# Exercise 2.6

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In case representing pairs as procedures wasn’t mind-boggling enough, consider that, in a language that can manipulate procedures, we can get by without numbers (at least insofar as nonnegative integers are concerned) by implementing 0 and the operation of adding 1 as

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

This representation is known as Church numerals, after its inventor, Alonzo Church, the logician who invented the λ calculus.

Define `one`

and `two`

directly (not in terms of `zero`

and `add-1`

). (Hint: Use substitution to evaluate `(add-1 zero)`

).
Give a direct definition of the addition procedure `+`

(not in
terms of repeated application of `add-1`

).

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