CristalCaveGem » LustreC

open Lustre_types

open Machine_code_types

open Machine_code_common

open Format

(* open Horn_backend_common

 * open Horn_backend *)

open Zustre_data

module HBC = Horn_backend_common

let node_name = HBC.node_name

let concat = HBC.concat

let rename_machine = HBC.rename_machine

let rename_machine_list = HBC.rename_machine_list

let rename_next = HBC.rename_next

let rename_mid = HBC.rename_mid

let rename_current = HBC.rename_current

let rename_current_list = HBC.rename_current_list

let rename_mid_list = HBC.rename_mid_list

let rename_next_list = HBC.rename_next_list

let full_memory_vars = HBC.full_memory_vars

let inout_vars = HBC.inout_vars

let reset_vars = HBC.reset_vars

let step_vars = HBC.step_vars

let local_memory_vars = HBC.local_memory_vars

let step_vars_m_x = HBC.step_vars_m_x

let step_vars_c_m_x = HBC.step_vars_c_m_x

let machine_reset_name = HBC.machine_reset_name 

let machine_step_name = HBC.machine_step_name 

let machine_stateless_name = HBC.machine_stateless_name 

let preprocess = Horn_backend.preprocess

(** Sorts

A sort is introduced for each basic type and each enumerated type.

A hashtbl records these and allow easy access to sort values, when

   provided with a enumerated type name. 

*)

let bool_sort = Z3.Boolean.mk_sort !ctx

let int_sort = Z3.Arithmetic.Integer.mk_sort !ctx

let real_sort = Z3.Arithmetic.Real.mk_sort !ctx

let get_const_sort = Hashtbl.find const_sorts 

let get_sort_elems = Hashtbl.find sort_elems

let get_tag_sort = Hashtbl.find const_tags

let decl_sorts () =

  Hashtbl.iter (fun typ decl ->

    match typ with

    | Tydec_const var ->

      (match decl.top_decl_desc with

      | TypeDef tdef -> (

	match tdef.tydef_desc with

	| Tydec_enum tl ->

	  let new_sort = Z3.Enumeration.mk_sort_s !ctx var tl in

          Hashtbl.add const_sorts var new_sort;

          Hashtbl.add sort_elems new_sort tl;

          List.iter (fun t -> Hashtbl.add const_tags t new_sort) tl

	| _ -> Format.eprintf "Unknown type : %a@.@?" Printers.pp_var_type_dec_desc typ; assert false

      )

      | _ -> assert false

      )

    | _        -> ()) Corelang.type_table

let rec type_to_sort t =

  if Types.is_bool_type t  then bool_sort else

    if Types.is_int_type t then int_sort else 

  if Types.is_real_type t then real_sort else 

  match (Types.repr t).Types.tdesc with

  | Types.Tconst ty       -> get_const_sort ty

  | Types.Tclock t        -> type_to_sort t

  | Types.Tarray(dim,ty)   -> Z3.Z3Array.mk_sort !ctx int_sort (type_to_sort ty)

  | Types.Tstatic(d, ty)-> type_to_sort ty

  | Types.Tarrow _

  | _                     -> Format.eprintf "internal error: pp_type %a@."

                               Types.print_ty t; assert false

(** Func decls

Similarly fun_decls are registerd, by their name, into a hashtbl. The

   proposed encoding introduces a 0-ary fun_decl to model variables

   and fun_decl with arguments to declare reset and step predicates.

 *)

let register_fdecl id fd = Hashtbl.add decls id fd

let get_fdecl id =

  try

    Hashtbl.find decls id

  with Not_found -> (Format.eprintf "Unable to find func_decl %s@.@?" id; raise Not_found)

let pp_fdecls fmt =

  Format.fprintf fmt "Registered fdecls: @[%a@]@ "

    (Utils.fprintf_list ~sep:"@ " Format.pp_print_string)  (Hashtbl.fold (fun id _ accu -> id::accu) decls [])

let decl_var id =

  Format.eprintf "Declaring var %s@." id.var_id;

  let fdecl = Z3.FuncDecl.mk_func_decl_s !ctx id.var_id [] (type_to_sort id.var_type) in

  register_fdecl id.var_id fdecl;

  fdecl

let decl_rel name args =

  (*verifier ce qui est construit. On veut un declare-rel *)

  let args_sorts = List.map (fun v -> type_to_sort v.var_type) args in

  let fdecl = Z3.FuncDecl.mk_func_decl_s !ctx name args_sorts bool_sort in

  Z3.Fixedpoint.register_relation !fp fdecl;

  register_fdecl name fdecl;

  fdecl

(** Conversion functions

The following is similar to the Horn backend. Each printing function

   is rephrased from pp_xx to xx_to_expr and produces a Z3 value.

