _)))
  | DEF_fixity (_, _, Id_aux (_, l))
  | DEF_overload (Id_aux (_, l), _) -> l
  | DEF_internal_mutrec _ -> Parse_ast.Unknown
  | DEF_pragma (_, _, l) -> l
  | DEF_measure (id, _, _) -> id_loc id
  | DEF_loop_measures (id, _) -> id_loc id

let string_of_id = function
  | Id_aux (Id v, _) -> v
  | Id_aux (Operator v, _) -> "(operator " ^ v ^ ")"

let id_of_kid = function
  | Kid_aux (Var v, l) -> Id_aux (Id (String.sub v 1 (String.length v - 1)), l)

let kid_of_id = function
  | Id_aux (Id v, l) -> Kid_aux (Var ("'" ^ v), l)
  | Id_aux (Operator v, _) -> assert false

let prepend_id str = function
  | Id_aux (Id v, l) -> Id_aux (Id (str ^ v), l)
  | Id_aux (Operator v, l) -> Id_aux (Operator (str ^ v), l)

let append_id id str =
  match id with
  | Id_aux (Id v, l) -> Id_aux (Id (v ^ str), l)
  | Id_aux (Operator v, l) -> Id_aux (Operator (v ^ str), l)

let prepend_kid str = function
  | Kid_aux (Var v, l) -> Kid_aux (Var ("'" ^ str ^ String.sub v 1 (String.length v - 1)), l)

let string_of_base_effect_aux = function
  | BE_rreg -> "rreg"
  | BE_wreg -> "wreg"
  | BE_rmem -> "rmem"
  | BE_rmemt -> "rmemt"
  | BE_wmem -> "wmem"
  | BE_eamem -> "eamem"
  | BE_exmem -> "exmem"
  | BE_wmv -> "wmv"
  | BE_wmvt -> "wmvt"
  | BE_barr -> "barr"
  | BE_depend -> "depend"
  | BE_undef -> "undef"
  | BE_unspec -> "unspec"
  | BE_nondet -> "nondet"
  | BE_escape -> "escape"
  | BE_config -> "configuration"
  (*| BE_lset -> "lset"
  | BE_lret -> "lret"*)

let string_of_kind_aux = function
  | K_type -> "Type"
  | K_int -> "Int"
  | K_order -> "Order"
  | K_bool -> "Bool"

let string_of_kind (K_aux (k, _)) = string_of_kind_aux k

let string_of_kinded_id (KOpt_aux (KOpt_kind (k, kid), _)) =
  "(" ^ string_of_kid kid ^ " : " ^ string_of_kind k ^ ")"

let string_of_base_effect = function
  | BE_aux (beff, _) -> string_of_base_effect_aux beff

let string_of_effect = function
  | Effect_aux (Effect_set [], _) -> "pure"
  | Effect_aux (Effect_set beffs, _) ->
     "{" ^ string_of_list ", " string_of_base_effect beffs ^ "}"

let string_of_order = function
  | Ord_aux (Ord_var kid, _) -> string_of_kid kid
  | Ord_aux (Ord_inc, _) -> "inc"
  | Ord_aux (Ord_dec, _) -> "dec"

let rec string_of_nexp = function
  | Nexp_aux (nexp, _) -> string_of_nexp_aux nexp
and string_of_nexp_aux = function
  | Nexp_id id -> string_of_id id
  | Nexp_var kid -> string_of_kid kid
  | Nexp_constant c -> Big_int.to_string c
  | Nexp_times (n1, n2) -> "(" ^ string_of_nexp n1 ^ " * " ^ string_of_nexp n2 ^ ")"
  | Nexp_sum (n1, n2) -> "(" ^ string_of_nexp n1 ^ " + " ^ string_of_nexp n2 ^ ")"
  | Nexp_minus (n1, n2) -> "(" ^ string_of_nexp n1 ^ " - " ^ string_of_nexp n2 ^ ")"
  | Nexp_app (id, nexps) -> string_of_id id ^ "(" ^ string_of_list ", " string_of_nexp nexps ^ ")"
  | Nexp_exp n -> "2 ^ " ^ string_of_nexp n
  | Nexp_neg n -> "- " ^ string_of_nexp n

let rec string_of_typ = function
  | Typ_aux (typ, l) -> string_of_typ_aux typ
and string_of_typ_aux = function
  | Typ_internal_unknown -> "<UNKNOWN TYPE>"
  | Typ_id id -> string_of_id id
  | Typ_var kid -> string_of_kid kid
  | Typ_tup typs -> "(" ^ string_of_list ", " string_of_typ typs ^ ")"
  | Typ_app (id, args) when Id.compare id (mk_id "atom") = 0 -> "int(" ^ string_of_list ", " string_of_typ_arg args ^ ")"
  | Typ_app (id, args) when Id.compare id (mk_id "atom_bool") = 0 -> "bool(" ^ string_of_list ", " string_of_typ_arg args ^ ")"
  | Typ_app (id, args) -> string_of_id id ^ "(" ^ string_of_list ", " string_of_typ_arg args ^ ")"
  | Typ_fn ([typ_arg], typ_ret, eff) ->
     string_of_typ typ_arg ^ " -> " ^ string_of_typ typ_ret ^ " effect " ^ string_of_effect eff
  | Typ_fn (typ_args, typ_ret, eff) ->
     "(" ^ string_of_list ", " string_of_typ typ_args ^ ") -> "
     ^ string_of_typ typ_ret ^ " effect " ^ string_of_effect eff
  | Typ_bidir (typ1, typ2) -> string_of_typ typ1 ^ " <-> " ^ string_of_typ typ2
  | Typ_exist (kids, nc, typ) ->
     "{" ^ string_of_list " " string_of_kinded_id kids ^ ", " ^ string_of_n_constraint nc ^ ". " ^ string_of_typ typ ^ "}"
and string_of_typ_arg = function
  | A_aux (typ_arg, l) -> string_of_typ_arg_aux typ_arg
and string_of_typ_arg_aux = function
  | A_nexp n -> string_of_nexp n
  | A_typ typ -> string_of_typ typ
  | A_order o -> string_of_order o
  | A_bool nc -> string_of_n_constraint nc
and string_of_n_constraint = function
  | NC_aux (NC_equal (n1, n2), _) -> string_of_nexp n1 ^ " == " ^ string_of_nexp n2
  | NC_aux (NC_not_equal (n1, n2), _) -> string_of_nexp n1 ^ " != " ^ string_of_nexp n2
  | NC_aux (NC_bounded_ge (n1, n2), _) -> string_of_nexp n1 ^ " >= " ^ string_of_nexp n2
  | NC_aux (NC_bounded_le (n1, n2), _) -> string_of_nexp n1 ^ " <= " ^ string_of_nexp n2
  | NC_aux (NC_or (nc1, nc2), _) ->
     "(" ^ string_of_n_constraint nc1 ^ " | " ^ string_of_n_constraint nc2 ^ ")"
  | NC_aux (NC_and (nc1, nc2), _) ->
     "(" ^ string_of_n_constraint nc1 ^ " & " ^ string_of_n_constraint nc2 ^ ")"
  | NC_aux (NC_set (kid, ns), _) ->
     string_of_kid kid ^ " in {" ^ string_of_list ", " Big_int.to_string ns ^ "}"
  | NC_aux (NC_app (Id_aux (Operator op, _), [arg1; arg2]), _) ->
     "(" ^ string_of_typ_arg arg1 ^ " " ^ op ^ " " ^ string_of_typ_arg arg2 ^ ")"
  | NC_aux (NC_app (id, args), _) -> string_of_id id ^ "(" ^ string_of_list ", " string_of_typ_arg args ^ ")"
  | NC_aux (NC_var v, _) -> string_of_kid v
  | NC_aux (NC_true, _) -> "true"
  | NC_aux (NC_false, _) -> "false"

let string_of_kinded_id (KOpt_aux (KOpt_kind (k, kid), _)) = "(" ^ string_of_kid kid ^ " : " ^ string_of_kind k ^ ")"

let string_of_quant_item_aux = function
  | QI_id kopt -> string_of_kinded_id kopt
  | QI_constant kopts -> "is_constant(" ^ Util.string_of_list ", " string_of_kinded_id kopts ^ ")"
  | QI_constraint constr -> string_of_n_constraint constr

let string_of_quant_item = function
  | QI_aux (qi, _) -> string_of_quant_item_aux qi

let string_of_typquant_aux = function
  | TypQ_tq quants -> "forall " ^ string_of_list ", " string_of_quant_item quants
  | TypQ_no_forall -> ""

let string_of_typquant = function
  | TypQ_aux (quant, _) -> string_of_typquant_aux quant

let string_of_typschm (TypSchm_aux (TypSchm_ts (quant, typ), _)) =
  string_of_typquant quant ^ ". " ^ string_of_typ typ
let string_of_lit (L_aux (lit, _)) =
  match lit with
  | L_unit -> "()"
  | L_zero -> "bitzero"
  | L_one -> "bitone"
  | L_true -> "true"
  | L_false -> "false"
  | L_num n -> Big_int.to_string n
  | L_hex n -> "0x" ^ n
  | L_bin n -> "0b" ^ n
  | L_undef -> "undefined"
  | L_real r -> r
  | L_string str -> "\"" ^ str ^ "\""

