Problem Set 5– Abstractions and Paradigms

1. Write a macro to implement C-style while loops in drracket. In general, the syntax of while
is:
(while boolean-expression one-or-more-statements )
The example below illustrates the use of the while macro:
(define i 10)
(define y 0)
(while ( i 0)
(set! y (+ y i))
(set! i (- i 1)))
2. Consider a non-terminating system which keeps on accepting a sequence of numbers as inputs from the keyboard using the function called (read). Read about read (pun intended)
from the racket documentation. The system, on receiving an input, (display)s the sum of
the last three inputs read. Write a function called which simulates the system. Once again,
clearly identify the state variable.
3. Write a function to-decimal to convert a list of characters into decimal numbers. Your
number should, for instance, convert (#\2 #\4 #\3 #\. #\6 #\5) into 243.65. If you
think some variable represents the state of the system, name the variable as state.
4. Exercise 3.3 of SICP.
5. Exercise 3.7 of SICP.
6. If the language is without side-effects, we do not have to specify the order in which the
sub-expressions should be evaluated (e.g., left to right or right to left). When we introduce
assignment, the order in which the arguments to a procedure are evaluated can make a
difference to the result. Define a simple procedure f such that evaluating (+ (f 0) (f
1)) will return 0 if the arguments to + are evaluated from left to right but will return 1 if
the arguments are evaluated from right to left.
(+ (f 0) (f 1))
0
Since drracket evaluates expressions from left to right, I shall simulate a right-to-left evaluation by flipping the arguments:
(+ (f 1) (f 0))
1
A second time evaluation also produces the same result
(+ (f 1) (f 0))
1
(+ (f 0) (f 1))
0

7. Pen and paper exercise: Using the environmental model of execution, explain the
output of the following program:
(define (f i q)
(define (p) @i)
(if ( i 3) (f (-i 2) p)
(begin
(+ (p)(q)))))
(define (g) ())
(define (main) (f 4 g))
(main)
Your explanation should include the figures of the environment at the point marked with @
every time it is visited.