CristalCaveGem » LustreC

(********************************************************************)

(*                                                                  *)

(*  The LustreC compiler toolset   /  The LustreC Development Team  *)

(*  Copyright 2012 -    --   ONERA - CNRS - INPT                    *)

(*                                                                  *)

(*  LustreC is free software, distributed WITHOUT ANY WARRANTY      *)

(*  under the terms of the GNU Lesser General Public License        *)

(*  version 2.1.                                                    *)

(*                                                                  *)

(********************************************************************)

open Utils

open Lustre_types

open Corelang

open Format

(* To update thank to some command line options *)

let debug = ref false

(** Normalisation iters through the AST of expressions and bind fresh definition

    when some criteria are met. This creation of fresh definition is performed by

    the function mk_expr_alias_opt when the alias argument is on.

    Initial expressions, ie expressions attached a variable in an equation

    definition are not aliased. This non-alias feature is propagated in the

    expression AST for array access and power construct, tuple, and some special

    cases of arrows.

    Two global variables may impact the normalization process:

    - unfold_arrow_active

    - force_alias_ite: when set, bind a fresh alias for then and else

      definitions.

*)

type param_t =

  {

    unfold_arrow_active: bool;

    force_alias_ite: bool;

    force_alias_internal_fun: bool;

  }

let params = ref

               {

                 unfold_arrow_active = false;

                 force_alias_ite = false;

                 force_alias_internal_fun =false;

               }

type norm_ctx_t =

  {

    parentid: ident;

    vars: var_decl list;

    is_output: ident -> bool; 

  }

let expr_true loc ck =

{ expr_tag = Utils.new_tag ();

  expr_desc = Expr_const (Const_tag tag_true);

  expr_type = Type_predef.type_bool;

  expr_clock = ck;

  expr_delay = Delay.new_var ();

  expr_annot = None;

  expr_loc = loc }

let expr_false loc ck =

{ expr_tag = Utils.new_tag ();

  expr_desc = Expr_const (Const_tag tag_false);

  expr_type = Type_predef.type_bool;

  expr_clock = ck;

  expr_delay = Delay.new_var ();

  expr_annot = None;

  expr_loc = loc }

let expr_once loc ck =

 { expr_tag = Utils.new_tag ();

  expr_desc = Expr_arrow (expr_true loc ck, expr_false loc ck);

  expr_type = Type_predef.type_bool;

  expr_clock = ck;

  expr_delay = Delay.new_var ();

  expr_annot = None;

  expr_loc = loc }

let is_expr_once =

  let dummy_expr_once = expr_once Location.dummy_loc (Clocks.new_var true) in

  fun expr -> Corelang.is_eq_expr expr dummy_expr_once

let unfold_arrow expr =

 match expr.expr_desc with

 | Expr_arrow (e1, e2) ->

    let loc = expr.expr_loc in

    let ck = List.hd (Clocks.clock_list_of_clock expr.expr_clock) in

    { expr with expr_desc = Expr_ite (expr_once loc ck, e1, e2) }

 | _                   -> assert false

(* Get the equation in [defs] with [expr] as rhs, if any *)

let get_expr_alias defs expr =

 try Some (List.find (fun eq -> Clocks.eq_clock expr.expr_clock eq.eq_rhs.expr_clock && is_eq_expr eq.eq_rhs expr) defs)

 with

 | Not_found -> None

(* Replace [expr] with (tuple of) [locals] *)

let replace_expr locals expr =

 match locals with

 | []  -> assert false

 | [v] -> { expr with

   expr_tag = Utils.new_tag ();

   expr_desc = Expr_ident v.var_id }

 | _   -> { expr with

   expr_tag = Utils.new_tag ();

   expr_desc = Expr_tuple (List.map expr_of_vdecl locals) }

(* IS IT USED ? TODO 

(* Create an alias for [expr], if none exists yet *)

let mk_expr_alias (parentid, vars) (defs, vars) expr =

(*Format.eprintf "mk_expr_alias %a %a %a@." Printers.pp_expr expr Types.print_ty expr.expr_type Clocks.print_ck expr.expr_clock;*)

  match get_expr_alias defs expr with

  | Some eq ->

    let aliases = List.map (fun id -> List.find (fun v -> v.var_id = id) vars) eq.eq_lhs in

    (defs, vars), replace_expr aliases expr

  | None    ->

    let new_aliases =

      List.map2

	(mk_fresh_var (parentid, vars) expr.expr_loc)

	(Types.type_list_of_type expr.expr_type)