let rec string_of_exp (E_aux (exp, _)) =
  match exp with
  | E_block exps -> "{ " ^ string_of_list "; " string_of_exp exps ^ " }"
  | E_id v -> string_of_id v
  | E_ref id -> "ref " ^ string_of_id id
  | E_sizeof nexp -> "sizeof " ^ string_of_nexp nexp
  | E_constraint nc -> "constraint(" ^ string_of_n_constraint nc ^ ")"
  | E_lit lit -> string_of_lit lit
  | E_return exp -> "return " ^ string_of_exp exp
  | E_app (f, args) -> string_of_id f ^ "(" ^ string_of_list ", " string_of_exp args ^ ")"
  | E_app_infix (x, op, y) -> "(" ^ string_of_exp x ^ " " ^ string_of_id op ^ " " ^ string_of_exp y ^ ")"
  | E_tuple exps -> "(" ^ string_of_list ", " string_of_exp exps ^ ")"
  | E_case (exp, cases) ->
     "match " ^ string_of_exp exp ^ " { " ^ string_of_list ", " string_of_pexp cases ^ " }"
  | E_try (exp, cases) ->
     "try " ^ string_of_exp exp ^ " catch { case " ^ string_of_list " case " string_of_pexp cases ^ "}"
  | E_let (letbind, exp) -> "let " ^ string_of_letbind letbind ^ " in " ^ string_of_exp exp
  | E_assign (lexp, bind) -> string_of_lexp lexp ^ " = " ^ string_of_exp bind
  | E_cast (typ, exp) -> string_of_exp exp ^ " : " ^ string_of_typ typ
  | E_vector vec -> "[" ^ string_of_list ", " string_of_exp vec ^ "]"
  | E_vector_access (v, n) -> string_of_exp v ^ "[" ^ string_of_exp n ^ "]"
  | E_vector_update (v, n, exp) -> "[" ^ string_of_exp v ^ " with " ^ string_of_exp n ^ " = " ^ string_of_exp exp ^ "]"
  | E_vector_update_subrange (v, n, m, exp) -> "[" ^ string_of_exp v ^ " with " ^ string_of_exp n ^ " .. " ^ string_of_exp m ^ " = " ^ string_of_exp exp ^ "]"
  | E_vector_subrange (v, n1, n2) -> string_of_exp v ^ "[" ^ string_of_exp n1 ^ " .. " ^ string_of_exp n2 ^ "]"
  | E_vector_append (v1, v2) -> string_of_exp v1 ^ " @ " ^ string_of_exp v2
  | E_if (cond, then_branch, else_branch) ->
     "if " ^ string_of_exp cond ^ " then " ^ string_of_exp then_branch ^ " else " ^ string_of_exp else_branch
  | E_field (exp, id) -> string_of_exp exp ^ "." ^ string_of_id id
  | E_for (id, f, t, u, ord, body) ->
     "foreach ("
     ^ string_of_id id ^ " from " ^ string_of_exp f ^ " to " ^ string_of_exp t
     ^ " by " ^ string_of_exp u ^ " order " ^ string_of_order ord
     ^ ") { "
     ^ string_of_exp body
  | E_loop (While, measure, cond, body) -> "while " ^ string_of_measure measure ^ string_of_exp cond ^ " do " ^ string_of_exp body
  | E_loop (Until, measure, cond, body) -> "repeat " ^ string_of_measure measure  ^ string_of_exp body ^ " until " ^ string_of_exp cond
  | E_assert (test, msg) -> "assert(" ^ string_of_exp test ^ ", " ^ string_of_exp msg ^ ")"
  | E_exit exp -> "exit " ^ string_of_exp exp
  | E_throw exp -> "throw " ^ string_of_exp exp
  | E_cons (x, xs) -> string_of_exp x ^ " :: " ^ string_of_exp xs
  | E_list xs -> "[|" ^ string_of_list ", " string_of_exp xs ^ "|]"
  | E_record_update (exp, fexps) ->
     "{ " ^ string_of_exp exp ^ " with " ^ string_of_list "; " string_of_fexp fexps ^ " }"
  | E_record fexps ->
     "{ " ^ string_of_list "; " string_of_fexp fexps ^ " }"
  | E_var (lexp, binding, exp) -> "var " ^ string_of_lexp lexp ^ " = " ^ string_of_exp binding ^ " in " ^ string_of_exp exp
  | E_internal_return exp -> "internal_return (" ^ string_of_exp exp ^ ")"
  | E_internal_plet (pat, exp, body) -> "internal_plet " ^ string_of_pat pat ^ " = " ^ string_of_exp exp ^ " in " ^ string_of_exp body
  | E_nondet _ -> "NONDET"
  | E_internal_value v -> "INTERNAL_VALUE(" ^ Value.string_of_value v ^ ")"

and string_of_measure (Measure_aux (m,_)) =
  match m with
  | Measure_none -> ""
  | Measure_some exp -> "termination_measure { " ^ string_of_exp exp ^ "}"

and string_of_fexp (FE_aux (FE_Fexp (field, exp), _)) =
  string_of_id field ^ " = " ^ string_of_exp exp
and string_of_pexp (Pat_aux (pexp, _)) =
  match pexp with
  | Pat_exp (pat, exp) -> string_of_pat pat ^ " -> " ^ string_of_exp exp
  | Pat_when (pat, guard, exp) -> string_of_pat pat ^ " when " ^ string_of_exp guard ^ " -> " ^ string_of_exp exp
and string_of_typ_pat (TP_aux (tpat_aux, _)) =
  match tpat_aux with
  | TP_wild -> "_"
  | TP_var kid -> string_of_kid kid
  | TP_app (f, tpats) -> string_of_id f ^ "(" ^ string_of_list ", " string_of_typ_pat tpats ^ ")"
and string_of_pat (P_aux (pat, l)) =
  match pat with
  | P_lit lit -> string_of_lit lit
  | P_wild -> "_"
  | P_or (pat1, pat2) -> "(" ^ string_of_pat pat1 ^ " | " ^ string_of_pat pat2
  ^ ")"
  | P_not pat         -> "(!" ^ string_of_pat pat ^ ")"
  | P_id v -> string_of_id v
  | P_var (pat, tpat) -> string_of_pat pat ^ " as " ^ string_of_typ_pat tpat
  | P_typ (typ, pat) -> string_of_pat pat ^ " : " ^ string_of_typ typ
  | P_tup pats -> "(" ^ string_of_list ", " string_of_pat pats ^ ")"
  | P_app (f, pats) -> string_of_id f ^ "(" ^ string_of_list ", " string_of_pat pats ^ ")"
  | P_cons (pat1, pat2) -> string_of_pat pat1 ^ " :: " ^ string_of_pat pat2
  | P_list pats -> "[||" ^ string_of_list "," string_of_pat pats ^ "||]"
  | P_vector_concat pats -> string_of_list " @ " string_of_pat pats
  | P_vector pats -> "[" ^ string_of_list ", " string_of_pat pats ^ "]"
  | P_as (pat, id) -> "(" ^ string_of_pat pat ^ " as " ^ string_of_id id ^ ")"
  | P_string_append [] -> "\"\""
  | P_string_append pats -> string_of_list " ^ " string_of_pat pats
  | P_record _ -> "PAT"

and string_of_mpat (MP_aux (pat, l)) =
  match pat with
  | MP_lit lit -> string_of_lit lit
  | MP_id v -> string_of_id v
  | MP_tup pats -> "(" ^ string_of_list ", " string_of_mpat pats ^ ")"
  | MP_app (f, pats) -> string_of_id f ^ "(" ^ string_of_list ", " string_of_mpat pats ^ ")"
  | MP_cons (pat1, pat2) -> string_of_mpat pat1 ^ " :: " ^ string_of_mpat pat2
  | MP_list pats -> "[||" ^ string_of_list "," string_of_mpat pats ^ "||]"
  | MP_vector_concat pats -> string_of_list " @ " string_of_mpat pats
  | MP_vector pats -> "[" ^ string_of_list ", " string_of_mpat pats ^ "]"
  | MP_string_append pats -> string_of_list " ^ " string_of_mpat pats
  | MP_typ (mpat, typ) -> "(" ^ string_of_mpat mpat ^ " : " ^ string_of_typ typ ^ ")"
  | MP_as (mpat, id) -> "((" ^ string_of_mpat mpat ^ ") as " ^ string_of_id id ^ ")"
  | _ -> "MPAT"

and string_of_lexp (LEXP_aux (lexp, _)) =
  match lexp with
  | LEXP_id v -> string_of_id v
  | LEXP_deref exp -> "*(" ^ string_of_exp exp ^ ")"
  | LEXP_cast (typ, v) -> "(" ^ string_of_typ typ ^ ") " ^ string_of_id v
  | LEXP_tup lexps -> "(" ^ string_of_list ", " string_of_lexp lexps ^ ")"
  | LEXP_vector (lexp, exp) -> string_of_lexp lexp ^ "[" ^ string_of_exp exp ^ "]"
  | LEXP_vector_range (lexp, exp1, exp2) ->
     string_of_lexp lexp ^ "[" ^ string_of_exp exp1 ^ " .. " ^ string_of_exp exp2 ^ "]"
  | LEXP_vector_concat lexps ->
     string_of_list " @ " string_of_lexp lexps
  | LEXP_field (lexp, id) -> string_of_lexp lexp ^ "." ^ string_of_id id
  | LEXP_memory (f, xs) -> string_of_id f ^ "(" ^ string_of_list ", " string_of_exp xs ^ ")"
and string_of_letbind (LB_aux (lb, l)) =
  match lb with
  | LB_val (pat, exp) -> string_of_pat pat ^ " = " ^ string_of_exp exp

let rec string_of_index_range (BF_aux (ir, _)) =
  match ir with
  | BF_single n -> string_of_nexp n
  | BF_range (n, m) -> string_of_nexp n ^ " .. " ^ string_of_nexp m
  | BF_concat (ir1, ir2) -> "(" ^ string_of_index_range ir1 ^ ") : (" ^ string_of_index_range ir2 ^ ")"


let rec pat_ids (P_aux (pat_aux, _)) =
  match pat_aux with
  | P_lit _ | P_wild -> IdSet.empty
  | P_id id -> IdSet.singleton id
  | P_as (pat, id) -> IdSet.add id (pat_ids pat)
  | P_or (pat1, pat2) -> IdSet.union (pat_ids pat1) (pat_ids pat2)
  | P_not (pat)       -> pat_ids pat
  | P_var (pat, _) | P_typ (_, pat) -> pat_ids pat
  | P_app (_, pats) | P_tup pats | P_vector pats | P_vector_concat pats | P_list pats ->
     List.fold_right IdSet.union (List.map pat_ids pats) IdSet.empty
  | P_cons (pat1, pat2) ->
     IdSet.union (pat_ids pat1) (pat_ids pat2)
  | P_record (fpats, _) ->
     List.fold_right IdSet.union (List.map fpat_ids fpats) IdSet.empty
  | P_string_append pats ->
     List.fold_right IdSet.union (List.map pat_ids pats) IdSet.empty

