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(********************************************************************)
(*                                                                  *)
(*  The Why3 Verification Platform   /   The Why3 Development Team  *)
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(*  Copyright 2010-2017   --   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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  | Dvar of dvar ref          (* destructible "fresh" type variable *)
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  | Dutv of tvsymbol          (* undestructible "user" type variable *)
  | Durg of dity * region     (* undestructible "user" region *)
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  | Dapp of itysymbol * dity list * dity list

and dvar =
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  | Dval of dity              (* i am equal to dity *)
  | Dpur of dity              (* i am equal to the purified dity *)
  | Dsim of dity * tvsymbol   (* our purified types are equal *)
  | Dreg of dity * tvsymbol   (* unassigned region *)
  | Dtvs of        tvsymbol   (* unassigned variable *)
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(* In Dreg and Durg, the dity field is a Dapp of the region's type. *)
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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 dity_fresh () =
  Dvar (ref (Dtvs (create_tvsymbol (id_fresh "mu"))))

let dity_reg d =
  Dvar (ref (Dreg (d, create_tvsymbol (id_fresh "rho"))))

let rec dity_sim = function
  | Dvar {contents = (Dval d|Dpur d|Dsim (d,_)|Dreg (d,_))}
  | Durg (d,_) -> dity_sim d
  | d -> Dvar (ref (Dsim (d, create_tvsymbol (id_fresh "eta"))))
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let rec dity_pur = function
  | Dvar {contents = (Dval d|Dpur d|Dsim (d,_)|Dreg (d,_))}
  | Durg (d,_) -> dity_pur d
  | d -> Dvar (ref (Dpur d))

let app_map fn s tl rl = Dapp (s, List.map fn tl, List.map fn rl)
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let dity_of_ity ity =
  let hr = Hreg.create 3 in
  let rec dity ity = match ity.ity_node with
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    | Ityvar (v,false) -> Dutv v
    | Ityvar (v,true)  -> dity_pur (Dutv v)
    | Ityapp (s,tl,rl) -> app_map dity s tl rl
    | Ityreg ({reg_its = s; reg_args = tl; reg_regs = rl} as r) ->
        try Hreg.find hr r with Not_found ->
        let d = dity_reg (app_map dity s tl rl) in
        Hreg.add hr r d; d in
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  dity ity

let rec ity_of_dity = function
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  | Dutv v -> ity_var v
  | Durg (_,r) -> ity_reg r
  | Dvar {contents = Dval d} -> ity_of_dity d
  | Dvar {contents = Dpur d} -> ity_purify (ity_of_dity d)
  | Dvar ({contents = Dsim (d,_)} as r) ->
      let rec refresh ity = match ity.ity_node with
        | Ityreg {reg_its = s; reg_args = tl} | Ityapp (s,tl,_) ->
            ity_app s (List.map refresh tl) []
        | Ityvar (v,_) -> ity_var v in
      let rec dity ity = match ity.ity_node with
        | Ityreg r ->
            Durg (app_map dity r.reg_its r.reg_args r.reg_regs, r)
        | Ityapp (s,tl,rl) -> app_map dity s tl rl
        | Ityvar (v,true)  -> dity_pur (Dutv v)
        | Ityvar (v,false) -> Dutv v in
      let t = refresh (ity_of_dity d) in
      r := Dval (dity t); t
  | Dvar ({contents = Dreg (Dapp (s,tl,rl) as d,_)} as r) ->
      let reg = create_region (id_fresh "rho") s
        (List.map ity_of_dity tl) (List.map ity_of_dity rl) in
      r := Dval (Durg (d, reg)); ity_reg reg
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  | Dvar r ->
      let v = create_tvsymbol (id_fresh "xi") in
      r := Dval (Dutv v); ity_var v
  | Dapp (s,tl,rl) ->
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      ity_app_pure s (List.map ity_of_dity tl) (List.map ity_of_dity rl)
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(** Destructive type unification *)