 *)

(* Returns the f_decl associated to the variable v *)

let horn_var_to_expr v =

  Z3.Expr.mk_const_f !ctx (get_fdecl v.var_id)

  (* Used to print boolean constants *)

let horn_tag_to_expr t =

  if t = Corelang.tag_true then

    Z3.Boolean.mk_true !ctx

  else if t = Corelang.tag_false then

    Z3.Boolean.mk_false !ctx

  else

    (* Finding the associated sort *)

    let sort = get_tag_sort t in

    let elems = get_sort_elems sort in 

    let res : Z3.Expr.expr option =

      List.fold_left2 (fun res cst expr ->

          match res with

          | Some _ -> res

          | None -> if t = cst then Some (expr:Z3.Expr.expr) else None

        ) None elems (Z3.Enumeration.get_consts sort)

    in

    match res with None -> assert false | Some s -> s

(* Prints a constant value *)

let rec horn_const_to_expr c =

  match c with

    | Const_int i    -> Z3.Arithmetic.Integer.mk_numeral_i !ctx i

    | Const_real (_,_,s)   -> Z3.Arithmetic.Real.mk_numeral_i !ctx 0

    | Const_tag t    -> horn_tag_to_expr t

    | _              -> assert false

(* Default value for each type, used when building arrays. Eg integer array

   [2;7] is defined as (store (store (0) 1 7) 0 2) where 0 is this default value

   for the type integer (arrays).

*)

let rec horn_default_val t =

  let t = Types.dynamic_type t in

  if Types.is_bool_type t  then Z3.Boolean.mk_true !ctx else

  if Types.is_int_type t then Z3.Arithmetic.Integer.mk_numeral_i !ctx 0 else 

  if Types.is_real_type t then Z3.Arithmetic.Real.mk_numeral_i !ctx 0 else 

  (* match (Types.dynamic_type t).Types.tdesc with

   * | Types.Tarray(dim, l) -> (\* TODO PL: this strange code has to be (heavily) checked *\)

   *    let valt = Types.array_element_type t in

   *    fprintf fmt "((as const (Array Int %a)) %a)"

   *      pp_type valt 

   *      pp_default_val valt

   * | Types.Tstruct(l) -> assert false

   * | Types.Ttuple(l) -> assert false

   * |_ -> *) assert false

(* Conversion of basic library functions *)

let horn_basic_app i val_to_expr vl =

  match i, vl with

  | "ite", [v1; v2; v3] ->

     Z3.Boolean.mk_ite

       !ctx

       (val_to_expr v1)

       (val_to_expr v2)

       (val_to_expr v3)

  | "uminus", [v] ->

     Z3.Arithmetic.mk_unary_minus

       !ctx

       (val_to_expr v)

  | "not", [v] ->

     Z3.Boolean.mk_not

       !ctx

       (val_to_expr v)

  | "=", [v1; v2] ->

     Z3.Boolean.mk_eq

       !ctx

       (val_to_expr v1)

       (val_to_expr v2)

  | "&&", [v1; v2] ->

     Z3.Boolean.mk_and

       !ctx

       [val_to_expr v1;

        val_to_expr v2]

  | "||", [v1; v2] ->

          Z3.Boolean.mk_or

       !ctx

       [val_to_expr v1;

        val_to_expr v2]

  | "impl", [v1; v2] ->

     Z3.Boolean.mk_implies

       !ctx

       (val_to_expr v1)

       (val_to_expr v2)

 | "mod", [v1; v2] ->

          Z3.Arithmetic.Integer.mk_mod

       !ctx

       (val_to_expr v1)

       (val_to_expr v2)

  | "equi", [v1; v2] ->

          Z3.Boolean.mk_eq

       !ctx

       (val_to_expr v1)