and fpat_ids (FP_aux (FP_Fpat (_, pat), _)) = pat_ids pat

let id_of_fundef (FD_aux (FD_function (_, _, _, funcls), (l, _))) =
  match (List.fold_right
           (fun (FCL_aux (FCL_Funcl (id, _), _)) id' ->
             match id' with
             | Some id' -> if string_of_id id' = string_of_id id then Some id'
                           else raise (Reporting.err_typ l
                             ("Function declaration expects all definitions to have the same name, "
                              ^ string_of_id id ^ " differs from other definitions of " ^ string_of_id id'))
             | None -> Some id) funcls None)
  with
  | Some id -> id
  | None -> raise (Reporting.err_typ l "funcl list is empty")

let id_of_type_def_aux = function
  | TD_abbrev (id, _, _)
  | TD_record (id, _, _, _)
  | TD_variant (id, _, _, _)
  | TD_enum (id, _, _)
  | TD_bitfield (id, _, _) -> id
let id_of_type_def (TD_aux (td_aux, _)) = id_of_type_def_aux td_aux

let id_of_val_spec (VS_aux (VS_val_spec (_, id, _, _), _)) = id

let id_of_dec_spec (DEC_aux (ds_aux, _)) =
  match ds_aux with
  | DEC_reg (_, _, _, id) -> id
  | DEC_config (id, _, _) -> id
  | DEC_alias (id, _) -> id
  | DEC_typ_alias (_, id, _) -> id

let ids_of_def = function
  | DEF_type td -> IdSet.singleton (id_of_type_def td)
  | DEF_fundef fd -> IdSet.singleton (id_of_fundef fd)
  | DEF_val (LB_aux (LB_val (pat, _), _)) -> pat_ids pat
  | DEF_reg_dec (DEC_aux (DEC_reg (_, _, _, id), _)) -> IdSet.singleton id
  | DEF_spec vs -> IdSet.singleton (id_of_val_spec vs)
  | DEF_internal_mutrec fds -> IdSet.of_list (List.map id_of_fundef fds)
  | _ -> IdSet.empty
let ids_of_defs (Defs defs) =
  List.fold_left IdSet.union IdSet.empty (List.map ids_of_def defs)

let val_spec_ids (Defs defs) =
  let val_spec_id (VS_aux (vs_aux, _)) =
    match vs_aux with
    | VS_val_spec (_, id, _, _) -> id
  in
  let rec vs_ids = function
    | DEF_spec vs :: defs -> val_spec_id vs :: vs_ids defs
    | def :: defs -> vs_ids defs
    | [] -> []
  in
  IdSet.of_list (vs_ids defs)

module BE = struct
  type t = base_effect
  let compare be1 be2 = String.compare (string_of_base_effect be1) (string_of_base_effect be2)
end

module BESet = Set.Make(BE)

let effect_compare (Effect_aux (Effect_set l1,_)) (Effect_aux (Effect_set l2,_)) =
  match compare (List.length l1) (List.length l2) with
  | 0 -> Util.compare_list BE.compare l1 l2
  | n -> n
let order_compare (Ord_aux (o1,_)) (Ord_aux (o2,_)) =
  match o1, o2 with
  | Ord_var k1, Ord_var k2 -> Kid.compare k1 k2
  | Ord_inc, Ord_inc -> 0
  | Ord_dec, Ord_dec -> 0
  | Ord_var _, _ -> -1 | _, Ord_var _ -> 1
  | Ord_inc, _ -> -1   | _, Ord_inc -> 1
let lex_ord f g x1 x2 y1 y2 =
  match f x1 x2 with
  | 0 -> g y1 y2
  | n -> n

let rec nc_compare (NC_aux (nc1,_)) (NC_aux (nc2,_)) =
  match nc1, nc2 with
  | NC_equal (n1,n2), NC_equal (n3,n4)
  | NC_bounded_ge (n1,n2), NC_bounded_ge (n3,n4)
  | NC_bounded_le (n1,n2), NC_bounded_le (n3,n4)
  | NC_not_equal (n1,n2), NC_not_equal (n3,n4)
    -> lex_ord Nexp.compare Nexp.compare n1 n3 n2 n4
  | NC_set (k1,s1), NC_set (k2,s2) ->
     lex_ord Kid.compare (Util.compare_list Nat_big_num.compare) k1 k2 s1 s2
  | NC_or (nc1,nc2), NC_or (nc3,nc4)
  | NC_and (nc1,nc2), NC_and (nc3,nc4)
    -> lex_ord nc_compare nc_compare nc1 nc3 nc2 nc4
  | NC_app (f1,args1), NC_app (f2,args2)
    -> lex_ord Id.compare (Util.compare_list typ_arg_compare) f1 f2 args1 args2
  | NC_var v1, NC_var v2
    -> Kid.compare v1 v2
  | NC_true, NC_true
  | NC_false, NC_false
    -> 0
  | NC_equal _, _ -> -1      | _, NC_equal _ -> 1
  | NC_bounded_ge _, _ -> -1 | _, NC_bounded_ge _ -> 1
  | NC_bounded_le _, _ -> -1 | _, NC_bounded_le _ -> 1
  | NC_not_equal _, _ -> -1  | _, NC_not_equal _ -> 1
  | NC_set _, _ -> -1        | _, NC_set _ -> 1
  | NC_or _, _ -> -1         | _, NC_or _ -> 1
  | NC_and _, _ -> -1        | _, NC_and _ -> 1
  | NC_app _, _ -> -1        | _, NC_app _ -> 1
  | NC_var _, _ -> -1        | _, NC_var _ -> 1
  | NC_true, _ -> -1         | _, NC_true -> 1

and typ_compare (Typ_aux (t1,_)) (Typ_aux (t2,_)) =
  match t1,t2 with
  | Typ_internal_unknown, Typ_internal_unknown -> 0
  | Typ_id id1, Typ_id id2 -> Id.compare id1 id2
  | Typ_var kid1, Typ_var kid2 -> Kid.compare kid1 kid2
  | Typ_fn (ts1,t2,e1), Typ_fn (ts3,t4,e2) ->
     (match Util.compare_list typ_compare ts1 ts3 with
     | 0 -> (match typ_compare t2 t4 with
       | 0 -> effect_compare e1 e2
       | n -> n)
     | n -> n)
  | Typ_bidir (t1,t2), Typ_bidir (t3,t4) ->
     (match typ_compare t1 t3 with
     | 0 -> typ_compare t2 t3
     | n -> n)
  | Typ_tup ts1, Typ_tup ts2 -> Util.compare_list typ_compare ts1 ts2
  | Typ_exist (ks1,nc1,t1), Typ_exist (ks2,nc2,t2) ->
     (match Util.compare_list KOpt.compare ks1 ks2 with
     | 0 -> (match nc_compare nc1 nc2 with
       | 0 -> typ_compare t1 t2
       | n -> n)
     | n -> n)
  | Typ_app (id1,ts1), Typ_app (id2,ts2) ->
     (match Id.compare id1 id2 with
     | 0 -> Util.compare_list typ_arg_compare ts1 ts2
     | n -> n)
  | Typ_internal_unknown, _ -> -1 | _, Typ_internal_unknown -> 1
  | Typ_id _, _ -> -1    | _, Typ_id _ -> 1
  | Typ_var _, _ -> -1   | _, Typ_var _ -> 1
  | Typ_fn _, _ -> -1    | _, Typ_fn _ -> 1
  | Typ_bidir _, _ -> -1 | _, Typ_bidir _ -> 1
  | Typ_tup _, _ -> -1   | _, Typ_tup _ -> 1
  | Typ_exist _, _ -> -1 | _, Typ_exist _ -> 1

and typ_arg_compare (A_aux (ta1,_)) (A_aux (ta2,_)) =
  match ta1, ta2 with
  | A_nexp n1,  A_nexp n2  -> Nexp.compare n1 n2
  | A_typ t1,   A_typ t2   -> typ_compare t1 t2
  | A_order o1, A_order o2 -> order_compare o1 o2
  | A_bool nc1, A_bool nc2 -> nc_compare nc1 nc2
  | A_nexp _, _ -> -1  | _, A_nexp _ -> 1
  | A_typ _, _  -> -1  | _, A_typ _ -> 1
  | A_order _, _ -> -1 | _, A_order _ -> 1

module NC = struct
  type t = n_constraint
  let compare = nc_compare
end

module NCMap = Map.Make(NC)

module Typ = struct
  type t = typ
  let compare = typ_compare
end

module TypMap = Map.Make(Typ)

let rec nexp_frees (Nexp_aux (nexp, l)) =
  match nexp with
  | Nexp_id _ -> raise (Reporting.err_typ l "Unimplemented Nexp_id in nexp_frees")
  | Nexp_var kid -> KidSet.singleton kid
  | Nexp_constant _ -> KidSet.empty
  | Nexp_times (n1, n2) -> KidSet.union (nexp_frees n1) (nexp_frees n2)
  | Nexp_sum (n1, n2) -> KidSet.union (nexp_frees n1) (nexp_frees n2)
  | Nexp_minus (n1, n2) -> KidSet.union (nexp_frees n1) (nexp_frees n2)
  | Nexp_exp n -> nexp_frees n
  | Nexp_neg n -> nexp_frees n
  | Nexp_app (_, nexps) -> List.fold_left KidSet.union KidSet.empty (List.map nexp_frees nexps)

let rec lexp_to_exp (LEXP_aux (lexp_aux, annot) as le) =
  let rewrap e_aux = E_aux (e_aux, annot) in
  match lexp_aux with
  | LEXP_id id | LEXP_cast (_, id) -> rewrap (E_id id)
  | LEXP_tup les ->
    let get_id (LEXP_aux(lexp,((l,_) as annot)) as le) = match lexp with
      | LEXP_id id | LEXP_cast (_, id) -> E_aux (E_id id, annot)
      | _ ->
        raise (Reporting.err_unreachable l __POS__
         ("Unsupported sub-lexp " ^ string_of_lexp le ^ " in tuple")) in
    rewrap (E_tuple (List.map get_id les))
  | LEXP_vector (lexp, e) -> rewrap (E_vector_access (lexp_to_exp lexp, e))
  | LEXP_vector_range (lexp, e1, e2) -> rewrap (E_vector_subrange (lexp_to_exp lexp, e1, e2))
  | LEXP_field (lexp, id) -> rewrap (E_field (lexp_to_exp lexp, id))
  | LEXP_memory (id, exps) -> rewrap (E_app (id, exps))
  | LEXP_vector_concat [] -> rewrap (E_vector [])
  | LEXP_vector_concat (lexp :: lexps) ->
     List.fold_left (fun exp lexp -> rewrap (E_vector_append (exp, lexp_to_exp lexp))) (lexp_to_exp lexp) lexps
  | LEXP_deref exp -> rewrap (E_app (mk_id "reg_deref", [exp]))

