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Else exp)) Consider the following definition of sign, which returns -1 for negative inputs, +1 for positive inputs, and 0 for zero. 3 The two if expressions may be replaced by a single cond expression as follows. 33 (define sign (lambda (n) (cond ((< n 0) -1) ((> n 0) +1) (else 0)))) Sometimes it is clearer to leave out the else clause. This should be done only when there is no possibility that all the tests will fail, as in the new version of sign below. (define sign (lambda (n) (cond ((< n 0) -1) ((> n 0) +1) ((= n 0) 0)))) These definitions of sign do not depend on the order in which the tests are performed, since only one of the tests can be true for any value of n.

Make-list 7 '()) 38 (() () () () () () ()) [Hint: The base test should be (= n 0), and the recursion step should involve (- n 1). Whereas () is the natural base case for recursion on lists, 0 is the natural base case for recursion on nonnegative integers. 4 The procedures list-ref and list-tail return the nth element and nth tail of a list ls. (list-ref '(1 2 3 4) 0) 1 (list-tail '(1 2 3 4) 0) (1 2 3 4) (list-ref '(a short (nested) list) 2) (list-tail '(a short (nested) list) 2) (nested) ((nested) list) Define both procedures.

T #t (stack1 'push! ) #t (stack1 (stack2 (stack1 (stack2 'push! 'b) 'push! ) #f #t 43 As with the counters created by make-counter, the state maintained by each stack object is directly accessible only within the object. Each reference or change to this state is made explicitly by the object itself. 7) instead of a list to hold the elements, without changing its external behavior. Because the behavior of the object is known abstractly (not operationally), it is known as an abstract object. 8 for more about creating abstract objects.