       (val_to_expr v2)

  | "xor", [v1; v2] ->

          Z3.Boolean.mk_xor

       !ctx

       (val_to_expr v1)

       (val_to_expr v2)

  | "!=", [v1; v2] ->

     Z3.Boolean.mk_not

       !ctx

       (

         Z3.Boolean.mk_eq

           !ctx

           (val_to_expr v1)

           (val_to_expr v2)

       )

  | "/", [v1; v2] ->

     Z3.Arithmetic.mk_div

       !ctx

       (val_to_expr v1)

       (val_to_expr v2)

  | "+", [v1; v2] ->

     Z3.Arithmetic.mk_add

       !ctx

       [val_to_expr v1; val_to_expr v2]

  | "-", [v1; v2] ->

     Z3.Arithmetic.mk_sub

       !ctx

       [val_to_expr v1 ; val_to_expr v2]

  | "*", [v1; v2] ->

     Z3.Arithmetic.mk_mul

       !ctx

       [val_to_expr v1; val_to_expr v2]

  | "<", [v1; v2] ->

     Z3.Arithmetic.mk_lt

       !ctx

       (val_to_expr v1)

       (val_to_expr v2)

  | "<=", [v1; v2] ->

     Z3.Arithmetic.mk_le

       !ctx

       (val_to_expr v1)

       (val_to_expr v2)

  | ">", [v1; v2] ->

     Z3.Arithmetic.mk_gt

       !ctx

       (val_to_expr v1)

       (val_to_expr v2)

  | ">=", [v1; v2] ->

     Z3.Arithmetic.mk_ge

       !ctx

       (val_to_expr v1)

       (val_to_expr v2)

  (* | _, [v1; v2] ->      Z3.Boolean.mk_and

   *      !ctx

   *      (val_to_expr v1)

   *      (val_to_expr v2)

   * 

   *      Format.fprintf fmt "(%s %a %a)" i val_to_exprr v1 val_to_expr v2 *)

  | _ -> (

    Format.eprintf

      "internal error: zustre unkown function %s@." i;

    assert false)

(* Convert a value expression [v], with internal function calls only.

   [pp_var] is a printer for variables (typically [pp_c_var_read]),

   but an offset suffix may be added for array variables

*)

let rec horn_val_to_expr ?(is_lhs=false) self v =

  match v.value_desc with

  | Cst c       -> horn_const_to_expr c

  (* Code specific for arrays *)

  | Array il    ->

     (* An array definition: 

	(store (

	  ...

 	    (store (

	       store (

	          default_val

	       ) 

	       idx_n val_n

	    ) 

	    idx_n-1 val_n-1)

	  ... 

	  idx_1 val_1

	) *)

     let rec build_array (tab, x) =

       match tab with

       | [] -> horn_default_val v.value_type(* (get_type v) *)

       | h::t ->

	  Z3.Z3Array.mk_store

            !ctx

	    (build_array (t, (x+1)))

	    (Z3.Arithmetic.Integer.mk_numeral_i !ctx x)

	    (horn_val_to_expr ~is_lhs:is_lhs self h)

     in

     build_array (il, 0)

  | Access(tab,index) ->

     Z3.Z3Array.mk_select !ctx 

       (horn_val_to_expr ~is_lhs:is_lhs self tab)

       (horn_val_to_expr ~is_lhs:is_lhs self index)

  (* Code specific for arrays *)

  | Power (v, n)  -> assert false

  | LocalVar v    ->

     horn_var_to_expr

       (rename_machine

          self

          v)

  | StateVar v    ->

     if Types.is_array_type v.var_type

     then assert false

     else horn_var_to_expr (rename_machine self ((if is_lhs then rename_next else rename_current) (* self *) v))

  | Fun (n, vl)   -> horn_basic_app n (horn_val_to_expr self) vl

let no_reset_to_exprs machines m i =

  let (n,_) = List.assoc i m.minstances in

  let target_machine = List.find (fun m  -> m.mname.node_id = (Corelang.node_name n)) machines in

  let m_list = 

    rename_machine_list

      (concat m.mname.node_id i)

      (rename_mid_list (full_memory_vars machines target_machine))

  in

  let c_list =

    rename_machine_list

      (concat m.mname.node_id i)

