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|
(* From the SML/NJ benchmark suite. *)
(* term.sml *)
structure Term =
struct
datatype term
= STR of string * term list
| INT of int
| CON of string
| REF of term option ref
exception BadArg of string
end;
(* trail.sml *)
structure Trail =
struct
local
open Term
val global_trail = ref (nil : term option ref list)
val trail_counter = ref 0
in
fun unwind_trail (0, tr) = tr
| unwind_trail (n, r::tr) =
( r := NONE ; unwind_trail (n-1, tr) )
| unwind_trail (_, nil) =
raise BadArg "unwind_trail"
fun reset_trail () = ( global_trail := nil )
fun trail func =
let
val tc0 = !trail_counter
in
( func () ;
global_trail :=
unwind_trail (!trail_counter-tc0, !global_trail) ;
trail_counter := tc0 )
end
fun bind (r, t) =
( r := SOME t ;
global_trail := r::(!global_trail) ;
trail_counter := !trail_counter+1 )
end (* local *)
end; (* Trail *)
(* unify.sml *)
structure Unify =
struct
local
open Term Trail
fun same_ref (r, REF(r')) = (r = r')
| same_ref _ = false
fun occurs_check r t =
let
fun oc (STR(_,ts)) = ocs ts
| oc (REF(r')) =
(case !r' of
SOME(s) => oc s
| _ => r <> r')
| oc (CON _) = true
| oc (INT _) = true
and ocs nil = true
| ocs (t::ts) = oc t andalso ocs ts
in
oc t
end
fun deref (t as (REF(x))) =
(case !x of
SOME(s) => deref s
| _ => t)
| deref t = t
fun unify' (REF(r), t) sc = unify_REF (r,t) sc
| unify' (s, REF(r)) sc = unify_REF (r,s) sc
| unify' (STR(f,ts), STR(g,ss)) sc =
if (f = g)
then unifys (ts,ss) sc
else ()
| unify' (CON(f), CON(g)) sc =
if (f = g) then
sc ()
else
()
| unify' (INT(f), INT(g)) sc =
if (f = g) then
sc ()
else
()
| unify' (_, _) sc = ()
and unifys (nil, nil) sc = sc ()
| unifys (t::ts, s::ss) sc =
unify' (deref(t), deref(s))
(fn () => unifys (ts, ss) sc)
| unifys _ sc = ()
and unify_REF (r, t) sc =
if same_ref (r, t)
then sc ()
else if occurs_check r t
then ( bind(r, t) ; sc () )
else ()
in
val deref = deref
fun unify (s, t) = unify' (deref(s), deref(t))
end (* local *)
end; (* Unify *)
(* data.sml *)
structure Data =
struct
local
open Term Trail Unify
val cons_s = "cons"
val x_s = "x"
val nil_s = "nil"
val o_s = "o"
val s_s = "s"
val CON_o_s = CON(o_s)
val CON_nil_s = CON(nil_s)
val CON_x_s = CON(x_s)
in
fun exists sc = sc (REF(ref(NONE)))
fun move_horiz (T_1, T_2) sc =
(
trail (fn () =>
(
trail (fn () =>
(
trail (fn () =>
(
trail (fn () =>
(
trail (fn () =>
(
trail (fn () =>
(
trail (fn () =>
(
trail (fn () =>
(
trail (fn () =>
(
trail (fn () =>
(
trail (fn () =>
exists (fn T =>
exists (fn TT =>
unify (T_1, STR(cons_s, [STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_o_s, T])])]), TT])) (fn () =>
unify (T_2, STR(cons_s, [STR(cons_s, [CON_o_s, STR(cons_s, [CON_o_s, STR(cons_s, [CON_x_s, T])])]), TT])) (fn () =>
sc ())))))
;
exists (fn P1 =>
