T x y := x
F x y := y
if b t e := (b t e)

pair a b := \c.(c a b)
left p := (p T)
right p := (p F)

print n := (n 0 1 end)

fix f := (\x.(f (x x)) \x.(f (x x)))

some x := (pair T x)
none := \.F
isfull := left
unwrap := right

nil := none
push i l := (some (pair i l))
peek l := (left (unwrap l))
pop l := (right (unwrap l))
 
inc := (fix \self l.{
  (if (isfull l)
    (if (peek l)
      (push F (self (pop l)))
      (push T (pop l))
    )
    (push T nil)
  )
})

print := (fix \self l.{
  (if (isfull l)
    ((if (peek l) 1 0) (self (pop l)))
    END
  )
})

one := (push T nil)
double N := (push F N)

N :=
  (double (double (double (double (double
  (double (double (double (double (double
  (double (double (double (double (double
  (double (double (double (double (double
  (double (double (double (double (double
  (double (double (double (double (double
  one))))))))))))))))))))))))))))))

(print N)