Dear lispers,
i have created a page on the lambda logo tour.
http://xahlee.org/UnixResource_dir/lambda_logo.html
comment welcome.
Xah
···@xahlee.org
http://xahlee.org/PageTwo_dir/more.html
···@xahlee.org (Xah Lee) wrote ...
> http://xahlee.org/UnixResource_dir/lambda_logo.html
Nice logo collection. In particular I like the 3D renderings.
But I hate to tell you, there is nothing majestic or divine about the
letter lambda. Mathematics simply borrowed the Greek letter for "l"
(amongst many others). For the Greek, who invented it, to this day,
this is just an ordinary letter. Go visit Athens sometime -it is a
very exciting place- and you will see what you describe as
"mathematical symbols" all over the place, on coffee shops,
supermarkets, banks, tabac street-shops, in newspapers etc etc.
If you have a mathematics background, you will find that you can
actually read what is written there and the meanings of many words
become clear. For example, you will often see the word "ethnik" and
realise that the English word ethnic has a Greek origin. In Greek it
means "national" as in "National Bank of Greece". The name Greece
itself ("Hellas") has two lambdas in it ;-)
And if you're into symbolism, well, considering your purist comments,
that's so unscientific, so much against everything mathematics stands
for, don't go there.
rgds
bk
Xah Lee wrote:
> i have created a page on the lambda logo tour.
>
> http://xahlee.org/UnixResource_dir/lambda_logo.html
>
> comment welcome.
The above page raises objections to the perceived use of the lambda
character in vain:
> The lambda character, always struck an awe in me, as with
> other mathematical symbols. In my mind, i imagine that those
> obscure math symbolism are etched in stone by god. [...]
>
> These symbols are not to be trifled with. If any one puff in as much
> half a snicker, i wish god strike a thunder upon their disrespect.
This will not be news to many, but anyone wishing to construct a religion
around the lambda character in particular may wish to reflect upon the
character's origins in the functional context. Barendregt describes these
origins in his paper "The Impact of the Lambda Calculus in Logic and
Computer Science" (http://citeseer.nj.nec.com/423413.html). In the quote
below, the character sequence x^ is intended to represent an x with a hat
accent above it, and [lambda] represents the lambda character:
------
"We end this introduction by telling what seems to be the story how the
letter [lambda] was chosen to denote function abstraction. In Principia
Mathematica the notation for the function f with f(x) = 2x + 1 is 2x^ + 1.
Church originally intended to use the notation x^.2x+1. The typesetter
could not position the hat on top of the x and placed it in front of it,
resulting in:
^x.2x+1.
"Then another typesetter changed it to [lambda]x.2x + 1."
------
Of course, deities are often said to work in mysterious ways, so perhaps
these inauspicious beginnings, in the limitations and errors of typesetters,
were merely some deity's way of transmitting the appropriate use of the holy
lambda character into the mortal sphere (with the aid of a mortal
appropriately named Church).
Without this divine act, we might now be basing our programming languages on
something called "the hat calculus". I guess that deity knew what she was
doing!
Anton
Anton van Straaten writes:
> Without this divine act, we might now be basing our programming
> languages on something called "the hat calculus".
Well, make that "circumflex calculus" and it doesn't sound too bad,
does it? :-)
On Mon, 05 May 2003 18:49:51 GMT, "Anton van Straaten"
<·····@appsolutions.com> wrote:
>This will not be news to many, but anyone wishing to construct a religion
>around the lambda character in particular may wish to reflect upon the
That, of course, doesn't explain, how lambda came into LISP. McCarthy
wrote in his 'History of LISP'
http://portal.acm.org/citation.cfm?id=808387&dl=ACM&coll=portal
that
"to use functions as arguments, one needs a notation for functions,
and it seemed natural to use the [lambda]-notation of Church... I
didn't understand the rest of his book, so I wasn't tempted to try to
implement his more general mechanism for defining functions."
I am not sure what he means by that, because I thought lambda
expressions in LISP are merely anonymous functions, and can be used
anywhere you would use any other function as well.
What he does say however is that LISP wasn't really much influenced
by, let alone based on, lambda calculus.
