Making Scheme Lazier

Chapter: Making Scheme Lazier

Now we're going to add just one special form to Scheme so that we will be able to work in Scheme with infinite lists such as we met in the previous chapter. At this stage, we are going to stop calling them "infinite lists" and instead use the term "streams". This more accurately reflects the true significance of streams in programming: They are used to model streams of data such as those emanating from a keyboard or being sent to a video or printing device. There are clear applications of this week's lab work in the area of data communications.

Recall that

(define billgates (cons "dollar" billgates))

failed because Scheme wants to evaluate that second argument to cons. But recall the discussion of delay and force from class: (delay <exp>) produces a promise <p> such that (force <p>) evaluates <exp>.

Using delay on the second argument to cons prevents its evaluation:

(define billgates (cons "dollar" (delay billgates)))

Now Scheme is happy. With the understanding that if we ever need the cdr of the stream billgates we will need to force the promise produced by (delay billgates), we now have a way to represent streams in Scheme.

But always surrounding the second argument to a cons with a (delay ...), and always having to force it when we need the cdr is inconvenient. We will define three new forms car$, cdr$ and cons$ to enable us to work with streams. just as The Little Schemer showed us how to work with lists using the three forms car, cdr, cons.

Q. 5: Can cons$ be a function?

Q. 6: So what can we do?

The file stream.ss contains the basic code for setting up streams. In addition to car$, cdr$ and cons$, we've also implemented the following.

(print$ s) ; prints a stream, prompting after each line
(printn$ n s) ; prints the first n members of s
(show$ n s) ; builds a list out of the first n members of s
(map$ f s) ; applies f to each member of s
(filter$ p s) ; selects those members of s satisfying predicate p
(+$ s1 s2) ; adds corresponding members of s1 and s2
(fold$ recur-case base-case base-test lyst) ; stream fold
(nth$ n s) ; selects the nth member of s

Notice how easy it is to program with streams as compared to lists. For a start, you can forget about The Little Schemer's "The First Commandment": Always ask null? as the first question in expressing any function.

Q. 7: Why can you forget about the First Commandment?

We have created some sample streams that you may find useful for testing stream functions that you write. You can find the code to create these in somestreams.ss

Exercise 1

Write the functions

(rember-all $x s)$ ; returns a stream with all occurrences of x removed from the stream s
(subst-all x y s); returns a stream with all occurrences of x in the stream s replaced with y

Save your solutions in ex1.ss.

Here is a transcript showing how your functions should work:

> (print$ (rember-all$ 5 (randoms 10)))
0 7 3 1 6 2 2 1 1 4 
Want more? y
8 3 3 1 0 0 8 4 1 9 
Want more? y
6 4 0 2 9 2 8 8 0 4 
Want more? y
3 8 0 4 9 3 7 3 8 7 
Want more? n
done
> (print$ (rember-all$ #\e (random-chars)))
#\i #\k #\n #\i #\y #\j #\n #\a #\s #\m 
Want more? y
#\z #\y #\z #\h #\y #\z #\y #\d #\y #\g 
Want more? y
#\u #\i #\a #\a #\c #\n #\f #\f #\r #\s 
Want more? y
#\w #\i #\z #\d #\a #\j #\r #\c #\f #\j 
Want more? y
#\n #\u #\q #\f #\m #\q #\c #\k #\o #\a 
Want more? n
done
> (print$ (rember-all$ 'e (keyboard-stream)))
? a
a ? b
b ? c
c ? d
d ? e
? f
f ? g
g ? a
a ? b
b ? c
c ? d
d ? e
? f

Want more? n
done
> (print$ (subst-all$ #\e 'the-letter-e (random-chars)))
#\v #\p #\b #\f #\l #\u #\h #\l #\t #\v 
Want more? y
#\d #\l #\p #\j #\q #\a #\i #\i #\n #\l 
Want more? y
#\j #\w the-letter-e #\f #\m #\r #\o #\l #\f #\d 
Want more? y
#\g #\i #\b #\n #\i #\p #\l #\l #\c #\q 
Want more? y
#\l #\l #\u #\f #\l #\b #\u #\c #\u #\o 
Want more? y
#\h #\x #\k #\f #\f the-letter-e #\i the-letter-e #\p #\a 
Want more? n
done
> (print$ (subst-all$ 'e 'I-hate-the-letter-e (keyboard-stream)))
? a
a ? b
b ? c
c ? d
d ? e
I-hate-the-letter-e ? f
f ? g
g ? h
h ? i
i ? j
j ? k

Want more? n
done
>

rms@cs.oberlin.edu