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

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

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let dity_app_fresh s dl =
  let mv = List.fold_right2 Mtv.add s.its_ts.ts_args dl Mtv.empty in
  let hr = Hreg.create 3 in
  let rec ity_inst ity = match ity.ity_node with
    | Ityreg r -> reg_inst r
    | Ityvar (v, false) -> Mtv.find v mv
    | Ityvar (v, true) -> dity_pur (Mtv.find v mv)
    | Ityapp (s,tl,rl) -> app_map ity_inst s tl rl
  and reg_inst ({reg_its = s; reg_args = tl; reg_regs = rl} as r) =
    try Hreg.find hr r with Not_found ->
    let d = dity_reg (app_map ity_inst s tl rl) in
    Hreg.replace hr r d; d in
  Dapp (s, dl, List.map reg_inst s.its_regions)

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let rec dity_refresh = function
  | Dvar {contents = (Dval d|Dpur d|Dsim (d,_)|Dreg (d,_))}
  | Durg (d,_) -> dity_refresh d
  | Dutv _ as d -> d
  | Dvar {contents = Dtvs _} -> dity_fresh ()
  | Dapp (s,dl,_) ->
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      let d = dity_app_fresh s (List.map dity_refresh dl) in
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      if its_immutable s then d else dity_reg d

let rec dity_unify_asym d1 d2 = match d1,d2 with
  | Durg _, _ | Dutv _, _ -> raise Exit (* we cannot be pure then *)
  | d1, Dvar {contents = (Dval d2|Dpur d2|Dsim (d2,_)|Dreg (d2,_))}
  | d1, Durg (d2,_)
  | Dvar {contents = Dval d1}, d2 ->
      dity_unify_asym d1 d2
  | Dvar {contents = Dpur d1}, d2 ->
      dity_unify_weak d1 d2
  | Dvar ({contents = Dsim (d1,_)} as r), d2 ->
      dity_unify_weak d1 d2;
      r := Dpur d1
  | Dvar ({contents = Dreg (d1,_)} as r), d2 ->
      dity_unify_asym d1 d2;
      r := Dval d1
  | Dvar ({contents = Dtvs u} as r),
    Dvar {contents = Dtvs v} when tv_equal u v ->
      r := Dpur (dity_fresh ())
  | Dvar ({contents = Dtvs v} as r), d ->
      occur_check v d;
      r := Dpur d
  | d (* not a Dvar! *), Dvar ({contents = Dtvs v} as r) ->
      occur_check v d;
      let d2 = dity_refresh d in
      dity_unify_asym d d2;
      r := Dval d2
  | Dapp (s1,dl1,rl1), Dapp (s2,dl2,rl2) when its_equal s1 s2 ->
      List.iter2 dity_unify_asym dl1 dl2;
      List.iter2 dity_unify_asym rl1 rl2
  | _ -> raise Exit
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let rec dity_unify d1 d2 = match d1,d2 with
  | Dvar {contents = Dval d1}, d2 | d1, Dvar {contents = Dval d2} ->
      dity_unify d1 d2
  | Dvar ({contents = Dpur d2}), d1 (* yes, it's d2 on the left *)
  | d1, Dvar ({contents = Dpur d2}) ->
      dity_unify_asym d1 d2
  | Dvar ({contents = Dsim (_,u)}),
    Dvar ({contents = Dsim (_,v)}) when tv_equal u v ->
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      ()
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  | Dvar ({contents = Dsim (d1,v)} as r), d
  | d, Dvar ({contents = Dsim (d1,v)} as r) ->
      occur_check v d; (* not necessary? *)
      dity_unify_weak d1 d;
      r := Dval d
  | Dvar {contents = Dreg (_,u)},
    Dvar {contents = Dreg (_,v)} when tv_equal u v ->
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      ()
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  | Dvar ({contents = Dreg (d1,v)} as r),
    ((Dapp _ as d2 | Durg (d2,_) | Dvar {contents = Dreg (d2,_)}) as d)
  | ((Dapp _ as d1 | Durg (d1,_)) as d),
    Dvar ({contents = Dreg (d2,v)} as r) ->
      occur_check v d; (* not necessary! *)
      dity_unify d1 d2;
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      r := Dval d
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  | 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 ->
      ()
  | Durg (_,r1), Durg (_,r2) when reg_equal r1 r2 ->
      ()
  | Dapp (s1,dl1,rl1), Dapp (s2,dl2,rl2) when its_equal s1 s2 ->
      List.iter2 dity_unify dl1 dl2;
      List.iter2 dity_unify rl1 rl2
  | _ -> raise Exit
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(** 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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(*
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let dvty_int  = [], dity_int
let dvty_real = [], dity_real
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*)
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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

