(******************************************************************************
 * SNU 4190.310 Programming Languages (Fall 2006)
 *
 * HW 1: nML exercise I
 ******************************************************************************)

(******************************************************************************
 * Exercise 1.
 * nML exercise I: merge
 ******************************************************************************)

fun merge ([] : int list, r) = r
  | merge (l, []) = l
  | merge (l as (lh :: lt), r as (rh :: rt)) =
    if lh < rh then lh :: (merge (lt, r)) else rh :: (merge (l, rt))


(******************************************************************************
 * Exercise 2.
 * nML exercise I: sigma
 ******************************************************************************)

fun sigma (a, b, f) = 
  if b < a then 0 
  else f a + sigma (a + 1, b, f)


(******************************************************************************
 * Exercise 3.
 * nML exercise I: vocalize
 ******************************************************************************)

exception Error of string

val vocalize : string -> string list list =
let 
  val invalid : string -> bool =
    fn s => not String.length(s)=7
  
  val split : string -> int -> string list =
    fn s i => [(String.sub s 0 i),(String.sub s i ((String.length s)-i))]

  val vocalize_digit : string -> int ->  string list = 
    let
      fun vocalize_table_1 s = 
        (case s of "1" => "ÀÏ" | "2" => "ÀÌ" | "3" => "»ï" | "4" => "»ç"
                 | "5" => "¿À" | "6" => "À°" | "7" => "Ä¥" | "8" => "ÆÈ" | "9" => "±¸" 
                 | _ => raise Error "vocalize_digit : fist argument is not integer string")            
      fun vocalize_table_2 i = 
        (case i of 1 => "½Ê"   | 2 => "¹é"   | 3 => "õ"   | 4 => "¸¸" 
                 | 5 => "½Ê¸¸" | 6 => "¹é¸¸" | 7 => "õ¸¸" | 8 => "¾ï"
                 | _ => raise Error "vocalize_digit : second argument out of range(1-8)")
    in
        fn "0" _ => []
         | s 0   => [(vocalize_table_1 s)]
         | s i   => [(vocalize_table_1 s),(vocalize_table_2 i)]
    end

  val vocalize_string : string -> string list = 
    let
      val rec vocalize_stringb : string -> string list =
        fn s => 
          if String.length(s) = 0 then []
          else (List.append 
                (vocalize_digit (String.sub s 0 1) (String.length(s) - 1))
                (vocalize_stringb (String.sub s 1 (String.length(s)-1))))
    in
      fn s => if (vocalize_stringb s) = [] then ["¿µ"] else (vocalize_stringb s)
    end
in
  fn s => 
    if invalid(s) then raise Error "invalid input : length of first argument string must be 7" 
    else (List.map vocalize_string (split s 3))
end


(******************************************************************************
 * Exercise 4.
 * nML exercise I: crazy2val
 ******************************************************************************)

type crazy2 
  = NIL 
  | ZERO of crazy2
  | ONE of crazy2
  | MONE of crazy2

val rec crazy2val : crazy2 -> int 
=fn NIL => 0
  | ONE(c) => 1 + 2 * (crazy2val c)
  | MONE(c) => -1 + 2 * (crazy2val c)
  | ZERO(c) => 2 * (crazy2val c)


(******************************************************************************
 * Exercise 5.
 * nML exercise I: crazy2add
 ******************************************************************************)

fun merge ([] : int list, r) = r
type crazy2 
  = NIL 
  | ZERO of crazy2
  | ONE of crazy2
  | MONE of crazy2

val rec crazy2val : crazy2 -> int
=fn NIL => 0
  | ONE(c) => 1 + 2 * (crazy2val c)
  | MONE(c) => -1 + 2 * (crazy2val c)
  | ZERO(c) => 2 * (crazy2val c)

val rec crazy2add : crazy2 * crazy2 -> crazy2
=fn (NIL, c) => c
  | (c, NIL) => c
  | (ONE(c1), ONE(c2)) => ZERO(crazy2add(crazy2add(c1, c2),ONE(NIL)))
  | (ONE(c1), ZERO(c2)) => ONE(crazy2add (c1, c2))
  | (ONE(c1), MONE(c2)) => ZERO(crazy2add(c1,c2))
  | (ZERO(c1), ZERO(c2)) => ZERO(crazy2add(c1,c2))
  | (ZERO(c1), MONE(c2)) => MONE(crazy2add(c1,c2))
  | (MONE(c1), MONE(c2)) => ZERO(crazy2add(crazy2add(c1,c2),MONE(NIL)))
  | (c1,c2) => crazy2add(c2,c1)