(a) Write (delay ) as a special form for (lambda () ) and (force ), as discussed in class.

(b) Write (stream-cons x y) as a special form, as discussed in class.

(c) Write stream analogues of some familiar list processing functions, including:

(stream-car str)

(stream-cdr str)

(stream-nullfi str)

(stream-ref str n) --- returns the nth

element in stream str

(stream-filter pred str)    --- makes a new stream of

elements satisfying pred

(stream-for-each proc str) --- applies proc to each

element of str for side effect

(first n str)    --- makes a stream of the

first n items in str

(list->stream lis) --- makes a stream from

list lis

(stream->list str) --- opposite coercion

For example, if you have defined a stream of even integers called evens, you can display the first 50 even integers as follows:

(stream-for-each (lambda (x) (display x)(display " ")) (first 50 evens)).

Test your functions convincingly!

(d) Now define a bunch of streams to test your functions:

(i) an infinite stream of 1's

(ii) an infinite stream of all even integers

(iii) an infinite stream of random numbers between 1 and 100

(iv) write a predicate (primefi n) that tests for primality and use it to create