Cheers,
Steffen
Steffen Haugk wrote:
>
> [Quoting McCarthy]
> "to use functions as arguments, one needs a notation for functions,
> and it seemed natural to use the [lambda]-notation of Church... I
> didn't understand the rest of his book, so I wasn't tempted to try to
> implement his more general mechanism for defining functions."
>
> I am not sure what he means by that, because I thought lambda
> expressions in LISP are merely anonymous functions, and can be used
> anywhere you would use any other function as well.
>
> What he does say however is that LISP wasn't really much influenced
> by, let alone based on, lambda calculus.
It's true. Scheme is much more closely based on Lambda Calculus
than were the earlier LISPS. But it's largely a case of retroactive
continuity....
Bear
····@sonic.net writes:
> Scheme is much more closely based on Lambda Calculus
> than were the earlier LISPS. But it's largely a case of retroactive
> continuity....
Too bad it's the 21st century. `retroactive continuity' surely deserves
a place in the '90s sound-bite hall of fame right along with Bill
Clinton's famous obfuscations on his relationships with his younger
employees.
I like the phrase 'retroactive continuity' mind you...I'm plannning to
use it the next time I have to justify a code change to management
without telling themm first.
david rush
--
Finding a needle in a haystack is a lot easier if you burn down the
haystack and scan the ashes with a metal detector.
-- the Silicon Valley Tarot
David Rush <·····@aol.net> writes:
> ····@sonic.net writes:
> > Scheme is much more closely based on Lambda Calculus
> > than were the earlier LISPS. But it's largely a case of retroactive
> > continuity....
>
> Too bad it's the 21st century. `retroactive continuity' surely deserves
> a place in the '90s sound-bite hall of fame right along with Bill
> Clinton's famous obfuscations on his relationships with his younger
> employees.
>
> I like the phrase 'retroactive continuity' mind you...I'm plannning to
> use it the next time I have to justify a code change to management
> without telling themm first.
I don't think it's a particularly 90s phrase, actually. I gather the idea
has been in use (in its shortened form, `retcon') among science fiction
fans and comic fans for longer than that; see the jargon file for a
definition and brief etymology:
<http://catb.org/esr/jargon/html/entry/retcon.html>.
Just in case the definition cited above doesn't make this clear, it's not
usually regarded as a good thing to retcon something. Indeed, this most
frequently happens when the people responsible have `written themselves
into a corner,' if you will, and need to get some way out while preserving
continuity at a superficial level.
Richard
·····@ccs.neu.edu (Richard C. Cobbe) writes:
> Indeed, this most frequently happens when the people responsible
> have `written themselves into a corner,' if you will, and need to
> get some way out while preserving continuity at a superficial level.
This sounds related to the "Deus Ex Machina" device, perhaps at a
different scale.
--
Steven E. Harris :: ········@raytheon.com
Raytheon :: http://www.raytheon.com
Steffen Haugk wrote:
> "to use functions as arguments, one needs a notation for functions,
> and it seemed natural to use the [lambda]-notation of Church... I
> didn't understand the rest of his book, so I wasn't tempted to try to
> implement his more general mechanism for defining functions."
...
> What he does say however is that LISP wasn't really much influenced
> by, let alone based on, lambda calculus.
He may not have consciously based LISP on lambda calculus, but as a
consequence of not understanding Church's book, he proceeded to reinvent
parts of the lambda calculus, but with a number of mistakes. There's some
material about this in "The Influence of the Designer on the Design -- J.
McCarthy and LISP" at
http://www8.informatik.uni-erlangen.de/html/lisp/mcc91.html :
------
"The universal S-function 'eval' given in [McC59b] is a complete interpreter
of LISP -- a substituting call-by-name realization of an applied
lambda-calculus. McCarthy did not know this. He realized LISP -- and LISP
used lambda-notation. This may explain why he forgot a clause for
lambda-expression in this 'eval'. It was the fourth time he forgot lambda.
There are two main errors: McCarthy ignored the computation of functions and
he used a too general substitution procedure. He corrected the latter a
little but it remained incorrect because of forgotten variable lists in
lambda-expressions.
"This leads to the question of McCarthy's knowledge of the lambda-calculus.
McCarthy always pointed out that he did not know much about this. It is
obvious that he has read the first pages of Church's paper. The 'eval' of
March 1958 proves that he did know about substitution. However, there is no
sign of renaming variables, no sign of normalization. One cannot believe
that McCarthy did not study carefully the substitution procedures of the
lambda-calculus for his realization, but this is the only explanation for a
series of errors that were not apparent in the simple examples of 1958.
