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.                                                    *)

(*                                                                  *)

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

(* The compilation presented here was first defined in Garoche, Gurfinkel,

   Kahsai, HCSV'14.

   This is a modified version that handle reset

*)

open Format

open Lustre_types

open Machine_code_types

open Corelang

open Machine_code_common

open Horn_backend_common

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

(*                    Instruction Printing functions                                        *)

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

let pp_horn_var m fmt id =

  (*if Types.is_array_type id.var_type

  then

    assert false (* no arrays in Horn output *)

  else*)

    fprintf fmt "%s" id.var_id

(* Used to print boolean constants *)

let pp_horn_tag fmt t =

  pp_print_string fmt (if t = tag_true then "true" else if t = tag_false then "false" else t)

(* Prints a constant value *)

let rec pp_horn_const fmt c =

  match c with

    | Const_int i    -> pp_print_int fmt i

    | Const_real (_,_,s)   -> pp_print_string fmt s

    | Const_tag t    -> pp_horn_tag fmt 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 pp_default_val fmt t =

  let t = Types.dynamic_type t in

  if Types.is_bool_type t  then fprintf fmt "true" else

  if Types.is_int_type t then fprintf fmt "0" else 

  if Types.is_real_type t then fprintf fmt "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

let pp_mod pp_val v1 v2 fmt =

  if Types.is_int_type v1.value_type &&  not !Options.integer_div_euclidean then

    (* C semantics: converting it from Euclidean operators

       (a mod_M b) - ((a mod_M b > 0 && a < 0) ? abs(b) : 0)            

    *)

    Format.fprintf fmt "(- (mod %a %a) (ite (and (> (mod %a %a) 0) (< %a 0)) (abs %a) 0))"

      pp_val v1 pp_val v2

      pp_val v1 pp_val v2

      pp_val v1

      pp_val v2

  else

    Format.fprintf fmt "(mod %a %a)" pp_val v1 pp_val v2

let pp_div pp_val v1 v2 fmt =

  if Types.is_int_type v1.value_type &&  not !Options.integer_div_euclidean then

    (* C semantics: converting it from Euclidean operators

       (a - (a mod_C b)) div_M b

    *)

    Format.fprintf fmt "(div (- %a %t) %a)"

      pp_val v1

      (pp_mod pp_val v1 v2)

      pp_val v2

  else

    Format.fprintf fmt "(div %a %a)" pp_val v1 pp_val v2

let pp_basic_lib_fun i pp_val fmt vl =

  match i, vl with

  | "ite", [v1; v2; v3] -> Format.fprintf fmt "(@[<hov 2>ite %a@ %a@ %a@])" pp_val v1 pp_val v2 pp_val v3

  | "uminus", [v] -> Format.fprintf fmt "(- %a)" pp_val v

  | "not", [v] -> Format.fprintf fmt "(not %a)" pp_val v

  | "=", [v1; v2] -> Format.fprintf fmt "(= %a %a)" pp_val v1 pp_val v2

  | "&&", [v1; v2] -> Format.fprintf fmt "(and %a %a)" pp_val v1 pp_val v2

  | "||", [v1; v2] -> Format.fprintf fmt "(or %a %a)" pp_val v1 pp_val v2

  | "impl", [v1; v2] -> Format.fprintf fmt "(=> %a %a)" pp_val v1 pp_val v2

  | "equi", [v1; v2] -> Format.fprintf fmt "(%a = %a)" pp_val v1 pp_val v2

  | "xor", [v1; v2] -> Format.fprintf fmt "(%a xor %a)" pp_val v1 pp_val v2

  | "!=", [v1; v2] -> Format.fprintf fmt "(not (= %a %a))" pp_val v1 pp_val v2

  | "mod", [v1; v2] -> pp_mod pp_val v1 v2 fmt

  | "/", [v1; v2] -> pp_div pp_val v1 v2 fmt

  | _, [v1; v2] -> Format.fprintf fmt "(%s %a %a)" i pp_val v1 pp_val v2

  | _ -> (Format.eprintf "internal error: Basic_library.pp_horn %s@." i; assert false)

