This does not seem relevant to the discussion. In any case, "matrix multiplication" usually means the inner product or the matrix product as in linear algebra, and in such multiplication the matrix arguments need not have the same shape.
----- Original Message ----- From: Donna Y <[email protected]> Date: Monday, October 25, 2010 20:15 Subject: Re: [Jgeneral] "J In A Day" --crits please To: General forum <[email protected]> > Think about matrix multiplication - a scalar can multiply any > matrix but to multiply two matrix - they need to be the same shape > Donna > [email protected] > > > On 2010-10-25, at 10:54 PM, Roger Hui wrote: > > >> But if I mean 'any scalar or array', I have the > >> word 'noun' for that. > > > > They don't have the word "noun" in APL. > > > >> I just don't see why the word 'array', which in plain English > denotes > >> an arrangement of (multiple) things, should have to include > scalars.>> Sue me. Or change the standard. > > > > Look at the texts I quoted. For example, the function > > + takes arrays arguments, scalar or arrays of higher rank. > > If arrays don't include scalars you'd constantly have to > > say "arrays or scalars". You can not use > "multiple" to > > determine whether something is or is not an array, > > for surely you would not say that ,99 or 1 1$99 or 1 1 1$99 > > are not arrays? > > > > The APL standard uses "array" in that way for a good reason. > > "Array or scalar" in APL is a fiction. I don't believe > there is > > anything in the APL literature that says that a scalar is > > not an array. For the same good reason. > > > > > > > > ----- Original Message ----- > > From: Henry Rich <[email protected]> > > Date: Monday, October 25, 2010 19:11 > > Subject: Re: [Jgeneral] "J In A Day" --crits please > > To: General forum <[email protected]> > > > >> I teach the kids that 'scalar' and 'atom' mean a rank-0 > thing, > >> and > >> 'array' means rank > 0. Yeah, I know it's not > >> standard. But if I mean > >> 'any scalar or array', I have the word 'noun' for that. > >> And the > >> distinction between scalar and array is important enough to > have > >> words for. > >> > >> My way, I can give them some simple things to memorize: > >> > >> An array is a list of its items. > >> > >> The items of an array have rank one less > than the array. > >> > >> #array is the same as {.$array. > >> > >> A DLL descriptor of *c matches an array of > characters.>> > >> I just don't see why the word 'array', which in plain English > >> denotes an > >> arrangement of (multiple) things, should have to include scalars. > >> Sue me. Or change the standard. > >> > >> Henry Rich > >> > >> > >> On 10/25/2010 9:19 PM, Roger Hui wrote: > >>> I had/have been an APLer for many years and I have > >>> never heard of scalars not being arrays. As far as > >>> I know 99 is not just now deemed an array but > >>> have always been deemed an array. I'd be interested > >>> in any APL reference you can find that says otherwise. > >>> > >>> A more ancient reference for that fact that a scalar is an array. > >>> Falkoff and Iverson, The APL\360 Terminal System, 1967-10-16. > >>> http://www.jsoftware.com/papers/APL360TerminalSystem.htm > >>> > >>> - A vector has a “rank” of one, the term being used, > >>> as in tensor analysis, to mean the number of indices > >>> required to identify a single element in an array. > >>> Hence, a scalar has rank zero and a matrix has rank two. > >>> > >>> - No special notational convention is required for the > >>> element-by-element extension, so that in the expression a+b , > >>> for example, a and b may be any pair of matching arrays. > >>> If one argument is a scalar the other may be any array, ... > >>> > >>> --- > >>> > >>> In any case, you have not addressed the practical point > >>> I raised: if a scalar is not an array, you are going to > >>> need a term for "array or scalar". Another way to > >>> look at it is, why is it useful to distinguish between > >>> an array and a scalar? > >>> > >>> Whether a scalar is an array is not a statement