(* Homemade boolean type *)

datatype boolean = True | False;

fun andB(True, True) = True
| andB(p, q) = False;

fun orB(False, False) = False
| orB(p, q) = True;

fun notB(True) = False
| notB(False) = True;

andB(orB(True, False), notB(andB(False, True)));


fun isEven(0) = true
  | isEven(1) = false 
  | isEven(n) = isEven(n-2);

fun isEven(0) = true
  | isEven(n) = not(isEven(n-1));

fun isEven(n) = n mod 2 = 0;

(* Ex 3.3.4, turnToInts *) 
fun turnToInts([]) = []
  | turnToInts(true::rest) = 1::turnToInts(rest)
  | turnToInts(false::rest) = 0::turnToInts(rest);

(* turnToBools *)
fun turnToBools([]) = []
  | turnToBools(0::rest) = false::turnToBools(rest)
  | turnToBools(x::rest) =  true::turnToBools(rest);



datatype bird = Robin | Sparrow | Crow | Cardinal | 
     Eagle | Mockingbird | Penguin | Flamingo ;

fun containsRobin([]) = false
  | containsRobin(Robin::rest) = true
  | containsRobin(x::rest) = containsRobin(rest);