1.

(define my-list (list 1 2 3 4))

(define (foo x)

(lambda (y)

(if (even? (+ x y))

(lambda (z) (* z 2))

(lambda (z) (* z 3)))))

(define (bar ls)

(if (empty? ls)

‘()

(cons ((car ls) 10) (bar (cdr ls)))))

Why is the output ‘(20 30 20 30)? To answer this question, trace and/or explain in detail the evaluation steps of (bar ( map (foo 3) my-list)) to show how the output ‘(20 30 20 30) is produced.

2.

A recursive, but not higher order function viral-growth that returns a list of the minute-by-minute growth when one person spreads a video to three other people per minute:

(define (viral-growth mins ppl)

(if (= 0 mins)

‘()

(cons (* 3 ppl) (viral-growth (- mins 1) (* 3 ppl)))))

> (viral-growth 4 1)

‘(3 9 27 81)

And a higher order function repeated that returns another function, f, applied count times:

(define (repeated f count)

(lambda (x)

(if (= count 0)

x

(f ((repeated f (- count 1)) x)))))

> ((repeated add-one 3) 1)

4

Rewrite viral-growth so that it can be passed to repeated and so that the count variable of repeated (rather than a mins variable in viral-growth) determines how many minutes of viral growth pass. Rewrite viral-growth to accept only one argument, the number of people who start the spread, and to return a lambda that accepts a list argument.

(define (viral-growth ppl)

(lambda (ls)

… your code goes here …

If you rewrite viral-growth correctly, you should be able to pass it to repeated as follows:

> ((repeated (viral-growth 1) 4) ‘())

‘(3 9 27 81)

An answer that returns the list in reverse order ‘(81 27 9 3) will be accepted but with an automatic deduction of 3 points. Also, do not use any built-in function except for empty?, *, cons, car, or cdr.