exists (fn P5 =>
exists (fn TT =>
unify (T_1, STR(cons_s, [STR(cons_s, [P1, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_o_s, STR(cons_s, [P5, CON_nil_s])])])])]), TT])) (fn () =>
unify (T_2, STR(cons_s, [STR(cons_s, [P1, STR(cons_s, [CON_o_s, STR(cons_s, [CON_o_s, STR(cons_s, [CON_x_s, STR(cons_s, [P5, CON_nil_s])])])])]), TT])) (fn () =>
sc ())))))
))
;
exists (fn P1 =>
exists (fn P2 =>
exists (fn TT =>
unify (T_1, STR(cons_s, [STR(cons_s, [P1, STR(cons_s, [P2, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_o_s, CON_nil_s])])])])]), TT])) (fn () =>
unify (T_2, STR(cons_s, [STR(cons_s, [P1, STR(cons_s, [P2, STR(cons_s, [CON_o_s, STR(cons_s, [CON_o_s, STR(cons_s, [CON_x_s, CON_nil_s])])])])]), TT])) (fn () =>
sc ())))))
))
;
exists (fn L1 =>
exists (fn P4 =>
exists (fn TT =>
unify (T_1, STR(cons_s, [L1, STR(cons_s, [STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_o_s, STR(cons_s, [P4, CON_nil_s])])])]), TT])])) (fn () =>
unify (T_2, STR(cons_s, [L1, STR(cons_s, [STR(cons_s, [CON_o_s, STR(cons_s, [CON_o_s, STR(cons_s, [CON_x_s, STR(cons_s, [P4, CON_nil_s])])])]), TT])])) (fn () =>
sc ())))))
))
;
exists (fn L1 =>
exists (fn P1 =>
exists (fn TT =>
unify (T_1, STR(cons_s, [L1, STR(cons_s, [STR(cons_s, [P1, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_o_s, CON_nil_s])])])]), TT])])) (fn () =>
unify (T_2, STR(cons_s, [L1, STR(cons_s, [STR(cons_s, [P1, STR(cons_s, [CON_o_s, STR(cons_s, [CON_o_s, STR(cons_s, [CON_x_s, CON_nil_s])])])]), TT])])) (fn () =>
sc ())))))
))
;
exists (fn L1 =>
exists (fn L2 =>
exists (fn TT =>
unify (T_1, STR(cons_s, [L1, STR(cons_s, [L2, STR(cons_s, [STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_o_s, CON_nil_s])])]), TT])])])) (fn () =>
unify (T_2, STR(cons_s, [L1, STR(cons_s, [L2, STR(cons_s, [STR(cons_s, [CON_o_s, STR(cons_s, [CON_o_s, STR(cons_s, [CON_x_s, CON_nil_s])])]), TT])])])) (fn () =>
sc ())))))
))
;
exists (fn T =>
exists (fn TT =>
unify (T_1, STR(cons_s, [STR(cons_s, [CON_o_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, T])])]), TT])) (fn () =>
unify (T_2, STR(cons_s, [STR(cons_s, [CON_x_s, STR(cons_s, [CON_o_s, STR(cons_s, [CON_o_s, T])])]), TT])) (fn () =>
sc ()))))
))
;
exists (fn P1 =>
exists (fn P5 =>
exists (fn TT =>
unify (T_1, STR(cons_s, [STR(cons_s, [P1, STR(cons_s, [CON_o_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [P5, CON_nil_s])])])])]), TT])) (fn () =>
unify (T_2, STR(cons_s, [STR(cons_s, [P1, STR(cons_s, [CON_x_s, STR(cons_s, [CON_o_s, STR(cons_s, [CON_o_s, STR(cons_s, [P5, CON_nil_s])])])])]), TT])) (fn () =>
sc ())))))
))
;
exists (fn P1 =>
exists (fn P2 =>
exists (fn TT =>
unify (T_1, STR(cons_s, [STR(cons_s, [P1, STR(cons_s, [P2, STR(cons_s, [CON_o_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, CON_nil_s])])])])]), TT])) (fn () =>
