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structure kernel :> kernel =
struct

open HolKernel Abbrev boolLib aiLib dir;
val ERR = mk_HOL_ERR "kernel";
               
val selfdir = dir.selfdir 

(* -------------------------------------------------------------------------
   Globals
   ------------------------------------------------------------------------- *)

val maxinput = ref 16
val simple_search = ref false

(* -------------------------------------------------------------------------
   Types
   ------------------------------------------------------------------------- *)

type oper2 = int * int -> int
type oper3 = int * int * int -> int
type exec = int * int -> int
type seq = int list
val seq_compare = list_compare Int.compare
fun string_of_seq il = String.concatWith " " (map its il)

(* -------------------------------------------------------------------------
   Composing semantics and executables
   ------------------------------------------------------------------------- *)

val error = valOf (Int.maxInt)

(* -------------------------------------------------------------------------
   Program
   ------------------------------------------------------------------------- *)

type id = int
datatype prog = Ins of (id * prog list);

fun prog_compare (Ins(s1,pl1),Ins(s2,pl2)) =
  cpl_compare Int.compare (list_compare prog_compare) ((s1,pl1),(s2,pl2))

fun equal_prog (a,b) = (prog_compare (a,b) = EQUAL)

fun prog_size (Ins(s,pl)) = 
  if null pl
  then 1 + sum_int (map prog_size pl) 
  else sum_int (map prog_size pl) 

fun all_subprog (p as Ins (_,pl)) = p :: List.concat (map all_subprog pl);

(* -------------------------------------------------------------------------
   Instructions
   ------------------------------------------------------------------------- *)

val zero_id = 0
val one_id = 1
val two_id = 2
val addi_id = 3
val diff_id = 4
val mult_id = 5
val divi_id = 6
val modu_id = 7
val cond_id = 8
val loop_id = 9
val var_id = 10
val ind_id = 11
val compr_id = 12

val alpha3 = rpt_fun_type 3 alpha
val alpha4 = rpt_fun_type 4 alpha
val operv = Vector.fromList 
  [
   mk_var ("zero",alpha),
   mk_var ("one",alpha),
   mk_var ("two",alpha),
   mk_var ("addi",alpha3),
   mk_var ("diff",alpha3),
   mk_var ("mult",alpha3),
   mk_var ("divi",alpha3),
   mk_var ("modu",alpha3),
   mk_var ("cond",alpha4),
   mk_var ("loop",alpha4),
   mk_var ("var",alpha),
   mk_var ("ind",alpha),
   mk_var ("compr",alpha3)
  ]

val maxoper = Vector.length operv

val operav = Vector.map arity_of operv

fun name_of_oper i = fst (dest_var (Vector.sub (operv,i)))

(* time limit per instruction *)
val timelimit = ref (16*16*16*16+1);
val counter = ref 0;
fun start f x = (counter := 0; f x)

(* nullary *)
val zero_f = (fn _ => 0)
val one_f = (fn _ => 1)
val two_f = (fn _ => 2)
val var_f = (fn (a:int,b:int) => a)
val ind_f = (fn (a:int,b:int) => b)

(* first-order *)
val addi_f = op +
val diff_f = op -
val mult_f = op *
val divi_f = op div
val modu_f = op mod
fun cond_f (a,b,c) = if a <= 0 then b else c

(* higher-order operator *)
fun loop_f_aux i f n x = 
   (
   incr counter;
   if !counter > !timelimit then raise Div
   else if n <= 0 then x 
   else loop_f_aux (i+1) f (n-1) (f (x,i))
   )

fun loop_f f (n,x) =
  if n > !timelimit then raise Div else loop_f_aux 1 f n x

fun compr_f_aux x f n0 n =
   (
   if x > (n0+1)*(n0+1)*256 then raise Div else ();
   incr counter;
   if !counter > !timelimit then raise Div
   else if f (x,0) <= 0 then 
     (if n0 >= n then x else compr_f_aux (x+1) f (n0+1) n)
   else compr_f_aux (x+1) f n0 n
   )

fun compr_f f n =
  if n > !timelimit orelse n < 0 then raise Div else compr_f_aux 0 f 0 n

(* regroup by arity *)
val nullaryl =
 [(zero_id,zero_f),(one_id,one_f),(two_id,two_f),(var_id,var_f),(ind_id,ind_f)]

val nullaryidl = map fst nullaryl
fun is_nullary id = mem id nullaryidl
fun find_nullaryf id = assoc id nullaryl
val nullaryv = Vector.tabulate (maxoper, fn i => 
  if can find_nullaryf i then find_nullaryf i else zero_f);

val binaryl = 
  [(addi_id,addi_f),(diff_id,diff_f),(mult_id,mult_f),(divi_id,divi_f),
   (modu_id,modu_f)]
val binaryidl = map fst binaryl
fun is_binary id = id >= addi_id andalso id <= modu_id
fun find_binaryf id = assoc id binaryl
val binaryv = Vector.tabulate (maxoper, fn i => 
  if can find_binaryf i then find_binaryf i else addi_f);

fun is_comm id = mem id [addi_id, mult_id]
val binaryidl_nocomm = filter (fn x => not (is_comm x)) binaryidl 

(* -------------------------------------------------------------------------
   Compressed programs
   ------------------------------------------------------------------------- *)

fun depend_on_i p = case p of 
    Ins (id,[]) => id = ind_id 
  | Ins (9,[p1,p2,p3]) => depend_on_i p2 orelse depend_on_i p3
  | Ins (_,pl) => exists depend_on_i pl  

fun under_lambda p = case p of
    Ins (id,[]) => []
  | Ins (9,[p1,p2,p3]) => p1 :: List.concat (map under_lambda [p1,p2,p3])
  | Ins (_,pl) => List.concat (map under_lambda pl)

fun has_lambdai p = case p of
    Ins (id,[]) => false
  | Ins (9,[p1,p2,p3]) => depend_on_i p1 
     orelse has_lambdai p2 orelse has_lambdai p3
  | Ins (_,pl) => exists has_lambdai pl

fun suc_prog n p = if n <= 0 then p else 
  Ins (addi_id, [suc_prog (n-1) p, Ins (one_id,[])])

fun shift_prog n p = case p of 
    Ins (id,[]) => if id = var_id then suc_prog n p else p 
  | Ins (9,[p1,p2,p3]) => Ins (9,[p1, shift_prog n p2, shift_prog n p3])
  | Ins (12,[p1,p2]) => Ins (12,[p1, shift_prog n p2])
  | Ins (id,pl) => Ins (id, map (shift_prog n) pl)

