Comments on A Neighborhood of Infinity: Eleven Reasons to use Haskell as a Mathematician

Typo: singled out element, the >>identitiy&l...

2010-07-02T13:58:08.139-07:00

Typo: singled out element, the >>identitiy<<

I think I should adopt the rule of always releasin...

2009-08-18T13:32:42.097-07:00

I think I should adopt the rule of always releasing my first draft. It may have a few typos but that's fine. When you go back to fix typos you start working locally rather than globally and you introduce structural errors. Have two threes is a good example of that :-)

Two threes ... See? That's what happens when y...

2009-08-18T13:23:08.836-07:00

Two threes ... See? That's what happens when you break the prime number list rule.

Less importantly, I'm going to have a deeper look at Haskell because of this well-argumented post.

Nice post! Thanks for writing it! ps. recusrion -...

2009-08-17T23:12:41.971-07:00

Nice post! Thanks for writing it!

ps. recusrion -> recursion

As one of the original authors of Macaulay, you ha...

2009-03-03T04:53:00.000-08:00

As one of the original authors of Macaulay, you had me at "hello"!

I've been teaching Haskell to anyone I can. With my student the other day, we wrote a screenful of one-liners (leavened by comments and type declarations) that reverse-search atomic lattices represented as bitfields. The result: Code that could find all instances on 5 atoms in a quarter second (Macaualay2 could only handle 4 atoms) and all 2^36 or so instances on 6 atoms in 14 hours. That's an instance per bit on my 8 GB linux box, all the while using a memory footprint measured instead in MB.

So Haskell can mix it up at the machine level with the best of them. With its lazy functional overhead, Haskell is often slower than C, step by step, but its conceptual clarity allows one to effortlessly combine steps to form algorithms that would be way too painful to write in procedural languages. People mired in language efficiency debates haven't moved on yet; I don't bother with the mere constant improvements of strictness annotations or overclocking my hardware, I instead look for better algorithms.

How efficiently does a language mind-meld with its user? That's the whole ball of wax. I'm in my 50s; if one could reject the language debate static and accept this principle in one's 20s, one would be way ahead.

As an engine author, I'd reverse your "giant engine" comparison. All languages and packages pick their engine and tune it. Macaulay2 optimizes Grobner bases, Prolog optimizes unification. Lisp optimizes the lambda calculus, while logicians have since moved on to merge the lambda calculus with type and category theory. This is the engine that Haskell optimizes; look under the hood of GHC Haskell, and one sees the biggest engine of them all, written by the best programmers of them all. Haskell made a better choice of domain for its engine.

Oh yeah, Integers are easy to use, but 32-bit Ints pervade the basic libraries. We're lucky we wrote "length64" on a hunch before our 14 hour run; the standard version would have overflowed.

@Jake: Really, you find letters less finite than ...

2009-01-13T15:04:00.000-08:00

@Jake: Really, you find letters less finite than numbers?

2, 3, whatever, who cares about that.

This ...

2007-09-28T23:35:00.000-07:00

2, 3, whatever, who cares about that.

This post is a very good resource for those interested in learning "those" details about programming languages that can make the difference and avoid missing a lot of time in the search for the appropiate one.

This information is totally worthy. :)
I'm considering learning Haskell...

Joe/Jake,

Tell that to the number theorists...

2007-07-02T08:23:00.000-07:00

Joe/Jake,

Tell that to the number theorists.

@ lemming

mathematician's don't work with n...

2007-07-02T08:21:00.000-07:00

@ lemming

mathematician's don't work with numbers, we work with letters.

Numbers are far to finite for us flighty math folk. We leave them to the Accountants and Statisticians.

~~Joe

"I think there's a rule against making lists with ...

2007-06-26T14:57:00.000-07:00

"I think there's a rule against making lists with prime numbers of elements but I'm ignoring it."

Counter-example: how about the (presentation) rule of three? See http://www.presentationhelper.co.uk/presentation_rule_of_3.htm

There are three kinds of mathematicians: Those who...

2006-11-22T05:17:00.000-08:00

There are three kinds of mathematicians:
Those who can count and those who cannot.

Apparently Haskell's Num is so bad, there are two ...

2006-11-15T02:05:00.000-08:00

Apparently Haskell's Num is so bad, there are two threes. :)

I appreciate this is tediously pedantic, but you m...

2006-11-04T16:43:00.000-08:00

I appreciate this is tediously pedantic, but you might want to count those reasons again.