F of x.......................Calculus.............functions..........................

Chapter: Philosophy of the infinite

Let's write a function to tell us if a given item x is a member of a stream s. It will be written just like the familiar member function, but we won't need to test for the null list.

(define member$
  (lambda (x s)
    (cond
      ((eq? x (car$ s)) #t)
      (else (member$ x (cdr$ s))))))

Q. 11

What does function member$ return if x is in the stream s?

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Well, that was an easy question wasn't it? Maybe the next question will be just as easy? Hah!

Q. 12

What does function member$ return if x is not in the stream s?

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All in all, member$ is a pretty useless function. If it returns #t that's nice. You know that you've got a member of the stream. But otherwise, you really don't know if the answer is "no" or if it's taking an awfully long time to tell you "yes".

Q. 13

Are there any conditions you can place on the stream s so that you can write a less useless member$ function?

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Exercise 2

Write a

(define member$
  (lambda (x s less-than-or-equal)

that takes an item x, a stream s and a compare operator less-than-or-equal. The compare operator should work like the mathematical <= operator in comparing items in the stream. You may assume that the items in the stream are ordered so that if item a1 precedes item a2 in the stream s, then (less-than-or-equal a1 a2) is true. The member$ function is looking for an item y such that (less-than-or-equal x y) and (less-than-or-equal y x) are both true.
You may find some of the definitions in memberex.ss useful.
Your function should work as indicated by the following transcript.

> (member$ 47 ints <=)
#t
> (member$ -21 ints <=)
#f
> (member$ 37.32 ints <=)
#f
> (member$ "rhys" words string<=?)
#f
> (reset-words)
> (member$ "barack" words string<=?)
#f
> (reset-words)
> (member$ "barrack" words string<=?)
#t
> (reset-words)
> (member$ "president" words string<=?)
#t
> (reset-words)
> (member$ "washington" words string<=?)
#t
> (reset-words)
> (member$ "george" words string<=?)
#t
> (reset-words)
> (member$ "gwu" words string<=?)
#f

You will notice that I have set up a file in this directory dict.txt as a stream. This is technically not quite right because it's not infinite. If you try to search for a word that's beyond the last word in the dictionary, it is ok for your function to fail because it's trying to read past end-of-file. Mine just sits there and stares back at you. So do not try to test words like "zzz" for membership. Do not spend time now trying to deal with end-of-file; this will be the topic of a later exercise.
You have to reset the words stream each time because a side-effect is involved in the member$ function. Each time you do a cdr$ you are performing a non-repeatable (read). Thus, when you have finished with the word stream you should reset it so it can begin reading at the beginning of the file again.

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When dealing with streams like words that involve a side-effect when computing a cdr$, you need to be careful that you are not trying to evaluate the same cdr$ more than once.

Q. 14

What happens if you do not (reset-words) in the above scenario?

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rhyspj@gwu.edu