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let rec print_dity pur pri fmt = function
  | Dvar {contents = Dval d} ->
      print_dity pur pri fmt d
  | Dvar {contents = (Dpur d|Dsim (d,_)|Dreg (d,_))}
  | Durg (d,_) when pur ->
      print_dity pur pri fmt d
  | Dvar {contents = Dtvs v} | Dutv v ->
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      Pretty.print_tv fmt v
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  | Dvar {contents = Dpur d} ->
      Format.fprintf fmt "{%a}" (print_dity true 0) d
  | Dvar {contents = Dsim (d,_)} ->
      Format.fprintf fmt "[%a]" (print_dity true 0) d
  | Dvar {contents = Dreg (Dapp (s,tl,rl),{tv_name = id})}
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  | Durg (Dapp (s,tl,rl),{reg_name = id}) ->
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      Format.fprintf fmt
        (protect_on (pri > 1 && (tl <> [] || rl <> [])) "%a%a%a@ @@%s")
        Pretty.print_ts s.its_ts (print_args (print_dity pur 2)) tl
          (print_regs (print_dity pur 0)) rl (Ident.id_unique rprinter id)
  | Dvar {contents = Dreg _} | Durg _ -> assert false
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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")
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        (print_dity pur 1) t1 (print_dity pur 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 pur 0)) tl
  | Dapp (s,tl,_) when pur ->
      Format.fprintf fmt (protect_on (pri > 1 && tl <> []) "%a%a")
        Pretty.print_ts s.its_ts (print_args (print_dity pur 2)) tl
  | Dapp (s,tl,rl) when its_immutable s ->
      Format.fprintf fmt
        (protect_on (pri > 1 && (tl <> [] || rl <> [])) "%a%a%a")
        Pretty.print_ts s.its_ts (print_args (print_dity pur 2)) tl
          (print_regs (print_dity pur 0)) rl
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  | Dapp (s,tl,rl) ->
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      Format.fprintf fmt
        (protect_on (pri > 1 && (tl <> [] || rl <> [])) "{%a}%a%a")
        Pretty.print_ts s.its_ts (print_args (print_dity pur 2)) tl
          (print_regs (print_dity pur 0)) rl
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let print_dity fmt d = print_dity false 0 fmt d
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(* Specialization of symbols *)

let specialize_scheme tvs (argl,res) =
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  let hv = Htv.create 3 in
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  let rec spec_dity = function
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    | Dvar {contents = Dval d} -> spec_dity d
    | Dvar {contents = Dpur d} -> dity_pur (spec_dity d)
    | Dvar {contents = Dsim (d,v)} ->
        (try Htv.find hv v with Not_found ->
        let nd = dity_sim (spec_dity d) in
        Htv.add hv v nd; nd)
    | Dvar {contents = Dreg (d,v)} ->
        (try Htv.find hv v with Not_found ->
        let nd = dity_reg (spec_dity d) in
        Htv.add hv v nd; nd)
    | Dvar {contents = Dtvs v} | Dutv v as d ->
        (try Htv.find hv v with Not_found ->
        (* even if v is frozen, it is polymorphic in its regions *)
        let nd = if Stv.mem v tvs then dity_fresh () else dity_sim d in
        Htv.add hv v nd; nd)
    | Dapp (s,dl,rl) -> app_map spec_dity s dl rl
    | Durg _ as d -> d in
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  List.map spec_dity argl, spec_dity res