(* -------------------------------------------------------------------------
   Compressed programs
   ------------------------------------------------------------------------- *)

type progi = Arbint.int

val progi_compare = Arbint.compare
fun equal_progi (a,b) = (progi_compare (a,b) = EQUAL)

fun suc x = x + 1
fun pred x = x - 1

local open Arbint in

val arbmaxoper = fromInt (suc maxoper)

fun zip_prog prog =
  let
    fun polish (Ins (id,pl)) = fromInt (suc id) :: List.concat (map polish pl)
    fun loop r il = case il of 
        [] => r 
      | a :: m => loop (r * arbmaxoper + a) m 
  in
    loop zero (rev (polish prog))
  end

fun unzip_progl arbi =
  let 
    val (q,r) = Arbint.divmod (arbi, arbmaxoper)
    val id = pred (toInt r)
    val a = Vector.sub (operav,id)
    val pl = if q = zero then [] else unzip_progl q
    val (pla,plb) = part_n a pl
  in
    Ins (id,pla) :: plb
  end

fun unzip_prog arbi = singleton_of_list (unzip_progl arbi)

val hseq_modw = fromInt 2115908027

fun pi_to_hseq pi =
  let val (q,r) = Arbint.divmod (pi, hseq_modw) in
    if q = zero 
    then [toInt r]
    else toInt r :: pi_to_hseq q
  end

end (* local *)

(* -------------------------------------------------------------------------
   Possible inputs
   ------------------------------------------------------------------------- *)

val entryl = List.concat [
  List.tabulate (16,fn x => (x,0)),
  List.tabulate (8,fn x => (x,1)),
  List.tabulate (4,fn x => (x,2)),
  List.tabulate (2,fn x => (x,3)),
  List.tabulate (1,fn x => (x,4))
  ];

val entryl16 = first_n 16 entryl

(* -------------------------------------------------------------------------
   Execute a program on some input
   ------------------------------------------------------------------------- *)

fun compose1 f f1 x = f (f1 x)
fun compose2 f f1 f2 x = f (f1 x, f2 x)
fun compose3 f f1 f2 f3 x = f (f1 x, f2 x, f3 x)

fun mk_exec_aux prog = case prog of
    Ins (id,[]) => Vector.sub (nullaryv,id) 
  | Ins (12,[p1,p2]) =>
    compose1 (compr_f (mk_exec_aux p1)) (mk_exec_aux p2)
  | Ins (id,[p1,p2]) => 
    compose2 (Vector.sub (binaryv,id)) (mk_exec_aux p1) (mk_exec_aux p2)
  | Ins (8,[p1,p2,p3]) => 
    compose3 cond_f (mk_exec_aux p1) (mk_exec_aux p2) (mk_exec_aux p3)
  | Ins (9,[p1,p2,p3]) =>
    compose2 (loop_f (mk_exec_aux p1)) (mk_exec_aux p2) (mk_exec_aux p3)
  | _ => raise ERR "mk_exec" ""  

fun mk_exec p =
  let val exec = start (mk_exec_aux p) in
    (fn x => ((exec x,!counter) handle Overflow => (error,!counter)))
  end 

fun not_semdep_on_i e31 =
  let
    val (e16,e15) = part_n 16 e31
    val (e8,e7) = part_n 8 e15
    val (e4,e3) = part_n 4 e7
    val (e2,e1) = part_n 2 e3
  in
    seq_compare (first_n 8 e16, e8) = EQUAL andalso
    seq_compare (first_n 4 e16, e4) = EQUAL andalso
    seq_compare (first_n 2 e16, e2) = EQUAL andalso
    seq_compare (first_n 1 e16, e1) = EQUAL
  end

fun semtimo_of_prog p =
  let val f = mk_exec p in
    if not (depend_on_i p) 
    then 
      let 
        val e16 = map f entryl16
        val r = 
          (e16 @ first_n 8 e16 @ first_n 4 e16 @ first_n 2 e16 @ first_n 1 e16)
        val (sem,timl) = split r
        val tim = 31 + sum_int timl
      in
        SOME (sem,tim)
      end
      handle Div => NONE
    else
      let 
        val r = map f entryl 
        val (sem,timl) = split r
        val tim = 31 + sum_int timl
      in
        if not_semdep_on_i sem then NONE else SOME (sem,tim)
      end
      handle Div => NONE
  end

fun semo_of_prog p = Option.map fst (semtimo_of_prog p)

fun same_sem p1 p2 = case (semo_of_prog p1, semo_of_prog p2) of
     (SOME l1, SOME l2) => seq_compare (l1,l2) = EQUAL
   | _ => false

val sem_of_prog = valOf o semo_of_prog

fun seq_of_prog p = first_n 16 (sem_of_prog p)

fun is_executable x = isSome (semo_of_prog x)

(* -------------------------------------------------------------------------
   Applications of an instruction syntactically from compressed programs
   ------------------------------------------------------------------------- *)

fun papp_nullop id = Ins (id,[])
fun papp_binop id (p1,p2) = Ins (id, [p1,p2])
fun papp_ternop id (p1,p2,p3) = Ins (id,[p1,p2,p3])

(* -------------------------------------------------------------------------
   Human readable output
   ------------------------------------------------------------------------- *)

val constnorm_flag = ref false
val polynorm_flag = ref true
val imperative_flag = ref false

fun itsm i = if i < 0 then "-" ^ its (~i) else its i

fun mk_xn vn = if vn = ~1 then "x" else "X"
fun mk_in vn = if vn = ~1 then "i" else "I"

fun constnorm prog = case prog of
    Ins (0,[]) => 0
  | Ins (1,[]) => 1
  | Ins (2,[]) => 2
  | Ins (3,[p1,p2]) => addi_f (constnorm p1,constnorm p2)
  | Ins (4,[p1,p2]) => diff_f (constnorm p1,constnorm p2)
  | Ins (5,[p1,p2]) => mult_f (constnorm p1,constnorm p2)
  | Ins (6,[p1,p2]) => divi_f (constnorm p1,constnorm p2)
  | Ins (7,[p1,p2]) => modu_f (constnorm p1,constnorm p2)
  | _ => raise ERR "constnorm" ""

fun polyaddi l1 l2 = case (l1,l2) of
    (l1,[]) => l1
  | ([],l2) => l2
  | (a1 :: m1, a2 :: m2) => addi_f (a1,a2) :: polyaddi m1 m2