      (rename_current_list (full_memory_vars machines target_machine))

  in

  match c_list, m_list with

  | [chd], [mhd] ->

     let expr =

       Z3.Boolean.mk_eq !ctx 

         (horn_var_to_expr mhd)

         (horn_var_to_expr chd)

     in

     [expr]

  | _ -> (

    let exprs =

      List.map2 (fun mhd chd -> 

          Z3.Boolean.mk_eq !ctx 

            (horn_var_to_expr mhd)

            (horn_var_to_expr chd)

        )

        m_list

        c_list

    in

    exprs

  )

let instance_reset_to_exprs machines m i =

  let (n,_) = List.assoc i m.minstances in

  let target_machine = List.find (fun m  -> m.mname.node_id = (Corelang.node_name n)) machines in

  let vars =

    (

      (rename_machine_list

	 (concat m.mname.node_id i)

	 (rename_current_list (full_memory_vars machines target_machine))

      ) 

      @

	(rename_machine_list

	   (concat m.mname.node_id i)

	   (rename_mid_list (full_memory_vars machines target_machine))

	)

    )

  in

  let expr =

    Z3.Expr.mk_app

      !ctx

      (get_fdecl (machine_reset_name (Corelang.node_name n)))

      (List.map (horn_var_to_expr) vars)

  in

  [expr]

let instance_call_to_exprs machines reset_instances m i inputs outputs =

  let self = m.mname.node_id in

  try (* stateful node instance *)

    begin

      let (n,_) = List.assoc i m.minstances in

      let target_machine = List.find (fun m  -> m.mname.node_id = Corelang.node_name n) machines in

      (* Checking whether this specific instances has been reset yet *)

      let reset_exprs = 

        if not (List.mem i reset_instances) then

	  (* If not, declare mem_m = mem_c *)

	  no_reset_to_exprs machines m i

        else

          [] (* Nothing to add yet *)

      in

      let mems = full_memory_vars machines target_machine in

      let rename_mems f = rename_machine_list (concat m.mname.node_id i) (f mems) in

      let mid_mems = rename_mems rename_mid_list in

      let next_mems = rename_mems rename_next_list in

      let call_expr = 

      match Corelang.node_name n, inputs, outputs, mid_mems, next_mems with

      | "_arrow", [i1; i2], [o], [mem_m], [mem_x] -> begin

          let stmt1 = (* out = ite mem_m then i1 else i2 *)

            Z3.Boolean.mk_eq !ctx

              ( (* output var *)

                horn_val_to_expr

                  ~is_lhs:true

                  self

                  (mk_val (LocalVar o) o.var_type)

              )

              (

                Z3.Boolean.mk_ite !ctx 

	          (horn_var_to_expr mem_m) 

	          (horn_val_to_expr self i1)

	          (horn_val_to_expr self i2)

              )

          in

          let stmt2 = (* mem_X = false *)

            Z3.Boolean.mk_eq !ctx

	      (horn_var_to_expr mem_x)

              (Z3.Boolean.mk_false !ctx)

          in

          [stmt1; stmt2]

      end

      | node_name_n ->

         let expr = 

           Z3.Expr.mk_app

             !ctx

             (get_fdecl (machine_step_name (node_name n)))

             ( (* Arguments are input, output, mid_mems, next_mems *)

               (

                 List.map (horn_val_to_expr self) (

                     inputs @

	               (List.map (fun v -> mk_val (LocalVar v) v.var_type) outputs)

                   )

               ) @ (

                 List.map (horn_var_to_expr) (mid_mems@next_mems)

	       )

             )

         in

         [expr]

      in

      reset_exprs@call_expr

    end

  with Not_found -> ( (* stateless node instance *)

    let (n,_) = List.assoc i m.mcalls in

    let expr = 

      Z3.Expr.mk_app

        !ctx

        (get_fdecl (machine_stateless_name (node_name n)))

        ((* Arguments are inputs, outputs *)

         List.map (horn_val_to_expr self)

           (

             inputs @ (List.map (fun v -> mk_val (LocalVar v) v.var_type) outputs)

           )

        )

    in

    [expr]

  )

(* (\* Prints a [value] indexed by the suffix list [loop_vars] *\) *)

