Consider the expression (see p.9 lecture notes lambda.ps)



     (lambda f. lambda x. f (f x)) (lambda x.x) z


Note that e1 e2 e3 is interpreted as (e1 e2) e3

Here e1 = (lambda f. lambda x. f (f x))
     e2 = (lambda x.x)
     e3 = z

Therefore,

    (lambda f. lambda x. f (f x)) (lambda x.x) z 

 -> (lambda x. (lambda x.x) ((lambda x.x) x)) z

    (f is replaced by (lambda x.x)

We rename some bound variables

    (lambda y. (lambda x.x) ((lambda x.x) y)) z

 ->  (lambda x.x) ((lambda x.x) z)

 -> (lambda x.x) z

 -> z