CristalCaveGem » LustreC

open Lustre_types

open Utils

open Seal_utils			

open Zustre_data (* Access to Z3 context *)

(* Switched system extraction: expression are memoized *)

(*let expr_mem = Hashtbl.create 13*)

let add_init defs vid =

  Hashtbl.add defs vid [[], IsInit]

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

(* Convert from Lustre expressions to Z3 expressions and back *)

(* All (free) variables have to be declared in the Z3 context *)

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

let is_init_name = "__is_init"

let const_defs = Hashtbl.create 13

let is_const id = Hashtbl.mem const_defs id

let is_enum_const id = Hashtbl.mem Zustre_data.const_tags id  

let get_const id = Hashtbl.find const_defs id

(* expressions are only basic constructs here, no more ite, tuples,

   arrows, fby, ... *)

(* Set of hash to support memoization *)

let expr_hash: (expr * Utils.tag) list ref = ref []

let ze_hash: (Z3.Expr.expr, Utils.tag) Hashtbl.t = Hashtbl.create 13

let e_hash: (Utils.tag, Z3.Expr.expr) Hashtbl.t = Hashtbl.create 13

let pp_hash pp_key pp_v fmt h = Hashtbl.iter (fun key v -> Format.fprintf fmt "%a -> %a@ " pp_key key pp_v v) h

let pp_e_map fmt = List.iter (fun (e,t) -> Format.fprintf fmt "%i -> %a@ " t Printers.pp_expr e) !expr_hash

let pp_ze_hash fmt = pp_hash

                      (fun fmt e -> Format.fprintf fmt "%s" (Z3.Expr.to_string e))

                      Format.pp_print_int

                      fmt

                      ze_hash

let pp_e_hash fmt = pp_hash

                      Format.pp_print_int

                      (fun fmt e -> Format.fprintf fmt "%s" (Z3.Expr.to_string e))

                      fmt

                      e_hash                              

let mem_expr e =

  (* Format.eprintf "Searching for %a in map: @[<v 0>%t@]"

   *   Printers.pp_expr e

   *   pp_e_map; *)

  let res = List.exists (fun (e',_) -> Corelang.is_eq_expr e e') !expr_hash in

  (* Format.eprintf "found?%b@." res; *)

  res

let mem_zexpr ze =

  Hashtbl.mem ze_hash ze

let get_zexpr e =

  let eref, uid = List.find (fun (e',_) -> Corelang.is_eq_expr e e') !expr_hash in

  (* Format.eprintf "found expr=%a id=%i@." Printers.pp_expr eref eref.expr_tag; *)

  Hashtbl.find e_hash uid

let get_expr ze =

  let uid = Hashtbl.find ze_hash ze in

  let e,_ = List.find (fun (e,t) -> t = uid) !expr_hash in

  e

let neg_ze z3e = Z3.Boolean.mk_not !ctx z3e 

let is_init_z3e =

  Z3.Expr.mk_const_s !ctx is_init_name  Zustre_common.bool_sort 

let get_zid (ze:Z3.Expr.expr) : Utils.tag = 

  try

    if Z3.Expr.equal ze is_init_z3e then -1 else

      if Z3.Expr.equal ze (neg_ze is_init_z3e) then -2 else

    Hashtbl.find ze_hash ze

  with _ -> (Format.eprintf "Looking for ze %s in Hash %a"

               (Z3.Expr.to_string ze)

               (fun fmt hash -> Hashtbl.iter (fun ze uid -> Format.fprintf fmt "%s -> %i@ " (Z3.Expr.to_string ze) uid) hash ) ze_hash;

             assert false)

let add_expr =

  let cpt = ref 0 in

  fun e ze ->

  incr cpt;

  let uid = !cpt in

  expr_hash := (e, uid)::!expr_hash;

  Hashtbl.add e_hash uid ze;

  Hashtbl.add ze_hash ze uid

let expr_to_z3_expr, zexpr_to_expr =

  (* List to store converted expression. *)

