CristalCaveGem » LustreC

open Format

open LustreSpec

open Corelang

open Machine_code

let pp_machine_init_name fmt id = fprintf fmt "%s_init" id

let pp_machine_step_name fmt id = fprintf fmt "%s_step" id

let pp_machine_stateless_name fmt id = fprintf fmt "%s" id

let pp_type fmt t =

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

  | Types.Tbool           -> Format.fprintf fmt "Bool"

  | Types.Tint            -> Format.fprintf fmt "Int"

  | Types.Treal           -> Format.fprintf fmt "Real"

  | Types.Tclock _

  | Types.Tarray _

  | Types.Tstatic _

  | Types.Tconst _

  | Types.Tarrow _

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

                             Types.print_ty t; assert false

let pp_decl_var fmt id = 

  Format.fprintf fmt "(declare-var %s %a)"

    id.var_id

    pp_type id.var_type

let pp_var fmt id = Format.pp_print_string fmt id.var_id

let pp_conj pp fmt l = 

  match l with 

    [] -> assert false

  | [x] -> pp fmt x

  | _ -> fprintf fmt "(and @[<v 0>%a@]@ )" (Utils.fprintf_list ~sep:" " pp) l

let concat prefix x = if prefix = "" then x else prefix ^ "." ^ x 

let rename f = (fun v -> {v with var_id = f v.var_id } )

let rename_machine p = rename (fun n -> concat p n)

let rename_machine_list p = List.map (rename_machine p)

let rename_current =  rename (fun n -> n ^ "_c")

let rename_current_list = List.map rename_current

let rename_next = rename (fun n -> n ^ "_x")

let rename_next_list = List.map rename_next

let get_machine machines node_name = 

  List.find (fun m  -> m.mname.node_id = node_name) machines 

let full_memory_vars machines machine =

  let rec aux fst prefix m =

    (rename_machine_list (if fst then prefix else concat prefix m.mname.node_id) m.mmemory) @

      List.fold_left (fun accu (id, (n, _)) -> 

	let name = node_name n in 

	if name = "_arrow" then accu else

	  let machine_n = get_machine machines name in

	( aux false (concat prefix (if fst then id else concat m.mname.node_id id)) machine_n ) @ accu

      ) [] (m.minstances) 

  in

  aux true machine.mname.node_id machine

let stateless_vars machines m = 

  (rename_machine_list m.mname.node_id m.mstep.step_inputs)@

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

let step_vars machines m = 

  (stateless_vars machines m)@

    (rename_current_list (full_memory_vars machines m)) @ 

    (rename_next_list (full_memory_vars machines m)) 

let init_vars machines m = 

  (stateless_vars machines m) @ (rename_next_list (full_memory_vars machines m)) 

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

(*                    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

    Format.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 r   -> pp_print_string fmt r

    | Const_float r  -> pp_print_float fmt r

    | Const_tag t    -> pp_horn_tag fmt t

    | _              -> assert false

(* 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) self pp_var fmt v =

  match v with

    | Cst c         -> pp_horn_const fmt c

    | Array _      

    | Access _ -> assert false (* no arrays *)

    | Power (v, n)  -> assert false

    | LocalVar v    -> pp_var fmt (rename_machine self v)

    | StateVar v    ->

      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))

    | Fun (n, vl)   -> Format.fprintf fmt "%a" (Basic_library.pp_horn n (pp_horn_val self pp_var)) vl

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

let rec pp_value_suffix self pp_value fmt value =

 match value with

 | Fun (n, vl)  ->

   Basic_library.pp_horn n (pp_value_suffix self pp_value) fmt vl

 |  _            ->

   pp_horn_val 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 self pp_var fmt var_type var_name value =

  fprintf fmt "(= %a %a)" (pp_horn_val ~is_lhs:true self pp_var) var_name (pp_value_suffix self pp_var) value

let pp_instance_call 

    machines ?(init=false) m self fmt i (inputs: value_t list) (outputs: var_decl list) =

  try (* stateful node instance *) 

    begin

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

      match node_name n, inputs, outputs with

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

        if init then

          pp_assign

   	    m

   	    self

   	    (pp_horn_var m) 

	    fmt

   	    o.var_type (LocalVar o) i1

        else

          pp_assign

   	    m self (pp_horn_var m) fmt

   	    o.var_type (LocalVar o) i2

      end

      | name, _, _ ->  

	begin

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

	  if init then

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

	      pp_machine_init_name (node_name n) 