(*  | "mod", [v1; v2] -> Format.fprintf fmt "(%a %% %a)" pp_val v1 pp_val v2

*)

(* Prints 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 pp_horn_val ?(is_lhs=false) m self pp_var fmt v =

  match v.value_desc with

  | Cst c       -> pp_horn_const fmt 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 print fmt (tab, x) =

       match tab with

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

       | h::t ->

	  fprintf fmt "(store %a %i %a)"

	    print (t, (x+1))

	    x

	    (pp_horn_val ~is_lhs:is_lhs m self pp_var) h

     in

     print fmt (il, 0)

  | Access(tab,index) ->

     fprintf fmt "(select %a %a)"

       (pp_horn_val ~is_lhs:is_lhs m self pp_var) tab

       (pp_horn_val ~is_lhs:is_lhs m self pp_var) index

  (* Code specific for arrays *)

  | Power (v, n)  -> assert false

  | Var v    ->

     if is_memory m v then

       if Types.is_array_type v.var_type

       then assert false

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

     else

       pp_var fmt (rename_machine self v)

  | Fun (n, vl)   -> fprintf fmt "%a" (pp_basic_lib_fun n (pp_horn_val m self pp_var)) vl

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

let rec pp_value_suffix m self pp_value fmt value =

 match value.value_desc with

 | Fun (n, vl)  ->

    pp_basic_lib_fun n (pp_value_suffix m self pp_value) fmt vl

 |  _            ->

   pp_horn_val m self pp_value fmt 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 pp_assign m pp_var fmt var_name value =

  let self = m.mname.node_id in

  fprintf fmt "(= %a %a)" 

    (pp_horn_val ~is_lhs:true m self pp_var) var_name

    (pp_value_suffix m self pp_var) value

(* In case of no reset call, we define mid_mem = current_mem *)

let pp_no_reset machines m fmt i =

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

  let target_machine = List.find (fun m  -> m.mname.node_id = (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] ->

    fprintf fmt "(= %a %a)"

      (pp_horn_var m) mhd

      (pp_horn_var m) chd

  | _ -> (

    fprintf fmt "@[<v 0>(and @[<v 0>";

    List.iter2 (fun mhd chd -> 

      fprintf fmt "(= %a %a)@ "

      (pp_horn_var m) mhd

      (pp_horn_var m) chd

    )

      m_list

      c_list      ;

    fprintf fmt ")@]@ @]"

  )

let pp_instance_reset machines m fmt i =

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

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

  fprintf fmt "(%a @[<v 0>%a)@]"

    pp_machine_reset_name (node_name n)

    (Utils.fprintf_list ~sep:"@ " (pp_horn_var m)) 

    (

      (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))

	)

    )

let pp_instance_call machines reset_instances m fmt 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 = node_name n) machines in

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

      if not (List.mem i reset_instances) then

	(* If not, declare mem_m = mem_c *)

	pp_no_reset machines m fmt i;

      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

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

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

	fprintf fmt "@[<v 5>(and ";

	fprintf fmt "(= %a (ite %a %a %a))"

	  (pp_horn_val ~is_lhs:true m self (pp_horn_var m)) (mk_val (Var o) o.var_type) (* output var *)

	  (pp_horn_var m) mem_m 

	  (pp_horn_val m self (pp_horn_var m)) i1

	  (pp_horn_val m self (pp_horn_var m)) i2

	;

	fprintf fmt "@ ";

	fprintf fmt "(= %a false)" (pp_horn_var m) mem_x;

	fprintf fmt ")@]"

      end

      | node_name_n -> begin

	fprintf fmt "(%a @[<v 0>%a%t%a%t%a)@]"

	  pp_machine_step_name (node_name n)

	  (Utils.fprintf_list ~sep:"@ " (pp_horn_val m self (pp_horn_var m))) inputs

	  (Utils.pp_final_char_if_non_empty "@ " inputs)

	  (Utils.fprintf_list ~sep:"@ " (pp_horn_val m self (pp_horn_var m)))

