Because all-true and all-false are both all-something, they are both written (and), not (or). If you want something corresponding to (or), you need at-least-one-true or at-least-one-false. In general, all-true is the negation of at-least-one-false, and all-false is the negation of at-least-one-true.
On Sat, Jan 3, 2015 at 2:06 PM, Jos Koot <jos.k...@gmail.com> wrote: > Matthias, you write: > > all-true is the same as cannot-find-a-false-on-the-list. > > Then I take an inverse: > > all-false is the same as cannot-find-a-true-on-the-list. > > But we have (in Racket): > > (and) -> #t > (or) -> #f > > Something is wrong with the inversion. But what? > > Happy new year to all, Jos > > -----Original Message----- > From: users [mailto:users-boun...@racket-lang.org] On Behalf Of Matthias > Felleisen > Sent: 03 January 2015 03:12 > To: Frank Weytjens > Cc: users Users > Subject: Re: [racket] Little Schemer, lat? > > > Frank, happy new year. It's good to hear from people like you because TLS > is > for you. > > Now I'd like to say that I am unbelievably unhappy about Chapter 2 but I > could not convince Dan to change the book that much. Let's look at lists in > the "How to Design Programs" way, the TLS for adults if you so wish. Here > is > the definition: > > A LAT is either > -- the empty list > or > -- a LAT l extended with one ATOM. > > And we don't care what an ATOM is. > > This definition is unusual because it refers to itself. You haven't seen > such definitions in your high school courses, and it's best to make sure > this definition generates some LATs (whatever those are). > > * Clearly one thing is a LAT. T > - he empty list. > > * Now suppose we take ATOM1 (whatever atoms are) and extend the empty list > with ATOM1. > - What do we get? > > * Yes, we get a different LAT. > - Should we give it a name? > > * Sure, what would you like to call it? > - LAT1. > > * Great name. What do you think happens if we extend LAT1 with ATOM2? > - Then we get LAT2, which is like LAT1 but extended with ATOM2. > > And so on. But the key is, we started by simply defining the empty list to > be a LAT. Note how we also don't need any "Scheme" or "Racket" things to > express the ideas. Plain English and an agreement to treat 'extend with' > and > 'the empty list" as special phrases. > > Time to look the second aspect of your question. Here is a definition for > LOB: > > A LOB is either > -- the empty list > or > -- a LOB extended with one Boolean. > A Boolean is either #t or #f. > > * Are these LOBs? > the empty list > the empty list extended with #f > the empty list extended with #f extended with #t > - Yes they are. > > * Are all Booleans on this list #t > the empty list extended with #t extended with #t > - They sure are. > > * Are all Booleans on this list #t > the empty list extended with #t > - Still. > > * Are all Booleans on this list #t > the empty list > - It all depends on what "are" means. [Famous quote. Who said that?] > > * How many options do we have? > - Two: The answer is either true or false. > > * How do you define the function for answer 1 [true] > - Easy > (define (all-true?-1 lob) > (cond > [(null? lob) #t] ;; by definition, right? > [else (and (true? (car lob)) (all-true?-1 (cdr lob)))])) ;; <--- this > is > now functions should be defined > > * What about answer 2 [false]? > - Here is a start: > (define (all-true?-2 lob) > (cond > [(null? lob) #f] ;; by definition, right? > [else ...])) > > * This function works for the empty list but how about lists with one or > two > or three ... Booleans? > - For all those, all-true?-1 gives the correct answer. > (define (all-true?-2 lob) > (cond > [(null? lob) #f] ;; by definition, right? > [else (all-true?-1 lob)])) > > * How come? > - Because all-true?-2 makes sure that all-true?-1 never sees the empty > list. > > > * But doesn't all-true?-1 look for the empty list? > - Yes, but only after it has seen at least one Boolean. > > * Which answer is simpler, elegant, satisfying? > - The first one. It's a two-line function and it's easily explained. > > * So what is the better choice? > - It's better to say that all Booleans on the empty list are true, even > though there aren't any. > > * Is this weird? > - A little bit but it makes everything easy. > > * So let's use this convention from now on. > - Good. > > That's one explanation for considering it correct to say that the empty > list > contains only #t Booleans. Another one: > > all-true is the same as cannot-find-a-false-on-the-list. > > Can you deal with this explanation? -- Matthias > > > > > > > > On Jan 2, 2015, at 5:58 PM, Frank Weytjens wrote: > > > Happy new year Racketeers, > > > > The Little Schemer is my favorite book. > > I have a kind of Sisyphus relationship with it. > > In the preface they advice to not read it, in less then 3 times. > > The jokers! It's more then 3 years I read this book, from time to time. > > Hoping to get further and further, each time. > > I enjoy to start over and over, without completely understanding it. > > Like if: once it 's completely understood, there is no more interesting > stuff on earth. > > This time i got stuck much earlier, then normal, extremely early. > > > > (define lat? > > (lambda (l) > > (cond > > ((null? l) #t) > > ((atom? (car l)) (lat? (cdr l))) > > (else #f)))) > > > > An empty list is a list, but is it a lat ? > > If you give an empty list as argument to the lat?-function, the answer > > is yes. But an atom must be a string of characters or numbers, or even > > one character, or a combination of special characters as long as it is > > not an ( or an ). The empty list contains no characters at all, so it > > can not be a list of atoms. It would be OK, if you recur at least > > once. But when you feed an empty list, this is not the case. Then the > > answer of (null? l) should be #f > > > > Rewriting the function that way, would never give #t as answer > > > > (define lat? > > (lambda (l) > > (cond > > ((null? l) #f) > > ((atom? (car l)) (lat? (cdr l))) > > (else #f)))) > > > > > > So an empty list has to be a lat, and it is not. > > Or is it? Then an empty list can be anything. > > > > > > Thanks, > > > > Frank > > ____________________ > > Racket Users list: > > http://lists.racket-lang.org/users > > > ____________________ > Racket Users list: > http://lists.racket-lang.org/users > > ____________________ > Racket Users list: > http://lists.racket-lang.org/users > >
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