include "Prelude.e"

{- Depending how much memory you have, you may need to reduce 'nine' -}

main () -> Unit = 
  printInt(natToInt(fact(eight)))

zero () -> Data = Con 0 ()
one () -> Data = Con 1 (zero)
two () -> Data = Con 1 (one)
three () -> Data = Con 1 (two)
four () -> Data = Con 1 (three)
five () -> Data = Con 1 (four)
six () -> Data = Con 1 (five)
seven () -> Data = Con 1 (six)
eight () -> Data = Con 1 (seven)
nine () -> Data = Con 1 (eight)
ten () -> Data = Con 1 (nine)

natToInt (x:Data) -> Int =
  case x of {
     Con 0 () -> 0
   | Con 1 (k:Data) -> 1+natToInt(k)
  }

plus (x:Data, y:Data) -> Data = 
  case x of {
     Con 0 () -> y
   | Con 1 (k:Data) -> Con 1 (plus(k, y))
  }

mult (x:Data, y:Data) -> Data = 
  case x of {
     Con 0 () -> Con 0 ()
   | Con 1 (k:Data) -> plus(y, (mult(k, y)))
  }

fact (x:Data) -> Data =
  case x of {
     Con 0 () -> one()
   | Con 1 (k:Data) -> mult(x, fact(k))
  }

apply (f:Fun, a:Any) -> Any =
  f(a)