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Read SICP 3.5.1, then answer the following:
(delay (+ 1 27))?
(force (delay (+ 1 27)))?
Evaluating this expression produces an error:
(stream-cdr (stream-cdr (cons-stream 1 '(2 3))))
Consider the following:
(define (enumerate-interval low high) (if (> low high) '() (cons low (enumerate-interval (+ low 1) high)) ) ) (define (stream-enumerate-interval low high) (if (> low high) the-empty-stream (cons-stream low (stream-enumerate-interval (+ low 1) high)) ) )
What's the difference between the following two expressions?
(delay (enumerate-interval 1 3)) (stream-enumerate-interval 1 3)
An unsolved problem in number theory concerns the following algorithm for creating a sequence of positive integers [mathjaxinline]s_1, s_2, \ldots[/mathjaxinline] where [mathjaxinline]s_1[/mathjaxinline] is some positive integer and, for all [mathjaxinline]n > 1[/mathjaxinline],
No matter what starting value [mathjaxinline]s_1[/mathjaxinline] is chosen, the sequence (called a hailstone sequence) always seems to end with the repeating values 1, 4, 2, 1, 4, 2, 1, .... However, it is not known if this is always the case.
Write a procedure
num-seq that, given a positive integer
n as argument,
returns the hailstone sequence for
(num-seq 7) should return the stream representing the sequence 7,
22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, ...
Write a procedure
seq-length that, given a stream produced by
returns the number of values that occur in the sequence up to and including
the first 1. For example,
(seq-length (num-seq 7)) should return 17. You
should assume that there is a 1 somewhere in the sequence.
It's that time of the homework—SICP!
Write and test two functions to manipulate nonnegative proper fractions.
fract-stream, will take as its argument a list of two
nonnegative integers, the numerator and the denominator, in which the
numerator is less than the denominator. It will return an infinite stream of
decimal digits representing the decimal expansion of the fraction.
approximation, will take two arguments: a fraction stream and a
nonnegative integer numdigits. It will return a list (not a stream) containing
the first numdigits digits of the decimal expansion.
(fract-stream '(1 7))should return the stream representing the decimal
(stream-car (fract-stream '(1 7)))should return
(stream-car (stream-cdr (stream-cdr (fract-stream '(1 7)))))should return
(approximation (fract-stream '(1 7)) 4)should return
(1 4 2 8).
(approximation (fract-stream '(1 2)) 4)should return
(5 0 0 0).
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