[plt-scheme] HtDP newbie question, 12.4.2

From: Cooke Kelsey (cookekelsey at yahoo.com)
Date: Fri Mar 28 12:34:10 EDT 2008

OK, here's a simple function that adds a letter to a word:
  (define (add-first-letter first-letter word)
  (append (list first-letter) word))
(add-first-letter 'A (list 'X 'T 'E))=(list 'A 'X 'T 'E')

  So my question is, where does (list 'A 'T 'E) come from?  In your table below, you say "the recursion: "X" "TE" --> "XTE" "TXE" "TEX".  Actually I have never been able to create such a recursion.  That's the big mystery to me.  
  I just read Dave Yrueta's encouraging note, and he says I need to focus on your hint about adding 'A to the list, "in the simplest and most natural way."  Well, all I can think of is to append it, like I did above.  But there is no recursive element, and I cannot call it or plug it into the main recursive function.  It is floating out in space.
Matthias Felleisen <matthias at ccs.neu.edu> wrote:

  Okay you have gotten to the point where you're jumping even faster. Slogan: 

   furiously fast programming leads to nowhere. 

  ;; --- 

  All I was getting at is a simple point: 

  Your recursive calls in insert-everywhere/one-word produced almost all the work in the recursion. Indeed, it always produces all but one word, except that the first letter from the original word is missing. Example: 

     given:          the recursion                           in the final result I want                    plus 
    'X   "ATE"     "X" "TE" --> "XTE" "TXE" "TEX"     "AXTE" "ATXE" "ATXE" "ATEX"           "XATE" 

  Given the recursive result (the list of words that are too short by the first letter in the orginal word) can you design a function that adds this letter (no matter what it is) to the front of all these words you have gotten back? 


  After that: what is missing? 

  -- Matthias




  On Mar 28, 2008, at 11:51 AM, Cooke Kelsey wrote:
    OK, that helps me a little.  If I insert "cons (first word)," then I can rebuild the word:
  (define (cons-function word)
    [(empty? (rest word)) word]
    [else (cons (first word) (cons-function (rest word)))]))
  (cons-function (list 'A 'T 'W)) = (list 'A 'T 'W)
  The problem is how to add this to a shrinking function:
  (define (shrinking-function s word)
    [(empty? (rest word)) empty]
    [else (list (append (list s) word) (shrinking-function s (rest word)))]))

  (This shrinking function isn't exactly what I want, but at least it gives me (list 'X 'A 'T 'W) and (list 'X 'T 'W)).
  So I append them together: 
  (append (cons-function (list 'A 'T 'W)) (shrinking-function 'X (list 'A 'T 'W)))
  And I get this:
  (list (list 'X 'A 'T 'W) (list (list 'X 'T 'W) empty)) (list 'A 'T 'W (list 'X 'A 'T 'W) (list (list 'X 'T 'W) empty))
  As a last resort, I try to combine cons and shrinking functions together:
  (define (cons+shrinking-function s word)
    [(empty? (rest word)) word]
    [else (append (cons (first word) (cons+shrinking-function 'X (rest word))) (list s) (rest word))]))
  (cons+shrinking-function 'X (list 'A 'T 'W)) = (list 'A 'T 'W 'X 'W 'X 'T 'W)
  It looks kind of nice, but it is even further from the expected result.
Matthias Felleisen <matthias at ccs.neu.edu> wrote:

  How about (cons 'A (list 'X 'T)) = (list 'A 'X 'T)



  On Mar 28, 2008, at 10:53 AM, Cooke Kelsey wrote:
  (append (list 'A) (list 'X 'T)) = (list 'A 'X 'T)

Matthias Felleisen <matthias at ccs.neu.edu> wrote:     

  Here is a definition of 'adding in the missing element': 

  * If a list X misses the symbol 'A (at the front), how do you get a list that has the 'A and all of X? 

  * X = (list 'X 'T) and 'A --> I want (list 'A 'X 'T). How do I do that? 

  -- Matthias


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