unify (T_2, STR(cons_s, [STR(cons_s, [P1, STR(cons_s, [P2, STR(cons_s, [CON_x_s, STR(cons_s, [CON_o_s, STR(cons_s, [CON_o_s, CON_nil_s])])])])]), TT])) (fn () =>
sc ())))))
))
;
exists (fn L1 =>
exists (fn P4 =>
exists (fn TT =>
unify (T_1, STR(cons_s, [L1, STR(cons_s, [STR(cons_s, [CON_o_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [P4, CON_nil_s])])])]), TT])])) (fn () =>
unify (T_2, STR(cons_s, [L1, STR(cons_s, [STR(cons_s, [CON_x_s, STR(cons_s, [CON_o_s, STR(cons_s, [CON_o_s, STR(cons_s, [P4, CON_nil_s])])])]), TT])])) (fn () =>
sc ())))))
))
;
exists (fn L1 =>
exists (fn P1 =>
exists (fn TT =>
unify (T_1, STR(cons_s, [L1, STR(cons_s, [STR(cons_s, [P1, STR(cons_s, [CON_o_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, CON_nil_s])])])]), TT])])) (fn () =>
unify (T_2, STR(cons_s, [L1, STR(cons_s, [STR(cons_s, [P1, STR(cons_s, [CON_x_s, STR(cons_s, [CON_o_s, STR(cons_s, [CON_o_s, CON_nil_s])])])]), TT])])) (fn () =>
sc ())))))
))
;
exists (fn L1 =>
exists (fn L2 =>
exists (fn TT =>
unify (T_1, STR(cons_s, [L1, STR(cons_s, [L2, STR(cons_s, [STR(cons_s, [CON_o_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, CON_nil_s])])]), TT])])])) (fn () =>
unify (T_2, STR(cons_s, [L1, STR(cons_s, [L2, STR(cons_s, [STR(cons_s, [CON_x_s, STR(cons_s, [CON_o_s, STR(cons_s, [CON_o_s, CON_nil_s])])]), TT])])])) (fn () =>
sc ())))))
)
(* | move_horiz _ _ = () *)
and rotate (T_1, T_2) sc =
exists (fn P11 =>
exists (fn P12 =>
exists (fn P13 =>
exists (fn P14 =>
exists (fn P15 =>
exists (fn P21 =>
exists (fn P22 =>
exists (fn P23 =>
exists (fn P24 =>
exists (fn P31 =>
exists (fn P32 =>
exists (fn P33 =>
exists (fn P41 =>
exists (fn P42 =>
exists (fn P51 =>
unify (T_1, STR(cons_s, [STR(cons_s, [P11, STR(cons_s, [P12, STR(cons_s, [P13, STR(cons_s, [P14, STR(cons_s, [P15, CON_nil_s])])])])]), STR(cons_s, [STR(cons_s, [P21, STR(cons_s, [P22, STR(cons_s, [P23, STR(cons_s, [P24, CON_nil_s])])])]), STR(cons_s, [STR(cons_s, [P31, STR(cons_s, [P32, STR(cons_s, [P33, CON_nil_s])])]), STR(cons_s, [STR(cons_s, [P41, STR(cons_s, [P42, CON_nil_s])]), STR(cons_s, [STR(cons_s, [P51, CON_nil_s]), CON_nil_s])])])])])) (fn () =>
unify (T_2, STR(cons_s, [STR(cons_s, [P51, STR(cons_s, [P41, STR(cons_s, [P31, STR(cons_s, [P21, STR(cons_s, [P11, CON_nil_s])])])])]), STR(cons_s, [STR(cons_s, [P42, STR(cons_s, [P32, STR(cons_s, [P22, STR(cons_s, [P12, CON_nil_s])])])]), STR(cons_s, [STR(cons_s, [P33, STR(cons_s, [P23, STR(cons_s, [P13, CON_nil_s])])]), STR(cons_s, [STR(cons_s, [P24, STR(cons_s, [P14, CON_nil_s])]), STR(cons_s, [STR(cons_s, [P15, CON_nil_s]), CON_nil_s])])])])])) (fn () =>
sc ())))))))))))))))))
(* | rotate _ _ = () *)
and move (T_1, T_2) sc =
(
trail (fn () =>
(
trail (fn () =>
exists (fn X =>