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

	  (Utils.pp_final_char_if_non_empty "@ " outputs)

	  (Utils.fprintf_list ~sep:"@ " (pp_horn_var m)) (mid_mems@next_mems)

      end

    end

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

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

    fprintf fmt "(%a @[<v 0>%a%t%a)@]"

      pp_machine_stateless_name (node_name n)

      (Utils.fprintf_list ~sep:"@ " (pp_horn_val m self (pp_horn_var m)))

      inputs

      (Utils.pp_final_char_if_non_empty "@ " inputs)

      (Utils.fprintf_list ~sep:"@ " (pp_horn_val m self (pp_horn_var m)))

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

  )

(* Print the instruction and update the set of reset instances *)

let rec pp_machine_instr machines reset_instances (m: machine_t) fmt instr : ident list =

  match get_instr_desc instr with

  | MSpec _ | MComment _ -> reset_instances

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

    pp_no_reset machines m fmt i;

    i::reset_instances

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

    pp_instance_reset machines m fmt i;

    i::reset_instances

  | MLocalAssign (i,v) ->

    pp_assign

      m (pp_horn_var m) fmt

      (mk_val (Var i) i.var_type) v;

    reset_instances

  | MStateAssign (i,v) ->

    pp_assign

      m (pp_horn_var m) fmt

      (mk_val (Var 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 *)

    pp_instance_call machines reset_instances m fmt 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 pp_branch fmt (tag, instrs) =

      fprintf fmt 

	"@[<v 3>(or (not (= %a %a))@ " 

	(*"@[<v 3>(=> (= %a %s)@ "*)  (* Issues with some versions of Z3. It

					  seems that => within Horn predicate

					  may cause trouble. I have hard time

					  producing a MWE, so I'll just keep the

					  fix here as (not a) or b *)

	(pp_horn_val m self (pp_horn_var m)) g

	pp_horn_tag tag;

      let _ (* rs *) = pp_machine_instrs machines reset_instances m fmt instrs in 

      fprintf fmt "@])";

      () (* rs *)

    in

    pp_conj pp_branch fmt hl;

    reset_instances 

and pp_machine_instrs machines reset_instances m fmt instrs = 

  let ppi rs fmt i = pp_machine_instr machines rs m fmt i in

  match instrs with

  | [x] -> ppi reset_instances fmt x 

  | _::_ ->

    fprintf fmt "(and @[<v 0>";

    let rs = List.fold_left (fun rs i -> 

      let rs = ppi rs fmt i in

      fprintf fmt "@ ";

      rs

    )

      reset_instances instrs 

    in

    fprintf fmt "@])";

    rs

  | [] -> fprintf fmt "true"; reset_instances

let pp_machine_reset machines fmt m =

  let locals = local_memory_vars machines m in

  fprintf fmt "@[<v 5>(and @ ";

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

  (Utils.fprintf_list ~sep:"@ " (fun fmt v -> 

    fprintf fmt "(= %a %a)"

      (pp_horn_var m) (rename_mid v)

      (pp_horn_var m) (rename_current v)

   )) fmt locals;

  fprintf fmt "@ ";

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

     Special treatment for _arrow: _first = true

  *)

  (Utils.fprintf_list ~sep:"@ " (fun fmt (id, (n, _)) ->

    let name = node_name n in

    if name = "_arrow" then ( 

      fprintf fmt "(= %s._arrow._first_m true)"

	(concat m.mname.node_id id)  

    ) else (

      let machine_n = get_machine machines name in 

      fprintf fmt "(%s_reset @[<hov 0>%a@])" 

	name

	(Utils.fprintf_list ~sep:"@ " (pp_horn_var m)) 

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

    )

   )) fmt m.minstances;

  fprintf fmt "@]@ )"

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

(* Print the machine m:

   two functions: m_init and m_step

   - m_init is a predicate over m memories

   - m_step is a predicate over old_memories, inputs, new_memories, outputs

   We first declare all variables then the two /rules/.