that > >>> you can prove one way or the other, and you have to > >>> decide on considerations in the preceding paragraph, > >>> or considerations similar to same. > >>> > >>> Finally, why is it counter-intuitive that a scalar is > >>> an array? > >>> > >>> > >>> > >>> ----- Original Message ----- > >>> From: Ian Clark<[email protected]> > >>> Date: Monday, October 25, 2010 17:44 > >>> Subject: Re: [Jgeneral] "J In A Day" --crits please > >>> To: General forum<[email protected]> > >>> > >>>> Thanks, Roger, for the ref to the ISO standard: ISO 13751. Wow, > >>>> haven't things moved on since I was involved with the draft ISO > >>>> standard in 1992. I'd buy myself a copy, but they want $292 just > >>>> for a > >>>> lousy PDF. But yes: thanks for reminding me the Dyalog > >> manuals are > >>>> free. > >>>> > >>>> No, I didn't really think you'd get it wrong. But I confess > >> I'm amazed > >>>> that scalar 99 is now deemed an "array"! I thought I knew APL, > >>>> but I'd > >>>> never heard that one. (Yes, I knew about rank zero.) > >>>> > >>>> I'm now going to ask all my APL friends: "did you know 99 > is an > >>>> array?" -- and see what they say. > >>>> > >>>> But you know what I think? I think it's counter-intuitive, > >> and that's > >>>> the sort of thing that gets APL a bad name. And not just APL... > >>>> > >>>> I refuse to get into disputes about which is the better > >>>> language: APL > >>>> or J. What's more, "reductio" arguments don't work with me > either,>>>> unless I'm convinced we start from the same premises > -- which > >>>> I'm not. > >>>> I've spent my programming career porting > code, > >> and there > >>>> is no > >>>> "better" or "worse" language for me. There is just a source > >> and a > >>>> target language. Which is which? Well, (1) who's paying? (2) > >>>> which way > >>>> does he want to migrate his code? > >>>> > >>>> I haven't touched APL for over a year now, but I've coded > >>>> heavily in > >>>> J. The reasons for that won't impress you. If you ask me > >> which I have > >>>> any warm feeling for, I have to say APL... in the same way > a doctor > >>>> prefers a sick patient to a healthy one. It's made me a living, > >>>> and a > >>>> good one. > >>>> > >>>> I've offered to write this crash-course for APLers. Some of > >> them are > >>>> proud of their skill in the language -- and they don't respond > >>>> positively to having it dissed. I'm going to need to purge > my > >> answers>> of all insinuation that APL is rubbish. People will > be > >> so relieved! > >>>> "It's about J and it doesn't rubbish APL...!" > >>>> > >>>> But I know what they're going to ask: what's with all these > >>>> nouns and pronouns? > >>>> > >>>> I've asked on this list: "what's a pronoun"? I still don't > >> know the > >>>> answer (with my APL hat on, let me stress). I'm going to > have > >> to say: > >>>> "it's only metalanguage." (...right: where's it formally > >>>> defined?) "It > >>>> isn't. The documenters want you to read their minds." (...ok, > >>>> give me > >>>> a clue.) "I can't. In two year's time you'll think it's all > >> perfectly>> natural" (...meanwhile...?) > >>>> > >>>> Ian > >>>> > >>>> > >>>> On Mon, Oct 25, 2010 at 3:39 PM, Roger > >> Hui<[email protected]> wrote: > >>>>> No, I don't mean "array or scalar", I meant "array". > >>>>> Let me cite two sources: > >>>>> > >>>>> 0. Dyalog APL Language Reference/Variables/Arrays: - > >>>>> A Dyalog APL data structure is called an array. ... An array > >>>>> may have 0 or more axes. > >>>>> > >>>>> 1. ISO/IEC 13751-2001, ISO Standard on Extended APL, > >>>>> Section 5.3.2: Scalar: An array whose rank is zero. > >>>>> > >>>>> As well, in practice, if a scalar in APL is if not an array, > >>>>> then when you talk about APL you'd be constantly saying > >>>>> "array or scalar" rather than just "array". (I was > >>>>> once asked by non-mathematicians why 1 is not > >>>>> a prime. After 5 seconds of thought I said, > >>>>> "because it makes lots of statements simpler". > >>>>> (As it is, you already have statements