datatype tree = Oak | Elm | Maple | Spruce | Fir | 
                Pine | Willow;

datatype vegetable = Carrot | Zucchini | Tomato | Cucumber | 
                     Lettuce;

datatype grain = Wheat | Oat | Barley | Maize;

datatype plot = Grove of tree | Garden of vegetable | 
                Field of grain | Vacant;


datatype bread = White | MultiGrain | Rye | Kaiser;

datatype spread = Mayo | Mustard;

datatype vegetable = Cucumber | Lettuce | Tomato;

datatype deliMeat = Ham | Turkey | RoastBeef | ExtraVeg of vegetable ;

datatype noodle = Spaghetti | Penne | Fusilli | Gemelli | Farfalle;

datatype sauce = Pesto | Marinara | Creamy;

datatype protein = MeatBalls | Sausage | Chicken | Tofu;


datatype entree = Sandwich of bread * spread * vegetable * deliMeat 
                              | Pasta of noodle * sauce * protein;

datatype salad = Caesar | Garden;

datatype side = Fries | Chips | CarrotSticks | GarlicBread | Salad of salad;

datatype beverage = Water | Coffee | Pop | Lemonade | IceTea;

datatype meal = Meal of entree * side * beverage;


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
  ...



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);



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


fun plotYield(Garden(Carrot)) = 100
  | plotYield(Garden(Zucchini)) = 3
  | plotYield(Garden(Tomato)) = 1000
  | plotYield(Garden(Cucumber)) = 1200
  | plotYield(Garden(Lettuce)) = 800
  | plotYield(Field(Maize)) = 10000
  | plotYield(Field(x)) = 5000
  | plotYield(x) = 0;

(* 1.11.5 *)
fun replaceFries(Meal(x, Fries, y)) = Meal(x, Chips, y)
  | replaceFries(Meal(x, z, y)) = Meal(x, z, y);

(* 1.11.3 *)
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));

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;