fun polydiff l1 l2 = case (l1,l2) of
    (l1,[]) => l1
  | ([],l2) => polydiff (List.tabulate (length l2, fn _ => 0)) l2
  | (a1 :: m1, a2 :: m2) => diff_f (a1,a2) :: polydiff m1 m2

fun polymult l1 l2 = case (l1,l2) of 
    (l1,[]) => raise ERR "polymult" ""
  | ([],l2) => raise ERR "polymult" ""
  | (l1,[a]) => map (fn x => mult_f (a,x)) l1
  | ([a],l2) => map (fn x => mult_f (a,x)) l2
  | (a1 :: m1, l2) => 
    polyaddi (map (fn x => mult_f (a1,x)) l2)  (polymult m1 (0 :: l2))

fun polydivi l1 l2 = case (l1,l2) of
    ([a],[b]) => [divi_f (a,b)]
  | _ => raise ERR "polydivi" ""
fun polymodu l1 l2 = case (l1,l2) of
    ([a],[b]) => [modu_f (a,b)]
  | _ => raise ERR "polymodu" ""

fun polynorm prog = case prog of
    Ins (0,[]) => [0]
  | Ins (1,[]) => [1]
  | Ins (2,[]) => [2]
  | Ins (3,[p1,p2]) => polyaddi (polynorm p1) (polynorm p2)
  | Ins (4,[p1,p2]) => polydiff (polynorm p1) (polynorm p2)
  | Ins (5,[p1,p2]) => polymult (polynorm p1) (polynorm p2)
  | Ins (6,[p1,p2]) => polydivi (polynorm p1) (polynorm p2)
  | Ins (7,[p1,p2]) => polymodu (polynorm p1) (polynorm p2)
  | Ins (10,[]) => [0,1]
  | _ => raise ERR "polynorm" ""

fun string_of_mono vn (a,i) = 
  (if a = 1 andalso i <> 0 then "" else 
   if a = ~1 andalso i <> 0 then "-" else itsm a) ^
  (if (a = 1 andalso i <> 0) orelse
      (a = ~1 andalso i <> 0) orelse
      (i = 0)
   then "" else "*") ^
  (if i = 0 then "" else if i = 1 then mk_xn vn else mk_xn vn ^ 
     (if !imperative_flag then "**" else "^") ^ its i)

fun string_of_poly vn l = 
  let val l1 = filter (fn x => fst x <> 0) (number_snd 0 l) in
    if null l1 then "0" else
    let val s = String.concatWith " + " (map (string_of_mono vn) (rev l1)) in
      if length l1 = 1 then s else "(" ^ s ^ ")"
    end
  end

fun polyaddil l = case l of 
    [] => [] 
  | a :: m => polyaddi a (polyaddil m)

fun polymultl l = case l of 
    [] => raise ERR "polymultl" ""
  | [a] => a 
  | a :: m => polymult a (polymultl m)

fun rm_par s = 
  if String.size s = 0 then s else
  if String.sub (s,0) = #"(" andalso String.sub (s,String.size s - 1) =  #")" 
  then String.substring (s,1,String.size s - 2)
  else s;

(* regroup polynoms in repeated addition/substraction and
   multiplications *)

fun strip_addi p = case p of
    Ins (3,[p1,p2]) => 
    let 
      val (a1,b1) = strip_addi p1 
      val (a2,b2) = strip_addi p2
    in
      (a1 @ a2, b1 @ b2)
    end 
  | Ins (4,[p1,p2]) =>
    let 
      val (a1,b1) = strip_addi p1
      val (a2,b2) = strip_addi p2
    in
      (a1 @ b2, a2 @ b1)
    end 
  | _ => ([p],[])

fun strip_mult p = case p of
    Ins (5,[p1,p2]) => strip_mult p1 @ strip_mult p2 
  | _ => [p]

fun is_loop (Ins(id,pl)) = (mem id [9,12])

val ctxt = ref []
val funn = ref 0
fun incrs s = s ^ " = " ^ s ^ " + 1";
fun decrs s = s ^ " = " ^ s ^ " - 1";

fun human vn prog =
  if !constnorm_flag andalso can constnorm prog then its (constnorm prog) else
  case prog of
    Ins (3,[p1,p2]) => 
    if !polynorm_flag 
    then reg_add vn prog
    else "(" ^ human vn p1 ^ " + " ^ human vn p2 ^ ")"   
  | Ins (4,[p1,p2]) =>  
    if !polynorm_flag 
    then reg_add vn prog
    else "(" ^ human vn p1 ^ " - " ^ human vn p2 ^ ")"   
  | Ins (5,[p1,p2]) =>
    if !polynorm_flag 
    then reg_mult vn prog
    else "(" ^ human vn p1 ^ " * " ^ human vn p2 ^ ")"
  | Ins (6,[p1,p2]) => 
    if !imperative_flag
    then "(" ^ human vn p1 ^ " // " ^ human vn p2 ^ ")"
    else "(" ^ human vn p1 ^ " div " ^ human vn p2 ^ ")"
  | Ins (7,[p1,p2]) => 
    if !imperative_flag
    then "(" ^ human vn p1 ^ " % " ^ human vn p2 ^ ")"
    else "(" ^ human vn p1 ^ " mod " ^ human vn p2 ^ ")"
  | Ins (8,[p1,p2,p3]) => 
     if !imperative_flag
     then "(" ^ rm_par (human vn p2) ^ " if " ^ 
                rm_par (human vn p1) ^ " <= 0 else " ^
                rm_par (human vn p3) ^ ")"
     else "(if " ^ 
       rm_par (human vn p1) ^ " <= 0 then " ^ rm_par (human vn p2)  ^ " else " ^ 
       rm_par (human vn p3) ^ ")"
  | Ins (9,[p1,p2,p3]) => 
      let
        val wn = (!funn)
        val _ = incr funn
        val s1 = rm_par (human (~1) p1)
        val s2 = human wn p2 ^ " + 1"
        val s3 = rm_par (human wn p3)
        val fs = "f" ^ its wn
        val fprev1 = if depend_on_i prog 
          then fs ^ "(" ^ mk_xn wn ^ "," ^ mk_in wn ^ ")"
          else fs ^ "(" ^ mk_xn wn ^ ")"
        val fprev2 = if depend_on_i prog 
          then fs ^ "(" ^ mk_xn vn ^ "," ^ mk_in vn ^ ")"
          else fs ^ "(" ^ mk_xn vn ^ ")"
        val fs_head = "def " ^ fprev1 ^ ":"
      in
        if !imperative_flag then
          let val cs = 
            [fs_head,
             "  x = " ^ s3,
             "  " ^ "for i in range (1," ^ s2 ^ "):",
             "    x = " ^ s1,
             "  return x", ""]
          in
            ctxt := !ctxt @ cs; fprev2
          end
        else
          "loop(\\(x,i)." ^ s1  ^ ", " ^ 
          rm_par (human (~1) p2)  ^ ", " ^ rm_par (human (~1) p3) ^ ")"
      end
  | Ins (10,[]) => mk_xn vn
  | Ins (11,[]) => mk_in vn
  | Ins (12,[p1,p2]) => 
    let
      val wn = (!funn)
      val _ = incr funn
      val s1 = rm_par (human (~1) p1)
      val s2 = rm_par (human wn p2)
      val fs = "f" ^ its wn
      val fprev1 = if depend_on_i prog 
        then fs ^ "(" ^ mk_xn wn ^ "," ^ mk_in wn ^ ")"
        else fs ^ "(" ^ mk_xn wn ^ ")"
      val fprev2 = if depend_on_i prog 
        then fs ^ "(" ^ mk_xn vn ^ "," ^ mk_in vn ^ ")"
        else fs ^ "(" ^ mk_xn vn ^ ")"
      val fs_head = "def " ^ fprev1 ^ ":"
    in
      if !imperative_flag then
        let val cs = [fs_head,
          "  x,i = 0,0",
          "  while i <= " ^ s2 ^ ":",
          "    if " ^ s1 ^ " <= 0:",
          "      i = i + 1",
          "    x = x + 1",
          "  return x - 1", ""]
        in
          ctxt := !ctxt @ cs; fprev2
        end
      else
        "compr(\\x." ^ s1 ^ ", " ^ rm_par (human (~1) p2) ^ ")" 
    end
  | Ins (s,[]) => its s
  | Ins (s,l) => "(" ^ its s ^ " " ^ 
      String.concatWith " " (map (human vn) l) ^ ")"

