OK, just one more addition to the J theme. Sorry to be noisy!
I wrote to the J forum two years ago on the topic:
http://www.jsoftware.com/pipermail/general/2004-July/017809.html
Some of the responses were quite interesting. For example, J has a
"Tacit" mode which lets you prove equivalence of certain operations
like commutativity of addition. I.e. J allows "meta operations" on
algorithms.
Just click on the "next message" link in the above to follow the
conversation. Note that Ken himself, along with Roger Hui jumped
into the fray!
I *gotta* write all this up!
-- Owen
Owen Densmore http://backspaces.net
On Dec 28, 2006, at 12:15 PM, Owen Densmore wrote:
> Here's a more recent Ken Iverson discussion on Computers and
> Mathematical Notation:
> http://tinyurl.com/ym8r64
> or
> http://www.cacs.louisiana.edu/~mgr/404/burks/language/apl/camnweb/
> camn.htm
>
> This is J based, rather than APL.
>
> -- Owen
>
> Owen Densmore http://backspaces.net
>
>
> On Dec 28, 2006, at 12:00 PM, Owen Densmore wrote:
>
>> First of all, a big THANKS for all the interesting ideas. I've been
>> trying to get my brain around all this for quite some time. And I
>> think its time I sit down and start writing on the divide between
>> Math and Computing.
>>
>> One of the more interesting discussions on this topic comes from the
>> APL/Ken Iverson world. APL (A Programming Language) used a concise
>> mathematical notation for its syntax. It was quite a hit at Xerox in
>> the early to mid '70s and indeed was considered a great rapid
>> prototyping language.
>>
>> One of Iverson's ideas was that mathematical notation was flawed and
>> could easily be fixed by focusing on making it more parseable and
>> less ambiguous. His 1979 Turing Award lecture was a wonderful
>> summary of these ideas:
>> Notation as a Tool of Thought (1979 Turing Award Lecture)
>> by Kenneth E. Iverson, Communications of the ACM,
>> Volume 23, Number 8, August 1980.
>> http://elliscave.com/APL_J/tool.pdf
>>
>> In a sense, Ken was the one of the pioneers poking at the topic we're
>> discussing. I suspect Turing, Von Neuman, and others were there too.
>>
>> Ken's APL work has been carried on by Ken's son Eric and Roger Hui,
>> both of whom worked closely with Ken. APL has been morphed into the
>> J Programming Language:
>> http://en.wikipedia.org/wiki/J_programming_language
>>
>> I've taken a run at J with some success. Its reasonably cross
>> platform. But boy, the learning curve is steep! The power of J,
>> however, is considerable. If any FRIAMers start in on J, let me
>> know. These sites are representative of the leaders of the J
>> community:
>> http://olegykj.sourceforge.net/
>> .. and all the External links at the end of the Wikipedia article.
>>
>> -- Owen
>>
>> Owen Densmore http://backspaces.net
>>
>>
>>
>>
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>
>
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> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
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