New Science Discovery: Perl Idiots Remain Idiots After A Decade!New

Discussion in 'Python' started by Xah Lee, Feb 29, 2012.

  1. Xah Lee

    Xah Lee Guest

    New Science Discovery: Perl Idiots Remain Idiots After A Decade!

    A excerpt from the new book 〈Modern Perl〉, just published, chapter 4
    on “Operatorsâ€. Quote:

    «The associativity of an operator governs whether it evaluates from
    left to right or right to left. Addition is left associative, such
    that 2 + 3 + 4 evaluates 2 + 3 first, then adds 4 to the result.
    Exponentiation is right associative, such that 2 ** 3 ** 4 evaluates 3
    ** 4 first, then raises 2 to the 81st power. »

    LOL. Looks like the perl folks haven't changed. Fundamentals of
    serious math got botched so badly.

    Let me explain the idiocy.

    It says “The associativity of an operator governs whether it evaluates
    from left to right or right to left.â€. Ok, so let's say we have 2
    operators: a white triangle â–³ and a black triangle â–². Now, by the
    perl's teaching above, let's suppose the white triangle is “right
    associative†and the black triangle is “left associativeâ€. Now, look
    at this:

    3 â–³ 6 â–² 5

    seems like the white and black triangles are going to draw a pistol
    and fight for the chick 6 there. LOL.

    Now, let me tell you what operator precedence is. First of all, let's
    limit ourselfs to discuss operators that are so-called binary
    operators, which, in our context, basically means single symbol
    operator that takes it's left and right side as operands. Now, each
    symbol have a “precedenceâ€, or in other words, the set of operators
    has a order. (one easy way to think of this is that, suppose you have
    n symbols, then you give each a number, from 1 to n, as their order)
    So, when 2 symbols are placed side by side such as 「3 â–³ 6 â–² 5ã€, the
    symbol with higher precedence wins. Another easy way to think of this
    is that each operator has a stickiness level. The higher its level, it
    more sticky it is.

    the problem with the perl explanations is that it's one misleading
    confusion ball. It isn't about “left/right associativityâ€. It isn't
    about “evaluates from left to right or right to leftâ€. Worse, the word
    “associativity†is a math term that describe a property of algebra
    that has nothing to do with operator precedence, yet is easily
    confused with because it is a property about order of evaluation. (for
    example, the addition function is associative, meaning: 「(3+6)+5 =
    3+(6+5)ã€.)

    compare it with this:

    〈Perl & Python: Complex Numbers〉
    http://xahlee.org/perl-python/complex_numbers.html

    and for a good understanding of functions and operators, see:

    〈What's Function, What's Operator?〉
    http://xahlee.org/math/function_and_operators.html
     
    Xah Lee, Feb 29, 2012
    #1
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  2. Xah Lee

    Chiron Guest

    Re: New Science Discovery: Perl Idiots Remain Idiots After A

    On Wed, 29 Feb 2012 00:09:16 -0800, Xah Lee wrote:

    Personally, I think this whole issue of precedence in a programming
    language is over-rated. It seems to me that grouping of any non-trivial
    set of calculations should be done so as to remove any possible confusion
    as to intent. It is one more obstacle to accidental errors in logic,
    where you intend one thing, possibly overlook precedence, and get a
    strange result.

    Sure, mathematically it *should* go a particular way, and any programming
    language *should* follow that. Still... they don't, and since they don't
    it makes more sense to be really obvious what you meant to do.

    As someone pointed out, a programming language is for humans; computers
    don't need them. That being the case, it makes sense to keep things as
    clear as possible.

    --
    It's OKAY -- I'm an INTELLECTUAL, too.
     
    Chiron, Feb 29, 2012
    #2
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  3. Re: New Science Discovery: Perl Idiots Remain Idiots After A

    On Wed, Feb 29, 2012 at 6:43 AM, Chiron <> wrote:
    > Personally, I think this whole issue of precedence in a programming
    > language is over-rated.  It seems to me that grouping of any non-trivial
    > set of calculations should be done so as to remove any possible confusion
    > as to intent.


