[Haskell-beginners] Haskell and Category Theory
Simon Peter Nicholls
simon at mintsource.org
Tue Feb 12 16:32:47 CET 2013
I can't help the OP unfortunately, but I find this topic to be pretty
interesting. I'd be interested in exploring the mathematical foundations of
CT.
So, looking at this from a different aspect, what mathematics book /
knowledge would I need in order to make Mac Lane's "Categories for the
Working Mathematician" reasonably accessible, assuming UK A-Level further
mathematics level or equivalent has been attained?
Si
On Mon, Feb 11, 2013 at 2:47 PM, Joe Fredette <jfredett at gmail.com> wrote:
>
> While we await a reply, I will say that I found Benjamin Pierce's "Basic
> Category Theory for Computer Scientists" pretty readable, but will also
> readily admit my understanding of CT is not particularly deep or great.
> There are also some videos on youtube, particularly by [error792](1) which
> are worth watching, though they approach from a more math-oriented
> perspective (the video-author is a Mathematics Grad Student).
>
> One thing that helped me a lot was learning a bit about Combinatorial
> Species -- I come from a math background, so having something firmly
> abstract to grab onto wrt examples of CT in use was (and is) useful, Brent
> has a [nice suite of posts](2) on the matter, and I'm sure will have some
> book/paper recommendations, I linked to just one of the posts on his blog,
> I'm sure you can navigate to the others.
>
> The trick, I think, to learning CT is to realize it's a lot like Set
> theory -- there's a lot of abstract nonsense and definition shuffling
> (which error792's videos, iirc, note as "Soft Theorems"), and very little
> (immediate) connection to reality/more concrete tools. However, CT provides
> a framework of understanding which acts kind of like a
> highway-of-abstraction. When I can say, "A combinatorial species _is_ an
> endofunctor on the category of Sets and their Bijections", I necessarily
> know that if I can translate that category into another thing, then I can
> use my knowledge of species to inform my knowledge of that thing.
>
> I'm probably telling this story wrong in some way, perhaps (if we don't
> mind a bit of thread hijacking) someone can improve my understanding of CT
> by correcting my likely and inevitable mistakes.
>
> /Joe
>
>
> (1) http://www.youtube.com/user/error792
>
> (2)
> http://byorgey.wordpress.com/2012/11/20/combinatorial-species-definition/
>
>
>
>
> On Mon, Feb 11, 2013 at 10:37 AM, Brent Yorgey <byorgey at seas.upenn.edu>wrote:
>
>> On Sun, Feb 10, 2013 at 12:44:11PM -0500, Patrick Lynch wrote:
>> > Good morning,
>> > I've tried to read 5 books on Category Theory and finally have admitted
>> defeat.
>> > What I'm looking for is simply a book that is geared to Haskell and
>> Category that can be understood by mere mortals.
>> > I was trained as an Electrical Engineer, so my math is quite good, but
>> I just don't get Category Theory from these books.
>> > If anyone can recomment a book on Category Theory and Haskell, written
>> by a Computer Scientest [no more Mathematicians for me], I welcome it.
>> > Thanks,
>> > Patrick
>>
>> Can you tell us which books you've tried to read?
>>
>> -Brent
>>
>
> Well Brent is not going to say it I guess so someone needs to:
> Typeclassopedia http://www.haskell.org/haskellwiki/Typeclassopedia
> is required reading
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