*)

let print_machine machines fmt m =

  if m.mname.node_id = Arrow.arrow_id then

    (* We don't print arrow function *)

    ()

  else

    begin

      fprintf fmt "; %s@." m.mname.node_id;

      (* Printing variables *)

      Utils.fprintf_list ~sep:"@." pp_decl_var fmt

	(

	  (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)

	);

      pp_print_newline fmt ();

      if is_stateless m then

	begin

	  (* Declaring single predicate *)

	  fprintf fmt "(declare-rel %a (%a))@."

	    pp_machine_stateless_name m.mname.node_id

	    (Utils.fprintf_list ~sep:" " pp_type)

	    (List.map (fun v -> v.var_type) (inout_vars machines m));

          match m.mstep.step_asserts with

	  | [] ->

	     begin

	       (* Rule for single predicate *)

	       fprintf fmt "; Stateless step rule @.";

	       fprintf fmt "@[<v 2>(rule (=> @ ";

	       ignore (pp_machine_instrs machines ([] (* No reset info for stateless nodes *) )  m fmt m.mstep.step_instrs);

	       fprintf fmt "@ (%a @[<v 0>%a)@]@]@.))@.@."

		 pp_machine_stateless_name m.mname.node_id

		 (Utils.fprintf_list ~sep:" " (pp_horn_var m)) (inout_vars machines m);

	     end

	  | assertsl ->

	     begin

	       let pp_val = pp_horn_val ~is_lhs:true m m.mname.node_id (pp_horn_var m) in

	       fprintf fmt "; Stateless step rule with Assertions @.";

	       (*Rule for step*)

	       fprintf fmt "@[<v 2>(rule (=> @ (and @ ";

	       ignore (pp_machine_instrs machines [] m fmt m.mstep.step_instrs);

	       fprintf fmt "@. %a)@ (%a @[<v 0>%a)@]@]@.))@.@." (pp_conj pp_val) assertsl

		 pp_machine_stateless_name m.mname.node_id

		 (Utils.fprintf_list ~sep:" " (pp_horn_var m)) (step_vars machines m);

	     end

	end

      else

	begin

	  (* Declaring predicate *)

	  fprintf fmt "(declare-rel %a (%a))@."

	    pp_machine_reset_name m.mname.node_id

	    (Utils.fprintf_list ~sep:" " pp_type)

	    (List.map (fun v -> v.var_type) (reset_vars machines m));

	  fprintf fmt "(declare-rel %a (%a))@."

	    pp_machine_step_name m.mname.node_id

	    (Utils.fprintf_list ~sep:" " pp_type)

	    (List.map (fun v -> v.var_type) (step_vars machines m));

	  pp_print_newline fmt ();

	  (* Rule for reset *)

	  fprintf fmt "@[<v 2>(rule (=> @ %a@ (%a @[<v 0>%a)@]@]@.))@.@."

	    (pp_machine_reset machines) m 

	    pp_machine_reset_name m.mname.node_id

	    (Utils.fprintf_list ~sep:"@ " (pp_horn_var m)) (reset_vars machines m);

          match m.mstep.step_asserts with

	  | [] ->

	     begin

	       fprintf fmt "; Step rule @.";

	       (* Rule for step*)

	       fprintf fmt "@[<v 2>(rule (=> @ ";

	       ignore (pp_machine_instrs machines [] m fmt m.mstep.step_instrs);

	       fprintf fmt "@ (%a @[<v 0>%a)@]@]@.))@.@."

		 pp_machine_step_name m.mname.node_id

		 (Utils.fprintf_list ~sep:"@ " (pp_horn_var m)) (step_vars machines m);

	     end

	  | assertsl -> 

	     begin

	       let pp_val = pp_horn_val ~is_lhs:true m m.mname.node_id (pp_horn_var m) in

	       (* print_string pp_val; *)

	       fprintf fmt "; Step rule with Assertions @.";