	      (* inputs *)

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

	      inputs

	      (Utils.pp_final_char_if_non_empty " " inputs) 

	      (* outputs *)

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

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

	      (Utils.pp_final_char_if_non_empty " " outputs)

	      (* memories (next) *)

	      (Utils.fprintf_list ~sep:" " pp_var) (

  		rename_machine_list 

		  (concat m.mname.node_id i) 

		  (rename_next_list (full_memory_vars machines target_machine)

		  ) 

	       )

	  else

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

	      pp_machine_step_name (node_name n) 

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

	      (Utils.pp_final_char_if_non_empty " " inputs) 

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

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

	      (Utils.pp_final_char_if_non_empty " " outputs)

	      (Utils.fprintf_list ~sep:" " pp_var) (

		(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_next_list (full_memory_vars machines target_machine))

		  ) 

	       )

	end

    end

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

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

      Format.fprintf fmt "(%s %a%t%a)"

	(node_name n)

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

	inputs

	(Utils.pp_final_char_if_non_empty " " inputs) 

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

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

    )

let pp_machine_init (m: machine_t) self fmt inst =

  let (node, static) = List.assoc inst m.minstances in

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

    pp_machine_init_name (node_name node)

    (Utils.fprintf_list ~sep:" " Dimension.pp_dimension) static

    (Utils.pp_final_char_if_non_empty " " static)

    self inst

(* TODO *)

let rec pp_conditional machines ?(init=false)  (m: machine_t) self fmt c tl el =

  fprintf fmt "@[<v 2>if (%a) {%t%a@]@,@[<v 2>} else {%t%a@]@,}"

    (pp_horn_val self (pp_horn_var m)) c

    (Utils.pp_newline_if_non_empty tl)

    (Utils.fprintf_list ~sep:"@," (pp_machine_instr machines ~init:init  m self)) tl

    (Utils.pp_newline_if_non_empty el)

    (Utils.fprintf_list ~sep:"@," (pp_machine_instr machines ~init:init  m self)) el

and pp_machine_instr machines ?(init=false) (m: machine_t) self fmt instr =

  match instr with 

  | MReset i ->

    pp_machine_init m self fmt i

  | MLocalAssign (i,v) ->

    pp_assign

      m self (pp_horn_var m) fmt

      i.var_type (LocalVar i) v

  | MStateAssign (i,v) ->

    pp_assign

      m self (pp_horn_var m) fmt

      i.var_type (StateVar i) v

  | MStep ([i0], i, vl) when Basic_library.is_internal_fun i  -> 

    assert false (* This should not happen anymore *)

  | MStep (il, i, vl) ->

    pp_instance_call machines ~init:init m self fmt i vl il

  | MBranch (g,hl) ->

    if hl <> [] && let t = fst (List.hd hl) in t = tag_true || t = tag_false

    then (* boolean case, needs special treatment in C because truth value is not unique *)

      (* may disappear if we optimize code by replacing last branch test with default *)

      let tl = try List.assoc tag_true  hl with Not_found -> [] in

      let el = try List.assoc tag_false hl with Not_found -> [] in

      pp_conditional machines ~init:init m self fmt g tl el

    else assert false (* enum type case *)

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

let is_stateless m = m.minstances = [] && m.mmemory = [] 

(* 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 = 

  let pp_instr init = pp_machine_instr machines ~init:init m in

  if m.mname.node_id = arrow_id then 

    (* We don't print arrow function *)

    ()

  else 

    begin 

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

   (* 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 ();

   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) (stateless_vars machines m));

       (* Rule for single predicate *)

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

	 (pp_conj (pp_instr 

		     true (* In this case, the boolean init can be set to true or false. 

