Haskell and Category Theory

Previous Topic Next Topic
 
classic Classic list List threaded Threaded
8 messages Options
Reply | Threaded
Open this post in threaded view
|

Haskell and Category Theory

Patrick Lynch
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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://www.haskell.org/pipermail/beginners/attachments/20130210/8f36a6de/attachment.htm>

KC
Reply | Threaded
Open this post in threaded view
|

Haskell and Category Theory

KC
Category Theory turns function like entities (e.g. procedures -
functions with side effects) into functions so that they can be
composed like mathematical functions.


On Sun, Feb 10, 2013 at 9:44 AM, Patrick Lynch <kmandpjlynch at verizon.net> 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
>
> _______________________________________________
> Beginners mailing list
> Beginners at haskell.org
> http://www.haskell.org/mailman/listinfo/beginners
>



--
--
Regards,
KC


Reply | Threaded
Open this post in threaded view
|

Haskell and Category Theory

amindfv
In reply to this post by Patrick Lynch
I'm a fan of Basic Category Theory for Computer Scientists, by Benjamin Pierce.

I can't say it had an immediate payoff for learning Haskell, but it's been helpful longer-term.

Tom


On Feb 10, 2013, at 12:44 PM, "Patrick Lynch" <kmandpjlynch at verizon.net> 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
> _______________________________________________
> Beginners mailing list
> Beginners at haskell.org
> http://www.haskell.org/mailman/listinfo/beginners
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://www.haskell.org/pipermail/beginners/attachments/20130210/be484d35/attachment.htm>

KC
Reply | Threaded
Open this post in threaded view
|

Haskell and Category Theory

KC
In reply to this post by Patrick Lynch

Reply | Threaded
Open this post in threaded view
|

Haskell and Category Theory

Brent Yorgey-2
In reply to this post by Patrick Lynch
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


Reply | Threaded
Open this post in threaded view
|

Haskell and Category Theory

Rustom Mody
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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://www.haskell.org/pipermail/beginners/attachments/20130211/b8a154b7/attachment.htm>

Reply | Threaded
Open this post in threaded view
|

Haskell and Category Theory

jfredett

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
> _______________________________________________
> Beginners mailing list
> Beginners at haskell.org
> http://www.haskell.org/mailman/listinfo/beginners

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://www.haskell.org/pipermail/beginners/attachments/20130211/7d75e152/attachment.htm>

Reply | Threaded
Open this post in threaded view
|

Haskell and Category Theory

Simon Peter Nicholls
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
> _______________________________________________
> Beginners mailing list
> Beginners at haskell.org
> http://www.haskell.org/mailman/listinfo/beginners
>
>
>
> _______________________________________________
> Beginners mailing list
> Beginners at haskell.org
> http://www.haskell.org/mailman/listinfo/beginners
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://www.haskell.org/pipermail/beginners/attachments/20130212/cf04d48d/attachment.htm>