Chapter 1, Building Abstractions with Procedures

Section - Formulating Abstractions with Higher-Order Procedures

Exercise 1.37


Procedure definition that generates recursive process:

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(define (cont-frac num den k)
    (define (aux c)
        (cond ((> c k) 0)
              (else (/
                      (num c)
                      (+
                         (den c)
                         (aux (inc c))
                      )
                    )
              )
        )
    )
  (aux 1)
)

Value of needed to generate correct upto 4 decimal places:

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; Correct value: 0.618033988749894848204586834365638117720309179805762862135

> (cont-frac (lambda (i) 1.0) (lambda (i) 1.0) 10)
0.6179775280898876

> (cont-frac (lambda (i) 1.0) (lambda (i) 1.0) 11)
0.6180555555555556

Procedure definition that generates iterative process:

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(define (cont-frac-itr num den k)
    (define (itr rs c)
        (cond ((= c 0) rs)
              (else
                    (itr
                        (/
                           (num c)
                           (+ (den c) rs)
                        )
                        (dec c)
                    )
              )
        )
    )
  (itr 0 k)
)