Today, we all know much better."
------
The reason the LISP language ended up fairly close to the lambda calculus in
many respects is because it had similar goals to lambda calculus. For
example, to quote McCarthy from
http://www-formal.stanford.edu/jmc/history/lisp/node3.html :
"One mathematical consideration that influenced LISP was to express programs
as applicative expressions built up from variables and constants using
functions. I considered it important to make these expressions obey the
usual mathematical laws allowing replacement of expressions by expressions
giving the same value. The motive was to allow proofs of properties of
programs using ordinary mathematical methods."
This alone is likely to result in something quite a lot like lambda
calculus. But the connection goes further:
"I decided to write a paper describing LISP both as a programming language
and as a formalism for doing recursive function theory. [...] Another way
to show that LISP was neater than Turing machines was to write a universal
LISP function and show that it is briefer and more comprehensible than the
description of a universal Turing machine."
Of course, lambda calculus is an even better "formalism for doing recursive
function theory" than LISP. And the Church-Turing thesis, from 1936,
implied the equivalence of lambda calculus and Turing machines. Since many
of McCarthy's most important goals were so similar to those of the lambda
calculus, it's not surprising that he ended up with a rather similar system.
Of course, one enormous difference is that McCarthy & Russell implemented
LISP on a computer.
I mention all this because I think it's possible to draw wrong conclusions
from the claim that "LISP wasn't really much influenced by, let alone based
on, lambda calculus". In fact, there are very close connections between the
two, but it so happens that the original designer of LISP didn't understand
or exploit this. That was left to the designers of Scheme.
Anton
On Mon, 05 May 2003 18:49:51 GMT, "Anton van Straaten"
<·····@appsolutions.com> wrote:
>Without this divine act, we might now be basing our programming languages on
>something called "the hat calculus". I guess that deity knew what she was
>doing!
In another thread in this newsgroup John Atwood has been so kind to
give us this link to a newsgroup posting by Jonathan Seldin.
http://groups.google.com/groups?q=seldin+logic+curry&hl=en&lr=&ie=UTF-8&oe=UTF-8&scoring=d&selm=seldin-2709961738360001%40curry.concordia.ca&rnum=7
The x hat theory is there, and another, less awe inspiring one from
Church.
Cheers and Ta,
Stephan
Xah Lee wrote:
> Dear lispers,
>
> i have created a page on the lambda logo tour.
>
> http://xahlee.org/UnixResource_dir/lambda_logo.html
>
> comment welcome.
>
> Xah
> ···@xahlee.org
> http://xahlee.org/PageTwo_dir/more.html
Hey, don't forget:
http://www.call-with-current-continuation.org/chicken.png
On Mon, 05 May 2003 19:42:33 +0200, felix posted:
> Xah Lee wrote:
>> Dear lispers,
>>
>> i have created a page on the lambda logo tour.
>>
>> http://xahlee.org/UnixResource_dir/lambda_logo.html
>>
>> comment welcome.
>>
>> Xah
>> ···@xahlee.org
>> http://xahlee.org/PageTwo_dir/more.html
>
>
> Hey, don't forget:
>
> http://www.call-with-current-continuation.org/chicken.png
or
http://www.cse.unsw.edu.au/~pls/images/pls-small.png
mrak
--
realise your life was only bait for a bigger fish
-- aesop rock
Mark Alexander Wotton wrote:
> On Mon, 05 May 2003 19:42:33 +0200, felix posted:
>>Xah Lee wrote:
>>>Dear lispers,
>>>i have created a page on the lambda logo tour.
>>> http://xahlee.org/UnixResource_dir/lambda_logo.html
>>>comment welcome.
>>> Xah
>>> ···@xahlee.org
>>> http://xahlee.org/PageTwo_dir/more.html
>>Hey, don't forget:
>>http://www.call-with-current-continuation.org/chicken.png
> or
> http://www.cse.unsw.edu.au/~pls/images/pls-small.png
> mrak
or
http://www.pintus.de/mgrabmue/gallery/lambda-man.jpg
:-)
Jumping aboard the "me too" train...