    Some languages do this. e.g. all lisps.

    -- Devin
     
    Devin Jeanpierre, Feb 29, 2012
    #3
  4. Re: New Science Discovery: Perl Idiots Remain Idiots After A Decade!New Science Discovery: Perl Idiots Remain Idiots After A Decade!

    Xah Lee <> writes:
    > A excerpt from the new book 〈Modern Perl〉, just published, chapter 4
    > on “Operatorsâ€. Quote:
    >
    > «The associativity of an operator governs whether it evaluates from
    > left to right or right to left. Addition is left associative, such
    > that 2 + 3 + 4 evaluates 2 + 3 first, then adds 4 to the result.
    > Exponentiation is right associative, such that 2 ** 3 ** 4 evaluates 3
    > ** 4 first, then raises 2 to the 81st power. »
    >
    > LOL. Looks like the perl folks haven't changed. Fundamentals of
    > serious math got botched so badly.
    >
    > Let me explain the idiocy.
    >
    > It says “The associativity of an operator governs whether it evaluates
    > from left to right or right to left.â€. Ok, so let's say we have 2
    > operators: a white triangle â–³ and a black triangle â–². Now, by the
    > perl's teaching above, let's suppose the white triangle is “right
    > associative†and the black triangle is “left associativeâ€. Now, look
    > at this:
    >
    > 3 â–³ 6 â–² 5
    >
    > seems like the white and black triangles are going to draw a pistol
    > and fight for the chick 6 there. LOL.


    As the perlop manpage would have told you,

    Operator associativity defines what happens if a sequence of the same
    operators is used one after another

    Since this is not the case in your example, it doesn't seem to be
    applicable here. Also, the Perl I'm aware doesn't have 'white
    triangle' and 'black triangle' operators and it also doesn't have
    operators of equal precedence and different associativity. It can't,
    actually, since there would be no way to evaluate an expression like
    the mock one you invented above. Lastly, that something happens to be
    in one way or another way in the completely arbitrary set of rules and
    conventions commonly referred to as 'mathematics' (an essentially
    outdated write-only programming language dating back to the times
    when humans had to perform computations themselves) doesn't mean it is
    of any relevance anywhere else just because of this, no matter how
    dear it might be to lots of people.
     
    Rainer Weikusat, Feb 29, 2012
    #4
  5. Xah Lee

    namekuseijin Guest

    Re: New Science Discovery: Perl Idiots Remain Idiots After A

    On Feb 29, 5:09 am, Xah Lee <> wrote:
    > New Science Discovery: Perl Idiots Remain Idiots After A Decade!
    >
    > A excerpt from the new book 〈Modern Perl〉, just published, chapter 4
    > on “Operatorsâ€. Quote:
    >
    > «The associativity of an operator governs whether it evaluates from
    > left to right or right to left. Addition is left associative, such
    > that 2 + 3 + 4 evaluates 2 + 3 first, then adds 4 to the result.
    > Exponentiation is right associative, such that 2 ** 3 ** 4 evaluates 3
    > ** 4 first, then raises 2 to the 81st power. »
    >
    > LOL. Looks like the perl folks haven't changed. Fundamentals of
    > serious math got botched so badly.
    >
    > Let me explain the idiocy.
    >
    > It says “The associativity of an operator governs whether it evaluates
    > from left to right or right to left.â€. Ok, so let's say we have 2
    > operators: a white triangle â–³ and a black triangle â–². Now, by the
    > perl's teaching above, let's suppose the white triangle is “right
    > associative†and the black triangle is “left associativeâ€. Now, look
    > at this:
    >
    > 3 â–³ 6 â–² 5
    >
    > seems like the white and black triangles are going to draw a pistol
    > and fight for the chick 6 there. LOL.
    >
    > Now, let me tell you what operator precedence is. First of all, let's
    > limit ourselfs to discuss operators that are so-called binary
    > operators, which, in our context, basically means single symbol
    > operator that takes it's left and right side as operands. Now, each
    > symbol have a “precedenceâ€, or in other words, the set ofoperators
    > has a order. (one easy way to think of this is that, suppose you have
    > n symbols, then you give each a number, from 1 to n, as their order)
    > So, when 2 symbols are placed side by side such as 「3 â–³ 6â–² 5ã€, the
    > symbol with higher precedence wins. Another easy way to think of this
    > is that each operator has a stickiness level. The higher its level, it
    > more sticky it is.
    >
    > the problem with the perl explanations is that it's one misleading
    > confusion ball. It isn't about “left/right associativityâ€.. It isn't
    > about “evaluates from left to right or right to leftâ€. Worse, the word
    > “associativity†is a math term that describe a property of algebra
    > that has nothing to do with operator precedence, yet is easily
    > confused with because it is a property about order of evaluation. (for
    > example, the addition function is associative, meaning: 「(3+6)+5 =
    > 3+(6+5)ã€.)
    >
    > compare it with this:
    >
    > 〈Perl & Python: Complex Numbers〉http://xahlee.org/perl-python/complex_numbers.html
    >
    > and for a good understanding of functions and operators, see:
    >
    > 〈What's Function, What's Operator?〉http://xahlee.org/math/function_and_operators.html