and reg_add vn p = 
  let 
    val (pl1,pl2) = strip_addi p
    val (pl1a,pl1b) = partition (can polynorm) pl1
    val (pl2a,pl2b) = partition (can polynorm) pl2
    val pl1n = map polynorm pl1a
    val pl2n = map polynorm pl2a
    fun human_addl pl = case pl of 
         [] => raise ERR "reg_add" ""
       | [a] => human vn a 
       | _ => "(" ^ String.concatWith " + " (map (human vn) pl) ^ ")"
    val polyo = if null pl1n andalso null pl2n then NONE else 
      SOME (polydiff (polyaddil pl1n) (polyaddil pl2n)) 
  in
    case (polyo,pl1b,pl2b) of
      (NONE,[],[]) => raise ERR "reg_add 2" ""
    | (NONE,_,[]) => human_addl pl1b
    | (NONE,[],_) => "-" ^ human_addl pl2b
    | (NONE,_,_) => "(" ^ human_addl pl1b ^ " - " ^ human_addl pl2b ^ ")"
    | (SOME poly,[],[]) => string_of_poly vn poly 
    | (SOME poly,_,[]) => "(" ^ string_of_poly vn poly ^ 
      " + " ^ human_addl pl1b ^ ")"
    | (SOME poly,[],_) => "(" ^ string_of_poly vn poly ^ 
      " - " ^ human_addl pl2b ^ ")"
    | (SOME poly,_,_) => "(" ^ string_of_poly vn poly ^ 
      " + " ^ human_addl pl1b ^ " - " ^ human_addl pl2b ^ ")"
  end

and reg_mult vn p =
  let 
    val pl = strip_mult p 
    val (pla,plb) = partition (can polynorm) pl
    fun human_multl pl = case pl of 
         [] => raise ERR "reg_mult" ""
       | [a] => human vn a 
       | _ => "(" ^ String.concatWith " * " (map (human vn) pl) ^ ")"
    val polyo = if null pla then NONE else 
      SOME (polymultl (map polynorm pla))  
  in
    case (polyo,plb) of 
      (NONE,[]) => raise ERR "reg_mult 2" ""
    | (NONE,_) => human_multl plb
    | (SOME poly,[]) => string_of_poly vn poly
    | (SOME poly,_) => "(" ^ string_of_poly vn poly ^ " * " ^ 
      human_multl plb ^ ")"
  end

fun humanf p =
  let 
    val _ = imperative_flag := false
    val s = human (~1) p
    val _ = imperative_flag := false
  in s end

fun humani ntop p =
  let 
    val _ = imperative_flag := true
    val _ = ctxt := [] 
    val _ = funn := 0
    val ps = 
      if not (is_loop p) then
      let
        val wn = !funn
        val _ = incr funn
        val fs = "f" ^ its wn
        val xs = mk_xn wn
        val s = rm_par (human wn p)
        val head = "def " ^ fs ^ "(" ^ xs ^ "):\n  return " ^ s ^ "\n"
        val test = "for x in range(" ^ its ntop ^ 
          "):\n  print (" ^ fs ^ "(x))"    
        val ps' = String.concatWith "\n" (!ctxt @ [head,test])
      in ps' end
      else
      let
        val wn = !funn
        val fs = "f" ^ its wn
        val s = rm_par (human wn p)
        val test = "for x in range(" ^ its ntop ^ 
          "):\n  print (" ^ fs ^ "(x))"    
        val ps' = String.concatWith "\n" (!ctxt @ [test])
      in ps' end
    val _ = ctxt := [] 
    val _ = imperative_flag := false
  in
    ps
  end

(*
load "mcts"; open aiLib kernel mcts;
let val p = random_prog 20 in 
  print_endline (humanf p ^ "\n"); 
  print_endline (humani p) 
end;
*)

(* -------------------------------------------------------------------------
   Timer
   ------------------------------------------------------------------------- *)

val search_time = ref (Time.fromReal 60.0)
val search_steps = ref (valOf (Int.maxInt))
val rt_glob = ref (Timer.startRealTimer ())
val rti_glob = ref 0

exception SearchTimeout;

fun init_timer () = 
  (rti_glob := 0; rt_glob := Timer.startRealTimer ())

fun check_timer () = 
  (
  if !rti_glob mod 100000 = 0 then print "." else ();
  if !rti_glob > !search_steps orelse
     (!rti_glob mod 100 = 0 andalso 
      Timer.checkRealTimer (!rt_glob) > !search_time)
  then raise SearchTimeout 
  else incr rti_glob
  )

end (* struct *)

	structure kernel :> kernel =
	struct

	open HolKernel Abbrev boolLib aiLib dir;
	val ERR = mk_HOL_ERR "kernel";

	val selfdir = dir.selfdir

	(* -------------------------------------------------------------------------
	Globals
	------------------------------------------------------------------------- *)

	val maxinput = ref 16
	val simple_search = ref false

	(* -------------------------------------------------------------------------
	Types
	------------------------------------------------------------------------- *)

	type oper2 = int * int -> int
	type oper3 = int * int * int -> int
	type exec = int * int -> int
	type seq = int list
	val seq_compare = list_compare Int.compare
	fun string_of_seq il = String.concatWith " " (map its il)