	       (*Rule for step*)

	       fprintf fmt "@[<v 2>(rule (=> @ (and @ ";

	       ignore (pp_machine_instrs machines [] m fmt m.mstep.step_instrs);

	       fprintf fmt "@. %a)@ (%a @[<v 0>%a)@]@]@.))@.@." (pp_conj pp_val) assertsl

		 pp_machine_step_name m.mname.node_id

		 (Utils.fprintf_list ~sep:" " (pp_horn_var m)) (step_vars machines m);

	     end

	end

    end

let mk_flags arity =

  let b_range =

   let rec range i j =

     if i > arity then [] else i :: (range (i+1) j) in

   range 2 arity;

 in

 List.fold_left (fun acc x -> acc ^ " false") "true" b_range

  (*Get sfunction infos from command line*)

let get_sf_info() =

  let splitted = Str.split (Str.regexp "@") !Options.sfunction in

  Log.report ~level:1 (fun fmt -> fprintf fmt ".. sfunction name: %s@," !Options.sfunction);

  let sf_name, flags, arity = match splitted with

      [h;flg;par] -> h, flg, par

    | _ -> failwith "Wrong Sfunction info"

  in

  Log.report ~level:1 (fun fmt -> fprintf fmt "... sf_name: %s@, .. flags: %s@ .. arity: %s@," sf_name flags arity);

  sf_name, flags, arity

    (*a function to print the rules in case we have an s-function*)

  let print_sfunction machines fmt m =

      if m.mname.node_id = Arrow.arrow_id then

        (* We don't print arrow function *)

        ()

      else

        begin

          Format.fprintf fmt "; SFUNCTION@.";

          Format.fprintf fmt "; %s@." m.mname.node_id;

          Format.fprintf fmt "; EndPoint Predicate %s." !Options.sfunction;

          (* Check if there is annotation for s-function *)

          if m.mannot != [] then(

              Format.fprintf fmt "; @[%a@]@]@\n" (Utils.fprintf_list ~sep:"@ " Printers.pp_s_function) m.mannot;

            );

       (* Printing variables *)

          Utils.fprintf_list ~sep:"@." pp_decl_var fmt

                             ((step_vars machines m)@

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

          Format.pp_print_newline fmt ();

          let sf_name, flags, arity = get_sf_info() in

       if is_stateless m then

         begin

           (* Declaring single predicate *)

           Format.fprintf fmt "(declare-rel %a (%a))@."

    	                  pp_machine_stateless_name m.mname.node_id

    	                  (Utils.fprintf_list ~sep:" " pp_type)

    	                  (List.map (fun v -> v.var_type) (reset_vars machines m));

           Format.pp_print_newline fmt ();

           (* Rule for single predicate *)

           let str_flags = sf_name ^ " " ^ mk_flags (int_of_string flags) in

           Format.fprintf fmt "@[<v 2>(rule (=> @ (%s %a) (%a %a)@]@.))@.@."

                          str_flags

                          (Utils.fprintf_list ~sep:" " (pp_horn_var m)) (reset_vars machines m)

	                  pp_machine_stateless_name m.mname.node_id

	                  (Utils.fprintf_list ~sep:" " (pp_horn_var m)) (reset_vars machines m);

         end

      else

         begin

           (* Declaring predicate *)

           Format.fprintf fmt "(declare-rel %a (%a))@."

    	                  pp_machine_reset_name m.mname.node_id

    	                  (Utils.fprintf_list ~sep:" " pp_type)

    	                  (List.map (fun v -> v.var_type) (inout_vars machines m));

           Format.fprintf fmt "(declare-rel %a (%a))@."

    	                  pp_machine_step_name m.mname.node_id

    	                  (Utils.fprintf_list ~sep:" " pp_type)

    	                  (List.map (fun v -> v.var_type) (step_vars machines m));

           Format.pp_print_newline fmt ();

          (* Adding assertions *)

           match m.mstep.step_asserts with

	  | [] ->

	    begin

	      (* Rule for step*)

	      fprintf fmt "@[<v 2>(rule (=> @ ";

	      ignore (pp_machine_instrs machines [] m fmt m.mstep.step_instrs);

	      fprintf fmt "@ (%a @[<v 0>%a)@]@]@.))@.@."