	(Clocks.clock_list_of_clock expr.expr_clock) in

    let new_def =

      mkeq expr.expr_loc (List.map (fun v -> v.var_id) new_aliases, expr)

    in

    (* Format.eprintf "Checking def of alias: %a -> %a@." (fprintf_list ~sep:", " (fun fmt v -> Format.pp_print_string fmt v.var_id)) new_aliases Printers.pp_expr expr; *)

    (new_def::defs, new_aliases@vars), replace_expr new_aliases expr

 *)

(* Create an alias for [expr], if [expr] is not already an alias (i.e. an ident)

   and [opt] is true

 *)

let mk_expr_alias_opt opt norm_ctx (defs, vars) expr =

  if !debug then

    Log.report ~plugin:"normalization" ~level:2

      (fun fmt -> Format.fprintf  fmt "mk_expr_alias_opt %B %a %a %a@." opt Printers.pp_expr expr Types.print_ty expr.expr_type Clocks.print_ck expr.expr_clock);

  match expr.expr_desc with

  | Expr_ident alias ->

    (defs, vars), expr

  | _                ->

    match get_expr_alias defs expr with

    | Some eq ->

       (* Format.eprintf "Found a preexisting definition@."; *)

      let aliases = List.map (fun id -> List.find (fun v -> v.var_id = id) vars) eq.eq_lhs in

      (defs, vars), replace_expr aliases expr

    | None    ->

       (* Format.eprintf "Didnt found a preexisting definition (opt=%b)@." opt;

        * Format.eprintf "existing defs are: @[[%a@]]@."

        *   (fprintf_list ~sep:"@ "(fun fmt eq ->

        *        Format.fprintf fmt "ck:%a isckeq=%b, , iseq=%b, eq=%a"

        *          Clocks.print_ck eq.eq_rhs.expr_clock

        *          (Clocks.eq_clock expr.expr_clock eq.eq_rhs.expr_clock)

        *          (is_eq_expr eq.eq_rhs expr)

        *          Printers.pp_node_eq eq))

        *   defs; *)

      if opt

      then

	let new_aliases =

	  List.map2

	    (mk_fresh_var (norm_ctx.parentid, (norm_ctx.vars@vars)) expr.expr_loc)

	    (Types.type_list_of_type expr.expr_type)

	    (Clocks.clock_list_of_clock expr.expr_clock) in

	let new_def =

	  mkeq expr.expr_loc (List.map (fun v -> v.var_id) new_aliases, expr)

	in

	(* Typing and Registering machine type *) 

	let _ = if Machine_types.is_active then

                  Machine_types.type_def (norm_ctx.parentid, norm_ctx.vars) new_aliases expr

        in

	(new_def::defs, new_aliases@vars), replace_expr new_aliases expr

      else

	(defs, vars), expr

(* Similar fonctions for dimensions *) 

let mk_dim_alias opt norm_ctx (defs, vars) dim =

  match dim.Dimension.dim_desc with

  | Dimension.Dbool _ | Dint _ 

    | Dident _ -> (defs, vars), dim (* Keep the same *)

  | _ when opt -> (* Cast to expression, normalizing *)

     let e = expr_of_dimension dim in

     let defvars, e = mk_expr_alias_opt true norm_ctx (defs, vars) e in

     defvars, dimension_of_expr e

  | _ -> (defs, vars), dim (* Keep the same *)

let unfold_offsets norm_ctx defvars e offsets =

  let add_offset (defvars, e) d =

    (*Format.eprintf "add_offset %a(%a) %a @." Printers.pp_expr e Types.print_ty e.expr_type Dimension.pp_dimension d; *)

    let defvars, d = mk_dim_alias !params.force_alias_internal_fun norm_ctx defvars d in

    let new_e = 

      { e with

        expr_tag = Utils.new_tag ();

        expr_loc = d.Dimension.dim_loc;

        expr_type = Types.array_element_type e.expr_type;

        expr_desc = Expr_access (e, d) }

    in

    defvars, new_e

(*in (Format.eprintf "= %a @." Printers.pp_expr res; res) *)

  in

  List.fold_left add_offset (defvars, e) offsets 

(* Create a (normalized) expression from [ref_e],

   replacing description with [norm_d],

   taking propagated [offsets] into account

   in order to change expression type *)

let mk_norm_expr offsets ref_e norm_d =

  (*Format.eprintf "mk_norm_expr %a %a @." Printers.pp_expr ref_e Printers.pp_expr { ref_e with expr_desc = norm_d};*)

  let drop_array_type ty =

    Types.map_tuple_type Types.array_element_type ty in

  { ref_e with

    expr_desc = norm_d;

    expr_type = Utils.repeat (List.length offsets) drop_array_type ref_e.expr_type }

(* normalize_<foo> : defs * used vars -> <foo> -> (updated defs * updated vars) * normalized <foo> *)

let rec normalize_list alias norm_ctx offsets norm_element defvars elist =

  List.fold_right

    (fun t (defvars, qlist) ->

      let defvars, norm_t = norm_element alias norm_ctx offsets defvars t in

      (defvars, norm_t :: qlist)