in math of the > >>>>> sort "let n be an odd prime".)) > >>>>> > >>>>> In APL, if a "value" can only be an array, what word or > >>>>> words would you use when you need to say "the x of > >>>>> a phrase", when the phrase can be +/ or +/ 1 2 3 > >>>>> or . or ¨? > >>>>> > >>>>> Reading your statements about "variable" in APL, > >>>>> with descriptions of quad-nc, artificial restrictions on > >>>>> reassignment, quad-ex, etc. etc., it strikes > me that > >>>>> in contrast the meanings of "noun" and "pronoun" > >>>>> are simpler and more precise (less variable ...) than > >>>>> in APL. Even more so in any APLs which do not > >>>>> allow names be assigned to a function via ← . > >>>>> (Then functions can only be named as a side effect > >>>>> of ⎕fx or of an edit session.) One more thing: > >>>>> Dyalog APL, which does allow sum←+/, does not > >>>>> allow each←¨ . Explain that one. > >>>>> > >>>>> > >>>>> > >>>>> ----- Original Message ----- > >>>>> From: Ian Clark<[email protected]> > >>>>> Date: Monday, October 25, 2010 0:38 > >>>>> Subject: Re: [Jgeneral] "J In A Day" --crits please > >>>>> To: General forum<[email protected]> > >>>>> > >>>>>> Roger, > >>>>>> > >>>>>> I'd call sum a "variable" in APL if-and-only-if ([]NC 'sum') > >>>>>> returns 2. > >>>>>> > >>>>>> In Dyalog APL (I don't have it installed on my Mac) I > seem to > >>>> recall>> you can indeed write: > >>>>>> sum←+ > >>>>>> but []NC 'sum' would afterwards return 3, telling > me it's > >>>>>> a function > >>>>>> (...whatever else it might have been before). > >>>>>> > >>>>>> So... "what do you call a name in APL whose referent is a > >>>> function?">> -- A function name. > >>>>>> > >>>>>> Moreover I think most APLs won't let you change "sum", say, > >>>> from a > >>>>>> variable name to a function name by reassigning it. Even if > >>>> functional>> assignment is permitted. The statement (sum←+) > >>>> causes an error > >>>>>> if sum > >>>>>> is already defined in the workspace as a variable, and > you > >> haven't>>>> freed-up the name 'sum' for reuse by localisation > or []EX. > >>>>>> > >>>>>> I use "value" (...but only in an APL context, let me > >>>> emphasise) to > >>>>>> mean "something that can be assigned to a variable" (...and > >>>> it still > >>>>>> remains a variable). I think a lot of APLers would agree > >> with that. > >>>>>> It's a more restricted meaning of "value" than you imply in > >>>> the J > >>>>>> context, which it seems to me means anything acceptable to > >>>> the right > >>>>>> of a copula. Or, more precisely, any entity that is > >> returned by > >>>>>> evaluating a phrase which can validly stand to the right > of a > >>>> copula.>> > >>>>>> You say that "noun" in J corresponds directly and exactly > >>>> with "array" > >>>>>> in APL. Was that a mistake... don't you mean "array or scalar"? > >>>>>> (...commonly expressed as "vector or scalar" -- "array" not > >>>>>> being a > >>>>>> proper APL term, and [APL] "vector" not being restricted > to > >> 1-D > >>>>>> arrays.) Surely you don't mean me to infer that 99 is not > a noun > >>>>>> in J > >>>>>> because it is not an "array" in APL? > >>>>>> > >>>>>> I'm not interested in challenging Ken's appeal to his implicit > >>>>>> understanding of English Grammar (which I deny is necessarily > >>>>>> mine, or > >>>>>> indeed anyone else's) to convey programming ideas. He's allowed > >>>>>> to do > >>>>>> that. I just want a precise enough notion of > "noun/pronoun" > >> -- > >>>>>> as it > >>>>>> applies to J -- so I can point to something in J code and > >> say with > >>>>>> confidence "that's a noun" or "that's a pronoun". > >>>>>> > >>>>>> Ian > >>>>>> > >>>>>> > >>>>>> 2010/10/25 Roger Hui<[email protected]>: > >>>>>>>> But Ken talks of "analogies", and seems to use the word > "noun">>>>>>>> to mean a value or quantity: the result of an > expression,>>>> not the > >>>>>>>> variable -- or named memory location -- it's stored in. What, > >>>>>> in J, > >>>>>>>> corresponds to an APL "variable"? > >>>>>>> > >>>>>>> "Noun" in J does not mean