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(********************************************************************)
(*                                                                  *)
(*  The Why3 Verification Platform   /   The Why3 Development Team  *)
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(*  Copyright 2010-2015   --   INRIA - CNRS - Paris-Sud University  *)
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(*                                                                  *)
(*  This software is distributed under the terms of the GNU Lesser  *)
(*  General Public License version 2.1, with the special exception  *)
(*  on linking described in file LICENSE.                           *)
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(*                                                                  *)
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(********************************************************************)

open Stdlib
open Ident
open Ty
open Term
open Ity
open Expr

(** Program types *)

type dity =
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  | Dutv of tvsymbol          (* undestructible "user" type variable *)
  | Dvar of dvar ref          (* destructible "fresh" type variable *)
  | Durg of ity * dity        (* undestructible "user" region, for global refs *)
  | Dreg of dvar ref * dity   (* destructible "fresh" region *)
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  | Dapp of itysymbol * dity list * dity list
  | Dpur of itysymbol * dity list

and dvar =
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  | Dtvs of tvsymbol          (* unassigned fresh type variable *)
  | Dval of dity              (* destructive binding *)

(* In Dapp, the second dity list only contains Dreg's and Durg's.
   In Dreg and Durg, the dity field is a Dapp of the region's type.
   In Dreg, the dvar field leads to another Dreg or Durg.
   In Durg, the ity field is an Ityreg. *)
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type dvty = dity list * dity (* A -> B -> C == ([A;B],C) *)

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let dity_of_dvty (argl,res) =
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  List.fold_right (fun a d -> Dapp (its_func, [a;d], [])) argl res
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let dvar_fresh n = ref (Dtvs (create_tvsymbol (id_fresh n)))

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let dreg_fresh dity = Dreg (dvar_fresh "rho", dity)
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let dity_of_ity ity =
  let hr = Hreg.create 3 in
  let rec dity ity = match ity.ity_node with
    | Ityapp (s,tl,rl) -> Dapp (s, List.map dity tl, List.map dreg rl)
    | Itypur (s,tl)    -> Dpur (s, List.map dity tl)
    | Ityvar v -> Dutv v
    | Ityreg r -> dreg r
  and dreg reg =
    try Hreg.find hr reg with Not_found ->
    let {reg_its = s; reg_args = tl; reg_regs = rl} = reg in
    let d = Dapp (s, List.map dity tl, List.map dreg rl) in
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    let r = dreg_fresh d in Hreg.add hr reg r; r in
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  dity ity

let reg_of_ity = function
  | {ity_node = Ityreg reg} -> reg
  | _ -> assert false

let rec ity_of_dity = function
  | Dvar ({contents = Dval d})
  | Dreg ({contents = Dval d}, _) ->
      ity_of_dity d
  | Dvar r ->
      let v = create_tvsymbol (id_fresh "xi") in
      r := Dval (Dutv v); ity_var v
  | Dreg (r, d) ->
      let ity = ity_of_dity d in
      r := Dval (Durg (ity, d)); ity
  | Dutv v -> ity_var v
  | Durg (ity,_) -> ity
  | Dapp (s,tl,rl) ->
      let reg_of_dity r = reg_of_ity (ity_of_dity r) in
      ity_app s (List.map ity_of_dity tl) (List.map reg_of_dity rl)
  | Dpur (s,tl) ->
      ity_pur s (List.map ity_of_dity tl)

(** Destructive type unification *)

let rec occur_check v = function
  | Dvar {contents = Dval d} | Dreg (_,d) | Durg (_,d) -> occur_check v d
  | Dvar {contents = Dtvs u} | Dutv u -> if tv_equal u v then raise Exit
  | Dapp (_,dl,_) | Dpur (_,dl) -> List.iter (occur_check v) dl

let rec dity_unify d1 d2 = match d1,d2 with
  | Dvar {contents = Dval d1}, d2
  | d1, Dvar {contents = Dval d2}
  | Durg (_,d1), Durg (_,d2) | Durg (_,d1), Dreg (_,d2)
  | Dreg (_,d1), Durg (_,d2) | Dreg (_,d1), Dreg (_,d2) ->
      dity_unify d1 d2
  | Dvar {contents = Dtvs u},
    Dvar {contents = Dtvs v} when tv_equal u v ->
      ()
  | Dvar ({contents = Dtvs v} as r), d
  | d, Dvar ({contents = Dtvs v} as r) ->
      occur_check v d;
      r := Dval d
  | Dutv u, Dutv v when tv_equal u v ->
      ()
  |(Dapp (s1,dl1,_), Dapp (s2,dl2,_)
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  | Dpur (s1,dl1),   Dpur (s2,dl2)) when its_equal s1 s2 ->
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      List.iter2 dity_unify dl1 dl2
  | _ -> raise Exit

(** Reunify regions *)

let dtvs_queue : dvar ref Queue.t = Queue.create ()

let unify_queue : (dity * dity) Queue.t = Queue.create ()

let dity_fresh () =
  let r = dvar_fresh "mu" in
  Queue.add r dtvs_queue;
  Dvar r

let rec dity_refresh ht = function
  | Dreg ({contents = Dtvs v},d) ->
      begin try Htv.find ht v with Not_found ->
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      let r = dreg_fresh (dity_refresh ht d) in
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      Htv.add ht v r; r end
  | Dreg _ -> assert false
  | Dpur (s,dl) ->    Dpur (s, List.map (dity_refresh ht) dl)
  | Dapp (s,dl,rl) -> Dapp (s, List.map (dity_refresh ht) dl,
                               List.map (dity_refresh ht) rl)
  | Dvar {contents = Dval d} -> dity_refresh (Htv.create 3) d
  |(Dvar {contents = Dtvs _} | Dutv _ | Durg _) as d -> d

