[plt-scheme] HtDP newbie question, 12.4.2

Why did you throw away your progress (add-first-letter)?

Why did you not answer my second question?

(I'll give you that much: with the two you are about 10 keystrokes  
from the answer.)

I am getting the feeling your jumping again.

;; ---

Let's step back a bit. The purpose of this extended exercise is to  
practice the two ideas that the book has introduced at that point:

1. that the design recipe works on a per function basis -- BUT YOU  
NEED TO STICK TO IT;
2. that the 'wish list' works -- BUT YOU NEED TO STICK TO IT.  (If  
you are systematic about this, you just never forget where in the  
problem you are.)

;; ---

Another step back:

1. In case you're wondering:  most people would consider this  
exercise way beyond a first-semester exercise. (It was on my MS exam  
in 1981.)

2. HtDP/2e will use a simpler exercise than that and push back  
Arrangements until students have more practice. A lot of people have  
problems with it though in 1-1 meetings, it's much easier to tease  
out the answers to these questions because the speed is higher and  
less frustrating.



-- Matthias





On Mar 28, 2008, at 5:35 PM, Cooke Kelsey wrote:

> Dear Matthias / Marco,
>
> I read Marco's suggestions.  It was very helpful to read through  
> the whole problem again in clear English and remember how I got to  
> the function "insert-in-single-word."  I think I am near to the  
> answer.
>
> You both ask me a similar question:
> (1) Matthias:  Can you design a function that adds a letter (no  
> matter what it is) to the front of all these words you have gotten  
> back?...DONE? After that: what is missing?
>
>    given:          the recursion                           in the  
> final result I want
>   'X   "ATE"     "X" "TE" --> "XTE" "TXE" "TEX"     "AXTE" "ATXE"  
> "ATXE" "ATEX"
> (2) Marco: "Here is where I believe you are really stuck. It is  
> easy to see one member of the result: (letter a-word). This puts  
> letter before the first letter of a-word. Is that the only place it  
> can go? No, it can go before any of the letters in a word and at  
> the end of a-word. How do you insert a letter everywhere in (rest a- 
> word)? Once you have this list (call it R) all you need is to do  
> something with (first a-word).  Where does it have to go in each of  
> R?"
>
> OK, here is a function which I think answers these questions:
>
> (define (add-letter-to-recursive-list letter a-word)
>   (cond
>     [(empty? (rest a-word)) (cons (list letter (first a-word)) empty)]
>     [else (cons (cons letter a-word) (add-letter-to-recursive-list  
> letter (rest a-word)))]))
>
> ;example:
> (add-letter-to-recursive-list 'x (list 'w 'a 't 'e 'r))
> ;answer
> (list
>  (list 'x 'w 'a 't 'e 'r)
>  (list 'x 'a 't 'e 'r)
>  (list 'x 't 'e 'r)
>  (list 'x 'e 'r)
>  (list 'x 'r))
>
> Then next question is, how can I put the missing letters back on  
> the front of these words?
>
> For this, I can use the "add-first-letter" function which I sent  
> earlier to Matthias:
>
> (define (add-first-letter first-letter low)
>   (cond
>     [(empty? (rest low)) (cons (append (list first-letter) (first  
> low)) empty)]
>     [else (cons (append (list first-letter) (first low)) (add-first- 
> letter first-letter (rest low)))]))
>
> Now, I can combine the two functions into a main function, "add- 
> letter-plus-prefix":
>
> (define (add-letter-plus-prefix x a-word)
>   (add-first-letter (first a-word) (Rest x a-word)))
>
> ;example:
> (add-letter-plus-prefix 'x (list 'w 'a 't 'e 'r))
> ;answer:
> (list
>  (list 'w 'x 'w 'a 't 'e 'r)
>  (list 'w 'x 'a 't 'e 'r)
>  (list 'w 'x 't 'e 'r)
>  (list 'w 'x 'e 'r)
>  (list 'w 'x 'r))
>
> It looks nice, but the word is still shrinking away.  I have simply  
> added the first letter to the beginning of all the words.  My  
> problem is still, how can I increment the prefix in order: 'w, 'a,  
> 't, 'e, 'r?
>
> At this point, I think my problem is too many levels of  
> abstraction.  I think that you all can see the answer very clearly,  
> but I can't visualize multiple recursive functions.  The tables,  
> etc have been extremely helpful for me to develop the individual  
> functions.  As far as the final solution, perhaps I don't have the  
> ability to "see" it on that level of abstraction?
>
> Matthias Felleisen <matthias at ccs.neu.edu> wrote:
>
> On Mar 28, 2008, at 1:24 PM, Cooke Kelsey wrote:
>> Oh right, in order to include all the words I need more than an  
>> append.  Here's a function that adds a letter to ALL the words:
>>
>> (define (add-first-letter first-letter low)
>>   (cond
>>     [(empty? (rest low)) (list (cons first-letter low))]
>>     [else (cons (cons first-letter (list (first low))) (add-first- 
>> letter first-letter (rest low)))]))
>> ;example:
>> (add-first-letter 'X (list 'A 'T 'E 'Y 'W 'Z))
>> ;result:
>> (list (list 'X 'A) (list 'X 'T) (list 'X 'E) (list 'X 'Y) (list 'X  
>> 'W) (list 'X 'Z))
>
>
> So if you apply add-first-letter to (first word) and the result of  
> (insert-everywhere/in-one-word (rest word)), you get back all but  
> one of the word you want.  Which brings me to the second question:
>
>
>>  That was a lot more complicated than I thought.  I guess that  
>> should be a helper function.
>>
>> However, when I try to make a main function (insert-in-single- 
>> word) that calls add-first-letter, I end up going around in the  
>> same circle as before.
>
>
> Because you failed to read and answer my second question. -- Matthias
>
>
>
>
>
>>
>> Matthias Felleisen <matthias at ccs.neu.edu> wrote:
>>
>> On Mar 28, 2008, at 12:34 PM, Cooke Kelsey wrote:
>>> 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))
>>
>>
>> That's not what I asked you to _design_.  Please read the  
>> suggestion carefully. And again, (append (list foo) bar) is equal  
>> to (cons foo bar). Why do yu keep using append?
>>
>>
>>
>>> (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?
>>
>> It is your sample input to the function. It says "Given" in that  
>> column.
>>
>>
>>> 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.
>>
>>
>> The purpose statement of the function tells you what the recursive  
>> call should produce. So when you code, you may assume that the  
>> recursive call works properly.
>>
>>
>>>
>>> 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?
>>>
>>> DONE?
>>>
>>> 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)
>>>>   (cond
>>>>     [(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)
>>>>   (cond
>>>>     [(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))
>>>>
>>>> Garbage!
>>>>
>>>> As a last resort, I try to combine cons and shrinking functions  
>>>> together:
>>>>
>>>> (define (cons+shrinking-function s word)
>>>>   (cond
>>>>     [(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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