  (* let hash = ref [] in

   * let comp_expr e (e', _) = Corelang.is_eq_expr e e' in

   * let comp_zexpr ze (_, ze') = Z3.Expr.equal ze ze' in *)

  let rec e2ze e =

    if mem_expr e then (

      get_zexpr e

    )

    else (

      let res =

        match e.expr_desc with

        | Expr_const c ->

           let z3e = Zustre_common.horn_const_to_expr c in

           add_expr e z3e;

           z3e

        | Expr_ident id -> (

          if is_const id then (

            let c = get_const id in

            let z3e = Zustre_common.horn_const_to_expr c in

            add_expr e z3e;

            z3e

          )

          else if is_enum_const id then (

            let z3e = Zustre_common.horn_tag_to_expr id in

            add_expr e z3e;

            z3e

          )

          else (

            let fdecl_id = Zustre_common.get_fdecl id in

            let z3e = Z3.Expr.mk_const_f !ctx fdecl_id in

            add_expr e z3e;

            z3e

          )

        )

        | Expr_appl (id,args, None) (* no reset *) ->

           let z3e = Zustre_common.horn_basic_app id e2ze (Corelang.expr_list_of_expr args) in

           add_expr e z3e;

           z3e

        | Expr_tuple [e] ->

           let z3e = e2ze e in

           add_expr e z3e;

           z3e

        | _ -> ( match e.expr_desc with Expr_tuple _ -> Format.eprintf "tuple e2ze(%a)@.@?" Printers.pp_expr e

                                      | _ -> Format.eprintf "e2ze(%a)@.@?" Printers.pp_expr e)

             ; assert false

      in

      res

    )

  in

  let rec ze2e ze =

    let ze_name ze =

      let fd = Z3.Expr.get_func_decl ze in

      Z3.Symbol.to_string (Z3.FuncDecl.get_name fd)

    in

    if mem_zexpr ze then

      None, Some (get_expr ze)

    else

      let open Corelang in

      let fd = Z3.Expr.get_func_decl ze in

      let zel = Z3.Expr.get_args ze in

      match Z3.Symbol.to_string (Z3.FuncDecl.get_name fd), zel with

      (*      | var, [] -> (* should be in env *) get_e *)

      (* Extracting IsInit status *)

      | "not", [ze] when ze_name ze = is_init_name ->

         Some false, None

      | name, [] when name = is_init_name -> Some true, None

      (* Other constructs are converted to a lustre expression *)

      | op, _ -> (

        if Z3.Expr.is_numeral ze then

          let e =

            if Z3.Arithmetic.is_real ze then

              let num =  Num.num_of_ratio (Z3.Arithmetic.Real.get_ratio ze) in

              let s = Z3.Arithmetic.Real.numeral_to_string ze in

              mkexpr

                Location.dummy_loc

                (Expr_const

                   (Const_real

                      (num, 0, s)))

            else if Z3.Arithmetic.is_int ze then

              mkexpr

                Location.dummy_loc

                (Expr_const

                   (Const_int

                      (Big_int.int_of_big_int (Z3.Arithmetic.Integer.get_big_int ze))))

            else if Z3.Expr.is_const ze then

              match Z3.Expr.to_string ze with

              | "true" -> mkexpr Location.dummy_loc

                            (Expr_const (Const_tag (tag_true)))

              | "false" ->

                 mkexpr Location.dummy_loc

                   (Expr_const (Const_tag (tag_false)))

              | _ -> assert false

            else

              (

                Format.eprintf "Const err: %s %b@." (Z3.Expr.to_string ze) (Z3.Expr.is_const ze);

                assert false (* a numeral but no int nor real *)

              )

          in

          None, Some e

        else

          match op with

          | "not" | "=" | "-" | "*" | "/"

            | ">=" | "<=" | ">" | "<" 

            ->

             let args = List.map (fun ze -> Utils.desome (snd (ze2e ze))) zel in

             None, Some (mkpredef_call Location.dummy_loc op args)

          | "+" -> ( (* Special treatment of + for 2+ args *)

            let args = List.map (fun ze -> Utils.desome (snd (ze2e ze))) zel in

            let e = match args with

                [] -> assert false

              | [hd] -> hd

              | e1::e2::tl ->

                 let first_binary_and = mkpredef_call Location.dummy_loc op [e1;e2] in

                 if tl = [] then first_binary_and else

                   List.fold_left (fun e e_new ->

                       mkpredef_call Location.dummy_loc op [e;e_new]