	(* -------------------------------------------------------------------------
	Composing semantics and executables
	------------------------------------------------------------------------- *)

	val error = valOf (Int.maxInt)

	(* -------------------------------------------------------------------------
	Program
	------------------------------------------------------------------------- *)

	type id = int
	datatype prog = Ins of (id * prog list);

	fun prog_compare (Ins(s1,pl1),Ins(s2,pl2)) =
	cpl_compare Int.compare (list_compare prog_compare) ((s1,pl1),(s2,pl2))

	fun equal_prog (a,b) = (prog_compare (a,b) = EQUAL)

	fun prog_size (Ins(s,pl)) =
	if null pl
	then 1 + sum_int (map prog_size pl)
	else sum_int (map prog_size pl)

	fun all_subprog (p as Ins (_,pl)) = p :: List.concat (map all_subprog pl);

	(* -------------------------------------------------------------------------
	Instructions
	------------------------------------------------------------------------- *)

	val zero_id = 0
	val one_id = 1
	val two_id = 2
	val addi_id = 3
	val diff_id = 4
	val mult_id = 5
	val divi_id = 6
	val modu_id = 7
	val cond_id = 8
	val loop_id = 9
	val var_id = 10
	val ind_id = 11
	val compr_id = 12

	val alpha3 = rpt_fun_type 3 alpha
	val alpha4 = rpt_fun_type 4 alpha
	val operv = Vector.fromList
	[
	mk_var ("zero",alpha),
	mk_var ("one",alpha),
	mk_var ("two",alpha),
	mk_var ("addi",alpha3),
	mk_var ("diff",alpha3),
	mk_var ("mult",alpha3),
	mk_var ("divi",alpha3),
	mk_var ("modu",alpha3),
	mk_var ("cond",alpha4),
	mk_var ("loop",alpha4),
	mk_var ("var",alpha),
	mk_var ("ind",alpha),
	mk_var ("compr",alpha3)
	]

	val maxoper = Vector.length operv

	val operav = Vector.map arity_of operv

	fun name_of_oper i = fst (dest_var (Vector.sub (operv,i)))

	(* time limit per instruction *)
	val timelimit = ref (161616*16+1);
	val counter = ref 0;
	fun start f x = (counter := 0; f x)

	(* nullary *)
	val zero_f = (fn _ => 0)
	val one_f = (fn _ => 1)
	val two_f = (fn _ => 2)
	val var_f = (fn (a:int,b:int) => a)
	val ind_f = (fn (a:int,b:int) => b)

	(* first-order *)
	val addi_f = op +
	val diff_f = op -
	val mult_f = op *
	val divi_f = op div
	val modu_f = op mod
	fun cond_f (a,b,c) = if a <= 0 then b else c

	(* higher-order operator *)
	fun loop_f_aux i f n x =
	(
	incr counter;
	if !counter > !timelimit then raise Div
	else if n <= 0 then x
	else loop_f_aux (i+1) f (n-1) (f (x,i))
	)

	fun loop_f f (n,x) =
	if n > !timelimit then raise Div else loop_f_aux 1 f n x

	fun compr_f_aux x f n0 n =
	(
	if x > (n0+1)(n0+1)256 then raise Div else ();
	incr counter;
	if !counter > !timelimit then raise Div
	else if f (x,0) <= 0 then
	(if n0 >= n then x else compr_f_aux (x+1) f (n0+1) n)
	else compr_f_aux (x+1) f n0 n
	)

	fun compr_f f n =
	if n > !timelimit orelse n < 0 then raise Div else compr_f_aux 0 f 0 n

	(* regroup by arity *)
	val nullaryl =
	[(zero_id,zero_f),(one_id,one_f),(two_id,two_f),(var_id,var_f),(ind_id,ind_f)]

	val nullaryidl = map fst nullaryl
	fun is_nullary id = mem id nullaryidl
	fun find_nullaryf id = assoc id nullaryl
	val nullaryv = Vector.tabulate (maxoper, fn i =>
	if can find_nullaryf i then find_nullaryf i else zero_f);

	val binaryl =
	[(addi_id,addi_f),(diff_id,diff_f),(mult_id,mult_f),(divi_id,divi_f),
	(modu_id,modu_f)]
	val binaryidl = map fst binaryl
	fun is_binary id = id >= addi_id andalso id <= modu_id
	fun find_binaryf id = assoc id binaryl
	val binaryv = Vector.tabulate (maxoper, fn i =>
	if can find_binaryf i then find_binaryf i else addi_f);

	fun is_comm id = mem id [addi_id, mult_id]
	val binaryidl_nocomm = filter (fn x => not (is_comm x)) binaryidl

	(* -------------------------------------------------------------------------
	Compressed programs
	------------------------------------------------------------------------- *)

	fun depend_on_i p = case p of
	Ins (id,[]) => id = ind_id
	\| Ins (9,[p1,p2,p3]) => depend_on_i p2 orelse depend_on_i p3
	\| Ins (_,pl) => exists depend_on_i pl

	fun under_lambda p = case p of
	Ins (id,[]) => []
	\| Ins (9,[p1,p2,p3]) => p1 :: List.concat (map under_lambda [p1,p2,p3])
	\| Ins (_,pl) => List.concat (map under_lambda pl)

	fun has_lambdai p = case p of
	Ins (id,[]) => false
	\| Ins (9,[p1,p2,p3]) => depend_on_i p1
	orelse has_lambdai p2 orelse has_lambdai p3
	\| Ins (_,pl) => exists has_lambdai pl

	fun suc_prog n p = if n <= 0 then p else
	Ins (addi_id, [suc_prog (n-1) p, Ins (one_id,[])])

	fun shift_prog n p = case p of
	Ins (id,[]) => if id = var_id then suc_prog n p else p
	\| Ins (9,[p1,p2,p3]) => Ins (9,[p1, shift_prog n p2, shift_prog n p3])
	\| Ins (12,[p1,p2]) => Ins (12,[p1, shift_prog n p2])
	\| Ins (id,pl) => Ins (id, map (shift_prog n) pl)