			     The node is stateless. *)

		     m.mname.node_id)

	 )

	 m.mstep.step_instrs

	 pp_machine_stateless_name m.mname.node_id

	 (Utils.fprintf_list ~sep:" " pp_var) (stateless_vars machines m);

     end

   else 

     begin

       (* Declaring predicate *)

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

	 pp_machine_init_name m.mname.node_id

	 (Utils.fprintf_list ~sep:" " pp_type) 

	 (List.map (fun v -> v.var_type) (init_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 ();

       (* Rule for init *)

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

	 (pp_conj (pp_instr true m.mname.node_id)) m.mstep.step_instrs

	 pp_machine_init_name m.mname.node_id

	 (Utils.fprintf_list ~sep:" " pp_var) (init_vars machines m);

       (* Rule for step *)

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

	 (pp_conj (pp_instr false m.mname.node_id)) m.mstep.step_instrs

	 pp_machine_step_name m.mname.node_id

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

       (* Adding assertions *)

       (match m.mstep.step_asserts with

       | [] -> ()

       | assertsl -> begin

	 let pp_val = pp_horn_val ~is_lhs:true m.mname.node_id pp_var in

	 Format.fprintf fmt "; Asserts@.";

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

	   (pp_conj pp_val) assertsl;

	 (** TEME: the following code is the one we described. But it generates a segfault in z3 

	 Format.fprintf fmt "; Asserts for init@.";

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

	   (Utils.fprintf_list ~sep:"@ " (pp_instr true m.mname.node_id)) m.mstep.step_instrs

	   pp_machine_init_name m.mname.node_id

	   (Utils.fprintf_list ~sep:" " pp_var) (init_vars machines m)

	   (pp_conj pp_val) assertsl; 

	 Format.fprintf fmt "; Asserts for step@.";

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

	   (Utils.fprintf_list ~sep:"@ " (pp_instr false m.mname.node_id)) m.mstep.step_instrs

	   pp_machine_step_name m.mname.node_id

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

	   (pp_conj pp_val) assertsl

      	 *)

       end

       );

(*

       match m.mspec with

	 None -> () (* No node spec; we do nothing *)

       | Some {requires = []; ensures = [EnsuresExpr e]; behaviors = []} -> 

	 ( 

       (* For the moment, we only deal with simple case: single ensures, no other parameters *)

	   ()

	 )

       | _ -> () (* Other cases give nothing *)

*)      

     end

    end

let collecting_semantics machines fmt node machine =

    Format.fprintf fmt "; Collecting semantics for node %s@.@." node;

    (* We print the types of the main node "memory tree" TODO: add the output *)

    let main_output =

     rename_machine_list machine.mname.node_id machine.mstep.step_outputs

    in

    let main_output_dummy = 

     rename_machine_list ("dummy" ^ machine.mname.node_id) machine.mstep.step_outputs

    in

    let main_memory_next = 

      (rename_next_list (* machine.mname.node_id *) (full_memory_vars machines machine)) @

      main_output

    in

    let main_memory_current = 

      (rename_current_list (* machine.mname.node_id *) (full_memory_vars machines machine)) @

      main_output_dummy

    in

    (* Special case when the main node is stateless *)

    let init_name, step_name = 

      if is_stateless machine then

	pp_machine_stateless_name, pp_machine_stateless_name

      else

	pp_machine_init_name, pp_machine_step_name

    in

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

      (Utils.fprintf_list ~sep:" " pp_type) 

      (List.map (fun v -> v.var_type) main_memory_next);

    Format.fprintf fmt "; Initial set@.";

    Format.fprintf fmt "(declare-rel INIT_STATE ())@.";

    Format.fprintf fmt "(rule INIT_STATE)@.";

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

      init_name node

      (Utils.fprintf_list ~sep:" " pp_var) (init_vars machines machine)

      (Utils.fprintf_list ~sep:" " pp_var) main_memory_next ;

    Format.fprintf fmt "; Inductive def@.";

    (Utils.fprintf_list ~sep:" " (fun fmt v -> Format.fprintf fmt "%a@." pp_decl_var v)) fmt main_output_dummy;

    Format.fprintf fmt 

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

      (Utils.fprintf_list ~sep:" " pp_var) main_memory_current

      step_name node

      (Utils.fprintf_list ~sep:" " pp_var) (step_vars machines machine)

      (Utils.fprintf_list ~sep:" " pp_var) main_memory_next 

let check_prop machines fmt node machine =

  let main_output =

    rename_machine_list machine.mname.node_id machine.mstep.step_outputs

  in

  let main_memory_next = 

    (rename_next_list (full_memory_vars machines machine)) @ main_output

  in

  Format.fprintf fmt "; Property def@.";

  Format.fprintf fmt "(declare-rel ERR ())@.";

  Format.fprintf fmt "@[<v 2>(rule (=> @ (and @[<v 0>(not %a)@ (MAIN %a)@])@ ERR))@."