(* let rec value_suffix_to_expr self value = *)

(*  match value.value_desc with *)

(*  | Fun (n, vl)  ->  *)

(*     horn_basic_app n (horn_val_to_expr self) (value_suffix_to_expr self vl) *)

(*  |  _            -> *)

(*    horn_val_to_expr self value *)

(* type_directed assignment: array vs. statically sized type

   - [var_type]: type of variable to be assigned

   - [var_name]: name of variable to be assigned

   - [value]: assigned value

   - [pp_var]: printer for variables

*)

let assign_to_exprs m var_name value =

  let self = m.mname.node_id in

  let e =

    Z3.Boolean.mk_eq

      !ctx

      (horn_val_to_expr ~is_lhs:true self var_name)

      (horn_val_to_expr self value)

  (* was: TODO deal with array accesses       (value_suffix_to_expr self value) *)

  in

  [e]

(* Convert instruction to Z3.Expr and update the set of reset instances *)

let rec instr_to_exprs machines reset_instances (m: machine_t) instr : Z3.Expr.expr list * ident list =

  match Corelang.get_instr_desc instr with

  | MComment _ -> [], reset_instances

  | MNoReset i -> (* we assign middle_mem with mem_m. And declare i as reset *)

    no_reset_to_exprs machines m i,

    i::reset_instances

  | MReset i -> (* we assign middle_mem with reset: reset(mem_m) *)

    instance_reset_to_exprs machines m i,

    i::reset_instances

  | MLocalAssign (i,v) ->

    assign_to_exprs

      m  

      (mk_val (LocalVar i) i.var_type) v,

    reset_instances

  | MStateAssign (i,v) ->

    assign_to_exprs

      m 

      (mk_val (StateVar i) i.var_type) v,

    reset_instances

  | MStep ([i0], i, vl) when Basic_library.is_internal_fun i (List.map (fun v -> v.value_type) vl) ->

    assert false (* This should not happen anymore *)

  | MStep (il, i, vl) ->

    (* if reset instance, just print the call over mem_m , otherwise declare mem_m =

       mem_c and print the call to mem_m *)

    instance_call_to_exprs machines reset_instances m i vl il,

    reset_instances (* Since this instance call will only happen once, we

		       don't have to update reset_instances *)

  | MBranch (g,hl) -> (* (g = tag1 => expr1) and (g = tag2 => expr2) ...

			 should not be produced yet. Later, we will have to

			 compare the reset_instances of each branch and

			 introduced the mem_m = mem_c for branches to do not

			 address it while other did. Am I clear ? *)

    (* For each branch we obtain the logical encoding, and the information

       whether a sub node has been reset or not. If a node has been reset in one

       of the branch, then all others have to have the mem_m = mem_c

       statement. *)

    let self = m.mname.node_id in

    let branch_to_expr (tag, instrs) =

      let branch_def, branch_resets = instrs_to_expr machines reset_instances m instrs in

      let e =

	Z3.Boolean.mk_implies !ctx

          (Z3.Boolean.mk_eq !ctx 

             (horn_val_to_expr self g)

	     (horn_tag_to_expr tag))

          branch_def in

      [e], branch_resets

    in

    List.fold_left (fun (instrs, resets) b ->

      let b_instrs, b_resets = branch_to_expr b in

      instrs@b_instrs, resets@b_resets 

    ) ([], reset_instances) hl 

and instrs_to_expr machines reset_instances m instrs = 

  let instr_to_exprs rs i = instr_to_exprs machines rs m i in

  let e_list, rs = 

    match instrs with

    | [x] -> instr_to_exprs reset_instances x 

    | _::_ -> (* TODO: check whether we should compuyte a AND on the exprs (expr list) built here. It was performed in the printer setting but seems to be useless here since the output is a list of exprs *)

       List.fold_left (fun (exprs, rs) i -> 

         let exprs_i, rs_i = instr_to_exprs rs i in

         exprs@exprs_i, rs@rs_i

       )

         ([], reset_instances) instrs 

    | [] -> [], reset_instances

  in

  let e = 

    match e_list with

    | [e] -> e

    | [] -> Z3.Boolean.mk_true !ctx

    | _ -> Z3.Boolean.mk_and !ctx e_list

  in

  e, rs

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

(* Quantifiying universally all occuring variables *)

let add_rule ?(dont_touch=[]) vars  expr =

  (* let fds = Z3.Expr.get_args expr in *)