    associativity of operators mean little in the Lisp world obviously, so
    why was this posted here? Sorry, perl, python and emacs folks...

    BTW, it's the same in javascript: it is so such that 2 + 3 + "4" is
    "54" and "2" + 3 + 4 is "234". Blame weak typing and + overloading,
    though it may be a blessing.
     
    namekuseijin, Feb 29, 2012
    #5
  6. Xah Lee

    Xah Lee Guest

    Re: New Science Discovery: Perl Idiots Remain Idiots After A

    i missed a point in my original post. That is, when the same operator
    are adjacent. e.g. 「3 â–² 6 â–² 5ã€.

    This is pointed out by Kiuhnm 〔kiuhnm03.4t.yahoo.it〕 and Tim Bradshaw.
    Thanks.

    though, i disagree the way they expressed it, or any sense this is
    different from math.

    to clarify, amend my original post, here's what's needed for binary
    operator precedence:

    â‘  the symbols are ordered. (e.g. given a unique integer)

    â‘¡ each symbol is has either one of left-side stickness or right-side
    stickness spec. (needed when adjacent symbols are the same.)

    About the lisp case mentioned by Tim, e.g. in「(f a b c)ã€, whether it
    means 「(f (f a b) c)〠or 「(f a (f b c))〠. It is not directly relevant
    to the context of my original post, because it isn't about to
    operators. It's about function argument eval order. Good point,
    nevertheless.

    the perl doc, is still misleading, terribly bad written. Becha ass!

    Xah

    On Feb 29, 4:08 am, Kiuhnm <kiuhnm03.4t.yahoo.it> wrote:
    > On 2/29/2012 9:09, Xah Lee wrote:
    >
    >
    > > New Science Discovery: Perl Idiots Remain Idiots After A Decade!

    >
    > > A excerpt from the new book 〈Modern Perl〉, just published, chapter 4
    > > on “Operatorsâ€. Quote:

    >
    > > «The associativity of an operator governs whether it evaluates from
    > > left to right or right to left. Addition is left associative, such
    > > that 2 + 3 + 4 evaluates 2 + 3 first, then adds 4 to the result.
    > > Exponentiation is right associative, such that 2 ** 3 ** 4 evaluates 3
    > > ** 4 first, then raises 2 to the 81st power. »

    >
    > > LOL. Looks like the perl folks haven't changed. Fundamentals of
    > > serious math got botched so badly.

    >
    > > Let me explain the idiocy.

    >
    > > It says “The associativity of an operator governs whether it evaluates
    > > from left to right or right to left.â€. Ok, so let's say we have2
    > > operators: a white triangle â–³ and a black triangle â–². Now, by the
    > > perl's teaching above, let's suppose the white triangle is “right
    > > associative†and the black triangle is “left associativeâ€. Now, look
    > > at this:

    >
    > > 3 â–³ 6 â–² 5

    >
    > > seems like the white and black triangles are going to draw a pistol
    > > and fight for the chick 6 there. LOL.