let dity_refresh d = dity_refresh (Htv.create 3) d

let dity_unify_weak = dity_unify

let dity_unify d1 d2 = dity_unify d1 d2; Queue.add (d1,d2) unify_queue

let rec reunify d1 d2 = match d1,d2 with
  | Dvar {contents = Dval d1}, d2
  | d1, Dvar {contents = Dval d2}
  | Dreg ({contents = Dval d1},_), d2
  | d1, Dreg ({contents = Dval d2},_) ->
      reunify d1 d2
  | Dvar _, Dvar _ | Dutv _, Dutv _ | Durg _, Durg _ ->
      ()
  | Dreg ({contents = Dtvs u},_),
    Dreg ({contents = Dtvs v},_) when tv_equal u v ->
      ()
  | Dreg (r, d1), (Dreg (_, d2) as d)
  | Dreg (r, d1), (Durg (_, d2) as d)
  | (Durg (_, d1) as d), Dreg (r, d2) ->
      reunify d1 d2;
      r := Dval d
  | Dapp (_,dl1,rl1), Dapp (_,dl2,rl2) ->
      List.iter2 reunify dl1 dl2;
      List.iter2 reunify rl1 rl2
  | Dpur (_,dl1), Dpur (_,dl2) ->
      List.iter2 reunify dl1 dl2
  | _ -> assert false

let reunify_regions () =
  Queue.iter (fun r -> match !r with
    | Dval d -> r := Dval (dity_refresh d)
    | Dtvs _ -> ()) dtvs_queue;
  Queue.clear dtvs_queue;
  Queue.iter (fun (d1,d2) -> reunify d1 d2) unify_queue;
  Queue.clear unify_queue

(** Built-in types *)

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let dity_int  = Dapp (its_int,  [], [])
let dity_real = Dapp (its_real, [], [])
let dity_bool = Dapp (its_bool, [], [])
let dity_unit = Dapp (its_unit, [], [])
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let dvty_int  = [], dity_int
let dvty_real = [], dity_real
let dvty_bool = [], dity_bool
let dvty_unit = [], dity_unit

(** Pretty-printing *)

let rprinter =
  let sanitizer = Ident.sanitizer Ident.char_to_lalpha Ident.char_to_alnumus in
  Ident.create_ident_printer [] ~sanitizer

let print_args pr fmt tl = if tl <> [] then
  Format.fprintf fmt "@ %a" (Pp.print_list Pp.space pr) tl

let print_regs pr fmt rl = if rl <> [] then
  Format.fprintf fmt "@ <%a>" (Pp.print_list Pp.comma pr) rl

let protect_on x s = if x then "(" ^^ s ^^ ")" else s

let rec print_dity pri fmt = function
  | Dvar {contents = Dval d}
  | Dreg ({contents = Dval d},_) ->
      print_dity pri fmt d
  | Dvar {contents = Dtvs v}
  | Dutv v ->
      Pretty.print_tv fmt v
  | Dreg ({contents = Dtvs v},d) ->
      Format.fprintf fmt (protect_on (pri > 1) "%a@ @@%s")
        (print_dity 0) d (Ident.id_unique rprinter v.tv_name)
  | Durg (ity,d) ->
      Format.fprintf fmt (protect_on (pri > 1) "%a@ @@%s")
        (print_dity 0) d (Ident.id_unique rprinter (reg_of_ity ity).reg_name)
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  | Dapp (s,[t1;t2],[]) when its_equal s its_func ->
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      Format.fprintf fmt (protect_on (pri > 0) "%a@ ->@ %a")
        (print_dity 1) t1 (print_dity 0) t2
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  | Dapp (s,tl,[]) when is_ts_tuple s.its_ts ->
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      Format.fprintf fmt "(%a)" (Pp.print_list Pp.comma (print_dity 0)) tl
  | Dapp (s,tl,rl) ->
      Format.fprintf fmt (protect_on (pri > 1) "%a%a%a")
        Pretty.print_ts s.its_ts (print_args (print_dity 2)) tl
          (print_regs (print_dity 0)) rl
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  | Dpur (s,tl) ->
      Format.fprintf fmt (protect_on (pri > 1 && tl <> []) "{%a}%a")
        Pretty.print_ts s.its_ts (print_args (print_dity 2)) tl
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let print_dity fmt d = print_dity 0 fmt d

(* Specialization of symbols *)

let specialize_scheme tvs (argl,res) =
  let hv = Htv.create 3 and hr = Htv.create 3 in
  let rec spec_dity = function
    | Durg _ as d -> d
    | Dvar {contents = Dval d} | Dreg ({contents = Dval d},_) -> spec_dity d
    | Dvar {contents = Dtvs v} | Dutv v as d -> get_tv v d
    | Dreg ({contents = Dtvs v},d) -> get_reg v d
    | Dapp (s,dl,rl) -> Dapp (s, List.map spec_dity dl, List.map spec_dity rl)
    | Dpur (s,dl)    -> Dpur (s, List.map spec_dity dl)
  and get_tv v d = try Htv.find hv v with Not_found ->
    let nd = dity_fresh () in
    (* can't return d, might differ in regions *)
    if not (Stv.mem v tvs) then dity_unify_weak nd d;
    Htv.add hv v nd; nd
  and get_reg v d = try Htv.find hr v with Not_found ->
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    let r = dreg_fresh (spec_dity d) in
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    Htv.add hr v r; r in
  List.map spec_dity argl, spec_dity res

let spec_ity hv hr frz ity =
  let rec dity ity = match ity.ity_node with
    | Ityreg r -> dreg r
    | Ityvar v -> if Mtv.mem v frz.isb_tv then Dutv v else get_tv v
    | Ityapp (s,tl,rl) -> Dapp (s, List.map dity tl, List.map dreg rl)
    | Itypur (s,tl)    -> Dpur (s, List.map dity tl)
  and get_tv v = try Htv.find hv v with Not_found ->
    let nd = dity_fresh () in Htv.add hv v nd; nd
  and dreg reg = try Hreg.find hr reg with Not_found ->
    let {reg_its = s; reg_args = tl; reg_regs = rl} = reg in
    let d = Dapp (s, List.map dity tl, List.map dreg rl) in
    let r = if Mreg.mem reg frz.isb_reg then
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      Durg (ity_reg reg, d) else dreg_fresh d in
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    Hreg.add hr reg r; r in
  dity ity

