solve "send more money" in SML

sendmoremoney.sml

(*
 * "send more money" is quiz.
 * One character means one number.
 * All characters are different each other.
 * Numbers satisfy following condition.
 *
 *     send
 *  +) more
 *  --------
 *    money
 *
 * What are characters ?
 *  ... s,e,n,d,m,o,r,y
 *)
(*
 *  *** solver design ***
 *
 *    s,e,n,d,m,o,r,y
 * [ [0,0,0,0,0,0,0,0],
 *   [0,0,0,0,0,0,0,1],
 *                ... ,
 *   [9,9,9,9,9,9,9,9] ] : all list
 *          ||
 *          || filtered with conditions
 *          ||   > filter (condition : int list -> int list) allList
 *          vv
 *  [ [S,E,N,D,M,O,R,Y], ... ] : answer!!
 *)

(*
 * makeAll design : adding one by one
 * [] => [[0],[1],...,[9]] => [[0,0],[1,0],...,[9,0],
 *                             [0,1], ...     ,[9,1],
 *                             ...             [9,9]]
 *    => ... => ... ...
 *    => [[0,0,0,0,0,0,0,0], ... , [9,9,9,9,9,9,9,9]]
*)
fun addToAll nil _ = nil
  | addToAll (x::t) listlist =
    (map (fn list => x :: list) listlist) @ addToAll t listlist
fun makeAll () =
    (addToAll [0,1,2,3,4,5,6,7,8,9]
    (addToAll [0,1,2,3,4,5,6,7,8,9]
    (addToAll [0,1,2,3,4,5,6,7,8,9]
    (addToAll [0,1,2,3,4,5,6,7,8,9]
    (addToAll [0,1,2,3,4,5,6,7,8,9]
    (addToAll [0,1,2,3,4,5,6,7,8,9]
    (addToAll [0,1,2,3,4,5,6,7,8,9]
    (addToAll [0,1,2,3,4,5,6,7,8,9] [[]]))))))))
(* different each other *)
fun oneDiff x nil = true
  | oneDiff x (h::t) = x <> h andalso oneDiff x t
fun diff nil = true
  | diff (h::t) = oneDiff h t andalso diff t
(* d + e = y *)
fun oneCond [_,e,_,d,_,_,_,y] = d + e = y orelse d + e = y + 10
  | oneCond _ = raise Fail "oneCond"
(* n + r = e *)
fun tenCond [_,e,n,d,_,_,r,y] = n + r + ((d + e) div 10) = e orelse
                                n + r + ((d + e) div 10) = e + 10
  | tenCond _ = raise Fail "tenCond"
(* e + o = n *)
fun handCond [_,e,n,d,_,O,r,y] =
    e + O + ((n + r + ((d + e) div 10)) div 10) = n orelse
    e + O + ((n + r + ((d + e) div 10)) div 10) = n + 10
  | handCond _ = raise Fail "handCond"
(* s + m = o *)
fun thouCond [s,e,n,d,m,O,r,y] =
    s + m + ((e + O + ((n + r + ((d + e) div 10)) div 10)) div 10) = O orelse
    s + m + ((e + O + ((n + r + ((d + e) div 10)) div 10)) div 10) = O + 10
  | thouCond _ = raise Fail "thouCond"
(* carrng to m *)
fun tenthouCond [s,e,n,d,m,O,r,y] = (s + m) div 10 = m
  | tenthouCond _ = raise Fail "tenthouCond"

fun solve () =
    let
      val all = makeAll ()
      val tmp = List.filter diff all
      val tmp = List.filter oneCond tmp
      val tmp = List.filter tenCond tmp
      val tmp = List.filter thouCond tmp
      val ans = List.filter tenthouCond tmp
    in
      ans
    end

sendmoremoney2.sml

(*
 * "send more money" is quiz.
 * One character means one number.
 * All characters are different each other.
 * Numbers satisfy following condition.
 *
 *     send
 *  +) more
 *  --------
 *    money
 *
 * What are characters ?
 *  ... s,e,n,d,m,o,r,y
 *)
(*
 *  *** solver design ***
 *
 *    s,e,n,d,m,o,r,y
 * [ [0,0,0,0,0,0,0,0],
 *   [0,0,0,0,0,0,0,1],
 *                ... ,
 *   [9,9,9,9,9,9,9,9] ]
 *          ||
 *          || filtered with conditions
 *          ||   > filter (f : int list -> int list) all
 *          vv
 *  [ [S,E,N,D,M,O,R,Y], ... ]
 *)