let is_unit_typ = function
  | Typ_aux (Typ_id u, _) -> string_of_id u = "unit"
  | _ -> false

let rec is_number (Typ_aux (t,_)) =
  match t with
  | Typ_id (Id_aux (Id "int", _))
  | Typ_id (Id_aux (Id "nat", _))
  | Typ_app (Id_aux (Id "range", _),_)
  | Typ_app (Id_aux (Id "implicit", _),_)
  | Typ_app (Id_aux (Id "atom", _),_) -> true
  | _ -> false

let is_ref_typ (Typ_aux (typ_aux, _)) = match typ_aux with
  | Typ_app (id, _) -> string_of_id id = "register" || string_of_id id = "reg"
  | _ -> false

let rec is_vector_typ = function
  | Typ_aux (Typ_app (Id_aux (Id "vector",_), [_;_;_]), _) -> true
  | Typ_aux (Typ_app (Id_aux (Id "register",_), [A_aux (A_typ rtyp,_)]), _) ->
    is_vector_typ rtyp
  | _ -> false

let typ_app_args_of = function
  | Typ_aux (Typ_app (Id_aux (Id c,_), targs), l) ->
    (c, List.map (fun (A_aux (a,_)) -> a) targs, l)
  | Typ_aux (_, l) as typ ->
     raise (Reporting.err_typ l
       ("typ_app_args_of called on non-app type " ^ string_of_typ typ))

let rec vector_typ_args_of typ = match typ_app_args_of typ with
  | ("vector", [A_nexp len; A_order ord; A_typ etyp], l) ->
     (nexp_simp len, ord, etyp)
  | ("register", [A_typ rtyp], _) -> vector_typ_args_of rtyp
  | (_, _, l) ->
     raise (Reporting.err_typ l
       ("vector_typ_args_of called on non-vector type " ^ string_of_typ typ))

let vector_start_index typ =
  let (len, ord, etyp) = vector_typ_args_of typ in
  match ord with
  | Ord_aux (Ord_inc, _) -> nint 0
  | Ord_aux (Ord_dec, _) -> nexp_simp (nminus len (nint 1))
  | _ -> raise (Reporting.err_typ (typ_loc typ) "Can't calculate start index without order")

let is_order_inc = function
  | Ord_aux (Ord_inc, _) -> true
  | Ord_aux (Ord_dec, _) -> false
  | Ord_aux (Ord_var _, l) ->
    raise (Reporting.err_unreachable l __POS__ "is_order_inc called on vector with variable ordering")

let is_bit_typ = function
  | Typ_aux (Typ_id (Id_aux (Id "bit", _)), _) -> true
  | _ -> false

let is_bitvector_typ typ =
  if is_vector_typ typ then
    let (_,_,etyp) = vector_typ_args_of typ in
    is_bit_typ etyp
  else false

let has_effect (Effect_aux (eff,_)) searched_for = match eff with
  | Effect_set effs ->
    List.exists (fun (BE_aux (be,_)) -> be = searched_for) effs

let effect_set (Effect_aux (eff,_)) = match eff with
  | Effect_set effs -> BESet.of_list effs

(* Utilities for constructing effect sets *)

let union_effects e1 e2 =
  match e1, e2 with
  | Effect_aux (Effect_set base_effs1, _), Effect_aux (Effect_set base_effs2, _) ->
     let base_effs3 = BESet.elements (BESet.of_list (base_effs1 @ base_effs2)) in
     Effect_aux (Effect_set base_effs3, Parse_ast.Unknown)

let equal_effects e1 e2 =
  match e1, e2 with
  | Effect_aux (Effect_set base_effs1, _), Effect_aux (Effect_set base_effs2, _) ->
     BESet.compare (BESet.of_list base_effs1) (BESet.of_list base_effs2) = 0

let subseteq_effects e1 e2 =
  match e1, e2 with
  | Effect_aux (Effect_set base_effs1, _), Effect_aux (Effect_set base_effs2, _) ->
     BESet.subset (BESet.of_list base_effs1) (BESet.of_list base_effs2)

let rec kopts_of_nexp (Nexp_aux (nexp,_)) =
  match nexp with
  | Nexp_id _
  | Nexp_constant _ -> KOptSet.empty
  | Nexp_var kid -> KOptSet.singleton (mk_kopt K_int kid)
  | Nexp_times (n1,n2)
  | Nexp_sum (n1,n2)
  | Nexp_minus (n1,n2) -> KOptSet.union (kopts_of_nexp n1) (kopts_of_nexp n2)
  | Nexp_exp n
  | Nexp_neg n -> kopts_of_nexp n
  | Nexp_app (_, nexps) -> List.fold_left KOptSet.union KOptSet.empty (List.map kopts_of_nexp nexps)

let kopts_of_order (Ord_aux (ord, _)) =
  match ord with
  | Ord_var kid -> KOptSet.singleton (mk_kopt K_order kid)
  | Ord_inc | Ord_dec -> KOptSet.empty

let rec kopts_of_constraint (NC_aux (nc, _)) =
  match nc with
  | NC_equal (nexp1, nexp2)
  | NC_bounded_ge (nexp1, nexp2)
  | NC_bounded_le (nexp1, nexp2)
  | NC_not_equal (nexp1, nexp2) ->
     KOptSet.union (kopts_of_nexp nexp1) (kopts_of_nexp nexp2)
  | NC_set (kid, _) -> KOptSet.singleton (mk_kopt K_int kid)
  | NC_or (nc1, nc2)
  | NC_and (nc1, nc2) ->
     KOptSet.union (kopts_of_constraint nc1) (kopts_of_constraint nc2)
  | NC_app (id, args) ->
     List.fold_left (fun s t -> KOptSet.union s (kopts_of_typ_arg t)) KOptSet.empty args
  | NC_var kid -> KOptSet.singleton (mk_kopt K_bool kid)
  | NC_true | NC_false -> KOptSet.empty

and kopts_of_typ (Typ_aux (t,_)) =
  match t with
  | Typ_internal_unknown -> KOptSet.empty
  | Typ_id _ -> KOptSet.empty
  | Typ_var kid -> KOptSet.singleton (mk_kopt K_type kid)
  | Typ_fn (ts, t, _) -> List.fold_left KOptSet.union (kopts_of_typ t) (List.map kopts_of_typ ts)
  | Typ_bidir (t1, t2) -> KOptSet.union (kopts_of_typ t1) (kopts_of_typ t2)
  | Typ_tup ts ->
     List.fold_left (fun s t -> KOptSet.union s (kopts_of_typ t))
       KOptSet.empty ts
  | Typ_app (_,tas) ->
     List.fold_left (fun s ta -> KOptSet.union s (kopts_of_typ_arg ta))
       KOptSet.empty tas
  | Typ_exist (kopts, nc, t) ->
     let s = KOptSet.union (kopts_of_typ t) (kopts_of_constraint nc) in
     KOptSet.diff s (KOptSet.of_list kopts)
and kopts_of_typ_arg (A_aux (ta,_)) =
  match ta with
  | A_nexp nexp -> kopts_of_nexp nexp
  | A_typ typ -> kopts_of_typ typ
  | A_order ord -> kopts_of_order ord
  | A_bool nc -> kopts_of_constraint nc

let kopts_of_quant_item (QI_aux (qi, _)) = match qi with
  | QI_id kopt ->
     KOptSet.singleton kopt
  | QI_constant kopts -> KOptSet.of_list kopts
  | QI_constraint nc -> kopts_of_constraint nc

let rec tyvars_of_nexp (Nexp_aux (nexp,_)) =
  match nexp with
  | Nexp_id _
  | Nexp_constant _ -> KidSet.empty
  | Nexp_var kid -> KidSet.singleton kid
  | Nexp_times (n1,n2)
  | Nexp_sum (n1,n2)
  | Nexp_minus (n1,n2) -> KidSet.union (tyvars_of_nexp n1) (tyvars_of_nexp n2)
  | Nexp_exp n
  | Nexp_neg n -> tyvars_of_nexp n
  | Nexp_app (_, nexps) -> List.fold_left KidSet.union KidSet.empty (List.map tyvars_of_nexp nexps)

let rec tyvars_of_constraint (NC_aux (nc, _)) =
  match nc with
  | NC_equal (nexp1, nexp2)
  | NC_bounded_ge (nexp1, nexp2)
  | NC_bounded_le (nexp1, nexp2)
  | NC_not_equal (nexp1, nexp2) ->
     KidSet.union (tyvars_of_nexp nexp1) (tyvars_of_nexp nexp2)
  | NC_set (kid, _) -> KidSet.singleton kid
  | NC_or (nc1, nc2)
  | NC_and (nc1, nc2) ->
     KidSet.union (tyvars_of_constraint nc1) (tyvars_of_constraint nc2)
  | NC_app (id, args) ->
     List.fold_left (fun s t -> KidSet.union s (tyvars_of_typ_arg t)) KidSet.empty args
  | NC_var kid -> KidSet.singleton kid
  | NC_true
  | NC_false -> KidSet.empty

and tyvars_of_typ (Typ_aux (t,_)) =
  match t with
  | Typ_internal_unknown -> KidSet.empty
  | Typ_id _ -> KidSet.empty
  | Typ_var kid -> KidSet.singleton kid
  | Typ_fn (ts, t, _) -> List.fold_left KidSet.union (tyvars_of_typ t) (List.map tyvars_of_typ ts)
  | Typ_bidir (t1, t2) -> KidSet.union (tyvars_of_typ t1) (tyvars_of_typ t2)
  | Typ_tup ts ->
     List.fold_left (fun s t -> KidSet.union s (tyvars_of_typ t))
       KidSet.empty ts
  | Typ_app (_,tas) -> 
     List.fold_left (fun s ta -> KidSet.union s (tyvars_of_typ_arg ta))
       KidSet.empty tas
  | Typ_exist (kids, nc, t) ->
     let s = KidSet.union (tyvars_of_typ t) (tyvars_of_constraint nc) in
     List.fold_left (fun s k -> KidSet.remove k s) s (List.map kopt_kid kids)
and tyvars_of_typ_arg (A_aux (ta,_)) =
  match ta with
  | A_nexp nexp -> tyvars_of_nexp nexp
  | A_typ typ -> tyvars_of_typ typ
  | A_order _ -> KidSet.empty
  | A_bool nc -> tyvars_of_constraint nc