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let specialize_pv {pv_ity = ity} =
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  spec_ity (Htv.create 3) (Hreg.create 3) (ity_freeze isb_empty ity) ity

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let specialize_xs {xs_ity = ity} =
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  spec_ity (Htv.create 3) (Hreg.create 3) (ity_freeze isb_empty ity) ity

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let specialize_rs {rs_cty = cty} =
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  let hv = Htv.create 3 and hr = Hreg.create 3 in
  let spec ity = spec_ity hv hr cty.cty_freeze ity in
  List.map (fun v -> spec v.pv_ity) cty.cty_args, spec cty.cty_result

(** Patterns *)

type dpattern = {
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  dp_pat  : pre_pattern;
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  dp_dity : dity;
  dp_vars : dity Mstr.t;
  dp_loc  : Loc.position option;
}

type dpattern_node =
  | DPwild
  | DPvar  of preid
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  | DPapp  of rsymbol * dpattern list
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  | DPor   of dpattern * dpattern
  | DPas   of dpattern * preid
  | DPcast of dpattern * ity

(** Specifications *)

type ghost = bool

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type dbinder = preid option * ghost * dity
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type register_old = pvsymbol -> string -> pvsymbol

type 'a later = pvsymbol Mstr.t -> register_old -> 'a
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  (* specification terms are parsed and typechecked after the program
     expressions, when the types of locally bound program variables are
     already established. *)

type dspec_final = {
  ds_pre     : term list;
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  ds_post    : (pvsymbol * term) list;
  ds_xpost   : (pvsymbol * term) list Mexn.t;
  ds_reads   : pvsymbol list;
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  ds_writes  : term list;
  ds_diverge : bool;
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  ds_checkrw : bool;
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}

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type dspec = ity -> dspec_final
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  (* Computation specification is also parametrized by the result type.
     All vsymbols in the postcondition clauses in the [ds_post] field
     must have this type. All vsymbols in the exceptional postcondition
     clauses must have the type of the corresponding exception. *)

(** Expressions *)

type dinvariant = term list

type dexpr = {
  de_node : dexpr_node;
  de_dvty : dvty;
  de_loc  : Loc.position option;
}

and dexpr_node =
  | DEvar of string * dvty
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  | DEpv of pvsymbol
  | DErs of rsymbol
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  | DEconst of Number.constant
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  | DEapp of dexpr * dexpr
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  | DEfun of dbinder list * dspec later * dexpr
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  | DEany of dbinder list * dspec later * dity
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  | DElet of dlet_defn * dexpr
  | DErec of drec_defn * dexpr
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  | DEnot of dexpr
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  | DEand of dexpr * dexpr
  | DEor of dexpr * dexpr
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  | DEif of dexpr * dexpr * dexpr
  | DEcase of dexpr * (dpattern * dexpr) list
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  | DEassign of (dexpr * rsymbol * dexpr) list
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  | DEwhile of dexpr * dinvariant later * variant list later * dexpr
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  | DEfor of preid * dexpr * for_direction * dexpr * dinvariant later * dexpr
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  | DEtry of dexpr * (xsymbol * dpattern * dexpr) list
  | DEraise of xsymbol * dexpr
  | DEghost of dexpr
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  | DEassert of assertion_kind * term later
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  | DEpure of term later
  | DEabsurd
  | DEtrue
  | DEfalse
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  | DEmark of preid * dexpr
  | DEcast of dexpr * ity
  | DEuloc of dexpr * Loc.position
  | DElabel of dexpr * Slab.t

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and dlet_defn = preid * ghost * rs_kind * dexpr
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and drec_defn = { fds : dfun_defn list }

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and dfun_defn = preid * ghost * rs_kind *
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  dbinder list * dspec later * variant list later * dexpr
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(** Environment *)

type denv = {
  frozen : dity list;
  locals : (Stv.t option * dvty) Mstr.t;
}

let denv_empty = { frozen = []; locals = Mstr.empty }

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let is_frozen frozen v =
  try List.iter (occur_check v) frozen; false with Exit -> true
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let freeze_dvty frozen (argl,res) =
  let rec add l = function
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    | Dreg (_,d) | Durg (_,d)
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    | Dvar { contents = Dval d } -> add l d
    | Dvar { contents = Dtvs _ } as d -> d :: l
    | Dutv _ as d -> d :: l
    | Dapp (_,tl,_) | Dpur (_,tl) -> List.fold_left add l tl in
  List.fold_left add (add frozen res) argl

let free_vars frozen (argl,res) =
  let rec add s = function
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    | Dreg (_,d) | Durg (_,d)
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    | Dvar { contents = Dval d } -> add s d
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    | Dvar { contents = Dtvs v }
    | Dutv v -> if is_frozen frozen v then s else Stv.add v s
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    | Dapp (_,tl,_) | Dpur (_,tl) -> List.fold_left add s tl in
  List.fold_left add (add Stv.empty res) argl

let denv_add_mono { frozen = frozen; locals = locals } id dvty =
  let locals = Mstr.add id.pre_name (None, dvty) locals in
  { frozen = freeze_dvty frozen dvty; locals = locals }

let denv_add_poly { frozen = frozen; locals = locals } id dvty =
  let ftvs = free_vars frozen dvty in
  let locals = Mstr.add id.pre_name (Some ftvs, dvty) locals in
  { frozen = frozen; locals = locals }