value. It corresponds > >>>>>>> directly and exactly to "array" in APL. A value can > >>>>>>> be a verb (function), for example, "the value of the > >>>>>>> sentence +/ is a verb that does summation". > >>>>>>> > >>>>>>> Regarding your last question, It depends on how > >>>>>>> "variable" is used in APL. If you say sum←+/ 2 3 4, > >>>>>>> I think you'd call "sum" a variable. But if you say > >>>>>>> sum←+/, is "sum" still a variable? If not, what is > >>>>>>> the difference, and what do you call a name in APL > >>>>>>> whose referent is a function? If yes, doesn't it > >>>>>>> sound jarring to your ears? (It does to mine.) > >>>>>>> > >>>>>>> And, a question Ken used to ask: if sum←1 2 3, > >>>>>>> what is variable about "sum"? > >>>>>>> > >>>>>>> Some APL texts also calls .5 and 1 2 3 and 'abc' > >>>>>>> "variables, that is, used "variable" and "array" > >>>>>>> as synonyms. Ken's question is even more pertinent > >>>>>>> in those cases: If ever .5 has a different value > >>>>>>> ("varied"), I expect to get system errors shortly > >>>>>>> thereafter. > >>>>>>> > >>>>>>> There is a table in the dictionary section II. Grammar: > >>>>>>> http://www.jsoftware.com/help/dictionary/dict2.htm > >>>>>>> > >>>>>>> PARTS of SPEECH > >>>>>>> > >>>>>>> 50 > >> > fahrenheit Nouns/Pronouns > >>>>>>> + - * % bump Verbs/Proverbs > >>>>>>> / \ Adverbs > >>>>>>> & Conjunction > >>>>>>> ( ) Punctuation > >>>>>>> =: Copula > >>>>>>> > >>>>>>> > >>>>>>> > >>>>>>> ----- Original Message ----- > >>>>>>> From: Ian Clark<[email protected]> > >>>>>>> Date: Sunday, October 24, 2010 12:21 > >>>>>>> Subject: [Jgeneral] "J In A Day" --crits please > >>>>>>> To: General forum<[email protected]> > >>>>>>> > >>>>>>>> First draft of an article for eventual submission to VECTOR > >>>>>> entitled>> "J In A Day". > >>>>>>>> > >>>>>>>> http://www.jsoftware.com/jwiki/JinaDay > >>>>>>>> > >>>>>>>> It is "work-in-progress". It represents an "alpha" offering, > >>>>>> not a > >>>>>>>> "release" or "publication". It's aimed squarely at the > >>>> APLer who > >>>>>>>> doesn't know any J. > >>>>>>>> > >>>>>>>> There won't be many such on this list. But right now > I'm keen > >>>>>> to get > >>>>>>>> the J right. > >>>>>>>> > >>>>>>>> The prevalent message to APLers coming to J is: un-learn > >>>> everything>> >> you know about APL (it's not > >> helpful) and learn > >>>> J from first > >>>>>>>> principles. I think this erects an unnecessary barrier > to the > >>>>>>>> dwindling(?) band of APLers ignorant of J. > >>>>>>>> > >>>>>>>> Of course the barriers may be there anyway. I recall my first > >>>>>> exposure>> to J aroused antipathy in me. I can't > >> quite remember > >>>>>> why. A Kuhnian > >>>>>>>> paradigm-shift may be inescapable--or at least the need for > >>>>>> one. The > >>>>>>>> article deliberately avoids being starry-eyed so as not to > >>>>>> raise the > >>>>>>>> APLer's hackles. But this is not meant as provocation > to the > >>>>>> J-er. > >>>>>>>> > >>>>>>>> There's a fairly defiant "admonition" (as MoinMoin > calls it) > >>>>>> to J > >>>>>>>> experts -- but don't be put off. I would really > >> appreciate your > >>>>>>>> comments. So get your anoraks on... ;) > >>>>>>>> > >>>>>>>> Of course, if an APL-er knowing absolutely no J were to work > >>>>>> through>> it, and confirm (or deny) it was of use > to > >> them...>>>> that would > >>>>>>>> get me > >>>>>>>> on like 7-league boots. > >>>>>>>> > >>>>>>>> BTW I use the J terms "proverb" and "pronoun" in it. I > >>>> need to > >>>>>>>> know if > >>>>>>>> I'm using them correctly. See my separate posting. > >>>>>>>> > >>>>>>>> Thanks, Brian, for the Iverson ref. From the horse's mouth, > >>>>>> so to > >>>>>>>> speak. But Ken talks of "analogies", and seems to use the > >>>>>> word "noun" > >>>>>>>> to mean a value or quantity: the result of an expression, > >>>> not the > >>>>>>>> variable -- or named memory location -- it's stored in. What, > >>>>>> in J, > >>>>>>>> corresponds to an APL "variable"? ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