    ) elist (defvars, [])

let rec normalize_expr ?(alias=true) ?(alias_basic=false) norm_ctx offsets defvars expr =

  (* Format.eprintf "normalize %B %a:%a [%a]@." alias Printers.pp_expr expr Types.print_ty expr.expr_type (Utils.fprintf_list ~sep:"," Dimension.pp_dimension) offsets; *)

  match expr.expr_desc with

  | Expr_const _

    | Expr_ident _ ->

     unfold_offsets norm_ctx defvars expr offsets

  | Expr_array elist ->

     let defvars, norm_elist = normalize_list alias norm_ctx offsets (fun _ -> normalize_array_expr ~alias:true) defvars elist in

     let norm_expr = mk_norm_expr offsets expr (Expr_array norm_elist) in

     mk_expr_alias_opt alias norm_ctx defvars norm_expr

  | Expr_power (e1, d) when offsets = [] ->

     let defvars, norm_e1 = normalize_expr norm_ctx offsets defvars e1 in

     let norm_expr = mk_norm_expr offsets expr (Expr_power (norm_e1, d)) in

     mk_expr_alias_opt alias norm_ctx defvars norm_expr

  | Expr_power (e1, d) ->

     normalize_expr ~alias:alias norm_ctx (List.tl offsets) defvars e1

  | Expr_access (e1, d) ->

     normalize_expr ~alias:alias norm_ctx (d::offsets) defvars e1 

  | Expr_tuple elist ->

     let defvars, norm_elist =

       normalize_list alias norm_ctx offsets (fun alias -> normalize_expr ~alias:alias ~alias_basic:false) defvars elist in

     defvars, mk_norm_expr offsets expr (Expr_tuple norm_elist)

  | Expr_appl (id, args, None)

      when Basic_library.is_homomorphic_fun id 

	   && Types.is_array_type expr.expr_type ->

     let defvars, norm_args =

       normalize_list

	 alias

	 norm_ctx

	 offsets

	 (fun _ -> normalize_array_expr ~alias:true)

	 defvars

	 (expr_list_of_expr args)

     in

     defvars, mk_norm_expr offsets expr (Expr_appl (id, expr_of_expr_list args.expr_loc norm_args, None))

  | Expr_appl (id, args, None) when Basic_library.is_expr_internal_fun expr

      && not (!params.force_alias_internal_fun || alias_basic) ->

     let defvars, norm_args = normalize_expr ~alias:true norm_ctx offsets defvars args in

     defvars, mk_norm_expr offsets expr (Expr_appl (id, norm_args, None))

  | Expr_appl (id, args, r) ->

     let defvars, r =

       match r with

       | None -> defvars, None

       | Some r ->

	  let defvars, norm_r = normalize_expr ~alias_basic:true norm_ctx [] defvars r in

	  defvars, Some norm_r

     in

     let defvars, norm_args = normalize_expr norm_ctx [] defvars args in

     let norm_expr = mk_norm_expr [] expr (Expr_appl (id, norm_args, r)) in

     if offsets <> []

     then

       let defvars, norm_expr = normalize_expr norm_ctx [] defvars norm_expr in

       normalize_expr ~alias:alias norm_ctx offsets defvars norm_expr

     else

       mk_expr_alias_opt (alias && (!params.force_alias_internal_fun || alias_basic

				    || not (Basic_library.is_expr_internal_fun expr)))

	 norm_ctx defvars norm_expr

  | Expr_arrow (e1,e2) when !params.unfold_arrow_active && not (is_expr_once expr) ->

     (* Here we differ from Colaco paper: arrows are pushed to the top *)

     normalize_expr ~alias:alias norm_ctx offsets defvars (unfold_arrow expr)