let denv_add_rec_mono { frozen = frozen; locals = locals } id dvty =
  let locals = Mstr.add id.pre_name (Some Stv.empty, dvty) locals in
  { frozen = freeze_dvty frozen dvty; locals = locals }

let denv_add_rec_poly { frozen = frozen; locals = locals } frozen0 id dvty =
  let ftvs = free_vars frozen0 dvty in
  let locals = Mstr.add id.pre_name (Some ftvs, dvty) locals in
  { frozen = frozen; locals = locals }

let denv_add_rec denv frozen0 id ((argl,res) as dvty) =
  let rec is_explicit = function
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    | Dreg (_,d) | Durg (_,d)
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    | Dvar { contents = Dval d } -> is_explicit d
    | Dvar { contents = Dtvs _ } -> false
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    | Dutv _ -> true
    | Dapp (_,tl,_) | Dpur (_,tl) -> List.for_all is_explicit tl in
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  if List.for_all is_explicit argl && is_explicit res
  then denv_add_rec_poly denv frozen0 id dvty
  else denv_add_rec_mono denv id dvty

let denv_add_var denv id dity = denv_add_mono denv id ([], dity)

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let denv_add_let denv (id,_,_,({de_dvty = dvty} as de)) =
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  if fst dvty = [] then denv_add_mono denv id dvty else
  let rec is_value de = match de.de_node with
    | DEghost de | DEuloc (de,_) | DElabel (de,_) -> is_value de
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    | DEvar _ | DErs _ | DEfun _ | DEany _ -> true
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    | _ -> false in
  if is_value de
  then denv_add_poly denv id dvty
  else denv_add_mono denv id dvty

let denv_add_args { frozen = frozen; locals = locals } bl =
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  let l = List.fold_left (fun l (_,_,t) -> t::l) frozen bl in
  let add s (id,_,t) = match id with
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    | Some {pre_name = n} ->
        Mstr.add_new (Dterm.DuplicateVar n) n (None, ([],t)) s
    | None -> s in
  let s = List.fold_left add Mstr.empty bl in
  { frozen = l; locals = Mstr.set_union s locals }

let denv_add_pat { frozen = frozen; locals = locals } dp =
  let l = Mstr.fold (fun _ t l -> t::l) dp.dp_vars frozen in
  let s = Mstr.map (fun t -> None, ([], t)) dp.dp_vars in
  { frozen = l; locals = Mstr.set_union s locals }

let mk_node n = function
  | Some tvs, dvty -> DEvar (n, specialize_scheme tvs dvty)
  | None,     dvty -> DEvar (n, dvty)

let denv_get denv n =
  mk_node n (Mstr.find_exn (Dterm.UnboundVar n) n denv.locals)

let denv_get_opt denv n =
  Opt.map (mk_node n) (Mstr.find_opt n denv.locals)

(** Unification tools *)

let dity_unify_app ls fn (l1: 'a list) (l2: dity list) =
  try List.iter2 fn l1 l2 with Invalid_argument _ ->
    raise (BadArity (ls, List.length l1))

let dpat_expected_type {dp_dity = dp_dity; dp_loc = loc} dity =
  try dity_unify dp_dity dity with Exit -> Loc.errorm ?loc
    "This pattern has type %a,@ but is expected to have type %a"
    print_dity dp_dity print_dity dity

let dpat_expected_type_weak {dp_dity = dp_dity; dp_loc = loc} dity =
  try dity_unify_weak dp_dity dity with Exit -> Loc.errorm ?loc
    "This pattern has type %a,@ but is expected to have type %a"
    print_dity dp_dity print_dity dity

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let dexpr_expected_type {de_dvty = dvty; de_loc = loc} dity =
  let res = dity_of_dvty dvty in
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  try dity_unify res dity with Exit -> Loc.errorm ?loc
    "This expression has type %a,@ but is expected to have type %a"
    print_dity res print_dity dity

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let dexpr_expected_type_weak {de_dvty = dvty; de_loc = loc} dity =
  let res = dity_of_dvty dvty in
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  try dity_unify_weak res dity with Exit -> Loc.errorm ?loc
    "This expression has type %a,@ but is expected to have type %a"
    print_dity res print_dity dity

(** Generation of letrec blocks *)

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type pre_fun_defn = preid * ghost * rs_kind * dbinder list *
  dity * (denv -> dspec later * variant list later * dexpr)
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exception DupId of preid

let drec_defn denv0 prel =
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  if prel = [] then invalid_arg "Dexpr.drec_defn: empty function list";
  let add s (id,_,_,_,_,_) = Sstr.add_new (DupId id) id.pre_name s in
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  let _ = try List.fold_left add Sstr.empty prel with DupId id ->
    Loc.errorm ?loc:id.pre_loc "duplicate function name %s" id.pre_name in
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  let add denv (id,_,_,bl,res,_) =
    if bl = [] then invalid_arg "Dexpr.drec_defn: empty argument list";
    let argl = List.map (fun (_,_,t) -> t) bl in
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    denv_add_rec denv denv0.frozen id (argl,res) in
  let denv1 = List.fold_left add denv0 prel in
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  let parse (id,gh,pk,bl,res,pre) =
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    let dsp, dvl, de = pre (denv_add_args denv1 bl) in
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    dexpr_expected_type_weak de res;
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    (id,gh,pk,bl,dsp,dvl,de) in
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  let fdl = List.map parse prel in
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  let add denv (id,_,_,bl,_,_,{de_dvty = dvty}) =
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    (* just in case we linked some polymorphic type var to the outer context *)
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    let check tv = if is_frozen denv0.frozen tv then Loc.errorm ?loc:id.pre_loc
      "This function is expected to be polymorphic in type variable %a"
      Pretty.print_tv tv in
    begin match Mstr.find_opt id.pre_name denv1.locals with
    | Some (Some tvs, _) -> Stv.iter check tvs
    | Some (None, _) | None -> assert false
    end;
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    let argl = List.map (fun (_,_,t) -> t) bl in
    denv_add_poly denv id (argl, dity_of_dvty dvty) in
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  List.fold_left add denv0 fdl, { fds = fdl }