let spec_ity hv hr frz ity =
  let rec dity ity = match ity.ity_node with
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    | Ityreg r ->
        (try Hreg.find hr r with Not_found ->
        let d = app_map dity r.reg_its r.reg_args r.reg_regs in
        let nd = if Mreg.mem r frz.isb_reg then Durg (d,r) else dity_reg d in
        Hreg.add hr r nd; nd)
    | Ityvar (v,pure) ->
        let nd = try Htv.find hv v with Not_found ->
          let nd =
            if Mtv.mem v frz.isb_var then Dutv v else
            if Mtv.mem v frz.isb_pur then dity_sim (Dutv v) else
            dity_fresh () in
          Htv.add hv v nd; nd in
        if pure then dity_pur nd else nd
    | Ityapp (s,tl,rl) -> app_map dity s tl rl in
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  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

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let specialize_ls {ls_args = args; ls_value = res} =
  let hv = Htv.create 3 and hr = Hreg.create 3 in
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  let spec_val _ ty = spec_ity hv hr isb_empty (ity_of_ty_pure ty) in
  let spec_arg ty = dity_sim (spec_val () ty) in
  List.map spec_arg args, Opt.fold spec_val dity_bool res
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(** 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
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  | DPvar  of preid * bool
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  | DPapp  of rsymbol * dpattern list
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  | DPas   of dpattern * preid * bool
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  | DPor   of dpattern * dpattern
  | 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;
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  ds_xpost   : (pvsymbol * term) list Mxs.t;
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  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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  | DEls of lsymbol
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  | DEconst of Number.constant * dity
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  | DEapp of dexpr * dexpr
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  | DEfun of dbinder list * mask * dspec later * dexpr
  | DEany of dbinder list * mask * 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 * dity
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  | 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 * mask * dspec later * variant list later * dexpr
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(** Environment *)

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

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let denv_contents d = d.locals

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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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    | Dvar {contents = (Dval d|Dpur d|Dsim (d,_)|Dreg (d,_))}
    | Durg (d,_) -> add l d
    | Dvar {contents = Dtvs _}
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    | Dutv _ as d -> d :: l
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    | Dapp (_,tl,_) -> List.fold_left add l tl in
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  List.fold_left add (add frozen res) argl

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

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let denv_pure denv get_dty =
  let ht = Htv.create 3 in
  let hi = Hint.create 3 in
  let rec fold = function
    | Dvar {contents = (Dval d|Dpur d|Dsim (d,_)|Dreg (d,_))}
    | Durg (d,_) -> fold d
    | Dvar {contents = Dtvs v} as d ->
        begin try fst (Htv.find ht v) with Not_found ->
        let f = Dterm.dty_fresh () in Htv.add ht v (f,d); f end
    | Dapp (s,dl,_) -> Dterm.dty_app s.its_ts (List.map fold dl)
    | Dutv v -> Dterm.dty_var v in
  let pure_denv = Mstr.mapi (fun n (_, dvty) ->
    Dterm.DTvar (n, fold (dity_of_dvty dvty))) denv.locals in
  let dty = get_dty pure_denv in
  Htv.iter (fun v (f,_) ->
    try Dterm.dty_match f (ty_var v) with Exit -> ()) ht;
  let fnS s dl = dity_app_fresh (restore_its s) dl in
  let fnV v = try snd (Htv.find ht v) with Not_found -> Dutv v in
  let fnI i = try Hint.find hi i with Not_found ->
    let d = dity_fresh () in Hint.add hi i d; d in
  dity_pur (Dterm.dty_fold fnS fnV fnI dty)

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(** 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