		pp_machine_step_name m.mname.node_id

		(Utils.fprintf_list ~sep:"@ " (pp_horn_var m)) (step_vars machines m);

	    end

	  | assertsl ->

	    begin

	      let pp_val = pp_horn_val ~is_lhs:true m m.mname.node_id (pp_horn_var m) in

	      (* print_string pp_val; *)

	      fprintf fmt "; with Assertions @.";

	      (*Rule for step*)

	      fprintf fmt "@[<v 2>(rule (=> @ (and @ ";

	      ignore (pp_machine_instrs machines [] m fmt m.mstep.step_instrs);

	      fprintf fmt "@. %a)(%a @[<v 0>%a)@]@]@.))@.@." (pp_conj pp_val) assertsl

		pp_machine_step_name m.mname.node_id

		(Utils.fprintf_list ~sep:" " (pp_horn_var m)) (step_vars machines m);

	    end

         end

        end

(**************** XML printing functions *************)

	  let rec pp_xml_expr fmt expr =

  (match expr.expr_annot with 

  | None -> fprintf fmt "%t" 

  | Some ann -> fprintf fmt "@[(%a %t)@]" pp_xml_expr_annot ann)

    (fun fmt -> 

      match expr.expr_desc with

    | Expr_const c -> Printers.pp_const fmt c

    | Expr_ident id -> fprintf fmt "%s" id

    | Expr_array a -> fprintf fmt "[%a]" pp_xml_tuple a

    | Expr_access (a, d) -> fprintf fmt "%a[%a]" pp_xml_expr a Dimension.pp_dimension d

    | Expr_power (a, d) -> fprintf fmt "(%a^%a)" pp_xml_expr a Dimension.pp_dimension d

    | Expr_tuple el -> fprintf fmt "(%a)" pp_xml_tuple el

    | Expr_ite (c, t, e) -> fprintf fmt "@[<hov 1>(if %a then@ @[<hov 2>%a@]@ else@ @[<hov 2>%a@]@])" pp_xml_expr c pp_xml_expr t pp_xml_expr e

    | Expr_arrow (e1, e2) -> fprintf fmt "(%a -> %a)" pp_xml_expr e1 pp_xml_expr e2

    | Expr_fby (e1, e2) -> fprintf fmt "%a fby %a" pp_xml_expr e1 pp_xml_expr e2

    | Expr_pre e -> fprintf fmt "pre %a" pp_xml_expr e

    | Expr_when (e, id, l) -> fprintf fmt "%a when %s(%s)" pp_xml_expr e l id

    | Expr_merge (id, hl) -> 

      fprintf fmt "merge %s %a" id pp_xml_handlers hl

    | Expr_appl (id, e, r) -> pp_xml_app fmt id e r

    )

and pp_xml_tuple fmt el =

 Utils.fprintf_list ~sep:"," pp_xml_expr fmt el

and pp_xml_handler fmt (t, h) =

 fprintf fmt "(%s -> %a)" t pp_xml_expr h

and pp_xml_handlers fmt hl =

 Utils.fprintf_list ~sep:" " pp_xml_handler fmt hl

and pp_xml_app fmt id e r =

  match r with

  | None -> pp_xml_call fmt id e

  | Some c -> fprintf fmt "%t every (%a)" (fun fmt -> pp_xml_call fmt id e) pp_xml_expr c 

and pp_xml_call fmt id e =

  match id, e.expr_desc with

  | "+", Expr_tuple([e1;e2]) -> fprintf fmt "(%a + %a)" pp_xml_expr e1 pp_xml_expr e2

  | "uminus", _ -> fprintf fmt "(- %a)" pp_xml_expr e

  | "-", Expr_tuple([e1;e2]) -> fprintf fmt "(%a - %a)" pp_xml_expr e1 pp_xml_expr e2

  | "*", Expr_tuple([e1;e2]) -> fprintf fmt "(%a * %a)" pp_xml_expr e1 pp_xml_expr e2

  | "/", Expr_tuple([e1;e2]) -> fprintf fmt "(%a / %a)" pp_xml_expr e1 pp_xml_expr e2