let tyvars_of_quant_item (QI_aux (qi, _)) = match qi with
  | QI_id (KOpt_aux (KOpt_kind (_, kid), _)) ->
     KidSet.singleton kid
  | QI_constant kopts -> KidSet.of_list (List.map kopt_kid kopts)
  | QI_constraint nc -> tyvars_of_constraint nc

let is_kid_generated kid = String.contains (string_of_kid kid) '#'

let rec undefined_of_typ mwords l annot (Typ_aux (typ_aux, _) as typ) =
  let wrap e_aux typ = E_aux (e_aux, (l, annot typ)) in
  match typ_aux with
  | Typ_id id ->
     wrap (E_app (prepend_id "undefined_" id, [wrap (E_lit (mk_lit L_unit)) unit_typ])) typ
  | Typ_app (_,[size;_;_]) when mwords && is_bitvector_typ typ ->
     wrap (E_app (mk_id "undefined_bitvector",
       undefined_of_typ_args mwords l annot size)) typ
  | Typ_app (atom, [A_aux (A_nexp i, _)]) when string_of_id atom = "atom" ->
     wrap (E_sizeof i) typ
  | Typ_app (id, args) ->
     wrap (E_app (prepend_id "undefined_" id,
                  List.concat (List.map (undefined_of_typ_args mwords l annot) args))) typ
  | Typ_tup typs ->
     wrap (E_tuple (List.map (undefined_of_typ mwords l annot) typs)) typ
  | Typ_var kid ->
     (* Undefined monomorphism restriction in the type checker should
        guarantee that the typ_(kid) parameter was always one created
        in an undefined_(type) function created in
        initial_check.ml. i.e. the rewriter should only encounter this
        case when re-writing those functions. *)
     wrap (E_id (prepend_id "typ_" (id_of_kid kid))) typ
  | Typ_internal_unknown -> assert false
  | Typ_bidir _ -> assert false
  | Typ_fn _ -> assert false
  | Typ_exist _ -> assert false (* Typ_exist should be re-written *)
and undefined_of_typ_args mwords l annot (A_aux (typ_arg_aux, _) as typ_arg) =
  match typ_arg_aux with
  | A_nexp n -> [E_aux (E_sizeof n, (l, annot (atom_typ n)))]
  | A_typ typ -> [undefined_of_typ mwords l annot typ]
  | A_bool nc -> [E_aux (E_constraint nc, (l, annot (atom_bool_typ nc)))]
  | A_order _ -> []

let destruct_pexp (Pat_aux (pexp,ann)) =
  match pexp with
  | Pat_exp (pat,exp) -> pat,None,exp,ann
  | Pat_when (pat,guard,exp) -> pat,Some guard,exp,ann

let construct_pexp (pat,guard,exp,ann) =
  match guard with
  | None -> Pat_aux (Pat_exp (pat,exp),ann)
  | Some guard -> Pat_aux (Pat_when (pat,guard,exp),ann)

let destruct_mpexp (MPat_aux (mpexp,ann)) =
  match mpexp with
  | MPat_pat mpat -> mpat,None,ann
  | MPat_when (mpat,guard) -> mpat,Some guard,ann

let construct_mpexp (mpat,guard,ann) =
  match guard with
  | None -> MPat_aux (MPat_pat mpat,ann)
  | Some guard -> MPat_aux (MPat_when (mpat,guard),ann)


let is_valspec id = function
  | DEF_spec (VS_aux (VS_val_spec (_, id', _, _), _)) when Id.compare id id' = 0 -> true
  | _ -> false

let is_fundef id = function
  | DEF_fundef (FD_aux (FD_function (_, _, _, FCL_aux (FCL_Funcl (id', _), _) :: _), _)) when Id.compare id' id = 0 -> true
  | _ -> false

let rename_valspec id (VS_aux (VS_val_spec (typschm, _, externs, is_cast), annot)) =
  VS_aux (VS_val_spec (typschm, id, externs, is_cast), annot)

let rename_funcl id (FCL_aux (FCL_Funcl (_, pexp), annot)) = FCL_aux (FCL_Funcl (id, pexp), annot)

let rename_fundef id (FD_aux (FD_function (ropt, topt, eopt, funcls), annot)) =
  FD_aux (FD_function (ropt, topt, eopt, List.map (rename_funcl id) funcls), annot)

let rec split_defs' f defs acc =
  match defs with
  | [] -> None
  | def :: defs when f def -> Some (acc, def, defs)
  | def :: defs -> split_defs' f defs (def :: acc)

let split_defs f (Defs defs) =
  match split_defs' f defs [] with
  | None -> None
  | Some (pre_defs, def, post_defs) ->
     Some (Defs (List.rev pre_defs), def, Defs post_defs)

let append_ast (Defs ast1) (Defs ast2) = Defs (ast1 @ ast2)
let concat_ast asts = List.fold_right append_ast asts (Defs [])

let type_union_id (Tu_aux (Tu_ty_id (_, id), _)) = id

let rec subst id value (E_aux (e_aux, annot) as exp) =
  let wrap e_aux = E_aux (e_aux, annot) in
  let e_aux = match e_aux with
    | E_block exps -> E_block (List.map (subst id value) exps)
    | E_nondet exps -> E_nondet (List.map (subst id value) exps)
    | E_id id' -> if Id.compare id id' = 0 then unaux_exp value else E_id id'
    | E_lit lit -> E_lit lit
    | E_cast (typ, exp) -> E_cast (typ, subst id value exp)

    | E_app (fn, exps) -> E_app (fn, List.map (subst id value) exps)
    | E_app_infix (exp1, op, exp2) -> E_app_infix (subst id value exp1, op, subst id value exp2)

    | E_tuple exps -> E_tuple (List.map (subst id value) exps)

    | E_if (cond, then_exp, else_exp) ->
       E_if (subst id value cond, subst id value then_exp, subst id value else_exp)

    | E_loop (loop, measure, cond, body) ->
       E_loop (loop, subst_measure id value measure, subst id value cond, subst id value body)
    | E_for (id', exp1, exp2, exp3, order, body) when Id.compare id id' = 0 ->
       E_for (id', exp1, exp2, exp3, order, body)
    | E_for (id', exp1, exp2, exp3, order, body) ->
       E_for (id', subst id value exp1, subst id value exp2, subst id value exp3, order, subst id value body)

    | E_vector exps -> E_vector (List.map (subst id value) exps)
    | E_vector_access (exp1, exp2) -> E_vector_access (subst id value exp1, subst id value exp2)
    | E_vector_subrange (exp1, exp2, exp3) -> E_vector_subrange (subst id value exp1, subst id value exp2, subst id value exp3)
    | E_vector_update (exp1, exp2, exp3) -> E_vector_update (subst id value exp1, subst id value exp2, subst id value exp3)
    | E_vector_update_subrange (exp1, exp2, exp3, exp4) ->
       E_vector_update_subrange (subst id value exp1, subst id value exp2, subst id value exp3, subst id value exp4)
    | E_vector_append (exp1, exp2) -> E_vector_append (subst id value exp1, subst id value exp2)

    | E_list exps -> E_list (List.map (subst id value) exps)
    | E_cons (exp1, exp2) -> E_cons (subst id value exp1, subst id value exp2)

    | E_record fexps -> E_record (List.map (subst_fexp id value) fexps)
    | E_record_update (exp, fexps) -> E_record_update (subst id value exp, List.map (subst_fexp id value) fexps)
    | E_field (exp, id') -> E_field (subst id value exp, id')

    | E_case (exp, pexps) ->
       E_case (subst id value exp, List.map (subst_pexp id value) pexps)

    | E_let (LB_aux (LB_val (pat, bind), lb_annot), body) ->
       E_let (LB_aux (LB_val (pat, subst id value bind), lb_annot),
              if IdSet.mem id (pat_ids pat) then body else subst id value body)

    | E_assign (lexp, exp) -> E_assign (subst_lexp id value lexp, subst id value exp) (* Shadowing... *)

    (* Should be re-written *)
    | E_sizeof nexp -> E_sizeof nexp
    | E_constraint nc -> E_constraint nc

    | E_return exp -> E_return (subst id value exp)
    | E_exit exp -> E_exit (subst id value exp)

    (* id should always be immutable while id' must be mutable register name so should be ok to never substitute here *)
    | E_ref id' -> E_ref id'
    | E_throw exp -> E_throw (subst id value exp)

    | E_try (exp, pexps) ->
       E_try (subst id value exp, List.map (subst_pexp id value) pexps)

    | E_assert (exp1, exp2) -> E_assert (subst id value exp1, subst id value exp2)

    | E_internal_value v -> E_internal_value v

    | E_var (lexp, exp1, exp2) -> E_var (subst_lexp id value lexp, subst id value exp1, subst id value exp2)

    | E_internal_plet _ | E_internal_return _ -> failwith ("subst " ^ string_of_exp exp)
  in
  wrap e_aux

and subst_measure id value (Measure_aux (m_aux, l)) =
  match m_aux with
  | Measure_none -> Measure_aux (Measure_none, l)
  | Measure_some exp -> Measure_aux (Measure_some (subst id value exp), l)

and subst_pexp id value (Pat_aux (pexp_aux, annot)) =
  let pexp_aux = match pexp_aux with
    | Pat_exp (pat, exp) when IdSet.mem id (pat_ids pat) -> Pat_exp (pat, exp)
    | Pat_exp (pat, exp) -> Pat_exp (pat, subst id value exp)
    | Pat_when (pat, guard, exp) when IdSet.mem id (pat_ids pat) -> Pat_when (pat, guard, exp)
    | Pat_when (pat, guard, exp) -> Pat_when (pat, subst id value guard, subst id value exp)
  in
  Pat_aux (pexp_aux, annot)

and subst_fexp id value (FE_aux (FE_Fexp (id', exp), annot)) =
  FE_aux (FE_Fexp (id', subst id value exp), annot)

and subst_lexp id value (LEXP_aux (lexp_aux, annot) as lexp) =
  let wrap lexp_aux = LEXP_aux (lexp_aux, annot) in
  let lexp_aux = match lexp_aux with
    | LEXP_deref exp -> LEXP_deref (subst id value exp)
    | LEXP_id id' -> LEXP_id id'
    | LEXP_memory (f, exps) -> LEXP_memory (f, List.map (subst id value) exps)
    | LEXP_cast (typ, id') -> LEXP_cast (typ, id')
    | LEXP_tup lexps -> LEXP_tup (List.map (subst_lexp id value) lexps)
    | LEXP_vector (lexp, exp) -> LEXP_vector (subst_lexp id value lexp, subst id value exp)
    | LEXP_vector_range (lexp, exp1, exp2) -> LEXP_vector_range (subst_lexp id value lexp, subst id value exp1, subst id value exp2)
    | LEXP_vector_concat lexps ->
       LEXP_vector_concat (List.map (subst_lexp id value) lexps)
    | LEXP_field (lexp, id') -> LEXP_field (subst_lexp id value lexp, id')
  in
  wrap lexp_aux

let hex_to_bin hex =
  Util.string_to_list hex
  |> List.map Sail_lib.hex_char
  |> List.concat
  |> List.map Sail_lib.char_of_bit
  |> (fun bits -> String.init (List.length bits) (List.nth bits))