    (pp_conj pp_var) main_output

    (Utils.fprintf_list ~sep:" " pp_var) main_memory_next

    ;

  if !Options.horn_queries then

    Format.fprintf fmt "(query ERR)@."

let cex_computation machines fmt node machine =

    Format.fprintf fmt "; CounterExample computation for node %s@.@." node;

    (* We print the types of the cex node "memory tree" TODO: add the output *)

    let cex_input =

     rename_machine_list machine.mname.node_id machine.mstep.step_inputs

    in

    let cex_input_dummy = 

     rename_machine_list ("dummy" ^ machine.mname.node_id) machine.mstep.step_inputs

    in

    let cex_output =

     rename_machine_list machine.mname.node_id machine.mstep.step_outputs

    in

    let cex_output_dummy = 

     rename_machine_list ("dummy" ^ machine.mname.node_id) machine.mstep.step_outputs

    in

    let cex_memory_next = 

      cex_input @ (rename_next_list (full_memory_vars machines machine)) @ cex_output

    in

    let cex_memory_current = 

      cex_input_dummy @ (rename_current_list (full_memory_vars machines machine)) @ cex_output_dummy

    in

    (* Special case when the cex node is stateless *)

    let init_name, step_name = 

      if is_stateless machine then

	pp_machine_stateless_name, pp_machine_stateless_name

      else

	pp_machine_init_name, pp_machine_step_name

    in

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

      (Utils.fprintf_list ~sep:" " pp_type) 

      (List.map (fun v -> v.var_type) cex_memory_next);

    Format.fprintf fmt "; Initial set@.";

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

      init_name node

      (Utils.fprintf_list ~sep:" " pp_var) (init_vars machines machine)

      (Utils.fprintf_list ~sep:" " pp_var) cex_memory_next ;

    Format.fprintf fmt "; Inductive def@.";

    (* Declare dummy inputs. Outputs should have been declared previously with collecting sem *)

    (Utils.fprintf_list ~sep:" " (fun fmt v -> Format.fprintf fmt "%a@." pp_decl_var v)) fmt cex_input_dummy;

    Format.fprintf fmt "(declare-var cexcpt Int)@.";

    Format.fprintf fmt 

      "@[<v 2>(rule (=> @ (and @[<v 0>(CEX cexcpt %a)@ (@[<v 0>%a %a@])@]@ )@ (CEX (+ 1 cexcpt) %a)@]@.))@.@."

      (Utils.fprintf_list ~sep:" " pp_var) cex_memory_current

      step_name node

      (Utils.fprintf_list ~sep:" " pp_var) (step_vars machines machine)

      (Utils.fprintf_list ~sep:" " pp_var) cex_memory_next 

let get_cex machines fmt node machine =

    let cex_input =

     rename_machine_list machine.mname.node_id machine.mstep.step_inputs

    in

    let cex_output =

     rename_machine_list machine.mname.node_id machine.mstep.step_outputs

    in

  let cex_memory_next = 

    cex_input @ (rename_next_list (full_memory_vars machines machine)) @ cex_output

  in

  Format.fprintf fmt "; Property def@.";

  Format.fprintf fmt "(declare-rel CEXTRACE ())@.";

  Format.fprintf fmt "@[<v 2>(rule (=> @ (and @[<v 0>(not %a)@ (CEX cexcpt %a)@])@ CEXTRACE))@."

    (pp_conj pp_var) cex_output

    (Utils.fprintf_list ~sep:" " pp_var) cex_memory_next

    ;

  if !Options.horn_queries then

    Format.fprintf fmt "(query CEXTRACE)@."

let main_print machines fmt = 

if !Options.main_node <> "" then 

  begin

    let node = !Options.main_node in

    let machine = get_machine machines node in

    collecting_semantics machines fmt node machine;

    check_prop machines fmt node machine;

    cex_computation machines fmt node machine;

    get_cex machines fmt node machine 

end

let translate fmt basename prog machines =

  List.iter (print_machine machines fmt) (List.rev machines);

  main_print machines fmt 

let traces_file fmt basename prog machines =

  Format.fprintf fmt 

    "; Horn code traceability generated by %s@.; SVN version number %s@.@."