    >
    > Sorry, but you're wrong and they're right.
    > Associativity governs the order of evaluation of a group of operators
    > *OF THE SAME PRECEDENCE*.
    > If you write
    >    2**3**4
    > only the fact the '**' is right associative will tell you that the order is
    >    2**(3**4)
    > and not
    >    (2**3)**4
    > I remind you that 2^(3^4) != (2^3)^4.
    >
    > Kiuhnm
     
    Xah Lee, Mar 1, 2012
    #6
  7. Xah Lee

    Chiron Guest

    Re: New Science Discovery: Perl Detracters Remain Idiots After ADecade!

    On Wed, 29 Feb 2012 23:06:42 -0500, Shmuel (Seymour J.) Metz wrote:

    > In <ubo3r.20367$>, on 02/29/2012
    > at 11:43 AM, Chiron <> said:
    >
    >>Sure, mathematically it *should* go a particular way,

    >
    > No. Mathematically it should go the way that it is defined to go. There
    > is nothing in Mathematics that either requires or prohibits infix
    > notation in programming languages, or even in Mathematical notation.
    >

    Yes. That (the mathematically defined way) is a particular way, is it
    not?

    >>it makes sense to keep things as clear as possible.

    >
    > Often infix notation with well thought out precedence is the clearest
    > way to go. RPN and the like have their place, but often are difficult
    > for real people to read.


    However, I wasn't specifically referring to infix/postfix/prefix or
    anything of that nature. I wasn't limiting my comment to lisp notation
    in particular, since what I said applies to any language. I was
    referring to the placement of parentheses (or other groupings) to
    indicate to *humans* what the intended sequence of events was. The
    problem with precedence is that it is not always clear how it will go.
    Different languages have different rules, some of which depart from the
    rules in mathematics. Some implementations of languages are buggy in
    this regard.

    Mathematically, and in any language with which I am familiar, the
    sequence: 2 + 6 / 3 will yield 4. It is unnecessary, but harmless, to
    write this as 2 + (6 / 3). A naive reader (or just a tired or hurried
    one) might come up with 8 / 3 if there aren't any parentheses.

    Whenever there is *any* possibility of ambiguity, I see no reason not to
    clarify. Back in the days when the way you wrote your code affected how
    it was compiled, it made sense to rely heavily on language-specific
    features, thus saving a few bytes. With gigabyte memories, gigahertz
    clock speeds, and optimizing compilers, the pressure to try to optimize
    by hand is gone. A few extra parentheses, or even breaking down a
    complex sequence of events into discrete, simpler ones, is no longer a
    costly luxury. A few extra variables, if they help clarity, aren't going
    to hurt anything. Let the machine do the grunt work. Pamper your
    readers (which in a few weeks or months might be you) and show exactly
    what you had in mind. That's all I'm saying.

    --
    I'd just as soon kiss a Wookie.
    -- Princess Leia Organa
     
    Chiron, Mar 1, 2012
    #7
  8. Xah Lee

    Chiron Guest

    Re: New Science Discovery: Perl Idiots Remain Idiots After A

    On Wed, 29 Feb 2012 23:10:48 -0500, Shmuel (Seymour J.) Metz wrote:

    > ROTF,LMAO! You obviously don't have a clue as to what Mathematics means.
    > Free hint: it doesn't mean Arithmetic. You're as bigoted as Xah Lee,



    Hmm... maybe, instead of just ridiculing him, you could explain where he
    is mistaken. Of course, doing that is a *LOT* harder than just calling
    him a bigot.

    BTW, I happen to agree with you insofar as this poster not understanding
    the nature of mathematics. His comment reminds me of the article,
    "Transgressing the Boundaries: Towards a Transformative Hermeneutics of
    Quantum Gravity" (http://www.physics.nyu.edu/sokal/transgress_v2/
    transgress_v2_singlefile.html). Also known as the "Sokal Hoax."

