[Haskell-beginners] Beginners Digest, Vol 56, Issue 20
Patrick Lynch
kmandpjlynch at verizon.net
Tue Feb 12 16:02:14 CET 2013
Good morning,
I've actually have 6 books in my library. They are:
1. "Algebra Third Edition" by MacLane and Birkhoff
[I couldn't get anything out of this book]
2. "Categories for the Working Mathemetician - Second Edition" by Mac Lane
[I could get through the first chapter and then gave up]
3. "Conceptual Mathematics - A first introduction to categories" by Lawvere
and Schanuel
[The first chapter was understandable but the following chapters were
completely undecipherable]
4. " Basic Category Theory for Computer Scientists" by Pierce
[I could get through all three chapters but couldn't do the exercies -
and could not see how CT applies to Haskell {especially, Monoids, Monads and
Functors}]
5. "Categories and Computer Science" by Walters
[This one made me cry]
6. "Category Theory" by Awodey
[Again, I could only get through the first chapter]
I tried viewing the videos by Eugenia Cheng - but I just couldn't follow her
presentation.
I also viewed another video entitled Hasket and CT - but it was given by a
mathematican and I couldn't follow this fellow - I'll have to get the link
for this.
I finally viewed a video by Brian Beckman in regard to FP [eg: F# and
Haskell - and mentions C# as a comparison non-FP language], specifically, in
regard to Monoids and it was great - however, he didn't go into CT - but he
did recommend that the viewer pursue it.
I'm really not interested in all of the categories in the world...I
specifically am interested in how CT applies to Hask, Monoids, Monads and
Functors.
All of the Haskell authors that I've read have 'ducked' the CT issue -
mentioning that it is not necessary to understand Haskell. I often was left
with the thought: are they correct or do they simply not understand CT.
If you know of a Computer Scientist [and, please, not a Mathematician] who
has written in regard to Haskell and CT, please let me know.
Hopefully, there is a reference that is available that will help me - if
not, I plan on revisting my Haskell books ["Learn You a Haskell for Great
Good!..." by Lipovaca and "Real World Haskell" by O'Sullivan, etal] and
focus in on Functors, Monoids, Monads and Hask. I'll also view Brian
Beckman's video again and see if I can really follow his example.
Thank you
----- Original Message -----
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To: <beginners at haskell.org>
Sent: Tuesday, February 12, 2013 6:00 AM
Subject: Beginners Digest, Vol 56, Issue 20
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> Today's Topics:
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> 1. Re: Haskell and Category Theory (Rustom Mody)
> 2. Re: Haskell and Category Theory (Joe Fredette)
> 3. Re: Effective use of nested Monads (David Hinkes)
>
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> ----------------------------------------------------------------------
>
> Message: 1
> Date: Mon, 11 Feb 2013 19:01:51 +0530
> From: Rustom Mody <rustompmody at gmail.com>
> Subject: Re: [Haskell-beginners] Haskell and Category Theory
> To: The Haskell-Beginners Mailing List - Discussion of primarily
> beginner-level topics related to Haskell <beginners at haskell.org>
> Message-ID:
> <CAJ+Teoc=Yn9aWi-7OnOcLPPiywZ+rv__wiEjhTGdVD_0bP_qDg at mail.gmail.com>
> Content-Type: text/plain; charset="iso-8859-1"
>
> 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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> Message: 2
> Date: Mon, 11 Feb 2013 08:47:37 -0500
> From: Joe Fredette <jfredett at gmail.com>
> Subject: Re: [Haskell-beginners] Haskell and Category Theory
> To: The Haskell-Beginners Mailing List - Discussion of primarily
> beginner-level topics related to Haskell <beginners at haskell.org>
> Message-ID: <E437EA88-0456-4669-BDDC-FEECE93FD165 at gmail.com>
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>
>
> 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
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> Message: 3
> Date: Mon, 11 Feb 2013 10:30:56 -0800
> From: David Hinkes <david.hinkes at gmail.com>
> Subject: Re: [Haskell-beginners] Effective use of nested Monads
> To: The Haskell-Beginners Mailing List - Discussion of primarily
> beginner-level topics related to Haskell <beginners at haskell.org>
> Message-ID:
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>
> On Sun, Feb 10, 2013 at 9:17 PM, Brent Yorgey
> <byorgey at seas.upenn.edu>wrote:
>
>> On Sun, Feb 10, 2013 at 02:53:18PM -0800, David Hinkes wrote:
>> > Hi haskell-beginners,
>> >
>> > I'm starting to come to the idea of exposing a Monad as a means of
>> > controlling an API. So, I've started creating my own Monad data types
>> > based on classical monads. However, I'm running into a problem
>> > regarding
>> > creating monad definitions when using nested Monads.
>> >
>> > For example:
>> >
>> > newtype Example m o = Example {
>> > runExample :: State Int (m o)
>> > }
>> >
>> > Is there a clean way to make Example a monad?
>>
>> Actually, there isn't! This is one way in which monads turn out to be
>> *too* powerful: they don't compose very well. If m and n are monads,
>> then their composition (that is, a type like newtype Composed a =
>> Composed (m (n a))) is *not* necessarily a monad! So "nesting" monads
>> in this way is usually not a good idea.
>>
>> What you want are called "monad transformers", which give you a way to
>> "compose" certain monads (though it's more complicated than just
>> nesting them). You can do your Example type something like this:
>>
>> newtype Example m o = Example {
>> runExample :: StateT Int m o
>> }
>>
>> where StateT is the State monad transformer, defined in the
>> 'transformers' package (and also exported from the 'mtl' package). I
>> refer you to the typeclassopedia for more information and links to
>> further reading:
>>
> http://www.haskell.org/haskellwiki/Typeclassopedia#Monad_transformers
>
>
> Thanks Brent, I'll try to re-organize around the transforms.
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