(** Constructors *)

let dpattern ?loc node =
  let mk_dpat pre dity vars =
    { dp_pat = pre; dp_dity = dity; dp_vars = vars; dp_loc = loc } in
  let dpat = function
    | DPwild ->
        mk_dpat PPwild (dity_fresh ()) Mstr.empty
    | DPvar id ->
        let dity = dity_fresh () in
        mk_dpat (PPvar id) dity (Mstr.singleton id.pre_name dity)
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    | DPapp ({rs_logic = RLls ls} as rs, dpl) when ls.ls_constr > 0 ->
        let argl, res = specialize_rs rs in
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        dity_unify_app ls dpat_expected_type dpl argl;
        let join n _ _ = raise (Dterm.DuplicateVar n) in
        let add acc dp = Mstr.union join acc dp.dp_vars in
        let vars = List.fold_left add Mstr.empty dpl in
        let ppl = List.map (fun dp -> dp.dp_pat) dpl in
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        mk_dpat (PPapp (rs, ppl)) res vars
    | DPapp (rs,_) ->
        raise (ConstructorExpected rs);
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    | DPor (dp1,dp2) ->
        dpat_expected_type dp2 dp1.dp_dity;
        let join n dity1 dity2 = try dity_unify dity1 dity2; Some dity1
          with Exit -> Loc.errorm ?loc
            "Variable %s has type %a,@ but is expected to have type %a"
            n print_dity dity1 print_dity dity2 in
        let vars = Mstr.union join dp1.dp_vars dp2.dp_vars in
        mk_dpat (PPor (dp1.dp_pat, dp2.dp_pat)) dp1.dp_dity vars
    | DPas (dp, ({pre_name = n} as id)) ->
        let { dp_pat = pat; dp_dity = dity; dp_vars = vars } = dp in
        let vars = Mstr.add_new (Dterm.DuplicateVar n) n dity vars in
        mk_dpat (PPas (pat, id)) dity vars
    | DPcast (dp, ity) ->
        dpat_expected_type_weak dp (dity_of_ity ity);
        dp
  in
  Loc.try1 ?loc dpat node

let dexpr ?loc node =
  let get_dvty = function
    | DEvar (_,dvty) ->
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        dvty
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    | DEpv pv ->
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        [], specialize_pv pv
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    | DErs rs ->
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        specialize_rs rs
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    | DEconst (Number.ConstInt _) ->
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        dvty_int
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    | DEconst (Number.ConstReal _) ->
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        dvty_real
    | DEapp ({de_dvty = (arg::argl, res)}, de2) ->
        dexpr_expected_type de2 arg;
        argl, res
    | DEapp ({de_dvty = ([],res)} as de1, de2) ->
        let f,a,r = match specialize_rs rs_func_app with
          | [f;a],r -> f,a,r | _ -> assert false in
        begin try dity_unify res f with Exit ->
          let rec down n de = match de.de_node with
            | DEapp (de,_) -> down (succ n) de
            | _ when n = 0 -> Loc.errorm ?loc:de.de_loc
                "This expression has type %a,@ it cannot be applied"
                print_dity (dity_of_dvty de.de_dvty)
            | _ -> Loc.errorm ?loc:de.de_loc
                "This expression has type %a,@ but is applied to %d arguments"
                print_dity (dity_of_dvty de.de_dvty) (succ n) in
          down 0 de1
        end;
        dexpr_expected_type de2 a;
        [], r
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    | DEfun (bl,_,de) ->
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        List.map (fun (_,_,t) -> t) bl, dity_of_dvty de.de_dvty
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    | DEany (bl,_,res) ->
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        List.map (fun (_,_,t) -> t) bl, res
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    | DElet (_,de)
    | DErec (_,de) ->
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        de.de_dvty
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    | DEnot de ->
        dexpr_expected_type de dity_bool;
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        dvty_bool
    | DEand (de1,de2)
    | DEor (de1,de2) ->
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        dexpr_expected_type de1 dity_bool;
        dexpr_expected_type de2 dity_bool;
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        dvty_bool
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    | DEif (de1,de2,de3) ->
        let res = dity_fresh () in
        dexpr_expected_type de1 dity_bool;
        dexpr_expected_type de2 res;
        dexpr_expected_type de3 res;
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        [], res
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    | DEcase (_,[]) ->
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        invalid_arg "Dexpr.dexpr: empty branch list in DEcase"
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    | DEcase (de,bl) ->
        let ety = dity_fresh () in
        let res = dity_fresh () in
        dexpr_expected_type de ety;
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        List.iter (fun (dp,de) ->
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          dpat_expected_type dp ety;
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          dexpr_expected_type de res) bl;
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        [], res
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    | DEassign al ->
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        List.iter (fun (de1,rs,de2) ->
          let argl, res = specialize_rs rs in
          let ls = match rs.rs_logic with RLls ls -> ls
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            | _ -> invalid_arg "Dexpr.dexpr: not a field" in
          dity_unify_app ls dexpr_expected_type [de1] argl;
          dexpr_expected_type_weak de2 res) al;
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        dvty_unit
    | DEwhile (de1,_,_,de2) ->
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        dexpr_expected_type de1 dity_bool;
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        dexpr_expected_type de2 dity_unit;
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        dvty_unit
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    | DEfor (_,de_from,_,de_to,_,de) ->
        dexpr_expected_type de_from dity_int;
        dexpr_expected_type de_to dity_int;
        dexpr_expected_type de dity_unit;
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        dvty_unit
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    | DEtry (_,[]) ->
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        invalid_arg "Dexpr.dexpr: empty branch list in DEtry"
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    | DEtry (de,bl) ->
        let res = dity_fresh () in
        dexpr_expected_type de res;
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        List.iter (fun (xs,dp,de) ->
          dpat_expected_type dp (specialize_xs xs);
          dexpr_expected_type de res) bl;
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        [], res
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    | DEraise (xs,de) ->
        dexpr_expected_type de (specialize_xs xs);
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        [], dity_fresh ()
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    | DEghost de ->
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        de.de_dvty
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    | DEassert _ ->
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        dvty_unit
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    | DEpure _
    | DEabsurd ->
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        [], dity_fresh ()
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    | DEtrue
    | DEfalse ->
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        dvty_bool
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    | DEcast (de,ity) ->
        dexpr_expected_type_weak de (dity_of_ity ity);
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        de.de_dvty
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    | DEmark (_,de)
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    | DEuloc (de,_)
    | DElabel (de,_) ->
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        de.de_dvty in
  let dvty = Loc.try1 ?loc get_dvty node in
  { de_node = node; de_dvty = dvty; de_loc = loc }
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(** Final stage *)