    --
    Boling's postulate:
    If you're feeling good, don't worry. You'll get over it.
     
    Chiron, Mar 1, 2012
    #8
  9. Re: New Science Discovery: Perl Idiots Remain Idiots After A Decade!New Science Discovery: Perl Idiots Remain Idiots Af

    Shmuel (Seymour J.) Metz <> writes:
    > In <>, on 02/29/2012
    > at 03:15 PM, Rainer Weikusat <> said:
    >
    >>'mathematics' (an essentially outdated write-only programming
    >>language dating back to the times when humans had to perform
    >>computations themselves)

    >
    > ROTF,LMAO! You obviously don't have a clue as to what Mathematics
    > means. Free hint: it doesn't mean Arithmetic.


    You obviously don't have any sense of humour. But don't let this
    trouble you.
     
    Rainer Weikusat, Mar 1, 2012
    #9
  10. Re: New Science Discovery: Perl Idiots Remain Idiots After A

    First of all:

    http://www.youtube.com/watch?v=z5jKMEB4hHE

    On Wed, Feb 29, 2012 at 12:09:16AM -0800, Xah Lee wrote:
    > Now, let me tell you what operator precedence is. First of all, let's
    > limit ourselfs to discuss operators that are so-called binary
    > operators, which, in our context, basically means single symbol
    > operator that takes it's left and right side as operands. Now, each
    > symbol have a “precedenceâ€, or in other words, the set of operators
    > has a order. (one easy way to think of this is that, suppose you have
    > n symbols, then you give each a number, from 1 to n, as their order)
    > So, when 2 symbols are placed side by side such as 「3 â–³ 6 â–² 5ã€, the
    > symbol with higher precedence wins. Another easy way to think of this
    > is that each operator has a stickiness level. The higher its level, it
    > more sticky it is.


    You're absolutely correct.

    > the problem with the perl explanations is that it's one misleading
    > confusion ball. It isn't about “left/right associativityâ€. It isn't
    > about “evaluates from left to right or right to leftâ€. Worse, the word
    > “associativity†is a math term that describe a property of algebra
    > that has nothing to do with operator precedence, yet is easily
    > confused with because it is a property about order of evaluation. (for
    > example, the addition function is associative, meaning: 「(3+6)+5 =
    > 3+(6+5)ã€.)


    You're not getting it.

    Math is a language. Perl is a language. They have different rules for
    grammar. In Perl, C, Python, Java, and pretty much all procedural-based
    languages, operations are evaluated in two steps: the precedence /and/
    the associativity. Each level of precedence has its own associativity,
    either left-to-right or right-to-left. You can see this in table 2-1 in
    The C Programming Language. Whatever math does or what you think math
    does has nothing to do with the way Perl evaluates expressions.
     
    Westley Martínez, Mar 2, 2012
    #10
  11. Xah Lee

    Chiron Guest

    Re: New Science Discovery: Perl Idiots Remain Idiots After A

    On Wed, 29 Feb 2012 00:09:16 -0800, Xah Lee wrote:

    Xah, you won't grow even an inch taller by cutting others down.

    --
    I joined scientology at a garage sale!!
     
    Chiron, Mar 2, 2012
    #11
  12. Xah Lee

    Xah Lee Guest

    Re: New Science Discovery: Perl Idiots Remain Idiots After A

    On Mar 1, 3:00 am, Kiuhnm <kiuhnm03.4t.yahoo.it> wrote:
    > They did not make up the terminology, if that is what you are saying.
    > The concepts of left and right associativity are well-known and accepted
    > in TCS (Theoretical CS).



    > Aho, Sethi and Ullman explain it this way in "Compilers: Principles,
    > Techniques and Tools":
    > "We say that the operator + associates to the left because an operand
    > with plus signs on both sides of it is taken by the operator to its
    > left. [...]"
    > And they also show parse trees similar to the ones I wrote above.


    how do they explain when 2 operators are adjacent e.g. 「3 △6 ▲ 5 �

    do you happen to know some site that shows the relevant page i can
    have a look?

    thanks.