(* Functions for working with locations *)

let locate_id f (Id_aux (name, l)) = Id_aux (name, f l)

let locate_kid f (Kid_aux (name, l)) = Kid_aux (name, f l)

let locate_kind f (K_aux (kind, l)) = K_aux (kind, f l)

let locate_kinded_id f (KOpt_aux (KOpt_kind (k, kid), l)) =
  KOpt_aux (KOpt_kind (locate_kind f k, locate_kid f kid), f l)

let locate_lit f (L_aux (lit, l)) = L_aux (lit, f l)

let locate_base_effect f (BE_aux (base_effect, l)) = BE_aux (base_effect, f l)

let locate_effect f (Effect_aux (Effect_set effects, l)) =
  Effect_aux (Effect_set (List.map (locate_base_effect f) effects), f l)

let locate_order f (Ord_aux (ord_aux, l)) =
  let ord_aux = match ord_aux with
    | Ord_inc -> Ord_inc
    | Ord_dec -> Ord_dec
    | Ord_var v -> Ord_var (locate_kid f v)
  in
  Ord_aux (ord_aux, f l)

let rec locate_nexp f (Nexp_aux (nexp_aux, l)) =
  let nexp_aux = match nexp_aux with
    | Nexp_id id -> Nexp_id (locate_id f id)
    | Nexp_var kid -> Nexp_var (locate_kid f kid)
    | Nexp_constant n -> Nexp_constant n
    | Nexp_app (id, nexps) -> Nexp_app (locate_id f id, List.map (locate_nexp f) nexps)
    | Nexp_times (nexp1, nexp2) -> Nexp_times (locate_nexp f nexp1, locate_nexp f nexp2)
    | Nexp_sum (nexp1, nexp2) -> Nexp_sum (locate_nexp f nexp1, locate_nexp f nexp2)
    | Nexp_minus (nexp1, nexp2) -> Nexp_minus (locate_nexp f nexp1, locate_nexp f nexp2)
    | Nexp_exp nexp -> Nexp_exp (locate_nexp f nexp)
    | Nexp_neg nexp -> Nexp_neg (locate_nexp f nexp)
  in
  Nexp_aux (nexp_aux, f l)

let rec locate_nc f (NC_aux (nc_aux, l)) =
  let nc_aux = match nc_aux with
    | NC_equal (nexp1, nexp2) -> NC_equal (locate_nexp f nexp1, locate_nexp f nexp2)
    | NC_bounded_ge (nexp1, nexp2) -> NC_bounded_ge (locate_nexp f nexp1, locate_nexp f nexp2)
    | NC_bounded_le (nexp1, nexp2) -> NC_bounded_le (locate_nexp f nexp1, locate_nexp f nexp2)
    | NC_not_equal (nexp1, nexp2) -> NC_not_equal (locate_nexp f nexp1, locate_nexp f nexp2)
    | NC_set (kid, nums) -> NC_set (locate_kid f kid, nums)
    | NC_or (nc1, nc2) -> NC_or (locate_nc f nc1, locate_nc f nc2)
    | NC_and (nc1, nc2) -> NC_and (locate_nc f nc1, locate_nc f nc2)
    | NC_true -> NC_true
    | NC_false -> NC_false
    | NC_var v -> NC_var (locate_kid f v)
    | NC_app (id, args) -> NC_app (locate_id f id, List.map (locate_typ_arg f) args)
  in
  NC_aux (nc_aux, f l)

and locate_typ f (Typ_aux (typ_aux, l)) =
  let typ_aux = match typ_aux with
    | Typ_internal_unknown -> Typ_internal_unknown
    | Typ_id id -> Typ_id (locate_id f id)
    | Typ_var kid -> Typ_var (locate_kid f kid)
    | Typ_fn (arg_typs, ret_typ, effect) ->
       Typ_fn (List.map (locate_typ f) arg_typs, locate_typ f ret_typ, locate_effect f effect)
    | Typ_bidir (typ1, typ2) -> Typ_bidir (locate_typ f typ1, locate_typ f typ2)
    | Typ_tup typs -> Typ_tup (List.map (locate_typ f) typs)
    | Typ_exist (kopts, constr, typ) -> Typ_exist (List.map (locate_kinded_id f) kopts, locate_nc f constr, locate_typ f typ)
    | Typ_app (id, typ_args) -> Typ_app (locate_id f id, List.map (locate_typ_arg f) typ_args)
  in
  Typ_aux (typ_aux, f l)

and locate_typ_arg f (A_aux (typ_arg_aux, l)) =
  let typ_arg_aux = match typ_arg_aux with
    | A_nexp nexp -> A_nexp (locate_nexp f nexp)
    | A_typ typ -> A_typ (locate_typ f typ)
    | A_order ord -> A_order (locate_order f ord)
    | A_bool nc -> A_bool (locate_nc f nc)
  in
  A_aux (typ_arg_aux, f l)

let rec locate_typ_pat f (TP_aux (tp_aux, l)) =
  let tp_aux = match tp_aux with
    | TP_wild -> TP_wild
    | TP_var kid -> TP_var (locate_kid f kid)
    | TP_app (id, tps) -> TP_app (locate_id f id, List.map (locate_typ_pat f) tps)
  in
  TP_aux (tp_aux, f l)

let rec locate_pat : 'a. (l -> l) -> 'a pat -> 'a pat = fun f (P_aux (p_aux, (l, annot))) ->
  let p_aux = match p_aux with
    | P_lit lit -> P_lit (locate_lit f lit)
    | P_wild -> P_wild
    | P_or (pat1, pat2) -> P_or (locate_pat f pat1, locate_pat f pat2)
    | P_not pat -> P_not (locate_pat f pat)
    | P_as (pat, id) -> P_as (locate_pat f pat, locate_id f id)
    | P_typ (typ, pat) -> P_typ (locate_typ f typ, locate_pat f pat)
    | P_id id -> P_id (locate_id f id)
    | P_var (pat, typ_pat) -> P_var (locate_pat f pat, locate_typ_pat f typ_pat)
    | P_app (id, pats) -> P_app (locate_id f id, List.map (locate_pat f) pats)
    | P_record (fpats, semi) -> P_record (List.map (locate_fpat f) fpats, semi)
    | P_vector pats -> P_vector (List.map (locate_pat f) pats)
    | P_vector_concat pats -> P_vector_concat (List.map (locate_pat f) pats)
    | P_tup pats -> P_tup (List.map (locate_pat f) pats)
    | P_list pats -> P_list (List.map (locate_pat f) pats)
    | P_cons (hd_pat, tl_pat) -> P_cons (locate_pat f hd_pat, locate_pat f tl_pat)
    | P_string_append pats -> P_string_append (List.map (locate_pat f) pats)
  in
  P_aux (p_aux, (f l, annot))

and locate_fpat : 'a. (l -> l) -> 'a fpat -> 'a fpat = fun f (FP_aux (FP_Fpat (id, pat), (l, annot))) ->
  FP_aux (FP_Fpat (locate_id f id, locate_pat f pat), (f l, annot))

let rec locate : 'a. (l -> l) -> 'a exp -> 'a exp = fun f (E_aux (e_aux, (l, annot))) ->
  let e_aux = match e_aux with
    | E_block exps -> E_block (List.map (locate f) exps)
    | E_nondet exps -> E_nondet (List.map (locate f) exps)
    | E_id id -> E_id (locate_id f id)
    | E_lit lit -> E_lit (locate_lit f lit)
    | E_cast (typ, exp) -> E_cast (locate_typ f typ, locate f exp)
    | E_app (id, exps) -> E_app (locate_id f id, List.map (locate f) exps)
    | E_app_infix (exp1, op, exp2) -> E_app_infix (locate f exp1, locate_id f op, locate f exp2)
    | E_tuple exps -> E_tuple (List.map (locate f) exps)
    | E_if (cond_exp, then_exp, else_exp) -> E_if (locate f cond_exp, locate f then_exp, locate f else_exp)
    | E_loop (loop, measure, cond, body) -> E_loop (loop, locate_measure f measure, locate f cond, locate f body)
    | E_for (id, exp1, exp2, exp3, ord, exp4) ->
       E_for (locate_id f id, locate f exp1, locate f exp2, locate f exp3, ord, locate f exp4)
    | E_vector exps -> E_vector (List.map (locate f) exps)
    | E_vector_access (exp1, exp2) -> E_vector_access (locate f exp1, locate f exp2)
    | E_vector_subrange (exp1, exp2, exp3) -> E_vector_subrange (locate f exp1, locate f exp2, locate f exp3)
    | E_vector_update (exp1, exp2, exp3) -> E_vector_update (locate f exp1, locate f exp2, locate f exp3)
    | E_vector_update_subrange (exp1, exp2, exp3, exp4) ->
       E_vector_update_subrange (locate f exp1, locate f exp2, locate f exp3, locate f exp4)
    | E_vector_append (exp1, exp2) ->
       E_vector_append (locate f exp1, locate f exp2)
    | E_list exps -> E_list (List.map (locate f) exps)
    | E_cons (exp1, exp2) -> E_cons (locate f exp1, locate f exp2)
    | E_record fexps -> E_record (List.map (locate_fexp f) fexps)
    | E_record_update (exp, fexps) -> E_record_update (locate f exp, List.map (locate_fexp f) fexps)
    | E_field (exp, id) -> E_field (locate f exp, locate_id f id)
    | E_case (exp, cases) -> E_case (locate f exp, List.map (locate_pexp f) cases)
    | E_let (letbind, exp) -> E_let (locate_letbind f letbind, locate f exp)
    | E_assign (lexp, exp) -> E_assign (locate_lexp f lexp, locate f exp)
    | E_sizeof nexp -> E_sizeof (locate_nexp f nexp)
    | E_return exp -> E_return (locate f exp)
    | E_exit exp -> E_exit (locate f exp)
    | E_ref id -> E_ref (locate_id f id)
    | E_throw exp -> E_throw (locate f exp)
    | E_try (exp, cases) -> E_try (locate f exp, List.map (locate_pexp f) cases)
    | E_assert (exp, message) -> E_assert (locate f exp, locate f message)
    | E_constraint constr -> E_constraint (locate_nc f constr)
    | E_var (lexp, exp1, exp2) -> E_var (locate_lexp f lexp, locate f exp1, locate f exp2)
    | E_internal_plet (pat, exp1, exp2) -> E_internal_plet (locate_pat f pat, locate f exp1, locate f exp2)
    | E_internal_return exp -> E_internal_return (locate f exp)
    | E_internal_value value -> E_internal_value value
  in
  E_aux (e_aux, (f l, annot))

