You should prepare these exercises for oral presentation in tutorial.
The following procedure all-choices (which you will use in doing
this problem set) takes as argument a list of n lists 
and returns a list whose elements are all possible lists
of the form 
, where 
is chosen from
, 
is chosen from 
, ..., 
is chosen from 
.
(Mathematicians call this operation the Cartesian product of the
input lists.) For example, (all-choices '((1 2) (a b c)))
should return
((1 a) (1 b) (1 c) (2 a) (2 b) (2 c))
(define (all-choices possibilities-list)
(if (null? possibilities-list)
'(())
(let ((rest (all-choices (cdr possibilities-list))))
(flatten
(map
(lambda (choice-for-first)
(map (lambda (follow-on)
(cons choice-for-first follow-on))
rest))
(car possibilities-list))))))
Explain how this procedure works. In general, how many possible choices will there be as a function of the input list? How could you modify the procedure to produce a stream of choices rather than a list of choices. (Assume that the argument is still a list.)
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Using cons-stream, stream-map, stream-filter, create expressions that define an infinitely long stream of 1's and an infinitely long stream of the positive integers. Be prepared to explain why your expressions work.
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Using the same tools, create an expression that defines an infinitely long stream of the powers of 2 (i.e. 1, 2, 4, 8, 16, ...).
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Do exercise 3.54 from the text.
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Do exercise 3.55 from the text.
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