                     ) first_binary_and tl

            in

            None, Some e 

          )

          | "and" | "or" -> (

            (* Special case since it can contain is_init pred *)

            let args = List.map (fun ze -> ze2e ze) zel in

            let op = if op = "and" then "&&" else if op = "or" then "||" else assert false in 

            match args with

            | [] -> assert false

            | [hd] -> hd

            | hd::tl ->

               List.fold_left

                 (fun (is_init_opt1, expr_opt1) (is_init_opt2, expr_opt2) ->

                   (match is_init_opt1, is_init_opt2 with

                      None, x | x, None -> x

                      | Some _, Some _ -> assert false),

                   (match expr_opt1, expr_opt2 with

                    | None, x | x, None -> x

                    | Some e1, Some e2 ->

                       Some (mkpredef_call Location.dummy_loc op [e1; e2])

                 ))

                 hd tl 

          )

          | op -> 

             let args = List.map (fun ze ->  (snd (ze2e ze))) zel in

             Format.eprintf "deal with op %s (nb args: %i). Expr is %s@."  op (List.length args) (Z3.Expr.to_string ze); assert false

      )

  in

  (fun e -> e2ze e), (fun ze -> ze2e ze)

let zexpr_to_guard_list ze =

  let init_opt, expr_opt = zexpr_to_expr ze in

  (match init_opt with

   | None -> []

   |Some b -> [IsInit, b]

  ) @ (match expr_opt with

       | None -> []

       | Some e -> [Expr e, true]

      )

let simplify_neg_guard l =

  List.map (fun (g,posneg) ->

      match g with

      | IsInit -> g, posneg

      | Expr g ->

          if posneg then

            Expr (Corelang.push_negations g),

            true

          else

            (* Pushing the negation in the expression *)

            Expr(Corelang.push_negations ~neg:true g),

            true

    ) l 

(* TODO:

individuellement demander si g1 => g2. Si c'est le cas, on peut ne garder que g1 dans la liste

*)    

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

(* Checking sat(isfiability) of an expression and simplifying it *)

(* All (free) variables have to be declared in the Z3 context    *)

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

(*

let goal_simplify zl =

  let goal = Z3.Goal.mk_goal !ctx false false false in

  Z3.Goal.add goal zl;

  let goal' = Z3.Goal.simplify goal None in

  (* Format.eprintf "Goal before: %s@.Goal after : %s@.Sat? %s@."

   *   (Z3.Goal.to_string goal)

   *   (Z3.Goal.to_string goal')

   *   (Z3.Solver.string_of_status status_res) 

   * ; *)

  let ze = Z3.Goal.as_expr goal' in

  (* Format.eprintf "as an expr: %s@." (Z3.Expr.to_string ze); *)

  zexpr_to_guard_list ze

  *)

let implies =

  let ze_implies_hash : ((Utils.tag * Utils.tag), bool) Hashtbl.t  = Hashtbl.create 13 in

  fun ze1 ze2 ->

  let ze1_uid = get_zid ze1 in

  let ze2_uid = get_zid ze2 in

  if Hashtbl.mem ze_implies_hash (ze1_uid, ze2_uid) then

    Hashtbl.find ze_implies_hash (ze1_uid, ze2_uid)

  else

    begin

      if !seal_debug then (

        report ~level:6 (fun fmt -> Format.fprintf fmt "Checking implication: %s => %s?@ "

          (Z3.Expr.to_string ze1) (Z3.Expr.to_string ze2)

      )); 

      let solver = Z3.Solver.mk_simple_solver !ctx in

      let tgt = Z3.Boolean.mk_not !ctx (Z3.Boolean.mk_implies !ctx ze1 ze2) in

      let res =

        try

          let status_res = Z3.Solver.check solver [tgt] in

          match status_res with

          | Z3.Solver.UNSATISFIABLE -> if !seal_debug then

                                         report ~level:6 (fun fmt -> Format.fprintf fmt "Valid!@ "); 

             true

          | _ -> if !seal_debug then report ~level:6 (fun fmt -> Format.fprintf fmt "not proved valid@ "); 

             false

        with Zustre_common.UnknownFunction(id, msg) -> (

          report ~level:1 msg;

          false

        )

      in

      Hashtbl.add ze_implies_hash (ze1_uid,ze2_uid) res ;

      res

    end

let rec simplify zl =

  match zl with

  | [] | [_] -> zl

  | hd::tl -> (

    (* Forall e in tl, checking whether hd => e or e => hd, to keep hd

     in the first case and e in the second one *)

    let tl = simplify tl in

    let keep_hd, tl =

      List.fold_left (fun (keep_hd, accu) e ->

          if implies hd e then

            true, accu (* throwing away e *)

          else if implies e hd then

            false, e::accu (* throwing away hd *)

          else

            keep_hd, e::accu (* keeping both *)

        ) (true,[]) tl

    in

    (* Format.eprintf "keep_hd?%b hd=%s, tl=[%a]@."