(** Binders *)

let binders bl =
  let sn = ref Sstr.empty in
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  let binder (id, ghost, dity) =
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    let id = match id with
      | Some ({pre_name = n} as id) ->
          let exn = match id.pre_loc with
            | Some loc -> Loc.Located (loc, Dterm.DuplicateVar n)
            | None -> Dterm.DuplicateVar n in
          sn := Sstr.add_new exn n !sn; id
      | None -> id_fresh "_" in
    create_pvsymbol id ~ghost (ity_of_dity dity) in
  List.map binder bl

(** Specifications *)

let to_fmla f = match f.t_ty with
  | None -> f
  | Some ty when ty_equal ty ty_bool -> t_equ f t_bool_true
  | _ -> Loc.error ?loc:f.t_loc Dterm.FmlaExpected

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let create_assert = to_fmla

let create_invariant pl = List.map to_fmla pl

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let create_post ity ql = List.map (fun (v,f) ->
  ity_equal_check ity v.pv_ity; Ity.create_post v.pv_vs (to_fmla f)) ql
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let create_xpost xql = Mexn.mapi (fun xs ql -> create_post xs.xs_ity ql) xql
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(** User effects *)

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let rec effect_of_term t =
  let quit () = Loc.errorm ?loc:t.t_loc "unsupported effect expression" in
  match t.t_node with
  | Tapp (fs, [ta]) ->
      let v, ity, fa = effect_of_term ta in
      let ity = match fa with
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        | Some {rs_cty = {cty_args = [arg]; cty_result = res}} ->
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            ity_full_inst (ity_match isb_empty arg.pv_ity ity) res
        | Some _ -> assert false
        | None -> ity in
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      begin try match ity.ity_node, restore_rs fs with
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        | Ityreg {reg_its = ts}, ({rs_field = Some f} as rs)
          when List.exists (pv_equal f) ts.its_mfields -> v, ity, Some rs
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        | _, {rs_cty={cty_args=[arg]; cty_result=res; cty_freeze=frz}} ->
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            v, ity_full_inst (ity_match frz arg.pv_ity ity) res, None
        | _ -> quit () with Not_found -> quit () end
  | Tvar v ->
      let v = try restore_pv v with Not_found -> quit () in
      v, v.pv_ity, None
  | _ -> quit ()
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let effect_of_dspec dsp =
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  let pvs = Spv.of_list dsp.ds_reads in
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  let add_write (l,eff) t = match effect_of_term t with
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    | v, {ity_node = Ityreg reg}, fd ->
        let fs = match fd with
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          | Some fd -> Spv.singleton (Opt.get fd.rs_field)
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          | None -> Spv.of_list reg.reg_its.its_mfields in
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        let rd = Spv.singleton v and wr = Mreg.singleton reg fs in
        let e = Loc.try2 ?loc:t.t_loc eff_write rd wr in
        (e,t)::l, eff_union_par eff e
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    | _ ->
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        Loc.errorm ?loc:t.t_loc "mutable expression expected" in
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  let wl, eff = List.fold_left add_write ([], eff_read pvs) dsp.ds_writes in
  let eff = Mexn.fold (fun xs _ eff -> eff_raise eff xs) dsp.ds_xpost eff in
  let eff = if dsp.ds_diverge then eff_diverge eff else eff in
  wl, eff
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(* TODO: add warnings for empty postconditions (anywhere)
    and empty exceptional postconditions (toplevel). *)
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let check_spec dsp ecty e =
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  let bad_write weff eff = not (Mreg.submap (fun _ s1 s2 -> Spv.subset s1 s2)
                                            weff.eff_writes eff.eff_writes) in
  let bad_raise xeff eff = not (Sexn.subset xeff.eff_raises eff.eff_raises) in
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  (* computed effect vs user effect *)
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  let check_rwd = dsp.ds_checkrw in
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  let uwrl, ue = effect_of_dspec dsp in
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  let ucty = create_cty ecty.cty_args ecty.cty_pre ecty.cty_post
    ecty.cty_xpost ecty.cty_oldies ue ecty.cty_result in
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  let ueff = ucty.cty_effect and eeff = ecty.cty_effect in
  let urds = ueff.eff_reads and erds = eeff.eff_reads in
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  (* check that every user effect actually happens *)
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  if not (Spv.subset urds erds) then Loc.errorm ?loc:e.e_loc
    "variable@ %a@ does@ not@ occur@ in@ this@ expression"
    Pretty.print_vs (Spv.choose (Spv.diff urds erds)).pv_vs;
  if bad_write ueff eeff then List.iter (fun (weff,t) ->
    if bad_write weff eeff then Loc.errorm ?loc:t.t_loc
      "this@ write@ effect@ does@ not@ happen@ in@ the@ expression") uwrl;
  if bad_raise ueff eeff then Loc.errorm ?loc:e.e_loc
    "this@ expression@ does@ not@ raise@ exception@ %a"
    print_xs (Sexn.choose (Sexn.diff ueff.eff_raises eeff.eff_raises));
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  if ueff.eff_oneway && not eeff.eff_oneway then Loc.errorm ?loc:e.e_loc
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    "this@ expression@ does@ not@ diverge";
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  (* check that every computed effect is listed *)
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  if check_rwd && not (Spv.subset erds urds) then Spv.iter (fun v ->
    Loc.errorm ?loc:e.e_loc
      "this@ expression@ depends@ on@ variable@ %a@ left@ out@ in@ \
      the@ specification" Pretty.print_vs v.pv_vs) (Spv.diff erds urds);