  | Expr_arrow (e1,e2) ->

     let defvars, norm_e1 = normalize_expr norm_ctx offsets defvars e1 in

     let defvars, norm_e2 = normalize_expr norm_ctx offsets defvars e2 in

     let norm_expr = mk_norm_expr offsets expr (Expr_arrow (norm_e1, norm_e2)) in

     mk_expr_alias_opt alias norm_ctx defvars norm_expr

  | Expr_pre e ->

     let defvars, norm_e = normalize_expr norm_ctx offsets defvars e in

     let norm_expr = mk_norm_expr offsets expr (Expr_pre norm_e) in

     mk_expr_alias_opt alias norm_ctx defvars norm_expr

  | Expr_fby (e1, e2) ->

     let defvars, norm_e1 = normalize_expr norm_ctx offsets defvars e1 in

     let defvars, norm_e2 = normalize_expr norm_ctx offsets defvars e2 in

     let norm_expr = mk_norm_expr offsets expr (Expr_fby (norm_e1, norm_e2)) in

     mk_expr_alias_opt alias norm_ctx defvars norm_expr

  | Expr_when (e, c, l) ->

     let defvars, norm_e = normalize_expr norm_ctx offsets defvars e in

     defvars, mk_norm_expr offsets expr (Expr_when (norm_e, c, l))

  | Expr_ite (c, t, e) ->

     let defvars, norm_c = normalize_guard norm_ctx defvars c in

     let defvars, norm_t = normalize_cond_expr  norm_ctx offsets defvars t in

     let defvars, norm_e = normalize_cond_expr  norm_ctx offsets defvars e in

     let norm_expr = mk_norm_expr offsets expr (Expr_ite (norm_c, norm_t, norm_e)) in

     mk_expr_alias_opt alias norm_ctx defvars norm_expr

  | Expr_merge (c, hl) ->

     let defvars, norm_hl = normalize_branches norm_ctx offsets defvars hl in

     let norm_expr = mk_norm_expr offsets expr (Expr_merge (c, norm_hl)) in

     mk_expr_alias_opt alias norm_ctx defvars norm_expr

(* Creates a conditional with a merge construct, which is more lazy *)

(*

  let norm_conditional_as_merge alias node norm_expr offsets defvars expr =

  match expr.expr_desc with

  | Expr_ite (c, t, e) ->

  let defvars, norm_t = norm_expr (alias node offsets defvars t in

  | _ -> assert false

*)

and normalize_branches norm_ctx offsets defvars hl =

  List.fold_right

    (fun (t, h) (defvars, norm_q) ->

      let (defvars, norm_h) = normalize_cond_expr norm_ctx offsets defvars h in

      defvars, (t, norm_h) :: norm_q

    )

    hl (defvars, [])

and normalize_array_expr ?(alias=true) norm_ctx offsets defvars expr =

  (*Format.eprintf "normalize_array %B %a [%a]@." alias Printers.pp_expr expr (Utils.fprintf_list ~sep:"," Dimension.pp_dimension) offsets;*)

  match expr.expr_desc with

  | Expr_power (e1, d) when offsets = [] ->

     let defvars, norm_e1 = normalize_expr norm_ctx offsets defvars e1 in

     defvars, mk_norm_expr offsets expr (Expr_power (norm_e1, d))

  | Expr_power (e1, d) ->

     normalize_array_expr ~alias:alias norm_ctx (List.tl offsets) defvars e1

  | Expr_access (e1, d) -> normalize_array_expr ~alias:alias norm_ctx (d::offsets) defvars e1

  | Expr_array elist when offsets = [] ->

     let defvars, norm_elist = normalize_list alias norm_ctx offsets (fun _ -> normalize_array_expr ~alias:true) defvars elist in

     defvars, mk_norm_expr offsets expr (Expr_array norm_elist)

  | Expr_appl (id, args, None) when Basic_library.is_expr_internal_fun expr ->

     let defvars, norm_args = normalize_list alias norm_ctx offsets (fun _ -> normalize_array_expr ~alias:true) defvars (expr_list_of_expr args) in

     defvars, mk_norm_expr offsets expr (Expr_appl (id, expr_of_expr_list args.expr_loc norm_args, None))

  |  _ -> normalize_expr ~alias:alias norm_ctx offsets defvars expr

and normalize_cond_expr ?(alias=true) norm_ctx offsets defvars expr =

  (* Format.eprintf "normalize_cond %B %a [%a]@." alias Printers.pp_expr expr (Utils.fprintf_list ~sep:"," Dimension.pp_dimension) offsets; *)

  match expr.expr_desc with

  | Expr_access (e1, d) ->

     normalize_cond_expr ~alias:alias norm_ctx (d::offsets) defvars e1

  | Expr_ite (c, t, e) ->

     let defvars, norm_c = normalize_guard norm_ctx defvars c in

     let defvars, norm_t = normalize_cond_expr norm_ctx offsets defvars t in

     let defvars, norm_e = normalize_cond_expr norm_ctx offsets defvars e in

     defvars, mk_norm_expr offsets expr (Expr_ite (norm_c, norm_t, norm_e))

  | Expr_merge (c, hl) ->

     let defvars, norm_hl = normalize_branches norm_ctx offsets defvars hl in

     defvars, mk_norm_expr offsets expr (Expr_merge (c, norm_hl))