  | "mod", Expr_tuple([e1;e2]) -> fprintf fmt "(%a mod %a)" pp_xml_expr e1 pp_xml_expr e2

  | "&&", Expr_tuple([e1;e2]) -> fprintf fmt "(%a and %a)" pp_xml_expr e1 pp_xml_expr e2

  | "||", Expr_tuple([e1;e2]) -> fprintf fmt "(%a or %a)" pp_xml_expr e1 pp_xml_expr e2

  | "xor", Expr_tuple([e1;e2]) -> fprintf fmt "(%a xor %a)" pp_xml_expr e1 pp_xml_expr e2

  | "impl", Expr_tuple([e1;e2]) -> fprintf fmt "(%a => %a)" pp_xml_expr e1 pp_xml_expr e2

  | "<", Expr_tuple([e1;e2]) -> fprintf fmt "(%a &lt; %a)" pp_xml_expr e1 pp_xml_expr e2

  | "<=", Expr_tuple([e1;e2]) -> fprintf fmt "(%a &lt;= %a)" pp_xml_expr e1 pp_xml_expr e2

  | ">", Expr_tuple([e1;e2]) -> fprintf fmt "(%a > %a)" pp_xml_expr e1 pp_xml_expr e2

  | ">=", Expr_tuple([e1;e2]) -> fprintf fmt "(%a >= %a)" pp_xml_expr e1 pp_xml_expr e2

  | "!=", Expr_tuple([e1;e2]) -> fprintf fmt "(%a != %a)" pp_xml_expr e1 pp_xml_expr e2

  | "=", Expr_tuple([e1;e2]) -> fprintf fmt "(%a = %a)" pp_xml_expr e1 pp_xml_expr e2

  | "not", _ -> fprintf fmt "(not %a)" pp_xml_expr e

  | _, Expr_tuple _ -> fprintf fmt "%s %a" id pp_xml_expr e

  | _ -> fprintf fmt "%s (%a)" id pp_xml_expr e

and pp_xml_eexpr fmt e =

  fprintf fmt "%a%t %a"

    (Utils.fprintf_list ~sep:"; " Printers.pp_quantifiers) e.eexpr_quantifiers

    (fun fmt -> match e.eexpr_quantifiers with [] -> () | _ -> fprintf fmt ";")

    pp_xml_expr e.eexpr_qfexpr

and  pp_xml_sf_value fmt e =

   fprintf fmt "%a"

     (* (Utils.fprintf_list ~sep:"; " pp_xml_quantifiers) e.eexpr_quantifiers *)

     (* (fun fmt -> match e.eexpr_quantifiers *)

     (*             with [] -> () *)

     (*                | _ -> fprintf fmt ";") *)

     pp_xml_expr e.eexpr_qfexpr

and pp_xml_s_function fmt expr_ann =

  let pp_xml_annot fmt (kwds, ee) =

    Format.fprintf fmt " %t : %a"

                   (fun fmt -> match kwds with

                               | [] -> assert false

                               | [x] -> Format.pp_print_string fmt x

                               | _ -> Format.fprintf fmt "%a" (Utils.fprintf_list ~sep:"/" Format.pp_print_string) kwds)

                   pp_xml_sf_value ee

  in

  Utils.fprintf_list ~sep:"@ " pp_xml_annot fmt expr_ann.annots

and pp_xml_expr_annot fmt expr_ann =

  let pp_xml_annot fmt (kwds, ee) =

    Format.fprintf fmt "(*! %t: %a; *)"

      (fun fmt -> match kwds with | [] -> assert false | [x] -> Format.pp_print_string fmt x | _ -> Format.fprintf fmt "/%a/" (Utils.fprintf_list ~sep:"/" Format.pp_print_string) kwds)

      pp_xml_eexpr ee

  in

  Utils.fprintf_list ~sep:"@ " pp_xml_annot fmt expr_ann.annots

(* Local Variables: *)

(* compile-command:"make -C ../../.." *)

(* End: *)