(* --- In-class example --- *)


datatype icecream = VanillaIC | ChocolateIC | StrawberryIC | MintIC|
                        AnchovieIC;

datatype syrup = ChocolateS | CaramelS | StrawberryS | HotFudge |
                     TartarSauceS ;

datatype topping = RainbowSprinkles | ChocolateSprinkles 
               | ChocolateChips | Walnuts | Pecans | Cherry | Blueberries;

datatype cone = CakeC | SugarC | WaffleC;

datatype donutDough = CakeD | YeastD;

datatype donutFlavor = VanillaD | ChocolateD | BlueberryD | PumpkinD |
 CinnamonD;

datatype frostingFlavor = VanillaF | ChocolateF | StraberryF | MapleF;

datatype donutEncasement = Plain | Frosting of frostingFlavor | Glaze | Powder;

datatype pop = RootBeer | Cola | CreamSoda | DrSalt;

datatype treat = IcecreamCone of icecream * cone
                           | IcecreamSundae of icecream * syrup * topping
                           | Donut of donutDough * donutFlavor * donutEncasement
                           | Float of pop * icecream;


(* --- from the book --- *)


datatype number = Int of int | Real of real;

(* interpret the first int as numerator and second as denominator *)
datatype rational = Fraction of int * int;


(* 1.10.1 *)  (* A HW problem; this is just to get you started *)
datatype book = 
           (* author, title, pages *)
    Novel of string * string * int
          (* title, number of vols *)
  | RefBook of string * int  
          (* author, title, subject, pages *)
  | NonFiction of string * string * string * int
            (* author, title, subject, publisher *)
  | Textbook of string * string * string * string
  ...

datatype libraryItem =
  Book of book
  | Recording of recording


(* Simple function examples *)

fun fahrToCel(t) = (t - 32) * 5 div 9;

fun f(x) = 3.0 * x*x - 2.7 * x + 14.4;

fun capitalize(s) =
    str(Char.toUpper(String.sub(s, 0))) ^
    String.substring(s, 1, size(s) - 1);




(* Pattern matching *)

fun f(1) = 0
  | f(x) = (x * x - 1) div (x - 1);

fun asciiToppings(ChocolateChips) = "^ ^ ^ ^"
  | asciiToppings(Walnuts) = "(*#*)"
  | asciiToppings(Pecans) = "(||)"
  | asciiToppings(Cherry) = "o'"
  | asciiToppings(Blueberries) = "bbbbb"
  | asciiToppings(x) = "..|._.`";


fun outOfRainbowSprinkles(IcecreamSundae(x, y, RainbowSprinkles)) = 
                                       IcecreamSundae(x, y, ChocolateSprinkles) 
  | outOfRainbowSprinkles(somethingelse) = somethingelse;




(* 1.11.3 --- for the number datatype *)
fun add(Int(x), Int(y)) = Int(x + y)
  | add(Real(x), Real(y)) = Real(x + y)
  | add(Int(x), Real(y)) = Real(real(x) + y)
  | add(Real(x), Int(y)) = Real(x + real(y));


(* For the rational datatype *)

fun add(Fraction(a, b), Fraction(c, d)) =
   Fraction(a * d + c * b, b * d);


fun gcd(a, 0) = a
  | gcd(a, b) = gcd(b, a mod b);

fun add(Fraction(a, b) , Fraction(c, d)) =
    Fraction((a * d + c * b) div gcd(a * d + c * b, b * d),
    (b * d) div gcd(a * d + c * b, b * d));


fun add(Fraction(a, b), Fraction(c, d)) = 
  let 
      val numerator = a * d + c * b;
      val denominator = b * d;
      val divisor = gcd(numerator, denominator);
  in
     Fraction(numerator div divisor, denominator div divisor)
  end;

fun mul(Fraction(a, b), Fraction(c, d)) =
    let 
          val numerator = a * c;
          val denominator = b * d;
          val divisor = gcd(numerator, denominator);
  in
     Fraction(numerator div divisor, denominator div divisor)
  end;