  | _ when !params.force_alias_ite ->

     (* Forcing alias creation for then/else expressions *)

     let defvars, norm_expr =

       normalize_expr ~alias:alias norm_ctx offsets defvars expr

     in

     mk_expr_alias_opt true norm_ctx defvars norm_expr

  | _ -> (* default case without the force_alias_ite option *)

     normalize_expr ~alias:alias norm_ctx offsets defvars expr

and normalize_guard norm_ctx defvars expr =

  let defvars, norm_expr = normalize_expr ~alias_basic:true norm_ctx [] defvars expr in

  mk_expr_alias_opt true norm_ctx defvars norm_expr

(* outputs cannot be memories as well. If so, introduce new local variable.

*)

let decouple_outputs norm_ctx defvars eq =

  let rec fold_lhs defvars lhs tys cks =

    match lhs, tys, cks with

    | [], [], []          -> defvars, []

    | v::qv, t::qt, c::qc -> let (defs_q, vars_q), lhs_q = fold_lhs defvars qv qt qc in

			     if norm_ctx.is_output v

			     then

			       let newvar = mk_fresh_var (norm_ctx.parentid, norm_ctx.vars) eq.eq_loc t c in

			       let neweq  = mkeq eq.eq_loc ([v], expr_of_vdecl newvar) in

			       (neweq :: defs_q, newvar :: vars_q), newvar.var_id :: lhs_q

			     else

			       (defs_q, vars_q), v::lhs_q

    | _                   -> assert false in

  let defvars', lhs' =

    fold_lhs

      defvars

      eq.eq_lhs

      (Types.type_list_of_type eq.eq_rhs.expr_type)

      (Clocks.clock_list_of_clock eq.eq_rhs.expr_clock) in

  defvars', {eq with eq_lhs = lhs' }

let rec normalize_eq norm_ctx defvars eq =

(*Format.eprintf "normalize_eq %a@." Types.print_ty eq.eq_rhs.expr_type;*)

  match eq.eq_rhs.expr_desc with

  | Expr_pre _

  | Expr_fby _  ->

    let (defvars', eq') = decouple_outputs norm_ctx defvars eq in

    let (defs', vars'), norm_rhs = normalize_expr ~alias:false norm_ctx [] defvars' eq'.eq_rhs in

    let norm_eq = { eq' with eq_rhs = norm_rhs } in

    (norm_eq::defs', vars')

  | Expr_array _ ->

    let (defs', vars'), norm_rhs = normalize_array_expr ~alias:false norm_ctx [] defvars eq.eq_rhs in

    let norm_eq = { eq with eq_rhs = norm_rhs } in

    (norm_eq::defs', vars')

  | Expr_appl (id, _, None) when Basic_library.is_homomorphic_fun id && Types.is_array_type eq.eq_rhs.expr_type ->

    let (defs', vars'), norm_rhs = normalize_array_expr ~alias:false norm_ctx [] defvars eq.eq_rhs in

    let norm_eq = { eq with eq_rhs = norm_rhs } in

    (norm_eq::defs', vars')

  | Expr_appl _ ->

    let (defs', vars'), norm_rhs = normalize_expr ~alias:false norm_ctx [] defvars eq.eq_rhs in

    let norm_eq = { eq with eq_rhs = norm_rhs } in

    (norm_eq::defs', vars')

  | _ ->

    let (defs', vars'), norm_rhs = normalize_cond_expr ~alias:false norm_ctx [] defvars eq.eq_rhs in

    let norm_eq = { eq with eq_rhs = norm_rhs } in

    norm_eq::defs', vars'

let normalize_eq_split norm_ctx defvars eq =

  try

    let defs, vars = normalize_eq norm_ctx defvars eq in

    List.fold_right (fun eq (def, vars) -> 

        let eq_defs = Splitting.tuple_split_eq eq in

        if eq_defs = [eq] then

          eq::def, vars 

        else

          List.fold_left (normalize_eq norm_ctx) (def, vars) eq_defs

      ) defs ([], vars)  

  with ex -> (

    Format.eprintf "Issue normalizing eq split: %a@." Printers.pp_node_eq eq;

    raise ex

  )

(* Projecting an eexpr to an eexpr associated to a single

   variable. Returns the updated ee, the bounded variable and the

   associated statement *)

let normalize_pred_eexpr decls norm_ctx (def,vars) ee =

  assert (ee.eexpr_quantifiers = []); (* We do not normalize quantifiers yet. This is for very far future. *)

