Exercise 2.6

[Quux Man]

I don't remember going over this very thoroughly. Here's benny99's (from #haskell) solution:

( define (zero f)
    ( lambda (x) x))

( define (one f)
    ( lambda (x) (f x)))

(define (two f )
  (lambda (x) (f (f x))))


( define (add-1 n )
    (lambda (f)
      (lambda (x)
        (f ((n f ) x)))))

( define (add n m)
    ( lambda (f)
      ( lambda (x)
        ((compose (m f) (n f)) x))))

( define (chn->n c) ((c ( lambda (x) ( + x 1))) 0))

This brings up my original problem with the problem: it's not very well defined. Is he asking to define an add that's faster than adding 1 n or m times? Is this possible using Church Numerals? Or is the question asking something simpler?