    Xah

    On Mar 1, 3:00 am, Kiuhnm <kiuhnm03.4t.yahoo.it> wrote:
    > On 3/1/2012 1:02, Xah Lee wrote:
    >
    > > i missed a point in my original post. That is, when the same operator
    > > are adjacent. e.g. 「3 â–² 6 â–² 5ã€.

    >
    > > This is pointed out by Kiuhnm 〔kiuhnm03.4t.yahoo.it〕 and Tim Bradshaw.
    > > Thanks.

    >
    > > though, i disagree the way they expressed it, or any sense this is
    > > different from math.

    >
    > They did not make up the terminology, if that is what you are saying.
    > The concepts of left and right associativity are well-known and accepted
    > in TCS (Theoretical CS).
    >
    > If you change the terminology, no one will understand you unless you
    > provide your definitions every time (and then they may not accept them).
    >
    > Another way of saying that an operator is left-associative is that its
    > parse tree is a left-tree, i.e. a complete tree where each right child
    > is a leaf.
    > For instance, (use a monospaced font)
    >    1 + 2 + 3 + 4
    > gives you this left-tree:
    >        +
    >      +   4
    >    +   3
    >   1 2
    > while 1**2**3**4
    > gives you this right-tree:
    >    **
    > 1    **
    >     2    **
    >         3  4
    >
    > Aho, Sethi and Ullman explain it this way in "Compilers: Principles,
    > Techniques and Tools":
    > "We say that the operator + associates to the left because an operand
    > with plus signs on both sides of it is taken by the operator to its
    > left. [...]"
    > And they also show parse trees similar to the ones I wrote above.
    >
    > Kiuhnm
     
    Xah Lee, Mar 2, 2012
    #12
  13. Xah Lee

    Chiron Guest

    Re: New Science Discovery: Perl Idiots Remain Idiots After A

    On Thu, 01 Mar 2012 10:13:11 -0500, Shmuel (Seymour J.) Metz wrote:

    > In <DuD3r.21706$>, on 03/01/2012
    > at 05:07 AM, Chiron <> said:
    >
    >>Hmm... maybe, instead of just ridiculing him,

    >
    > I'm treating him as he treats others.


    OK.
    >
    >>BTW, I happen to agree with you insofar as this poster not understanding
    >> the nature of mathematics. His comment reminds me of the article,
    >>"Transgressing the Boundaries: Towards a Transformative Hermeneutics of
    >>Quantum Gravity"

    >
    > A brilliant piece of work. I greatly enjoyed it and the reaction to its
    > disclosure.


    What always gets me is how so many people criticized Sokal for doing it,
    instead of soundly condemning the editor for not bothering to verify what
    Sokal said. It's like the kid points out that the emperor has no
    clothes, so they shoot the kid. Of course, in real life, that's exactly
    what would happen, so I guess I shouldn't be too surprised...



    --
    It is a hard matter, my fellow citizens, to argue with the belly,
    since it has no ears.
    -- Marcus Porcius Cato
     
    Chiron, Mar 2, 2012
    #13
  14. Xah Lee

    Chiron Guest

    Re: New Science Discovery: Perl Detractors Remain Idiots After ADecade!

    On Fri, 02 Mar 2012 10:53:30 -0500, Shmuel (Seymour J.) Metz wrote:

    > In <OD44r.17949$>, on 03/02/2012
    > at 02:17 PM, Chiron <> said:
    >
    >>What always gets me is how so many people criticized Sokal for doing it,

    >
    > Google for Omerta. It's common for whistle blowers to be chastised or
    > even persecuted. I agree that the criticism of Prof Sokal was
    > outrageous, but it was also predictable.


    Yeah, omerta... I'm familiar with it. Talk and you're dead, and they put
    a canary in your mouth (well, some folks do, anyway).

    But of course you're right - it's a milder form of omerta. It's just so
    misguided. Kill the messenger. Imprison the whistle-blower.



    --
    Imitation is the sincerest form of plagiarism.
     