Abdulaziz Ghuloum <········@cs.indiana.edu> once said:
>Mark Alexander Wotton wrote:
>> On Mon, 05 May 2003 19:42:33 +0200, felix posted:
>>>Xah Lee wrote:
...
>>>> http://xahlee.org/UnixResource_dir/lambda_logo.html
>>>Hey, don't forget:
>>>http://www.call-with-current-continuation.org/chicken.png
>> or
>> http://www.cse.unsw.edu.au/~pls/images/pls-small.png
>or
>http://www.pintus.de/mgrabmue/gallery/lambda-man.jpg
or
http://www.cc.gatech.edu/~yannis/fc++/Logos/logos.html
--
Brian M. McNamara ······@acm.org : I am a parsing fool!
** Reduce - Reuse - Recycle ** : (Where's my medication? ;) )
Xah Lee wrote:
>
> i have created a page on the lambda logo tour.
>
> http://xahlee.org/UnixResource_dir/lambda_logo.html
>
[from that page]
> (btw, what does the _|_ symbol mean?)
This is the "bottom" element of a partial order. Denotational semantics
use it to represent the "meaning" of a non-terminating computation. Lazy
languages like Haskell need to reason about termination properties in
order to figure out where laziness is needed and where it can be
optimized away by the compiler.
--
Vilhelm
thanks all who have given feedback.
i have updated the page a bit with addendum.
http://xahlee.org/UnixResource_dir/lambda_logo.html
if you know some cool lambda logo, or other logos for functional
programing worthy of mention, please let me know.
thanks.
Xah
···@xahlee.org
http://xahlee.org/PageTwo_dir/more.html
> thanks all who have given feedback.
>
> i have updated the page a bit with addendum.
> http://xahlee.org/UnixResource_dir/lambda_logo.html
>
> if you know some cool lambda logo, or other logos for functional
> programing worthy of mention, please let me know.
>
> thanks.
>
well, there is my logo at:
http://bgb-sys.sourceforge.net/
I am not sure, figured I would make one, probably not that good though...
I probably need a logo for the system in general though.
I know I probably annoy people here with my near constant flogging and
incoherent, rambling, self-loathing style, but it is worth a shot...
> well, there is my logo at:
> http://bgb-sys.sourceforge.net/
>
> I am not sure, figured I would make one, probably not that good though...
>
> I probably need a logo for the system in general though.
>
> I know I probably annoy people here with my near constant flogging and
> incoherent, rambling, self-loathing style, but it is worth a shot...
>
lame: I forgot to take into account how old this thread was...
not really a logo, but i made the following for a haskell-related
t-shirt design: http://www.acooke.org/cgi-bin/photo.py?name=bugs
there's a detail, showing the faux-pixellation and anti-aliasing at
http://www.acooke.org/cgi-bin/photo.py?name=bugs-detail
andrew
"cr88192" <·······@hotmail.com> writes:
>> thanks all who have given feedback.
>>
>> i have updated the page a bit with addendum.
>> http://xahlee.org/UnixResource_dir/lambda_logo.html
>>
>> if you know some cool lambda logo, or other logos for functional
>> programing worthy of mention, please let me know.
>>
>> thanks.
>>
> well, there is my logo at:
> http://bgb-sys.sourceforge.net/
>
> I am not sure, figured I would make one, probably not that good though...
>
> I probably need a logo for the system in general though.
>
> I know I probably annoy people here with my near constant flogging and
> incoherent, rambling, self-loathing style, but it is worth a shot...
>
>
>
--
http://www.acooke.org
"andrew cooke" <······@acooke.org> wrote in message
···················@acooke.org...
>
> not really a logo, but i made the following for a haskell-related
> t-shirt design: http://www.acooke.org/cgi-bin/photo.py?name=bugs
>
> there's a detail, showing the faux-pixellation and anti-aliasing at
> http://www.acooke.org/cgi-bin/photo.py?name=bugs-detail
>
ok. kind of cool, likely more effort than mine which was created in a few
minutes with gimp (most effort thinking up what to make it look like...).
cr88192 wrote:
>>if you know some cool lambda logo, or other logos for functional
>>programing worthy of mention, please let me know.
You can choose from these two nearly-identical images I found by web
image search:
http://www.franz.com/~smh/nlambda.html