	(* -------------------------------------------------------------------------
	Compressed programs
	------------------------------------------------------------------------- *)

	type progi = Arbint.int

	val progi_compare = Arbint.compare
	fun equal_progi (a,b) = (progi_compare (a,b) = EQUAL)

	fun suc x = x + 1
	fun pred x = x - 1

	local open Arbint in

	val arbmaxoper = fromInt (suc maxoper)

	fun zip_prog prog =
	let
	fun polish (Ins (id,pl)) = fromInt (suc id) :: List.concat (map polish pl)
	fun loop r il = case il of
	[] => r
	\| a :: m => loop (r * arbmaxoper + a) m
	in
	loop zero (rev (polish prog))
	end

	fun unzip_progl arbi =
	let
	val (q,r) = Arbint.divmod (arbi, arbmaxoper)
	val id = pred (toInt r)
	val a = Vector.sub (operav,id)
	val pl = if q = zero then [] else unzip_progl q
	val (pla,plb) = part_n a pl
	in
	Ins (id,pla) :: plb
	end

	fun unzip_prog arbi = singleton_of_list (unzip_progl arbi)

	val hseq_modw = fromInt 2115908027

	fun pi_to_hseq pi =
	let val (q,r) = Arbint.divmod (pi, hseq_modw) in
	if q = zero
	then [toInt r]
	else toInt r :: pi_to_hseq q
	end

	end (* local *)

	(* -------------------------------------------------------------------------
	Possible inputs
	------------------------------------------------------------------------- *)

	val entryl = List.concat [
	List.tabulate (16,fn x => (x,0)),
	List.tabulate (8,fn x => (x,1)),
	List.tabulate (4,fn x => (x,2)),
	List.tabulate (2,fn x => (x,3)),
	List.tabulate (1,fn x => (x,4))
	];

	val entryl16 = first_n 16 entryl

	(* -------------------------------------------------------------------------
	Execute a program on some input
	------------------------------------------------------------------------- *)

	fun compose1 f f1 x = f (f1 x)
	fun compose2 f f1 f2 x = f (f1 x, f2 x)
	fun compose3 f f1 f2 f3 x = f (f1 x, f2 x, f3 x)

	fun mk_exec_aux prog = case prog of
	Ins (id,[]) => Vector.sub (nullaryv,id)
	\| Ins (12,[p1,p2]) =>
	compose1 (compr_f (mk_exec_aux p1)) (mk_exec_aux p2)
	\| Ins (id,[p1,p2]) =>
	compose2 (Vector.sub (binaryv,id)) (mk_exec_aux p1) (mk_exec_aux p2)
	\| Ins (8,[p1,p2,p3]) =>
	compose3 cond_f (mk_exec_aux p1) (mk_exec_aux p2) (mk_exec_aux p3)
	\| Ins (9,[p1,p2,p3]) =>
	compose2 (loop_f (mk_exec_aux p1)) (mk_exec_aux p2) (mk_exec_aux p3)
	\| _ => raise ERR "mk_exec" ""

	fun mk_exec p =
	let val exec = start (mk_exec_aux p) in
	(fn x => ((exec x,!counter) handle Overflow => (error,!counter)))
	end

	fun not_semdep_on_i e31 =
	let
	val (e16,e15) = part_n 16 e31
	val (e8,e7) = part_n 8 e15
	val (e4,e3) = part_n 4 e7
	val (e2,e1) = part_n 2 e3
	in
	seq_compare (first_n 8 e16, e8) = EQUAL andalso
	seq_compare (first_n 4 e16, e4) = EQUAL andalso
	seq_compare (first_n 2 e16, e2) = EQUAL andalso
	seq_compare (first_n 1 e16, e1) = EQUAL
	end

	fun semtimo_of_prog p =
	let val f = mk_exec p in
	if not (depend_on_i p)
	then
	let
	val e16 = map f entryl16
	val r =
	(e16 @ first_n 8 e16 @ first_n 4 e16 @ first_n 2 e16 @ first_n 1 e16)
	val (sem,timl) = split r
	val tim = 31 + sum_int timl
	in
	SOME (sem,tim)
	end
	handle Div => NONE
	else
	let
	val r = map f entryl
	val (sem,timl) = split r
	val tim = 31 + sum_int timl
	in
	if not_semdep_on_i sem then NONE else SOME (sem,tim)
	end
	handle Div => NONE
	end

	fun semo_of_prog p = Option.map fst (semtimo_of_prog p)

	fun same_sem p1 p2 = case (semo_of_prog p1, semo_of_prog p2) of
	(SOME l1, SOME l2) => seq_compare (l1,l2) = EQUAL
	\| _ => false

	val sem_of_prog = valOf o semo_of_prog

	fun seq_of_prog p = first_n 16 (sem_of_prog p)

	fun is_executable x = isSome (semo_of_prog x)

	(* -------------------------------------------------------------------------
	Applications of an instruction syntactically from compressed programs
	------------------------------------------------------------------------- *)

	fun papp_nullop id = Ins (id,[])
	fun papp_binop id (p1,p2) = Ins (id, [p1,p2])
	fun papp_ternop id (p1,p2,p3) = Ins (id,[p1,p2,p3])

	(* -------------------------------------------------------------------------
	Human readable output
	------------------------------------------------------------------------- *)

	val constnorm_flag = ref false
	val polynorm_flag = ref true
	val imperative_flag = ref false

	fun itsm i = if i < 0 then "-" ^ its (~i) else its i

	fun mk_xn vn = if vn = ~1 then "x" else "X"
	fun mk_in vn = if vn = ~1 then "i" else "I"

	fun constnorm prog = case prog of
	Ins (0,[]) => 0
	\| Ins (1,[]) => 1
	\| Ins (2,[]) => 2
	\| Ins (3,[p1,p2]) => addi_f (constnorm p1,constnorm p2)
	\| Ins (4,[p1,p2]) => diff_f (constnorm p1,constnorm p2)
	\| Ins (5,[p1,p2]) => mult_f (constnorm p1,constnorm p2)
	\| Ins (6,[p1,p2]) => divi_f (constnorm p1,constnorm p2)
	\| Ins (7,[p1,p2]) => modu_f (constnorm p1,constnorm p2)
	\| _ => raise ERR "constnorm" ""

	fun polyaddi l1 l2 = case (l1,l2) of
	(l1,[]) => l1
	\| ([],l2) => l2
	\| (a1 :: m1, a2 :: m2) => addi_f (a1,a2) :: polyaddi m1 m2