  (* don't do anything is eexpr is just a variable *)

  let skip =

    match ee.eexpr_qfexpr.expr_desc with

    | Expr_ident _ | Expr_const _ -> true

    | _ -> false

  in

  if skip then

    ee, (def, vars)

  else (

    (* New output variable *)

    let output_id = "spec" ^ string_of_int ee.eexpr_tag in

    let output_var = 

      mkvar_decl 

        ee.eexpr_loc 

        (output_id, 

         mktyp ee.eexpr_loc Tydec_bool, (* It is a predicate, hence a bool *)

         mkclock ee.eexpr_loc Ckdec_any, 

         false (* not a constant *),

         None,

         None

        ) 

    in

    let output_expr = expr_of_vdecl output_var in

    (* Rebuilding an eexpr with a silly expression, just a variable *)

    let ee' = { ee with eexpr_qfexpr = output_expr } in

    (* Now processing a fresh equation output_id = eexpr_qfexpr. We

       inline possible calls within, normalize it and type/clock the

       result.  *)

    let eq = mkeq ee.eexpr_loc ([output_id], ee.eexpr_qfexpr) in

    (* (\* Inlining any calls *\)

     * let nodes = get_nodes decls in

     * let calls = ISet.elements (get_expr_calls nodes ee.eexpr_qfexpr) in

     * let vars, eqs =

     *   if calls = [] && not (eq_has_arrows eq) then

     *     vars, [eq]    

     *   else

     *     assert false (\* TODO *\)

     * in *)

    (* Normalizing expr and eqs *)

    let defs, vars = List.fold_left (normalize_eq_split norm_ctx) (def, vars) [eq] in

    let vars = output_var :: vars in 

(*    let todefine =

      List.fold_left

        (fun m x-> if List.exists (fun y-> x.var_id = y.var_id) (locals) then m else ISet.add x.var_id m)

        (ISet.add output_id ISet.empty) vars in

 *)      

    (* Typing / Clocking *)

    try

      ignore (Typing.type_var_decl_list vars !Global.type_env vars);

        (*

    let env = Typing.type_var_decl [] !Global.type_env xxxx output_var in (* typing the variable *)

    (* Format.eprintf "typing var %s: %a@." output_id Types.print_ty output_var.var_type; *)

    let env = Typing.type_var_decl_list (vars@node.node_outputs@node.node_inputs) env (vars@node.node_outputs@node.node_inputs) in

    (*Format.eprintf "Env: %a@.@?" (Env.pp_env Types.print_ty) env;*)

    let undefined_vars = List.fold_left (Typing.type_eq (env, quant_vars@vars) false) todefine defs in

  (* check that table is empty *)

    if (not (ISet.is_empty undefined_vars)) then

      raise (Types.Error (ee.eexpr_loc, Types.Undefined_var undefined_vars));

    (*Format.eprintf "normalized eqs %a@.@?" 

      (Utils.fprintf_list ~sep:", " Printers.pp_node_eq) defs;  *)

         *)

    ee', (defs, vars)

  with (Types.Error (loc,err)) as exc ->

    eprintf "Typing error for eexpr %a: %a%a%a@."

      Printers.pp_eexpr ee

      Types.pp_error err

      (Utils.fprintf_list ~sep:", " Printers.pp_node_eq) defs

      Location.pp_loc loc

    ;

    raise exc

  )

   (*

  let quant_vars = List.flatten (List.map snd ee.eexpr_quantifiers) in

  (* Calls are first inlined *)

  (*Format.eprintf "eexpr %a@.calls: %a@.@?" Printers.pp_eexpr ee (Utils.fprintf_list ~sep:", " (fun fmt nd -> pp_print_string fmt nd.node_id)) calls;  *)

  let (new_locals, eqs) =

    if calls = [] && not (eq_has_arrows eq) then

      (locals, [eq])     

    else ( (* TODO remettre le code. Je l'ai enleve pour des dependances cycliques *)

(*      let new_locals, eqs, asserts = Inliner.inline_eq ~arrows:true eq locals calls in

      (*Format.eprintf "eqs %a@.@?" 