and locate_measure : 'a. (l -> l) -> 'a internal_loop_measure -> 'a internal_loop_measure = fun f (Measure_aux (m, l)) ->
  let m = match m with
    | Measure_none -> Measure_none
    | Measure_some exp -> Measure_some (locate f exp)
  in Measure_aux (m, f l)

and locate_letbind : 'a. (l -> l) -> 'a letbind -> 'a letbind = fun f (LB_aux (LB_val (pat, exp), (l, annot))) ->
  LB_aux (LB_val (locate_pat f pat, locate f exp), (f l, annot))

and locate_pexp : 'a. (l -> l) -> 'a pexp -> 'a pexp = fun f (Pat_aux (pexp_aux, (l, annot))) ->
  let pexp_aux = match pexp_aux with
    | Pat_exp (pat, exp) -> Pat_exp (locate_pat f pat, locate f exp)
    | Pat_when (pat, guard, exp) -> Pat_when (locate_pat f pat, locate f guard, locate f exp)
  in
  Pat_aux (pexp_aux, (f l, annot))

and locate_lexp : 'a. (l -> l) -> 'a lexp -> 'a lexp = fun f (LEXP_aux (lexp_aux, (l, annot))) ->
  let lexp_aux = match lexp_aux with
    | LEXP_id id -> LEXP_id (locate_id f id)
    | LEXP_deref exp -> LEXP_deref (locate f exp)
    | LEXP_memory (id, exps) -> LEXP_memory (locate_id f id, List.map (locate f) exps)
    | LEXP_cast (typ, id) -> LEXP_cast (locate_typ f typ, locate_id f id)
    | LEXP_tup lexps -> LEXP_tup (List.map (locate_lexp f) lexps)
    | LEXP_vector_concat lexps -> LEXP_vector_concat (List.map (locate_lexp f) lexps)
    | LEXP_vector (lexp, exp) -> LEXP_vector (locate_lexp f lexp, locate f exp)
    | LEXP_vector_range (lexp, exp1, exp2) -> LEXP_vector_range (locate_lexp f lexp, locate f exp1, locate f exp2)
    | LEXP_field (lexp, id) -> LEXP_field (locate_lexp f lexp, locate_id f id)
  in
  LEXP_aux (lexp_aux, (f l, annot))

and locate_fexp : 'a. (l -> l) -> 'a fexp -> 'a fexp = fun f (FE_aux (FE_Fexp (id, exp), (l, annot))) ->
  FE_aux (FE_Fexp (locate_id f id, locate f exp), (f l, annot))

let unique_ref = ref 0

let unique l =
  let l = Parse_ast.Unique (!unique_ref, l) in
  incr unique_ref;
  l

let extern_assoc backend exts =
  try
    try
      Some (List.assoc backend exts)
    with Not_found ->
      Some (List.assoc "_" exts)
  with Not_found ->
    None

(**************************************************************************)
(* 1. Substitutions                                                       *)
(**************************************************************************)

let order_subst_aux sv subst = function
  | Ord_var kid ->
     begin match subst with
     | A_aux (A_order ord, _) when Kid.compare kid sv = 0 ->
        unaux_order ord
     | _ -> Ord_var kid
     end
  | Ord_inc -> Ord_inc
  | Ord_dec -> Ord_dec

let order_subst sv subst (Ord_aux (ord, l)) = Ord_aux (order_subst_aux sv subst ord, l)

let rec nexp_subst sv subst (Nexp_aux (nexp, l)) = Nexp_aux (nexp_subst_aux sv subst nexp, l)
and nexp_subst_aux sv subst = function
  | Nexp_var kid ->
     begin match subst with
     | A_aux (A_nexp n, _) when Kid.compare kid sv = 0 -> unaux_nexp n
     | _ -> Nexp_var kid
     end
  | Nexp_id id -> Nexp_id id
  | Nexp_constant c -> Nexp_constant c
  | Nexp_times (nexp1, nexp2) -> Nexp_times (nexp_subst sv subst nexp1, nexp_subst sv subst nexp2)
  | Nexp_sum (nexp1, nexp2) -> Nexp_sum (nexp_subst sv subst nexp1, nexp_subst sv subst nexp2)
  | Nexp_minus (nexp1, nexp2) -> Nexp_minus (nexp_subst sv subst nexp1, nexp_subst sv subst nexp2)
  | Nexp_app (id, nexps) -> Nexp_app (id, List.map (nexp_subst sv subst) nexps)
  | Nexp_exp nexp -> Nexp_exp (nexp_subst sv subst nexp)
  | Nexp_neg nexp -> Nexp_neg (nexp_subst sv subst nexp)

let rec nexp_set_to_or l subst = function
  | [] -> raise (Reporting.err_unreachable l __POS__ "Empty set in constraint")
  | [int] -> NC_equal (subst, nconstant int)
  | (int :: ints) -> NC_or (mk_nc (NC_equal (subst, nconstant int)), mk_nc (nexp_set_to_or l subst ints))

let rec constraint_subst sv subst (NC_aux (nc, l)) = NC_aux (constraint_subst_aux l sv subst nc, l)
and constraint_subst_aux l sv subst = function
  | NC_equal (n1, n2) -> NC_equal (nexp_subst sv subst n1, nexp_subst sv subst n2)
  | NC_bounded_ge (n1, n2) -> NC_bounded_ge (nexp_subst sv subst n1, nexp_subst sv subst n2)
  | NC_bounded_le (n1, n2) -> NC_bounded_le (nexp_subst sv subst n1, nexp_subst sv subst n2)
  | NC_not_equal (n1, n2) -> NC_not_equal (nexp_subst sv subst n1, nexp_subst sv subst n2)
  | NC_set (kid, ints) as set_nc ->
     begin match subst with
     | A_aux (A_nexp (Nexp_aux (Nexp_var kid',_)), _) when Kid.compare kid sv = 0 ->
        NC_set (kid', ints)
     | A_aux (A_nexp n, _) when Kid.compare kid sv = 0 ->
        nexp_set_to_or l n ints
     | _ -> set_nc
     end
  | NC_or (nc1, nc2) -> NC_or (constraint_subst sv subst nc1, constraint_subst sv subst nc2)
  | NC_and (nc1, nc2) -> NC_and (constraint_subst sv subst nc1, constraint_subst sv subst nc2)
  | NC_app (id, args) -> NC_app (id, List.map (typ_arg_subst sv subst) args)
  | NC_var kid ->
     begin match subst with
     | A_aux (A_bool nc, _) when Kid.compare kid sv = 0 ->
        unaux_constraint nc
     | _ -> NC_var kid
     end
  | NC_false -> NC_false
  | NC_true -> NC_true

and typ_subst sv subst (Typ_aux (typ, l)) = Typ_aux (typ_subst_aux sv subst typ, l)
and typ_subst_aux sv subst = function
  | Typ_internal_unknown -> Typ_internal_unknown
  | Typ_id v -> Typ_id v
  | Typ_var kid ->
     begin match subst with
     | A_aux (A_typ typ, _) when Kid.compare kid sv = 0 ->
        unaux_typ typ
     | _ -> Typ_var kid
     end
  | Typ_fn (arg_typs, ret_typ, effs) -> Typ_fn (List.map (typ_subst sv subst) arg_typs, typ_subst sv subst ret_typ, effs)
  | Typ_bidir (typ1, typ2) -> Typ_bidir (typ_subst sv subst typ1, typ_subst sv subst typ2)
  | Typ_tup typs -> Typ_tup (List.map (typ_subst sv subst) typs)
  | Typ_app (f, args) -> Typ_app (f, List.map (typ_arg_subst sv subst) args)
  | Typ_exist (kopts, nc, typ) when KidSet.mem sv (KidSet.of_list (List.map kopt_kid kopts)) ->
     Typ_exist (kopts, nc, typ)
  | Typ_exist (kopts, nc, typ) ->
     Typ_exist (kopts, constraint_subst sv subst nc, typ_subst sv subst typ)

and typ_arg_subst sv subst (A_aux (arg, l)) = A_aux (typ_arg_subst_aux sv subst arg, l)
and typ_arg_subst_aux sv subst = function
  | A_nexp nexp -> A_nexp (nexp_subst sv subst nexp)
  | A_typ typ -> A_typ (typ_subst sv subst typ)
  | A_order ord -> A_order (order_subst sv subst ord)
  | A_bool nc -> A_bool (constraint_subst sv subst nc)

let subst_kid subst sv v x =
  x
  |> subst sv (mk_typ_arg (A_bool (nc_var v)))
  |> subst sv (mk_typ_arg (A_nexp (nvar v)))
  |> subst sv (mk_typ_arg (A_order (Ord_aux (Ord_var v, Parse_ast.Unknown))))
  |> subst sv (mk_typ_arg (A_typ (mk_typ (Typ_var v))))

let kopt_subst_kid sv subst (KOpt_aux (KOpt_kind (k, kid), l) as orig) =
  if Kid.compare kid sv = 0 then KOpt_aux (KOpt_kind (k, subst), l) else orig