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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 *
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  dity * mask * (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";
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  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,_,_) =
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    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,msk,pre) =
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    let dsp, dvl, de = pre (denv_add_args denv1 bl) in
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    dexpr_expected_type de res;
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    (id,gh,pk,bl,msk,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
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    | DPvar (id,gh) ->
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        let dity = dity_fresh () in
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        mk_dpat (PPvar (id,gh)) 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
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    | DPas (dp, ({pre_name = n} as id), gh) ->
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        let { dp_pat = pat; dp_dity = dity; dp_vars = vars } = dp in
        let vars = Mstr.add_new (Dterm.DuplicateVar n) n dity vars in
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        mk_dpat (PPas (pat, id, gh)) dity vars
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    | DPcast (dp, ity) ->
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        dpat_expected_type dp (dity_of_ity ity);
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        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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    | DEls ls ->
        specialize_ls ls
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    | DEconst (_, ity) -> [],ity
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    | 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 (_, dity) ->
        [], dity
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    | 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) ->
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        dexpr_expected_type 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 *)

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let binders ghost bl =
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  let sn = ref Sstr.empty in
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  let binder (id, gh, 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
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    create_pvsymbol id ~ghost:(ghost || gh) (ity_of_dity dity) in
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  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 = Mxs.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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        if not reg.reg_its.its_private && Spv.is_empty fs then
          Loc.errorm ?loc:t.t_loc "mutable expression expected";
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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
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  let eff = Mxs.fold (fun xs _ eff -> eff_raise eff xs) dsp.ds_xpost eff in
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  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 inr dsp ecty ({e_loc = loc} as e) =
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  let bad_read  reff eff = not (Spv.subset reff.eff_reads  eff.eff_reads) in
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  let bad_write weff eff = not (Mreg.submap (fun _ s1 s2 -> Spv.subset s1 s2)
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                                           weff.eff_writes eff.eff_writes) in
  let bad_raise xeff eff = not (Sxs.subset xeff.eff_raises eff.eff_raises) in
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  (* computed effect vs user effect *)
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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
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  let check_ue = not inr and check_rw = dsp.ds_checkrw in
  (* check that every user effect actually happens. We omit this
     for local functions inside recursive functions because if
     they call the parent function, they may have more effects
     than we know at this point: those will only be known after
     we finish constructing the parent function. TODO: make an
     effort to only disable the check for local functions that
     actually call their parent. *)
  if check_ue && bad_read ueff eeff then Loc.errorm ?loc
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    "variable@ %a@ does@ not@ occur@ in@ this@ expression"
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    Pretty.print_vs (Spv.choose (Spv.diff ueff.eff_reads eeff.eff_reads)).pv_vs;
  if check_ue && bad_write ueff eeff then List.iter (fun (weff,t) ->
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    if bad_write weff eeff then Loc.errorm ?loc:t.t_loc
      "this@ write@ effect@ does@ not@ happen@ in@ the@ expression") uwrl;
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  if check_ue && bad_raise ueff eeff then Loc.errorm ?loc
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    "this@ expression@ does@ not@ raise@ exception@ %a"
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    print_xs (Sxs.choose (Sxs.diff ueff.eff_raises eeff.eff_raises));
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  if check_ue && ueff.eff_oneway && not eeff.eff_oneway then Loc.errorm ?loc
      "this@ expression@ does@ not@ diverge";
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  (* check that every computed effect is listed *)
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  if check_rw && bad_read eeff ueff then Loc.errorm ?loc
    "this@ expression@ depends@ on@ variable@ %a,@ \
      which@ is@ left@ out@ in@ the@ specification"
    Pretty.print_vs (Spv.choose (Spv.diff eeff.eff_reads ueff.eff_reads)).pv_vs;
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  if check_rw && 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";
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  if ecty.cty_args <> [] && bad_raise eeff ueff then Sxs.iter (fun xs ->
    Loc.errorm ?loc:(e_locate_effect (fun eff -> Sxs.mem xs eff.eff_raises) e)
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      "this@ expression@ raises@ unlisted@ exception@ %a"
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      print_xs xs) (Sxs.diff eeff.eff_raises ueff.eff_raises);
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  if eeff.eff_oneway && not ueff.eff_oneway then
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    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 inr 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
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  check_spec inr dsp c e;
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  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;