	fun polydiff l1 l2 = case (l1,l2) of
	(l1,[]) => l1
	\| ([],l2) => polydiff (List.tabulate (length l2, fn _ => 0)) l2
	\| (a1 :: m1, a2 :: m2) => diff_f (a1,a2) :: polydiff m1 m2

	fun polymult l1 l2 = case (l1,l2) of
	(l1,[]) => raise ERR "polymult" ""
	\| ([],l2) => raise ERR "polymult" ""
	\| (l1,[a]) => map (fn x => mult_f (a,x)) l1
	\| ([a],l2) => map (fn x => mult_f (a,x)) l2
	\| (a1 :: m1, l2) =>
	polyaddi (map (fn x => mult_f (a1,x)) l2) (polymult m1 (0 :: l2))

	fun polydivi l1 l2 = case (l1,l2) of
	([a],[b]) => [divi_f (a,b)]
	\| _ => raise ERR "polydivi" ""
	fun polymodu l1 l2 = case (l1,l2) of
	([a],[b]) => [modu_f (a,b)]
	\| _ => raise ERR "polymodu" ""

	fun polynorm prog = case prog of
	Ins (0,[]) => [0]
	\| Ins (1,[]) => [1]
	\| Ins (2,[]) => [2]
	\| Ins (3,[p1,p2]) => polyaddi (polynorm p1) (polynorm p2)
	\| Ins (4,[p1,p2]) => polydiff (polynorm p1) (polynorm p2)
	\| Ins (5,[p1,p2]) => polymult (polynorm p1) (polynorm p2)
	\| Ins (6,[p1,p2]) => polydivi (polynorm p1) (polynorm p2)
	\| Ins (7,[p1,p2]) => polymodu (polynorm p1) (polynorm p2)
	\| Ins (10,[]) => [0,1]
	\| _ => raise ERR "polynorm" ""

	fun string_of_mono vn (a,i) =
	(if a = 1 andalso i <> 0 then "" else
	if a = ~1 andalso i <> 0 then "-" else itsm a) ^
	(if (a = 1 andalso i <> 0) orelse
	(a = ~1 andalso i <> 0) orelse
	(i = 0)
	then "" else "*") ^
	(if i = 0 then "" else if i = 1 then mk_xn vn else mk_xn vn ^
	(if !imperative_flag then "**" else "^") ^ its i)

	fun string_of_poly vn l =
	let val l1 = filter (fn x => fst x <> 0) (number_snd 0 l) in
	if null l1 then "0" else
	let val s = String.concatWith " + " (map (string_of_mono vn) (rev l1)) in
	if length l1 = 1 then s else "(" ^ s ^ ")"
	end
	end

	fun polyaddil l = case l of
	[] => []
	\| a :: m => polyaddi a (polyaddil m)

	fun polymultl l = case l of
	[] => raise ERR "polymultl" ""
	\| [a] => a
	\| a :: m => polymult a (polymultl m)

	fun rm_par s =
	if String.size s = 0 then s else
	if String.sub (s,0) = #"(" andalso String.sub (s,String.size s - 1) = #")"
	then String.substring (s,1,String.size s - 2)
	else s;

	(* regroup polynoms in repeated addition/substraction and
	multiplications *)

	fun strip_addi p = case p of
	Ins (3,[p1,p2]) =>
	let
	val (a1,b1) = strip_addi p1
	val (a2,b2) = strip_addi p2
	in
	(a1 @ a2, b1 @ b2)
	end
	\| Ins (4,[p1,p2]) =>
	let
	val (a1,b1) = strip_addi p1
	val (a2,b2) = strip_addi p2
	in
	(a1 @ b2, a2 @ b1)
	end
	\| _ => ([p],[])

	fun strip_mult p = case p of
	Ins (5,[p1,p2]) => strip_mult p1 @ strip_mult p2
	\| _ => [p]

	fun is_loop (Ins(id,pl)) = (mem id [9,12])

	val ctxt = ref []
	val funn = ref 0
	fun incrs s = s ^ " = " ^ s ^ " + 1";
	fun decrs s = s ^ " = " ^ s ^ " - 1";

	fun human vn prog =
	if !constnorm_flag andalso can constnorm prog then its (constnorm prog) else
	case prog of
	Ins (3,[p1,p2]) =>
	if !polynorm_flag
	then reg_add vn prog
	else "(" ^ human vn p1 ^ " + " ^ human vn p2 ^ ")"
	\| Ins (4,[p1,p2]) =>
	if !polynorm_flag
	then reg_add vn prog
	else "(" ^ human vn p1 ^ " - " ^ human vn p2 ^ ")"
	\| Ins (5,[p1,p2]) =>
	if !polynorm_flag
	then reg_mult vn prog
	else "(" ^ human vn p1 ^ " * " ^ human vn p2 ^ ")"
	\| Ins (6,[p1,p2]) =>
	if !imperative_flag
	then "(" ^ human vn p1 ^ " // " ^ human vn p2 ^ ")"
	else "(" ^ human vn p1 ^ " div " ^ human vn p2 ^ ")"
	\| Ins (7,[p1,p2]) =>
	if !imperative_flag
	then "(" ^ human vn p1 ^ " % " ^ human vn p2 ^ ")"
	else "(" ^ human vn p1 ^ " mod " ^ human vn p2 ^ ")"
	\| Ins (8,[p1,p2,p3]) =>
	if !imperative_flag
	then "(" ^ rm_par (human vn p2) ^ " if " ^
	rm_par (human vn p1) ^ " <= 0 else " ^
	rm_par (human vn p3) ^ ")"
	else "(if " ^
	rm_par (human vn p1) ^ " <= 0 then " ^ rm_par (human vn p2) ^ " else " ^
	rm_par (human vn p3) ^ ")"
	\| Ins (9,[p1,p2,p3]) =>
	let
	val wn = (!funn)
	val _ = incr funn
	val s1 = rm_par (human (~1) p1)
	val s2 = human wn p2 ^ " + 1"
	val s3 = rm_par (human wn p3)
	val fs = "f" ^ its wn
	val fprev1 = if depend_on_i prog
	then fs ^ "(" ^ mk_xn wn ^ "," ^ mk_in wn ^ ")"
	else fs ^ "(" ^ mk_xn wn ^ ")"
	val fprev2 = if depend_on_i prog
	then fs ^ "(" ^ mk_xn vn ^ "," ^ mk_in vn ^ ")"
	else fs ^ "(" ^ mk_xn vn ^ ")"
	val fs_head = "def " ^ fprev1 ^ ":"
	in
	if !imperative_flag then
	let val cs =
	[fs_head,
	" x = " ^ s3,
	" " ^ "for i in range (1," ^ s2 ^ "):",
	" x = " ^ s1,
	" return x", ""]
	in
	ctxt := !ctxt @ cs; fprev2
	end
	else
	"loop(\\(x,i)." ^ s1 ^ ", " ^
	rm_par (human (~1) p2) ^ ", " ^ rm_par (human (~1) p3) ^ ")"
	end
	\| Ins (10,[]) => mk_xn vn
	\| Ins (11,[]) => mk_in vn
	\| Ins (12,[p1,p2]) =>
	let
	val wn = (!funn)
	val _ = incr funn
	val s1 = rm_par (human (~1) p1)
	val s2 = rm_par (human wn p2)
	val fs = "f" ^ its wn
	val fprev1 = if depend_on_i prog
	then fs ^ "(" ^ mk_xn wn ^ "," ^ mk_in wn ^ ")"
	else fs ^ "(" ^ mk_xn wn ^ ")"
	val fprev2 = if depend_on_i prog
	then fs ^ "(" ^ mk_xn vn ^ "," ^ mk_in vn ^ ")"
	else fs ^ "(" ^ mk_xn vn ^ ")"
	val fs_head = "def " ^ fprev1 ^ ":"
	in
	if !imperative_flag then
	let val cs = [fs_head,
	" x,i = 0,0",
	" while i <= " ^ s2 ^ ":",
	" if " ^ s1 ^ " <= 0:",
	" i = i + 1",
	" x = x + 1",
	" return x - 1", ""]
	in
	ctxt := !ctxt @ cs; fprev2
	end
	else
	"compr(\\x." ^ s1 ^ ", " ^ rm_par (human (~1) p2) ^ ")"
	end
	\| Ins (s,[]) => its s
	\| Ins (s,l) => "(" ^ its s ^ " " ^
	String.concatWith " " (map (human vn) l) ^ ")"

