SICP Exercise 1.6

Exercise 1.6.  Alyssa P. Hacker doesn't see why if needs to be provided as a special form. ``Why can't I just define it as an ordinary procedure in terms of cond?'' she asks. Alyssa's friend Eva Lu Ator claims this can indeed be done, and she defines a new version of if:


(define (new-if predicate then-clause else-clause)
  (cond (predicate then-clause)
        (else else-clause)))

Eva demonstrates the program for Alyssa:


(new-if (= 2 3) 0 5)
5

(new-if (= 1 1) 0 5)
0

Delighted, Alyssa uses new-if to rewrite the square-root program:


(define (sqrt-iter guess x)
  (new-if (good-enough? guess x)
          guess
          (sqrt-iter (improve guess x)
                     x)))



What happens when Alyssa attempts to use this to compute square roots? Explain.

SOLUTION

The code is here:


Explanation: new-if is a procedure. So when it is called, it tries to evaluate all its arguments first (applicative order evaluation). One of the arguments is 'new-sqrt-iter' so this results in recursive calls that never end. 'new-if' does not fully execute and return even once.

Comments

Post a Comment

Popular posts from this blog

SICP Exercise 1.22 search-for-primes

Image
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, ...
Read more

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...
Read more

SICP Exercise 4.18 a alternative strategy for interpreting internal definitions

Exercise 4.18.   Consider an alternative strategy for scanning out definitions that translates the example in the text to (lambda < vars >   (let ((u '*unassigned*)         (v '*unassigned*))     (let ((a < e1 >)           (b < e2 >))       (set! u a)       (set! v b))     < e3 >)) Here  a  and  b  are meant to represent new variable names, created by the interpreter, that do not appear in the user's program. Consider the  solve  procedure from section  3.5.4 : (define (solve f y0 dt)   (define y (integral (delay dy) y0 dt))   (define dy (stream-map f y))   y) Will this ...
Read more