let quant_item_subst_kid_aux sv subst = function
  | QI_id kopt ->
     QI_id (kopt_subst_kid sv subst kopt)
  | QI_constant kopts ->
     QI_constant (List.map (kopt_subst_kid sv subst) kopts)
  | QI_constraint nc ->
     QI_constraint (subst_kid constraint_subst sv subst nc)

let quant_item_subst_kid sv subst (QI_aux (quant, l)) = QI_aux (quant_item_subst_kid_aux sv subst quant, l)

let typquant_subst_kid_aux sv subst = function
  | TypQ_tq quants -> TypQ_tq (List.map (quant_item_subst_kid sv subst) quants)
  | TypQ_no_forall -> TypQ_no_forall

let typquant_subst_kid sv subst (TypQ_aux (typq, l)) = TypQ_aux (typquant_subst_kid_aux sv subst typq, l)


let subst_kids_nexp substs nexp =
  let rec s_snexp substs (Nexp_aux (ne,l) as nexp) =
    let re ne = Nexp_aux (ne,l) in
    let s_snexp = s_snexp substs in
    match ne with
    | Nexp_var (Kid_aux (_,l) as kid) ->
       (try KBindings.find kid substs
       with Not_found -> nexp)
    | Nexp_id _
    | Nexp_constant _ -> nexp
    | Nexp_times (n1,n2) -> re (Nexp_times (s_snexp n1, s_snexp n2))
    | Nexp_sum (n1,n2)   -> re (Nexp_sum   (s_snexp n1, s_snexp n2))
    | Nexp_minus (n1,n2) -> re (Nexp_minus (s_snexp n1, s_snexp n2))
    | Nexp_exp ne -> re (Nexp_exp (s_snexp ne))
    | Nexp_neg ne -> re (Nexp_neg (s_snexp ne))
    | Nexp_app (id,args) -> re (Nexp_app (id,List.map s_snexp args))
  in s_snexp substs nexp

let subst_kids_nc, subst_kids_typ, subst_kids_typ_arg =
  let rec subst_kids_nc substs (NC_aux (nc,l) as n_constraint) =
    let snexp nexp = subst_kids_nexp substs nexp in
    let snc nc = subst_kids_nc substs nc in
    let re nc = NC_aux (nc,l) in
    match nc with
    | NC_equal (n1,n2) -> re (NC_equal (snexp n1, snexp n2))
    | NC_bounded_ge (n1,n2) -> re (NC_bounded_ge (snexp n1, snexp n2))
    | NC_bounded_le (n1,n2) -> re (NC_bounded_le (snexp n1, snexp n2))
    | NC_not_equal (n1,n2) -> re (NC_not_equal (snexp n1, snexp n2))
    | NC_set (kid,is) ->
       begin
         match KBindings.find kid substs with
         | Nexp_aux (Nexp_constant i,_) ->
            if List.exists (fun j -> Big_int.equal i j) is then re NC_true else re NC_false
         | nexp -> 
            raise (Reporting.err_general l
                     ("Unable to substitute " ^ string_of_nexp nexp ^
                        " into set constraint " ^ string_of_n_constraint n_constraint))
         | exception Not_found -> n_constraint
       end
    | NC_or (nc1,nc2) -> re (NC_or (snc nc1, snc nc2))
    | NC_and (nc1,nc2) -> re (NC_and (snc nc1, snc nc2))
    | NC_true
      | NC_false
      -> n_constraint
    | NC_var kid -> re (NC_var kid)
    | NC_app (f, args) ->
       re (NC_app (f, List.map (s_starg substs) args))
  and  s_styp substs ((Typ_aux (t,l)) as ty) =
    let re t = Typ_aux (t,l) in
    match t with
    | Typ_id _
    | Typ_var _
      -> ty
    | Typ_fn (t1,t2,e) -> re (Typ_fn (List.map (s_styp substs) t1, s_styp substs t2,e))
    | Typ_bidir (t1, t2) -> re (Typ_bidir (s_styp substs t1, s_styp substs t2))
    | Typ_tup ts -> re (Typ_tup (List.map (s_styp substs) ts))
    | Typ_app (id,tas) -> re (Typ_app (id,List.map (s_starg substs) tas))
    | Typ_exist (kopts,nc,t) ->
       let substs = List.fold_left (fun sub kopt -> KBindings.remove (kopt_kid kopt) sub) substs kopts in
       re (Typ_exist (kopts,subst_kids_nc substs nc,s_styp substs t))
    | Typ_internal_unknown -> Reporting.unreachable l __POS__ "escaped Typ_internal_unknown"
  and s_starg substs (A_aux (ta,l) as targ) =
    match ta with
    | A_nexp ne -> A_aux (A_nexp (subst_kids_nexp substs ne),l)
    | A_typ t -> A_aux (A_typ (s_styp substs t),l)
    | A_order _ -> targ
    | A_bool nc -> A_aux (A_bool (subst_kids_nc substs nc), l)
  in subst_kids_nc, s_styp, s_starg

let before p1 p2 =
  let open Lexing in
  p1.pos_fname = p2.pos_fname && p1.pos_cnum <= p2.pos_cnum

let subloc sl l =
  match sl, Reporting.simp_loc l with
  | _, None -> false
  | None, _ -> false
  | Some (p1a, p1b), Some (p2a, p2b) ->
     before p2a p1a && before p1b p2b

let rec option_mapm f = function
  | [] -> None
  | x :: xs ->
     begin match f x with
     | Some y -> Some y
     | None -> option_mapm f xs
     end

let option_chain opt1 opt2 =
  begin match opt1 with
  | None -> opt2
  | _ -> opt1
  end

let rec find_annot_exp sl (E_aux (aux, (l, annot)) as exp) =
  if not (subloc sl l) then None else
    let result = match aux with
      | E_block exps | E_tuple exps ->
         option_mapm (find_annot_exp sl) exps
      | E_app (id, exps) ->
         option_mapm (find_annot_exp sl) exps
      | E_let (LB_aux (LB_val (pat, exp), _), body) ->
         option_chain (find_annot_pat sl pat) (option_mapm (find_annot_exp sl) [exp; body])
      | E_assign (lexp, exp) ->
         option_chain (find_annot_lexp sl lexp) (find_annot_exp sl exp)
      | E_var (lexp, exp1, exp2) ->
         option_chain (find_annot_lexp sl lexp) (option_mapm (find_annot_exp sl) [exp1; exp2])
      | E_if (cond_exp, then_exp, else_exp) ->
         option_mapm (find_annot_exp sl) [cond_exp; then_exp; else_exp]
      | E_case (exp, cases) | E_try (exp, cases) ->
         option_chain (find_annot_exp sl exp) (option_mapm (find_annot_pexp sl) cases)
      | E_return exp | E_cast (_, exp) ->
         find_annot_exp sl exp
      | _ -> None
    in
    match result with
    | None -> Some (l, annot)
    | _ -> result

and find_annot_lexp sl (LEXP_aux (aux, (l, annot))) =
  if not (subloc sl l) then None else
    let result = match aux with
      | LEXP_vector_range (lexp, exp1, exp2) ->
         option_chain (find_annot_lexp sl lexp) (option_mapm (find_annot_exp sl) [exp1; exp2])
      | LEXP_deref exp ->
         find_annot_exp sl exp
      | LEXP_tup lexps ->
         option_mapm (find_annot_lexp sl) lexps
      | LEXP_memory (id, exps) ->
         option_mapm (find_annot_exp sl) exps
      | _ -> None
    in
    match result with
    | None -> Some (l, annot)
    | _ -> result

and find_annot_pat sl (P_aux (aux, (l, annot))) =
  if not (subloc sl l) then None else
    let result = match aux with
      | P_vector_concat pats ->
         option_mapm (find_annot_pat sl) pats
      | _ -> None
    in
    match result with
    | None -> Some (l, annot)
    | _ -> result

and find_annot_pexp sl (Pat_aux (aux, (l, annot))) =
  if not (subloc sl l) then None else
    match aux with
    | Pat_exp (pat, exp) ->
       option_chain (find_annot_pat sl pat) (find_annot_exp sl exp)
    | Pat_when (pat, guard, exp) ->
       option_chain (find_annot_pat sl pat) (option_mapm (find_annot_exp sl) [guard; exp])

let find_annot_funcl sl (FCL_aux (FCL_Funcl (id, pexp), (l, annot))) =
  if not (subloc sl l) then None else
    match find_annot_pexp sl pexp with
    | None -> Some (l, annot)
    | result -> result

let find_annot_fundef sl (FD_aux (FD_function (_, _, _, funcls), (l, annot))) =
  if not (subloc sl l) then None else
    match option_mapm (find_annot_funcl sl) funcls with
    | None -> Some (l, annot)
    | result -> result

let find_annot_scattered sl (SD_aux (aux, (l, annot))) =
  if not (subloc sl l) then None else
    let result = match aux with
      | SD_funcl fcl -> find_annot_funcl sl fcl
      | _ -> None
    in
    match result with
    | None -> Some (l, annot)
    | _ -> result

let rec find_annot_defs sl = function
  | DEF_fundef fdef :: defs ->
     begin match find_annot_fundef sl fdef with
     | None -> find_annot_defs sl defs
     | result -> result
     end
  | DEF_scattered sdef :: defs ->
     begin match find_annot_scattered sl sdef with
     | None -> find_annot_defs sl defs
     | result -> result
     end
  | _ :: defs ->
     find_annot_defs sl defs
  | [] -> None

let rec find_annot_ast sl (Defs defs) = find_annot_defs sl defs

let string_of_lx lx =
  let open Lexing in
  Printf.sprintf "%s,%d,%d,%d" lx.pos_fname lx.pos_lnum lx.pos_bol lx.pos_cnum

let rec simple_string_of_loc = function
  | Parse_ast.Unknown -> "Unknown"
  | Parse_ast.Unique (n, l) -> "Unique(" ^ string_of_int n ^ ", " ^ simple_string_of_loc l ^ ")"
  | Parse_ast.Generated l -> "Generated(" ^ simple_string_of_loc l ^ ")"
  | Parse_ast.Range (lx1,lx2) -> "Range(" ^ string_of_lx lx1 ^ "->" ^ string_of_lx lx2 ^ ")"
  | Parse_ast.Documented (_,l) -> "Documented(_," ^ simple_string_of_loc l ^ ")"