	(Utils.fprintf_list ~sep:", " Printers.pp_node_eq) eqs;  *)

      (new_locals, eqs)

*)

           (locals, [eq])     

    ) in

  (* Normalizing expr and eqs *)

    let defs, vars = List.fold_left (normalize_eq_split node) ([], new_locals) eqs in

    let todefine = List.fold_left

    (fun m x-> if List.exists (fun y-> x.var_id = y.var_id) (locals) then m else ISet.add x.var_id m)

    (ISet.add output_id ISet.empty) vars in

  try

    let env = Typing.type_var_decl_list quant_vars !Global.type_env quant_vars in

    let env = Typing.type_var_decl [] env output_var in (* typing the variable *)

    (* Format.eprintf "typing var %s: %a@." output_id Types.print_ty output_var.var_type; *)

    let env = Typing.type_var_decl_list (vars@node.node_outputs@node.node_inputs) env (vars@node.node_outputs@node.node_inputs) in

    (*Format.eprintf "Env: %a@.@?" (Env.pp_env Types.print_ty) env;*)

    let undefined_vars = List.fold_left (Typing.type_eq (env, quant_vars@vars) false) todefine defs in

  (* check that table is empty *)

    if (not (ISet.is_empty undefined_vars)) then

      raise (Types.Error (ee.eexpr_loc, Types.Undefined_var undefined_vars));

    (*Format.eprintf "normalized eqs %a@.@?" 

      (Utils.fprintf_list ~sep:", " Printers.pp_node_eq) defs;  *)

    ee.eexpr_normalized <- Some (output_var, defs, vars)

  with (Types.Error (loc,err)) as exc ->

    eprintf "Typing error for eexpr %a: %a%a%a@."

      Printers.pp_eexpr ee

      Types.pp_error err

      (Utils.fprintf_list ~sep:", " Printers.pp_node_eq) defs

      Location.pp_loc loc

    ;

    raise exc

                                                 *)    

(* We use node local vars to make sure we are creating fresh variables *) 

let normalize_spec decls parentid (in_vars, out_vars, l_vars) s =  

  (* Original set of variables actually visible from here: in/out and

     spec locals (no node locals) *)

  let orig_vars = in_vars @ out_vars @ s.locals in

  (* Format.eprintf "NormSpec: init locals: %a@." Printers.pp_vars s.locals; *)

  let not_is_orig_var v =

    List.for_all ((!=) v) orig_vars in

  let norm_ctx = {

      parentid = parentid;

      vars = in_vars @ out_vars @ l_vars;

      is_output = (fun _ -> false) (* no need to introduce fresh variables for outputs *);

    }

  in

  (* Normalizing existing stmts *)

  let eqs, auts = List.fold_right (fun s (el,al)  -> match s with Eq e -> e::el, al | Aut a -> el, a::al) s.stmts ([], []) in

  if auts != [] then assert false; (* Automata should be expanded by now. *)

  let defsvars = 

    List.fold_left (normalize_eq norm_ctx) ([], orig_vars) eqs

  in

  (* Iterate through predicates and normalize them on the go, creating

     fresh variables for any guarantees/assumes/require/ensure *)

  let process_predicates l defvars =

    (* Format.eprintf "ProcPred: vars: %a@." Printers.pp_vars (snd defvars); *)

    let res = List.fold_right (fun ee (accu, defvars) ->

        let ee', defvars = normalize_pred_eexpr decls norm_ctx defvars ee in

        ee'::accu, defvars

      ) l ([], defvars)

    in

    (* Format.eprintf "ProcStmt: %a@." Printers.pp_node_eqs (fst (snd res));

     * Format.eprintf "ProcPred: vars: %a@." Printers.pp_vars (snd (snd res)); *)

    res

  in

  let assume', defsvars = process_predicates s.assume defsvars in

  let guarantees', defsvars = process_predicates s.guarantees defsvars in

  let modes', (defs, vars) =

    List.fold_right (

        fun m (accu_m, defsvars) ->

        let require', defsvars = process_predicates m.require defsvars in

        let ensure', defsvars = process_predicates m.ensure defsvars in

        { m with require = require'; ensure = ensure' }:: accu_m, defsvars

      ) s.modes ([], defsvars)

  in

  let new_locals = List.filter not_is_orig_var vars in (* removing inouts and initial locals ones *)

  new_locals, defs,      

  {s with

    (* locals = s.locals @ new_locals; *)

    stmts = [];

    assume = assume';

    guarantees = guarantees';

    modes = modes'

  }

(* let nee _ = () in

 *   (\*normalize_eexpr decls iovars in *\)

 *   List.iter nee s.assume;

 *   List.iter nee s.guarantees;

 *   List.iter (fun m -> 

 *       List.iter nee m.require;

 *     List.iter nee m.ensure

 *     ) s.modes; *)

(* The normalization phase introduces new local variables

   - output cannot be memories. If this happen, new local variables acting as

   memories are introduced. 

   - array constants, pre, arrow, fby, ite, merge, calls to node with index

   access

   Thoses values are shared, ie. no duplicate expressions are introduced.

   Concerning specification, a similar process is applied, replacing an

   expression by a list of local variables and definitions

*)

(** normalize_node node returns a normalized node, 

    ie. 