    (Filename.basename Sys.executable_name) 

    Version.number;

  (* We extract the annotation dealing with traceability *)

  let machines_traces = List.map (fun m -> 

    let traces : (ident * expr) list= 

      let all_annots = List.flatten (List.map (fun ann -> ann.annots) m.mannot) in

      let filtered = 

	List.filter (fun (kwds, _) -> kwds = ["horn_backend";"trace"]) all_annots 

      in

      let content = List.map snd filtered in

      (* Elements are supposed to be a pair (tuple): variable, expression *)

      List.map (fun ee -> 

	match ee.eexpr_quantifiers, ee.eexpr_qfexpr.expr_desc with 

	| [], Expr_tuple [v;e] -> (

	  match v.expr_desc with 

	  | Expr_ident vid -> vid, e 

	  | _ -> assert false )

	| _ -> assert false)

	content

    in

    m, traces

  ) machines

  in

  (* Compute memories associated to each machine *)

  let compute_mems m =

    let rec aux fst prefix m =

      (List.map (fun mem -> (prefix, mem)) m.mmemory) @

	List.fold_left (fun accu (id, (n, _)) -> 

	  let name = node_name n in 

	  if name = "_arrow" then accu else

	    let machine_n = get_machine machines name in

	    ( aux false ((id,machine_n)::prefix) machine_n ) 

	    @ accu

	) [] m.minstances 

    in

    aux true [] m

  in

  List.iter (fun m ->

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

    let memories_old = 

      List.map (fun (p, v) -> 

	let machine = match p with | [] -> m | (_,m')::_ -> m' in

	let traces = List.assoc machine machines_traces in

	if List.mem_assoc v.var_id traces then

	  (* We take the expression associated to variable v in the trace info *)

	  p, List.assoc v.var_id traces

	else

	  (* We keep the variable as is: we create an expression v *)

	  p, mkexpr Location.dummy_loc (Expr_ident v.var_id)

      ) (compute_mems m) 

    in

    let memories_next = (* We remove the topest pre in each expression *)

      List.map 

	(fun (prefix, ee) -> 

	  match ee.expr_desc with 

	  | Expr_pre e -> prefix, e 

	  | _ -> Format.eprintf 

	    "Mem Failure: (prefix: %a, eexpr: %a)@.@?" 

	    (Utils.fprintf_list ~sep:"," 

	       (fun fmt (id,n) -> fprintf fmt "(%s,%s)" id n.mname.node_id )) 

	    (List.rev prefix) 

	    Printers.pp_expr ee; 

	    assert false)

	memories_old

    in

    let pp_prefix_rev fmt prefix =

      Utils.fprintf_list ~sep:"." (fun fmt (id,n) -> fprintf fmt "(%s,%s)" id n.mname.node_id) fmt (List.rev prefix)

    in

    Format.fprintf fmt "; Init predicate@.";

    Format.fprintf fmt "; horn encoding@.";

    Format.fprintf fmt "(%a %a)@."

      pp_machine_init_name m.mname.node_id

      (Utils.fprintf_list ~sep:" " pp_var) (init_vars machines m);

    Format.fprintf fmt "; original expressions@.";

    Format.fprintf fmt "(%a %a%t%a)@."

      pp_machine_init_name m.mname.node_id

      (Utils.fprintf_list ~sep:" " pp_var) (m.mstep.step_inputs@m.mstep.step_outputs)

      (fun fmt -> match memories_next with [] -> () | _ -> fprintf fmt " ")

      (Utils.fprintf_list ~sep:" " (fun fmt (prefix, ee) -> fprintf fmt "%a(%a)" pp_prefix_rev prefix Printers.pp_expr ee)) memories_next;

    Format.pp_print_newline fmt ();

    Format.fprintf fmt "; Step predicate@.";

    Format.fprintf fmt "; horn encoding@.";

    Format.fprintf fmt "(%a %a)@."

      pp_machine_step_name m.mname.node_id

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

    Format.fprintf fmt "; original expressions@.";

    Format.fprintf fmt "(%a %a%t%a)@."

      pp_machine_step_name m.mname.node_id

      (Utils.fprintf_list ~sep:" " pp_var) (m.mstep.step_inputs@m.mstep.step_outputs)

      (fun fmt -> match memories_old with [] -> () | _ -> fprintf fmt " ")

      (Utils.fprintf_list ~sep:" " (fun fmt (prefix,ee) -> fprintf fmt "%a(%a)" pp_prefix_rev prefix Printers.pp_expr ee)) (memories_old@memories_next);

    Format.pp_print_newline fmt ();    

  ) (List.rev machines);

(* Local Variables: *)

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

(* End: *)