    Chiron, Mar 2, 2012
    #14
  15. Re: New Science Discovery: Perl Idiots Remain Idiots After A Decade!New Science Discovery: Perl Idiots Remain Idiots After A Decade!

    In article <>,
    Xah Lee <> wrote:
    >New Science Discovery: Perl Idiots Remain Idiots After A Decade!
    >
    >A excerpt from the new book =E3=80=88Modern Perl=E3=80=89, just published, =
    >chapter 4
    >on =E2=80=9COperators=E2=80=9D. Quote:
    >
    >=C2=ABThe associativity of an operator governs whether it evaluates from
    >left to right or right to left. Addition is left associative, such
    >that 2 + 3 + 4 evaluates 2 + 3 first, then adds 4 to the result.
    >Exponentiation is right associative, such that 2 ** 3 ** 4 evaluates 3
    >** 4 first, then raises 2 to the 81st power. =C2=BB
    >
    >LOL. Looks like the perl folks haven't changed. Fundamentals of
    >serious math got botched so badly.


    You're confused.

    Associativity of operators is defined in mathematics.
    (The same concept may be used in programming).
    "left-associativity" and "right-associativity" are computer languages
    concept and their definitions are not from mathematics.

    Interestingly in mathematics associative means that it doesn't matter
    whether you use (a.b).c or a.(b.c).
    Using xxx-associativity to indicate that it *does* matter is
    a bit perverse, but the Perl people are not to blame if they use
    a term in their usual sense.

    Groetjes Albert

    --
    --
    Albert van der Horst, UTRECHT,THE NETHERLANDS
    Economic growth -- being exponential -- ultimately falters.
    albert@spe&ar&c.xs4all.nl &=n http://home.hccnet.nl/a.w.m.van.der.horst
     
    Albert van der Horst, Mar 12, 2012
    #15
  16. Re: New Science Discovery: Perl Detractors Remain Idiots After A Decade

    Shmuel (Seymour J.) Metz <> writes:

    > In <4all.nl>, on 03/12/2012
    > at 11:27 AM, Albert van der Horst <4all.nl> said:
    >
    >>You're confused.

    >
    > No, s/h/it is just an acephalic troll with delusions of adequacy.


    Another way to put it is to say that Xah is a legend in his
    own mind.
     
    Raymond Wiker, Mar 12, 2012
    #16
  17. Re: New Science Discovery: Perl Idiots Remain Idiots After A Decade!New Science Discovery: Perl Idiots Remain Idiots After A Decade!

    In article <4f5df4b3$0$1375$>,
    Kiuhnm <kiuhnm03.4t.yahoo.it> wrote:
    >On 3/12/2012 12:27, Albert van der Horst wrote:
    >> Interestingly in mathematics associative means that it doesn't matter
    >> whether you use (a.b).c or a.(b.c).
    >> Using xxx-associativity to indicate that it *does* matter is
    >> a bit perverse, but the Perl people are not to blame if they use
    >> a term in their usual sense.

    >
    >You may see it this way:
    >Def1. An operator +:SxS->S is left-associative iff
    > a+b+c = (a+b)+c for all a,b,c in S.
    >Def2. An operator +:SxS->S is right-associative iff
    > a+b+c = a+(b+c) for all a,b,c in S.
    >Def3. An operator +:SxS->S is associative iff it is both left and
    >right-associative.


    I know, but what the mathematicians do make so much more sense:
    (a+b)+c = a+(b+c) definition of associative.
    Henceforth we may leave out the brackets.

    Don't leave out the brackets if the operators if the operators is
    not associative.

    P.S. There is no need for the operators to be SxS->S.
    For example a b c may be m by n, n by l, l by k matrices respectively.

    >
    >Kiuhnm


    Groetjes Albert

    --
    --
    Albert van der Horst, UTRECHT,THE NETHERLANDS
    Economic growth -- being exponential -- ultimately falters.
    albert@spe&ar&c.xs4all.nl &=n http://home.hccnet.nl/a.w.m.van.der.horst
     
    Albert van der Horst, Mar 12, 2012
    #17
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