     *   keep_hd

     *   (Z3.Expr.to_string hd)

     * (Utils.fprintf_list ~sep:"; " (fun fmt e -> Format.fprintf fmt "%s" (Z3.Expr.to_string e))) tl

     *   ; *)

    if keep_hd then

      hd::tl

    else

      tl

  )

let check_sat ?(just_check=false) (l: elem_boolexpr guard) : bool * (elem_boolexpr guard) =

  (* Syntactic simplification *)

  if false then

    Format.eprintf "Before simplify: %a@." (pp_guard_list pp_elem) l; 

  let l = simplify_neg_guard l in

  if false then (

    Format.eprintf "After simplify: %a@." (pp_guard_list pp_elem) l; 

    Format.eprintf "@[<v 2>Z3 check sat: [%a]@ " (pp_guard_list pp_elem)l;

  );

  let solver = Z3.Solver.mk_simple_solver !ctx in

  try (

    let zl =

      List.map (fun (e, posneg) ->

          let ze =

            match e with

            | IsInit -> is_init_z3e

            | Expr e -> expr_to_z3_expr e 

          in

          if posneg then

            ze

          else

            neg_ze ze

        ) l

    in

    if false then Format.eprintf "Z3 exprs1: [%a]@ " (fprintf_list ~sep:",@ " (fun fmt e -> Format.fprintf fmt "%s" (Z3.Expr.to_string e))) zl; 

    let zl = simplify zl in

        if false then Format.eprintf "Z3 exprs2: [%a]@ " (fprintf_list ~sep:",@ " (fun fmt e -> Format.fprintf fmt "%s" (Z3.Expr.to_string e))) zl; 

    let status_res = Z3.Solver.check solver zl in

     if false then Format.eprintf "Z3 status: %s@ @]@. " (Z3.Solver.string_of_status status_res); 

    match status_res with

    | Z3.Solver.UNSATISFIABLE -> false, []

    | _ -> (

      if false && just_check then

        true, l

      else

        (* TODO: may be reactivate but it may create new expressions *)

        (* let l = goal_simplify zl in *)

        let l = List.fold_left

                  (fun accu ze -> accu @ (zexpr_to_guard_list ze))

                  []

                  zl

        in

  (* Format.eprintf "@.@[<v 2>Check_Sat:@ before: %a@ after:

       %a@. Goal precise? %b/%b@]@.@. " * pp_guard_list l

       pp_guard_list l' * (Z3.Goal.is_precise goal) *

       (Z3.Goal.is_precise goal'); *)

        true, l

    )

  )

  with Zustre_common.UnknownFunction(id, msg) -> (

    report ~level:1 msg;

    true, l (* keeping everything. *)

  )

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

let clean_sys sys =

  List.fold_left (fun accu (guards, updates) ->

      let sat, guards' =  check_sat (List.map (fun (g, pn) -> Expr g, pn) guards) in

      (*Format.eprintf "Guard: %a@.Guard cleaned: %a@.Sat? %b@."

        (fprintf_list ~sep:"@ " (pp_guard_expr Printers.pp_expr))  guards

        (fprintf_list ~sep:"@ " (pp_guard_expr Printers.pp_expr))  guards'

        sat

      ;*)

        if sat then

        (List.map (fun (e, b) -> (deelem e, b)) guards', updates)::accu

      else

        accu

    )

    [] sys

(* Most costly function: has the be efficiently implemented.  All

   registered guards are initially produced by the call to

   combine_guards. We csan normalize the guards to ease the

   comparisons.

   We assume that gl1 and gl2 are already both satisfiable and in a

   kind of reduced form. Let lshort and llong be the short and long

   list of gl1, gl2. We check whether each element elong of llong is

   satisfiable with lshort. If no, stop. If yes, we search to reduce

   the list. If elong => eshort_i, we can remove eshort_i from

   lshort. we can continue with this lshort shortened, lshort'; it is

   not necessary to add yet elong in lshort' since we already know

   rthat elong is somehow reduced with respect to other elements of

   llong. If eshort_i => elong, then we keep ehosrt_i in lshort and do

   not store elong.