  if check_rwd && bad_write eeff ueff then
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    Loc.errorm ?loc:(e_locate_effect (fun eff -> bad_write eff ueff) e)
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      "this@ expression@ produces@ an@ unlisted@ write@ effect";
  if ecty.cty_args <> [] && bad_raise eeff ueff then Sexn.iter (fun xs ->
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    Loc.errorm ?loc:(e_locate_effect (fun eff -> Sexn.mem xs eff.eff_raises) e)
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      "this@ expression@ raises@ unlisted@ exception@ %a"
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      print_xs xs) (Sexn.diff eeff.eff_raises ueff.eff_raises);
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  if check_rwd && eeff.eff_oneway && not ueff.eff_oneway then
    Loc.errorm ?loc:(e_locate_effect (fun eff -> eff.eff_oneway) e)
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      "this@ expression@ may@ diverge,@ but@ this@ is@ not@ \
        stated@ in@ the@ specification"
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let check_aliases recu c =
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  let rds_regs = c.cty_freeze.isb_reg in
  let report r _ _ =
    if Mreg.mem r rds_regs then let spv = Spv.filter
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        (fun v -> ity_r_occurs r v.pv_ity) (cty_reads c) in
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      Loc.errorm "The type of this function contains an alias with \
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        external variable %a" print_pv (Spv.choose spv)
    else Loc.errorm "The type of this function contains an alias" in
  (* we allow the value in a non-recursive function to contain
     regions coming the function's arguments, but not from the
     context. It is sometimes useful to write a function around
     a constructor or a projection. For recursive functions, we
     impose the full non-alias discipline, to ensure the safety
     of region polymorphism (see add_rec_mono). We do not track
     aliases inside the type of an argument or a result, which
     may break the type inference, but we have a safety net
     type checking in Expr. *)
  let add_ity regs ity =
    let frz = ity_freeze isb_empty ity in
    Mreg.union report regs frz.isb_reg in
  let add_arg regs v = add_ity regs v.pv_ity in
  let regs = List.fold_left add_arg rds_regs c.cty_args in
  ignore (add_ity (if recu then regs else rds_regs) c.cty_result)
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let check_fun rsym dsp e =
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  let c,e = match e with
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    | { c_node = Cfun e; c_cty = c } -> c,e
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    | _ -> invalid_arg "Dexpr.check_fun" in
  let c = match rsym with
    | Some s -> s.rs_cty
    | None -> c in
  check_spec dsp c e;
  check_aliases (rsym <> None) c

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(** Environment *)

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type env = {
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  rsm : rsymbol Mstr.t;
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  pvm : pvsymbol Mstr.t;
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  old : (pvsymbol Mstr.t * (let_defn * pvsymbol) Hpv.t) Mstr.t;
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}

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let env_empty = {
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  rsm = Mstr.empty;
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  pvm = Mstr.empty;
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  old = Mstr.empty;
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}

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exception UnboundLabel of string

let find_old pvm (ovm,old) v =
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  if v.pv_ity.ity_pure then v else
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  let n = v.pv_vs.vs_name.id_string in
  (* if v is top-level, both ov and pv are None.
     If v is local, ov and pv must be equal to v.
     If they are not equal, then v is defined under the label,
     so we return v and do not register an "oldie" for it. *)
  let ov = Mstr.find_opt n ovm in
  let pv = Mstr.find_opt n pvm in
  if not (Opt.equal pv_equal ov pv) then v
  else match Hpv.find_opt old v with
    | Some (_,o) -> o
    | None ->
        let e = e_pure (t_var v.pv_vs) in
        let id = id_clone v.pv_vs.vs_name in
        let ld = let_var id ~ghost:true e in
        Hpv.add old v ld; snd ld

let register_old env v l =
  find_old env.pvm (Mstr.find_exn (UnboundLabel l) l env.old) v

let get_later env later = later env.pvm (register_old env)

let add_label ({pvm = pvm; old = old} as env) l =
  let ht = Hpv.create 3 in
  { env with old = Mstr.add l (pvm, ht) old }, ht

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let rebase_old {pvm = pvm} preold old fvs =
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  let rebase v (_,{pv_vs = o}) sbs =
    if not (Mvs.mem o fvs) then sbs else match preold with
      | Some preold ->
          Mvs.add o (t_var (find_old pvm preold v).pv_vs) sbs
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      | None -> raise (UnboundLabel "0") in
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  Hpv.fold rebase old Mvs.empty

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let rebase_pre env preold old pl =
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  let pl = List.map to_fmla pl in
  let fvs = List.fold_left t_freevars Mvs.empty pl in
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  let sbs = rebase_old env preold old fvs in
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  List.map (t_subst sbs) pl

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let rebase_variant env preold old varl =
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  let add s (t,_) = t_freevars s t in
  let fvs = List.fold_left add Mvs.empty varl in
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  let sbs = rebase_old env preold old fvs in
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  let conv (t,rel) = t_subst sbs t, rel in
  List.map conv varl