  (* Format.eprintf "Expr %s: args: [%a]@." *)

  (*   (Z3.Expr.to_string expr) *)

  (*   (Utils.fprintf_list ~sep:", " (fun fmt e -> Format.pp_print_string fmt (Z3.Expr.to_string e))) fds; *)

  (* (\* Old code relying on provided vars *\) *)

  (* let sorts = (List.map (fun id -> type_to_sort id.var_type) vars) in *)

  (* let symbols = (List.map (fun id -> Z3.FuncDecl.get_name (get_fdecl id.var_id)) vars) in *)

  (* New code: we extract vars from expr *)

  let module FDSet = Set.Make (struct type t = Z3.FuncDecl.func_decl

				      let compare = compare

				      let hash = Hashtbl.hash

  end)

  in

  let rec get_expr_vars e =

    let open Utils in

    let nb_args = Z3.Expr.get_num_args e in

    if nb_args <= 0 then (

      let fdecl = Z3.Expr.get_func_decl e in

      (* let params = Z3.FuncDecl.get_parameters fdecl in *)

      Format.eprintf "Extracting info about %s: @." (Z3.Expr.to_string e);

      let dkind = Z3.FuncDecl.get_decl_kind fdecl in

      match dkind with Z3enums.OP_UNINTERPRETED -> (

	(* Format.eprintf "kind = %s, " (match dkind with Z3enums.OP_TRUE -> "true" | Z3enums.OP_UNINTERPRETED -> "uninter"); *)

	(* let open Z3.FuncDecl.Parameter in *)

	(* List.iter (fun p -> *)

	(*   match p with *)

        (*     P_Int i -> Format.eprintf "int %i" i *)

	(*   | P_Dbl f -> Format.eprintf "dbl %f" f *)

	(*   | P_Sym s -> Format.eprintf "symb"  *)

	(*   | P_Srt s -> Format.eprintf "sort"  *)

	(*   | P_Ast _ ->Format.eprintf "ast"  *)

	(*   | P_Fdl f -> Format.eprintf "fundecl"  *)

	(*   | P_Rat s -> Format.eprintf "rat %s" s  *)

	(* ) params; *)

	(* Format.eprintf "]@."; *)

	FDSet.singleton fdecl

      )

      | _ -> FDSet.empty

    )

    else (*if nb_args > 0 then*)

      List.fold_left

	(fun accu e ->  FDSet.union accu (get_expr_vars e))

	FDSet.empty (Z3.Expr.get_args e)

  in

  let extracted_vars = FDSet.elements (FDSet.diff (get_expr_vars expr) (FDSet.of_list dont_touch)) in

  let extracted_sorts = List.map Z3.FuncDecl.get_range extracted_vars in

  let extracted_symbols = List.map Z3.FuncDecl.get_name extracted_vars in

  Format.eprintf "Declaring rule: %s with variables %a@."

    (Z3.Expr.to_string expr)

    (Utils.fprintf_list ~sep:", " (fun fmt e -> Format.fprintf fmt "%s" (Z3.Expr.to_string e))) (List.map horn_var_to_expr vars)

    ;

  let expr = Z3.Quantifier.mk_forall_const

    !ctx  (* context *)

    (List.map horn_var_to_expr vars) (* TODO provide bounded variables as expr *)

    (* sorts           (\* sort list*\) *)

    (* symbols (\* symbol list *\) *)

    expr (* expression *)

    None (* quantifier weight, None means 1 *)

    [] (* pattern list ? *)

    [] (* ? *)

    None (* ? *)

    None (* ? *)

  in

  Format.eprintf "OK@.@?";

  TODO: bizarre la declaration de INIT tout seul semble poser pb.

  Z3.Fixedpoint.add_rule !fp

    (Z3.Quantifier.expr_of_quantifier expr)

    None

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

let machine_reset machines m =

  let locals = local_memory_vars machines m in

  (* print "x_m = x_c" for each local memory *)

  let mid_mem_def =

    List.map (fun v ->

      Z3.Boolean.mk_eq !ctx

	(horn_var_to_expr (rename_mid v))

	(horn_var_to_expr (rename_current v))

    ) locals

  in

  (* print "child_reset ( associated vars _ {c,m} )" for each subnode.

