Send Beginners mailing list submissions to
beginners@haskell.org
To subscribe or unsubscribe via the World Wide Web, visit
http://www.haskell.org/mailman/listinfo/beginners
or, via email, send a message with subject or body 'help' to
beginners-requ...@haskell.org
You can reach the person managing the list at
beginners-ow...@haskell.org
When replying, please edit your Subject line so it is more specific
than "Re: Contents of Beginners digest..."
Today's Topics:
1. Haskell and Category Theory (Patrick Lynch)
2. Re: Haskell and Category Theory (KC)
3. Re: Haskell and Category Theory (amin...@gmail.com)
4. Re: Haskell and Category Theory (KC)
5. Effective use of nested Monads (David Hinkes)
6. Re: Effective use of nested Monads (Ozgur Akgun)
7. Re: Haskell and Category Theory (Brent Yorgey)
8. Re: Effective use of nested Monads (Brent Yorgey)
----------------------------------------------------------------------
Message: 1
Date: Sun, 10 Feb 2013 12:44:11 -0500
From: "Patrick Lynch" <kmandpjly...@verizon.net>
Subject: [Haskell-beginners] Haskell and Category Theory
To: <beginners@haskell.org>
Message-ID: <B3165B70B11F41C185B9F06B6C6E3A46@UserPC>
Content-Type: text/plain; charset="iso-8859-1"
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-0001.htm>
------------------------------
Message: 2
Date: Sun, 10 Feb 2013 09:58:18 -0800
From: KC <kc1...@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@haskell.org>
Message-ID:
<CAMLKXy=+RJFBh5w3CAGYF6tKgzxuf43Jnib59axxaHN9Aks=s...@mail.gmail.com>
Content-Type: text/plain; charset=ISO-8859-1
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 <kmandpjly...@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@haskell.org
> http://www.haskell.org/mailman/listinfo/beginners
>
--
--
Regards,
KC
------------------------------
Message: 3
Date: Sun, 10 Feb 2013 13:49:28 -0500
From: amin...@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@haskell.org>
Cc: "<beginners@haskell.org>" <beginners@haskell.org>
Message-ID: <4722d1d6-fc2c-4712-aa62-86b6469bb...@gmail.com>
Content-Type: text/plain; charset="us-ascii"
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" <kmandpjly...@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@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-0001.htm>
------------------------------
Message: 4
Date: Sun, 10 Feb 2013 11:46:42 -0800
From: KC <kc1...@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@haskell.org>
Message-ID:
<CAMLKXykDrm2td4Z=bbb7o67gp0kb+t9nvfpke3dnr3aweti...@mail.gmail.com>
Content-Type: text/plain; charset=ISO-8859-1
>From "Steps in Scala - An Introduction to Obejct-Functional
Programming". Christos K. K. Loverdos and Apostolos Syropoulos, 2010.
Section 3.13 pages 163,164
Monads are mathematical structures that were introduced in homological algebra
and later they were introduced in category theory. Eugenio Moggi [53]
was probably
the first researcher who used monads in structuring semantic descriptions of
features such as state and exceptions. Philip Wadler [76] established
a connection
between list comprehensions and monads that led to a generalization of
list comprehensions to an arbitrary monad. This feature was employed
to express concisely in pure functional programming languages programs
that handle exceptions, parse text files, etc. Although it is not
necessary to have a solid background in category theory in order to
understand the various ideas described in the rest of this section,
still we believe it is better to be familiar with some basic notion of
category theory.
In this section we will introduce the reader to these ideas. Readers who are
either familiar with category theory or simply do not want to bother with these
mathematical notions, can safely skip this section and ignore all
future references
to categories.
Categories in a nutshell Categories were first introduced by Samuel Eilenberg
and Saunders Mac Lane. In a nutshell, a category can be viewed as a mathematical
universe. There are many categories and each of them consists of entities,
which have the same nature, and ways to pass from one entity to another. Also,
there are ways to pass from one category to another. In addition, it
is possible to
transform these ways from one category to another while preserving
their internal
structure.
A functor is away to go from one category to another that preserves
the categorical
structure of its domain.
There is a lot more.
On Sun, Feb 10, 2013 at 9:44 AM, Patrick Lynch <kmandpjly...@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@haskell.org
> http://www.haskell.org/mailman/listinfo/beginners
>
--
--
Regards,
KC
------------------------------
Message: 5
Date: Sun, 10 Feb 2013 14:53:18 -0800
From: David Hinkes <david.hin...@gmail.com>
Subject: [Haskell-beginners] Effective use of nested Monads
To: Haskell Beginners <beginners@haskell.org>
Message-ID:
<CA+_CxFPSsrygsJCX1g07VkNPT-TaNa3r=0hxabanwr2tlrf...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
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?
instance Monad m => Monad (Example m) where
-- return is easy
return = Example . return . return
-- bind is hard.
-- f :: o -> Example m p
-- a :: Example m o
a >>= f = ...
My intuition tells me that this should be simple, I should just use the
State's bind operation, but I can't seem to make it work.
Any advise would be great.
Thanks, Dave
--
David Hinkes
-------------- next part --------------
An HTML attachment was scrubbed...
URL:
<http://www.haskell.org/pipermail/beginners/attachments/20130210/9e66d97e/attachment-0001.htm>
------------------------------
Message: 6
Date: Sun, 10 Feb 2013 22:59:48 +0000
From: Ozgur Akgun <ozgurak...@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@haskell.org>
Message-ID:
<CALzazPCzJKntnWCF7UN_Mp2WoO=s037gqmesejr6r5emtyt...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
See http://hackage.haskell.org/trac/haskell-prime/wiki/NewtypeDeriving
HTH,
Ozgur
-------------- next part --------------
An HTML attachment was scrubbed...
URL:
<http://www.haskell.org/pipermail/beginners/attachments/20130210/52c4d150/attachment-0001.htm>
------------------------------
Message: 7
Date: Mon, 11 Feb 2013 00:07:46 -0500
From: Brent Yorgey <byor...@seas.upenn.edu>
Subject: Re: [Haskell-beginners] Haskell and Category Theory
To: beginners@haskell.org
Message-ID: <20130211050746.ga30...@seas.upenn.edu>
Content-Type: text/plain; charset=us-ascii
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
------------------------------
Message: 8
Date: Mon, 11 Feb 2013 00:17:46 -0500
From: Brent Yorgey <byor...@seas.upenn.edu>
Subject: Re: [Haskell-beginners] Effective use of nested Monads
To: beginners@haskell.org
Message-ID: <20130211051745.gb30...@seas.upenn.edu>
Content-Type: text/plain; charset=us-ascii
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
-Brent
------------------------------
_______________________________________________
Beginners mailing list
Beginners@haskell.org
http://www.haskell.org/mailman/listinfo/beginners
End of Beginners Digest, Vol 56, Issue 19
*****************************************