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let get_oldies old =
  Hpv.fold (fun v (_,o) sbs -> Mpv.add o v sbs) old Mpv.empty

let add_rsymbol ({rsm = rsm; pvm = pvm} as env) rs =
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  let n = rs.rs_name.id_string in
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  let pvm = match rs.rs_logic with
    | RLpv pv -> Mstr.add n pv pvm
    | _ -> pvm in
  { env with rsm = Mstr.add n rs rsm; pvm = pvm }
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let add_pvsymbol ({pvm = pvm} as env) pv =
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  let n = pv.pv_vs.vs_name.id_string in
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  { env with pvm = Mstr.add n pv pvm }
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let add_pv_map ({pvm = pvm} as env) vm =
  { env with pvm = Mstr.set_union vm pvm }
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let add_binders env pvl = List.fold_left add_pvsymbol env pvl

(** Abstract values *)

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let cty_of_spec env bl dsp dity =
  let ity = ity_of_dity dity in
  let bl = binders bl in
  let env = add_binders env bl in
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  let preold = Mstr.find_opt "0" env.old in
  let env, old = add_label env "0" in
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  let dsp = get_later env dsp ity in
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  let _, eff = effect_of_dspec dsp in
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  let eff = eff_reset_overwritten eff in
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  let p = rebase_pre env preold old dsp.ds_pre in
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  let q = create_post ity dsp.ds_post in
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  let xq = create_xpost dsp.ds_xpost in
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  create_cty bl p q xq (get_oldies old) eff ity
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(** Expressions *)

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let warn_unused s loc =
  if s = "" || s.[0] <> '_' then
  Warning.emit ?loc "unused variable %s" s

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let check_used_pv e pv = if not (Spv.mem pv e.e_effect.eff_reads) then
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  warn_unused pv.pv_vs.vs_name.id_string pv.pv_vs.vs_name.id_loc
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let e_let_check ld e = match ld with
  | LDvar (v,_) -> check_used_pv e v; e_let ld e
  | _           -> e_let ld e

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let rec strip uloc labs de = match de.de_node with
  | DEcast (de,_) -> strip uloc labs de
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  | DEuloc (de,loc) -> strip (Some (Some loc)) labs de
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  | DElabel (de,s) -> strip uloc (Slab.union labs s) de
  | _ -> uloc, labs, de

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let get_pv env n = Mstr.find_exn (Dterm.UnboundVar n) n env.pvm
let get_rs env n = Mstr.find_exn (Dterm.UnboundVar n) n env.rsm

let rec expr uloc env ({de_loc = loc} as de) =
  let uloc, labs, de = strip uloc Slab.empty de in
  let e = Loc.try3 ?loc try_expr uloc env de in
  let loc = Opt.get_def loc uloc in
  if loc = None && Slab.is_empty labs
  then e else e_label ?loc labs e
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and cexp uloc env ghost ({de_loc = loc} as de) =
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  let uloc, labs, de = strip uloc Slab.empty de in
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  if not (Slab.is_empty labs) then Warning.emit ?loc
    "Ignoring labels over a higher-order expression";
  Loc.try4 ?loc try_cexp uloc env ghost de

and try_cexp uloc env ghost de0 = match de0.de_node with
  | DEvar _ | DErs _ | DEapp _ ->
      let app (ldl,c) el =
        let argl, res = de0.de_dvty in
        ext_c_app (ldl, c_ghostify ghost c) el
          (List.map ity_of_dity argl) (ity_of_dity res) in
      let rec down de el = match de.de_node with
        | DEapp (de1,de2) -> down de1 (expr uloc env de2 :: el)
        | DEvar (n,_) -> app (ext_c_sym (get_rs env n)) el
        | DErs s -> app (ext_c_sym s) el
        | _ -> app (cexp uloc env ghost de) el in
      down de0 []
  | DEfun (bl,dsp,de) ->
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      let dvl _ _ = [] in
      let c, dsp, _ = lambda uloc env (binders bl) dsp dvl de in
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      check_fun None dsp c;
      [], c_ghostify ghost c
  | DEany (bl,dsp,dity) ->
      [], c_ghostify ghost (c_any (cty_of_spec env bl dsp dity))
  | DElet ((_,_,_,{de_dvty = ([],_)}) as dldf,de) ->
      let ld, env = var_defn uloc env ghost dldf in
      let ldl, c = cexp uloc env ghost de in
      ld::ldl, c
  | DElet (dldf,de) ->
      let ldl0, env = sym_defn uloc env ghost dldf in
      let ldl, c = cexp uloc env ghost de in
      ldl0 @ ldl, c
  | DErec (drdf,de) ->
      let ld, env = rec_defn uloc env ghost drdf in
      let ldl, c = cexp uloc env ghost de in
      ld::ldl, c
  | DEghost de -> cexp uloc env true de
  | DEmark _ ->
      Loc.errorm "Marks are not allowed over higher-order expressions"
  | DEpv _ | DEconst _ | DEnot _ | DEand _ | DEor _ | DEif _ | DEcase _
  | DEassign _ | DEwhile _ | DEfor _ | DEtry _ | DEraise _ | DEassert _
  | DEpure _ | DEabsurd | DEtrue | DEfalse -> assert false (* expr-only *)
  | DEcast _ | DEuloc _ | DElabel _ -> assert false (* already stripped *)

and try_expr uloc env ({de_dvty = argl,res} as de0) =
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  match de0.de_node with
  | DEvar (n,_) when argl = [] ->
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      e_var (get_pv env n)
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  | DEpv v ->
      e_var v
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  | DEconst c ->
      e_const c
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  | DEapp ({de_dvty = ([],_)} as de1, de2) ->