    - updated locals

    - new equations

    -

*)

let normalize_node decls node =

  reset_cpt_fresh ();

  let orig_vars = node.node_inputs@node.node_outputs@node.node_locals in

  let not_is_orig_var v =

    List.for_all ((!=) v) orig_vars in

  let norm_ctx = {

      parentid = node.node_id;

      vars = get_node_vars node;

      is_output = (fun vid -> List.exists (fun v -> v.var_id = vid) node.node_outputs);

    }

  in

  let eqs, auts = get_node_eqs node in

  if auts != [] then assert false; (* Automata should be expanded by now. *)

  let spec, new_vars, eqs =

    begin

      (* Update mutable fields of eexpr to perform normalization of

	 specification.

	 Careful: we do not normalize annotations, since they can have the form

	 x = (a, b, c) *)

      match node.node_spec with

      | None 

        | Some (NodeSpec _) -> node.node_spec, [], eqs

      | Some (Contract s) ->

         let new_locals, new_stmts, s' = normalize_spec

                    decls

                    node.node_id

                    (node.node_inputs, node.node_outputs, node.node_locals)

                    s

         in

         (* Format.eprintf "Normalization bounded new locals: %a@." Printers.pp_vars new_locals;

          * Format.eprintf "Normalization bounded stmts: %a@." Printers.pp_node_eqs new_stmts; *)

         Some (Contract s'), new_locals, new_stmts@eqs

    end

  in

  let defs, vars =

    List.fold_left (normalize_eq norm_ctx) ([], new_vars@orig_vars) eqs in

  (* Normalize the asserts *)

  let vars, assert_defs, asserts =

    List.fold_left (

        fun (vars, def_accu, assert_accu) assert_ ->

	let assert_expr = assert_.assert_expr in

	let (defs, vars'), expr = 

	  normalize_expr 

	    ~alias:true (* forcing introduction of new equations for fcn calls *) 

	    norm_ctx 

	    [] (* empty offset for arrays *)

	    ([], vars) (* defvar only contains vars *)

	    assert_expr

	in

        (*Format.eprintf "New assert vars: %a@.@?" (fprintf_list ~sep:", " Printers.pp_var) vars';*)

	vars', defs@def_accu, {assert_ with assert_expr = expr}::assert_accu

      ) (vars, [], []) node.node_asserts in

  let new_locals = List.filter not_is_orig_var vars in (* we filter out inout

							  vars and initial locals ones *)

  let all_locals = node.node_locals @ new_locals in (* we add again, at the

						       beginning of the list the

						       local declared ones *)

  (*Format.eprintf "New locals: %a@.@?" (fprintf_list ~sep:", " Printers.pp_var) new_locals;*)

  (* Updating annotations: traceability and machine types for fresh variables *)

  (* Compute traceability info:

     - gather newly bound variables

     - compute the associated expression without aliases

   *)

  let new_annots =

    if !Options.traces then

      begin

	let diff_vars = List.filter (fun v -> not (List.mem v node.node_locals) ) all_locals in

	let norm_traceability = {

	    annots = List.map (fun v ->

	                 let eq =

	                   try

		             List.find (fun eq -> List.exists (fun v' -> v' = v.var_id ) eq.eq_lhs) (defs@assert_defs) 

	                   with Not_found -> 

		             (

		               Format.eprintf "Traceability annotation generation: var %s not found@." v.var_id; 

		               assert false

		             ) 

	                 in

	                 let expr = substitute_expr diff_vars (defs@assert_defs) eq.eq_rhs in

	                 let pair = mkeexpr expr.expr_loc (mkexpr expr.expr_loc (Expr_tuple [expr_of_ident v.var_id expr.expr_loc; expr])) in

	                 Annotations.add_expr_ann node.node_id pair.eexpr_tag ["traceability"];

	                 (["traceability"], pair)

	               ) diff_vars;

	    annot_loc = Location.dummy_loc

	  }

	in

	norm_traceability::node.node_annot

      end

    else

      node.node_annot

  in

  let new_annots =

    List.fold_left (fun annots v ->

        if Machine_types.is_active && Machine_types.is_exportable v then

	  let typ = Machine_types.get_specified_type v in

  	  let typ_name = Machine_types.type_name typ in

	  let loc = v.var_loc in

	  let typ_as_string =

	    mkexpr

	      loc

	      (Expr_const

	         (Const_string typ_name))

	  in

	  let pair = expr_to_eexpr (expr_of_expr_list loc [expr_of_vdecl v; typ_as_string]) in

	  Annotations.add_expr_ann node.node_id pair.eexpr_tag Machine_types.keyword;

	  {annots = [Machine_types.keyword, pair]; annot_loc = loc}::annots

        else