Working Through SICP Exercises

As I work through SICP exercises, I will post them there.

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SICP Exercise 1.22 search-for-primes

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Exercise 1.22.    Most Lisp implementations include a primitive called  runtime  that returns an integer that specifies the amount of time the system has been running (measured, for example, in microseconds). The following  timed-prime-test  procedure, when called with an integer  n , prints  n  and checks to see if  n  is prime. If  n  is prime, the procedure prints three asterisks followed by the amount of time used in performing the test. (define (timed-prime-test n)   (newline)   (display n)   (start-prime-test n (runtime))) (define (start-prime-test n start-time)   (if (prime? n)       (report-prime (- (runtime) start-time)))) (define (report-prime elapsed-time)   (display " *** ")   (display elapsed-time)) Using this procedure, ...
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SICP Exercise 3.45 deadlock

Exercise 3.45.   Louis Reasoner thinks our bank-account system is unnecessarily complex and error-prone now that deposits and withdrawals aren't automatically serialized. He suggests that  make-account-and-serializer  should have exported the serializer (for use by such procedures as  serialized-exchange ) in addition to (rather than instead of) using it to serialize accounts and deposits as  make-account  did. He proposes to redefine accounts as follows: (define (make-account-and-serializer balance)   (define (withdraw amount)     (if (>= balance amount)         (begin (set! balance (- balance amount))                balance)         "Insufficient funds"))   (define (deposit amoun...
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SICP Exercise 3.78 solve-2nd

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Exercise 3.78.    Figure 3.35:   Signal-flow diagram for the solution to a second-order linear differential equation. Consider the problem of designing a signal-processing system to study the homogeneous second-order linear differential equation The output stream, modeling  y , is generated by a network that contains a loop. This is because the value of  d 2 y / d t 2 depends upon the values of  y  and  d y / d t  and both of these are determined by integrating  d 2 y / d t 2 . The diagram we would like to encode is shown in figure  3.35 . Write a procedure  solve-2nd  that takes as arguments the constants  a ,  b , and  d t and the initial values  y 0  and  d y 0  for  y  and  d y / d t  and generates the stream of successive values of  y . SOLUTION The code and tests are here . The plots are pasted below and also available  here ....
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