   After iterating through llong, we have a shortened version of

   lshort + some elements of llong that have to be remembered. We add

   them to this new consolidated list. 

 *)

(* combine_guards ~fresh:Some(e,b) gl1 gl2 returns ok, gl with ok=true

   when (e=b) ang gl1 and gl2 is satisfiable and gl is a consilidated

   version of it.  *)

let combine_guards ?(fresh=None) gl1 gl2 =

  (* Filtering out trivial cases. More semantics ones would have to be

     addressed later *)

  let check_sat e = (* temp function before we clean the original one *)

    let ok, _ = check_sat e in

    ok

  in

  let implies (e1,pn1) (e2,pn2) =

    let e2z e pn =

      match e with

        | IsInit -> if pn then is_init_z3e else neg_ze is_init_z3e

        | Expr e -> expr_to_z3_expr (if pn then e else (Corelang.push_negations ~neg:true e))

      in

    implies (e2z e1 pn1) (e2z e2 pn2)

  in

  let lshort, llong =

    if List.length gl1 > List.length gl2 then gl2, gl1 else gl1, gl2

  in

  let merge long short =

    let short, long_sel, ok = 

    List.fold_left (fun (short,long_sel, ok) long_e ->

        if not ok then

          [],[], false (* Propagating unsat case *)

        else if check_sat (long_e::short) then

          let short, keep_long_e =

            List.fold_left (fun (accu_short, keep_long_e) eshort_i ->

                if not keep_long_e then (* shorten the algo *)

                  eshort_i :: accu_short, false

                else (* keep_long_e = true in the following *)

                  if implies eshort_i long_e then

                    (* First case is trying to remove long_e!

                     Since short is already normalized, we can remove

                     long_e. If later long_e is stronger than another

                     element of short, then necessarily eshort_i =>

                     long_e ->

                     that_other_element_of_short. Contradiction. *)

                    eshort_i::accu_short, false

                  else if implies long_e eshort_i then 

                    (* removing eshort_i, keeping long_e. *)

                    accu_short, true

                  else (* Not comparable, keeping both *)

                    eshort_i::accu_short, true

              )

              ([],true) (* Initially we assume that we will keep long_e *)

              short

          in

          if keep_long_e then

            short, long_e::long_sel, true

          else

            short, long_sel, true

        else

          [],[],false

      ) (short, [], true) long

    in

    ok, long_sel@short

  in

  let ok, l = match fresh with

    | None -> true, []

    | Some g -> merge [g] []

  in

  if not ok then

    false, []

  else

    let ok, lshort = merge lshort l in

    if not ok then

      false, []

    else

      merge llong lshort

(* Encode "If gel1=posneg then gel2":

   - Compute the combination of guarded exprs in gel1 and gel2:

     - Each guarded_expr in gel1 is transformed as a guard: the

       expression is associated to posneg.

     - Existing guards in gel2 are concatenated to that list of guards

     - We keep expr in the ge of gel2 as the legitimate expression 

 *)

let concatenate_ge gel1 posneg gel2 =

  let l, all_invalid =

    List.fold_left (

        fun (accu, all_invalid) (g2,e2) ->

        List.fold_left (

            fun (accu, all_invalid) (g1,e1) ->

            (* Format.eprintf "@[<v 2>Combining guards: (%a=%b) AND [%a] AND [%a]@ "

             *  pp_elem e1

             *  posneg

             *  pp_guard_list g1

             *  pp_guard_list g2; *)

            let ok, gl = combine_guards ~fresh:(Some(e1,posneg)) g1 g2 in

            (* Format.eprintf "@]@ Result is [%a]@ "

             *   pp_guard_list gl; *)

            if ok then

              (gl, e2)::accu, false

            else (

              accu, all_invalid

            )

          ) (accu, all_invalid) gel1

      ) ([], true) gel2

  in

  not all_invalid, l

(* Transform the guard expressions ge = [gl1, e1; gl2, e2;...] as

   [gl1, e1=id; gl2, e2=id; ...]  *)

let mk_ge_eq_id ge id =

  List.map

    (fun (gl, g_e) ->

      gl,

      if id = "true" then

        g_e

      else

        match g_e with

        | Expr g_e ->

           if id = "false" then

             Expr (Corelang.push_negations ~neg:true g_e)

           else  

             let loc = g_e.expr_loc in

             Expr(Corelang.mk_eq loc

                    g_e

                    (Corelang.expr_of_ident id loc))

        | _ -> assert false

    )  ge 

    (* Rewrite the expression expr, replacing any occurence of a variable

   by its definition.