exists (fn Y =>
unify (T_1, X) (fn () =>
unify (T_2, Y) (fn () =>
move_horiz (X, Y) sc)))))
;
exists (fn X =>
exists (fn X1 =>
exists (fn Y =>
exists (fn Y1 =>
unify (T_1, X) (fn () =>
unify (T_2, Y) (fn () =>
rotate (X, X1) (fn () =>
move_horiz (X1, Y1) (fn () =>
rotate (Y, Y1) sc))))))))
))
;
exists (fn X =>
exists (fn X1 =>
exists (fn Y =>
exists (fn Y1 =>
unify (T_1, X) (fn () =>
unify (T_2, Y) (fn () =>
rotate (X1, X) (fn () =>
move_horiz (X1, Y1) (fn () =>
rotate (Y1, Y) sc))))))))
)
(* | move _ _ = () *)
and solitaire (T_1, T_2, T_3) sc =
(
trail (fn () =>
exists (fn X =>
unify (T_1, X) (fn () =>
unify (T_2, STR(cons_s, [X, CON_nil_s])) (fn () =>
unify (T_3, INT(0)) (fn () =>
sc ())))))
;
exists (fn N =>
exists (fn X =>
exists (fn Y =>
exists (fn Z =>
unify (T_1, X) (fn () =>
unify (T_2, STR(cons_s, [X, Z])) (fn () =>
unify (T_3, STR(s_s, [N])) (fn () =>
move (X, Y) (fn () =>
solitaire (Y, Z, N) sc))))))))
)
(* | solitaire _ _ = () *)
and solution1 (T_1) sc =
exists (fn X =>
unify (T_1, X) (fn () =>
solitaire (STR(cons_s, [STR(cons_s, [CON_o_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, CON_nil_s])])])])]), STR(cons_s, [STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s,
CON_nil_s])])])]), STR(cons_s, [STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, CON_nil_s])])]), STR(cons_s, [STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, CON_nil_s])]), STR(cons_s, [STR(cons_s, [CON_x_s, CON_nil_s]), CON_nil_s])])])])])
, X, STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [INT(0)])])])])])])])])])])])])])) sc))
(* | solution1 _ _ = () *)
and solution2 (T_1) sc =
exists (fn X =>
unify (T_1, X) (fn () =>
solitaire (STR(cons_s, [STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, CON_nil_s])])])])]), STR(cons_s, [STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s,
CON_nil_s])])])]), STR(cons_s, [STR(cons_s, [CON_x_s, STR(cons_s, [CON_o_s, STR(cons_s, [CON_x_s, CON_nil_s])])]), STR(cons_s, [STR(cons_s, [CON_x_s, STR(cons_s, [CON_x_s, CON_nil_s])]), STR(cons_s, [STR(cons_s, [CON_x_s, CON_nil_s]), CON_nil_s])])])])])
, X, STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [STR(s_s, [INT(0)])])])])])])])])])])])])])) sc))
(* | solution2 _ _ = () *)
end (* local *)
end; (* Data *)
signature BMARK =
sig
val doit : int -> unit
val testit : TextIO.outstream -> unit
end;
(* main.sml *)
structure Main : BMARK =
struct
val name = "Logic"
exception Done
fun testit strm = Data.exists(fn Z => Data.solution2 Z (fn () => raise Done))
handle Done => TextIO.output(strm, "yes\n")
fun doit () = Data.exists(fn Z => Data.solution2 Z (fn () => raise Done))
handle Done => ()
val doit =
fn size =>
let
fun loop n =
if n = 0
then ()
else (doit();
loop(n-1))
in loop size
end
end; (* Main *)
|