     Special treatment for _arrow: _first = true

  *)

  let reset_instances =

    List.map (fun (id, (n, _)) ->

      let name = node_name n in

      if name = "_arrow" then (

	Z3.Boolean.mk_eq !ctx

	  (

	    let vdecl = get_fdecl ((concat m.mname.node_id id) ^ "._arrow._first_m") in

	    Z3.Expr.mk_const_f !ctx vdecl

	  )

	  (Z3.Boolean.mk_true !ctx)

      ) else (

	let machine_n = get_machine machines name in 

	Z3.Expr.mk_app

	  !ctx

	  (get_fdecl (name ^ "_reset"))

	  (List.map (horn_var_to_expr)

	     (rename_machine_list (concat m.mname.node_id id) (reset_vars machines machine_n))

	  )

      )

    ) m.minstances

  in

  Z3.Boolean.mk_and !ctx (mid_mem_def @ reset_instances)

(*  TODO: empty list means true statement *)

let decl_machine machines m =

  if m.mname.node_id = Arrow.arrow_id then

    (* We don't do arrow function *)

    ()

  else

    begin

      let _ =

        List.map decl_var

      	  (

      	    (inout_vars machines m)@

      	      (rename_current_list (full_memory_vars machines m)) @

      	      (rename_mid_list (full_memory_vars machines m)) @

      	      (rename_next_list (full_memory_vars machines m)) @

      	      (rename_machine_list m.mname.node_id m.mstep.step_locals)

      	  )

      in

      if is_stateless m then

	begin

	  (* Declaring single predicate *)

	  let vars = inout_vars machines m in

	  let _ = decl_rel (machine_stateless_name m.mname.node_id) vars in

	  let horn_body, _ (* don't care for reset here *) =

	    instrs_to_expr

	      machines

	      ([] (* No reset info for stateless nodes *) )

	      m

	      m.mstep.step_instrs

	  in

	  let horn_head = 

	    Z3.Expr.mk_app

	      !ctx

	      (get_fdecl (machine_stateless_name m.mname.node_id))

	      (List.map (horn_var_to_expr) vars)

	  in

	  let vars = vars@(rename_machine_list m.mname.node_id m.mstep.step_locals) in

	  match m.mstep.step_asserts with

	  | [] ->

	     begin

	       (* Rule for single predicate : "; Stateless step rule @." *)

	       let vars = rename_machine_list m.mname.node_id m.mstep.step_locals in

	       add_rule vars (Z3.Boolean.mk_implies !ctx horn_body horn_head)

	     end

	  | assertsl ->

	     begin

	       (*Rule for step "; Stateless step rule with Assertions @.";*)

	       let body_with_asserts =

		 Z3.Boolean.mk_and !ctx (horn_body :: List.map (horn_val_to_expr m.mname.node_id) assertsl)

	       in

	       let vars = rename_machine_list m.mname.node_id m.mstep.step_locals in

	       add_rule vars (Z3.Boolean.mk_implies !ctx body_with_asserts horn_head)

	     end

	end

      else

	begin

	  (* Rule for reset *)

	  let vars = reset_vars machines m in

	  let _ = decl_rel (machine_reset_name m.mname.node_id) vars in

	  let horn_reset_body = machine_reset machines m in	    

	  let horn_reset_head = 

	    Z3.Expr.mk_app

	      !ctx

	      (get_fdecl (machine_reset_name m.mname.node_id))

	      (List.map (horn_var_to_expr) vars)

	  in

	  let _ =

	    add_rule vars (Z3.Boolean.mk_implies !ctx horn_reset_body horn_reset_head)

	  in

	  (* Rule for step*)

	  let vars = step_vars machines m in

          let _ = decl_rel (machine_step_name m.mname.node_id) vars in

	  let horn_step_body, _ (* don't care for reset here *) =

	    instrs_to_expr

	      machines

	      []

	      m

	      m.mstep.step_instrs

	  in

	  let horn_step_head = 

	    Z3.Expr.mk_app

	      !ctx

	      (get_fdecl (machine_step_name m.mname.node_id))