     *)

let rec rewrite defs expr : elem_guarded_expr list =

  let rewrite = rewrite defs in

  let res =

    match expr.expr_desc with

    | Expr_appl (id, args, None) ->

       let args = rewrite args in

       List.map (fun (guards, e) ->

           guards,

           Expr (Corelang.mkexpr expr.expr_loc (Expr_appl(id, deelem e, None)))

         ) args 

    | Expr_const _  -> [[], Expr expr]

    | Expr_ident id ->

       if Hashtbl.mem defs id then

         Hashtbl.find defs id

       else

         (* id should be an input *)

         [[], Expr expr]

    | Expr_ite (g, e1, e2) ->

       let g = rewrite g and

           e1 = rewrite e1 and

           e2 = rewrite e2 in

       let ok_then, g_then = concatenate_ge g true e1 in

       let ok_else, g_else = concatenate_ge g false e2 in

       (if ok_then then g_then else [])@

         (if ok_else then g_else else [])

    | Expr_merge (g_id, branches) ->

       if Hashtbl.mem defs g_id then

         let g = Hashtbl.find defs g_id in

         (* Format.eprintf "Expr_merge %s = %a@." g_id (pp_mdefs pp_elem) g ; *)

         List.fold_left (fun accu (id, e) ->

             let g = mk_ge_eq_id g id in

             let e = rewrite e in

             let ok, g_eq_id = concatenate_ge g true e in

             if ok then g_eq_id@accu else accu

           ) [] branches

       else

         assert false (* g should be defined already *)

    | Expr_when (e, id, l) ->

       let e = rewrite e in

       let id_def = Hashtbl.find defs id in

       let clock = mk_ge_eq_id id_def l in

       let ok, new_ge = concatenate_ge clock true e in

       if ok then new_ge else []

    | Expr_arrow _ -> [[], IsInit] (* At this point the only arrow should be true -> false *)

    | Expr_tuple el ->

       (* Each expr is associated to its flatten guarded expr list *)

       let gell = List.map rewrite el in

       (* Computing all combinations: we obtain a list of guarded tuple *)

       let rec aux gell : (elem_boolexpr guard * expr list) list =

         match gell with

         | [] -> assert false (* Not happening *)

         | [gel] -> List.map (fun (g,e) -> g, [deelem e]) gel

         | gel::getl ->

            let getl = aux getl in

            List.fold_left (

                fun accu (g,e) ->

                List.fold_left (

                    fun accu (gl, minituple) ->

                    let is_compat, guard_comb = combine_guards g gl in

                    if is_compat then

                      let new_gt : elem_boolexpr guard * expr list = (guard_comb, (deelem e)::minituple) in

                      new_gt::accu

                    else

                      accu

                  ) accu getl

              ) [] gel

       in

       let gtuples = aux gell in

       (* Rebuilding the valid type: guarded expr list (with tuple exprs) *)

       List.map

         (fun (g,tuple) -> g, Expr (Corelang.mkexpr expr.expr_loc (Expr_tuple tuple)))

         gtuples

    | Expr_fby _

      | Expr_appl _

                  (* Should be removed by mormalization and inlining *)

      -> Format.eprintf "Pb expr: %a@.@?" Printers.pp_expr expr; assert false

    | Expr_array _ | Expr_access _ | Expr_power _

                                                (* Arrays not handled here yet *)

      -> assert false

    | Expr_pre _ -> (* Not rewriting mem assign *)

       assert false

  in

  (* Format.eprintf "Rewriting %a as [@[<v 0>%a@]]@ "

   *   Printers.pp_expr expr

   *   (Utils.fprintf_list ~sep:"@ "

   *        pp_guard_expr) res; *)

  res

and add_def defs vid expr =

  (* Format.eprintf "Add_def: %s = %a@."

   *   vid

   *   Printers.pp_expr expr; *)

  let vid_defs = rewrite defs expr in

  (* Format.eprintf "-> @[<v 0>%a@]@."

   *   (Utils.fprintf_list ~sep:"@ "

   *      (pp_guard_expr pp_elem)) vid_defs;   *)

  (* Format.eprintf "Add_def: %s = %a@. -> @[<v 0>%a@]@."