(* different each other *)
fun oneDiff x nil = true
  | oneDiff x (h::t) = x <> h andalso oneDiff x t
fun diff nil = true
  | diff (h::t) = oneDiff h t andalso diff t
(*
 * [] => [[0],[1],...,[9]] => [[0,0],[1,0],...,[9,0],
 *                             [0,1], ...     ,[9,1],
 *                             ...             [9,9]]
 *    ...
 *    => [[0,0,0,0,0,0,0,0], ... , [9,9,9,9,9,9,9,9]]
*)
fun addToAll nil _ = nil
  | addToAll (x::t) listlist =
    (map (fn list => x :: list) listlist) @ addToAll t listlist
(*
 * delete list which have same number
 * [] => [[0],[1],...,[9]] => [[1,0],...      ,[9,0],
 *                             [0,1],[2,1],...,[9,1],
 *                             ...             [8,9]]
 *    ...
 *    => [[0,1,2,3,4,5,6,7], ... , [9,8,7,6,5,4,3,2]]
*)
fun addToAll nil _ = nil
  | addToAll (x::t) listlist =
    (foldl (fn (list, res) => if oneDiff x list
                              then (x :: list) :: res
                              else res)
           nil listlist)
    @ addToAll t listlist
fun makeAll () =
    (addToAll [0,1,2,3,4,5,6,7,8,9]
    (addToAll [0,1,2,3,4,5,6,7,8,9]
    (addToAll [0,1,2,3,4,5,6,7,8,9]
    (addToAll [0,1,2,3,4,5,6,7,8,9]
    (addToAll [0,1,2,3,4,5,6,7,8,9]
    (addToAll [0,1,2,3,4,5,6,7,8,9]
    (addToAll [0,1,2,3,4,5,6,7,8,9]
    (addToAll [0,1,2,3,4,5,6,7,8,9] [[]]))))))))
(* d + e = y *)
fun oneCond [_,e,_,d,_,_,_,y] = d + e = y orelse d + e = y + 10
  | oneCond _ = raise Fail "oneCond"
(* n + r = e *)
fun tenCond [_,e,n,d,_,_,r,y] = n + r + ((d + e) div 10) = e orelse
                                n + r + ((d + e) div 10) = e + 10
  | tenCond _ = raise Fail "tenCond"
(* e + o = n *)
fun handCond [_,e,n,d,_,O,r,y] =
    e + O + ((n + r + ((d + e) div 10)) div 10) = n orelse
    e + O + ((n + r + ((d + e) div 10)) div 10) = n + 10
  | handCond _ = raise Fail "handCond"
(* s + m = o *)
fun thouCond [s,e,n,d,m,O,r,y] =
    s + m + ((e + O + ((n + r + ((d + e) div 10)) div 10)) div 10) = O orelse
    s + m + ((e + O + ((n + r + ((d + e) div 10)) div 10)) div 10) = O + 10
  | thouCond _ = raise Fail "thouCond"
(* carrng to m *)
fun tenthouCond [s,e,n,d,m,O,r,y] = (s + m) div 10 = m
  | tenthouCond _ = raise Fail "tenthouCond"
(* m <> 0 *)
fun m [_,_,_,_,m,_,_,_] = m <> 0

fun solve () =
    let
      val all = makeAll ()
      (* val tmp = List.filter diff all *)
      val tmp = List.filter oneCond all
      val tmp = List.filter tenCond tmp
      val tmp = List.filter thouCond tmp
      val tmp = List.filter tenthouCond tmp
      val ans = List.filter m tmp
    in
      ans
    end