	and reg_add vn p =
	let
	val (pl1,pl2) = strip_addi p
	val (pl1a,pl1b) = partition (can polynorm) pl1
	val (pl2a,pl2b) = partition (can polynorm) pl2
	val pl1n = map polynorm pl1a
	val pl2n = map polynorm pl2a
	fun human_addl pl = case pl of
	[] => raise ERR "reg_add" ""
	\| [a] => human vn a
	\| _ => "(" ^ String.concatWith " + " (map (human vn) pl) ^ ")"
	val polyo = if null pl1n andalso null pl2n then NONE else
	SOME (polydiff (polyaddil pl1n) (polyaddil pl2n))
	in
	case (polyo,pl1b,pl2b) of
	(NONE,[],[]) => raise ERR "reg_add 2" ""
	\| (NONE,_,[]) => human_addl pl1b
	\| (NONE,[],_) => "-" ^ human_addl pl2b
	\| (NONE,_,_) => "(" ^ human_addl pl1b ^ " - " ^ human_addl pl2b ^ ")"
	\| (SOME poly,[],[]) => string_of_poly vn poly
	\| (SOME poly,_,[]) => "(" ^ string_of_poly vn poly ^
	" + " ^ human_addl pl1b ^ ")"
	\| (SOME poly,[],_) => "(" ^ string_of_poly vn poly ^
	" - " ^ human_addl pl2b ^ ")"
	\| (SOME poly,_,_) => "(" ^ string_of_poly vn poly ^
	" + " ^ human_addl pl1b ^ " - " ^ human_addl pl2b ^ ")"
	end

	and reg_mult vn p =
	let
	val pl = strip_mult p
	val (pla,plb) = partition (can polynorm) pl
	fun human_multl pl = case pl of
	[] => raise ERR "reg_mult" ""
	\| [a] => human vn a
	\| _ => "(" ^ String.concatWith " * " (map (human vn) pl) ^ ")"
	val polyo = if null pla then NONE else
	SOME (polymultl (map polynorm pla))
	in
	case (polyo,plb) of
	(NONE,[]) => raise ERR "reg_mult 2" ""
	\| (NONE,_) => human_multl plb
	\| (SOME poly,[]) => string_of_poly vn poly
	\| (SOME poly,_) => "(" ^ string_of_poly vn poly ^ " * " ^
	human_multl plb ^ ")"
	end

	fun humanf p =
	let
	val _ = imperative_flag := false
	val s = human (~1) p
	val _ = imperative_flag := false
	in s end

	fun humani ntop p =
	let
	val _ = imperative_flag := true
	val _ = ctxt := []
	val _ = funn := 0
	val ps =
	if not (is_loop p) then
	let
	val wn = !funn
	val _ = incr funn
	val fs = "f" ^ its wn
	val xs = mk_xn wn
	val s = rm_par (human wn p)
	val head = "def " ^ fs ^ "(" ^ xs ^ "):\n return " ^ s ^ "\n"
	val test = "for x in range(" ^ its ntop ^
	"):\n print (" ^ fs ^ "(x))"
	val ps' = String.concatWith "\n" (!ctxt @ [head,test])
	in ps' end
	else
	let
	val wn = !funn
	val fs = "f" ^ its wn
	val s = rm_par (human wn p)
	val test = "for x in range(" ^ its ntop ^
	"):\n print (" ^ fs ^ "(x))"
	val ps' = String.concatWith "\n" (!ctxt @ [test])
	in ps' end
	val _ = ctxt := []
	val _ = imperative_flag := false
	in
	ps
	end

	(*
	load "mcts"; open aiLib kernel mcts;
	let val p = random_prog 20 in
	print_endline (humanf p ^ "\n");
	print_endline (humani p)
	end;

	*)

	(* -------------------------------------------------------------------------
	Timer
	------------------------------------------------------------------------- *)

	val search_time = ref (Time.fromReal 60.0)
	val search_steps = ref (valOf (Int.maxInt))
	val rt_glob = ref (Timer.startRealTimer ())
	val rti_glob = ref 0

	exception SearchTimeout;

	fun init_timer () =
	(rti_glob := 0; rt_glob := Timer.startRealTimer ())

	fun check_timer () =
	(
	if !rti_glob mod 100000 = 0 then print "." else ();
	if !rti_glob > !search_steps orelse
	(!rti_glob mod 100 = 0 andalso
	Timer.checkRealTimer (!rt_glob) > !search_time)
	then raise SearchTimeout
	else incr rti_glob
	)

	end (* struct *)