   *     vid

   *     Printers.pp_expr expr

   *     (

   *       (Utils.fprintf_list ~sep:"@ "

   *          pp_guard_expr)) vid_defs;  *)

  Hashtbl.add defs vid vid_defs

(* Takes a list of guarded exprs (ge) and a guard

returns the same list of ge splited into the ones where the guard is true and the ones where it is false. In both lists the associated ge do not mention that guard anymore.

When a given ge doesn't mention positively or negatively such guards, it is duplicated in both lists *)

let split_mdefs elem (mdefs: elem_guarded_expr list) =

  List.fold_left (

      fun (selected, left_out)

          ((guards, expr) as ge) ->

      (* select the element of guards that match the argument elem *)

      let sel, others_guards = List.partition (select_elem elem) guards in

      match sel with

      (* we extract the element from the list and add it to the

         appropriate list *)

      | [_, sel_status] ->

         if sel_status then

           (others_guards,expr)::selected, left_out

         else selected, (others_guards,expr)::left_out

      | [] -> (* no such guard exists, we have to duplicate the

              guard_expr in both lists *)

         ge::selected, ge::left_out

      | _ -> (

        Format.eprintf "@.Spliting list on elem %a.@.List:%a@."

          pp_elem elem

          (pp_mdefs pp_elem) mdefs;

        assert false (* more then one element selected. Should

                          not happen , or trival dead code like if

                              x then if not x then dead code *)

      )

    ) ([],[]) mdefs

let split_mem_defs

      (elem: element)

      (mem_defs: (ident * elem_guarded_expr list) list)

      :

      ((ident * elem_guarded_expr mdef_t) list) * ((ident * elem_guarded_expr mdef_t) list)

  =

  List.fold_right (fun (m,mdefs)

                       (accu_pos, accu_neg) ->

      let pos, neg =

        split_mdefs elem mdefs 

      in

      (m, pos)::accu_pos,

      (m, neg)::accu_neg

    ) mem_defs ([],[])

(* Split a list of mem_defs into init and step lists of guarded

   expressions per memory. *)

let split_init mem_defs =

  split_mem_defs IsInit mem_defs 

(* Previous version of the function: way too costly 

let pick_guard mem_defs : expr option =  

  let gel = List.flatten (List.map snd mem_defs) in

  let gl = List.flatten (List.map fst gel) in

  let all_guards =

    List.map (

        (* selecting guards and getting rid of boolean *)

        fun (e,b) ->

        match e with

        | Expr e -> e

        | _ -> assert false

      (* should have been filtered out

                                      yet *)

      ) gl

  in

  (* TODO , one could sort by occurence and provided the most common

     one *)

  try

  Some (List.hd all_guards)  

  with _ -> None

   *)

(* Returning the first non empty guard expression *)

let rec pick_guard mem_defs : expr option =

  match mem_defs with

  | [] -> None

  | (_, gel)::tl -> (

    let found =

      List.fold_left (fun found (g,_) ->

          if found = None then

            match g with

            | [] -> None

            | (Expr e, _)::_ -> Some e

            | (IsInit, _)::_ -> assert false (* should be removed already *)

          else

            found

        ) None gel

    in

    if found = None then pick_guard tl else found

  )

(* Transform a list of variable * guarded exprs into a list of guarded pairs (variable, expressions)

*)

let rec build_switch_sys

          (mem_defs : (Utils.ident * elem_guarded_expr list) list )

          prefix

        :

          ((expr * bool) list * (ident * expr) list ) list =

  if !seal_debug then

    report ~level:4 (fun fmt -> Format.fprintf fmt "@[<v 2>Build_switch with@ %a@]@."

                                  pp_all_defs

                                  mem_defs);

  (* if all mem_defs have empty guards, we are done, return prefix,

     mem_defs expr.

     otherwise pick a guard in one of the mem, eg (g, b) then for each

     other mem, one need to select the same guard g with the same

     status b, *)

  let res =

  if List.for_all (fun (m,mdefs) ->

         (* All defs are unguarded *)

         match mdefs with

         | [[], _] -> true (* Regular unguarded expression *)

         | [] -> true (* A unbalanced definition of the memory. Here

                         we have m_{k+1} -> m_k *)

         | _ -> false

       ) mem_defs

  then

    [prefix ,

     List.map (fun (m,gel) ->

         match gel with

         | [_,e] ->

            let e =