[Haskell-beginners] Monads

[Patrick Lynch]

...i'm about half way thru "Real World Haskell" - I'm about to start its 
section on Monads...I'll let you know...
Thanks for your good advice...
Ciao

----- Original Message ----- 
From: "Brent Yorgey" <byorgey at seas.upenn.edu>
To: "Patrick Lynch" <kmandpjlynch at verizon.net>
Cc: <beginners at haskell.org>
Sent: Saturday, March 05, 2011 10:11 AM
Subject: Re: [Haskell-beginners] Monads


> On Sat, Mar 05, 2011 at 09:25:21AM -0500, Patrick Lynch wrote:
>> Brent,
>>
>> Eureeka! I'll be damned - I can create my own class...(I had a 'typo'
>> in my class MyCalculator class code -- that is, myadd::...should be
>> myAdd::...) it works just fine...thank you. You should of bet me...
>> I've purchased Awodey's book: "Category Theory"...thanks again...
>>
>> I've got the following books on my reading list:
>>    "Programming in Haskell" by Graham Hutton
>>    "Learn You a Haskell for Great Good!" by Miran Lipovaca
>>    "Real World Haskell" by Bryan O'Sullivan, etal
>>    "The Haskell Road to Logic, Maths and Programming" by Kees Doets, etal
>>    "An Introduction to Functioanl Programming Systems Using Haskell"
>> by A.J.T Davie
>>    "Introduction to Functional Programming using Haskell" by Richard Bird
>>    "The Craft of Functional Programming" by Simon Thompson
>> I've been working with Simon Thompson, so I'll start working his book
>> next...
>>
>> If you can recommend a book that covers Monads [for a mere practicing
>> software consultant], I'd welcome it...
>
> Real World Haskell is such a book -- I haven't read the part about
> monads but I've heard good things about it, that it introduces them in
> a quite practical, example-driven, no-nonsense way.
>
> -Brent
>
>>
>> Good weekend,
>> Pat
>>
>> ----- Original Message ----- From: "Brent Yorgey"
>> <byorgey at seas.upenn.edu>
>> To: "Patrick Lynch" <kmandpjlynch at verizon.net>
>> Cc: <beginners at haskell.org>
>> Sent: Friday, March 04, 2011 11:33 PM
>> Subject: Re: [Haskell-beginners] Monads
>>
>>
>> >On Fri, Mar 04, 2011 at 05:20:27PM -0500, Patrick Lynch wrote:
>> >>
>> >>I'd love to take a crack at Category Theory [my mathematics is good]
>> >>but this looks like a formidable task...
>> >
>> >It is not that formidable just to get started.  But it is so abstract
>> >that it can be difficult to gain intuition for.  If you want to learn
>> >some category theory I recommend Awodey's book.
>> >
>> >>I'll proceed using the Monad classes and instances as is - and hope
>> >>that at some point I'll be able to create my own Monads...
>> >
>> >Creating one's own monads is overrated.  I almost never do it.
>> >Usually I can just put something together using monad transformers
>> >that fits my needs.
>> >
>> >>
>> >>btw: can you create a class in Haskell -[I'm guessing the answer to
>> >>this is no -- see below, it doesn't work]?
>> >>
>> >>    class MyCalculator a where
>> >>    myadd::( Num a) => a -> a -> a
>> >>    myAdd x y = x + y
>> >
>> >Sure, you can do that.  What do you mean when you say that it doesn't
>> >work?
>> >
>> >-Brent
>> >
>> >>
>> >>----- Original Message ----- From: "Brent Yorgey"
>> >><byorgey at seas.upenn.edu>
>> >>To: <beginners at haskell.org>
>> >>Cc: "Patrick Lynch" <kmandpjlynch at verizon.net>
>> >>Sent: Friday, March 04, 2011 3:07 PM
>> >>Subject: Re: [Haskell-beginners] Monads
>> >>
>> >>
>> >>>On Wed, Mar 02, 2011 at 04:38:07PM -0500, Patrick Lynch wrote:
>> >>>>
>> >>>>----- Original Message ----- From: "Brent Yorgey"
>> >>>><byorgey at seas.upenn.edu>
>> >>>>To: <beginners at haskell.org>
>> >>>>Sent: Wednesday, March 02, 2011 10:37 AM
>> >>>>Subject: Re: [Haskell-beginners] Monads
>> >>>>
>> >>>>
>> >>>>>On Wed, Mar 02, 2011 at 10:04:38AM -0500, Patrick Lynch wrote:
>> >>>>>>Daniel,
>> >>>>>>Thank you...I understand now...
>> >>>>>>Good day
>> >>>>>>
>> >>>>>>    instance Functor Maybe where
>> >>>>>>      fmap f (Just x) = Just (f x)
>> >>>>>>      fmap f Nothing = Nothing
>> >>>>>
>> >>>>>So you are confused about this code?  Can you be more specific what
>> >>>>>you are confused about?  Try thinking carefully about all the types
>> >>>>>involved.  What is the type of f? (You already answered this: a -> 
>> >>>>>b.)
>> >>>>>What is the type of (Just x)? The type of x?  What type is required 
>> >>>>>on
>> >>>>>the right hand side of the = ?  And so on.
>> >>>>
>> >>>>
>> >>>>-Hi Brent
>> >>>>I know that Maybe type is: data Maybe a = Nothing | Just a
>> >>>>...so, I assume that the type to the right of the '=' should be
>> >>>>Maybe a..
>> >>>
>> >>>Not quite.  Let's look again at the type of fmap here:
>> >>>
>> >>> fmap :: (a -> b) -> Maybe a -> Maybe b
>> >>>
>> >>>So fmap will be taking *two* parameters, the first of type (a -> b),
>> >>>the second of type Maybe a.  Then it needs to return something of type
>> >>>Maybe b (so this is what will be on the right hand side of the =).
>> >>>
>> >>>>    instance Functor Maybe where
>> >>>>      fmap Nothing = Nothing
>> >>>>      fmap Just x = Just x
>> >>>
>> >>>You're missing the first argument to fmap (the one of type a -> b).
>> >>>Let's call it f.  Since the second argument is of type (Maybe a)
>> >>>you're right that we should handle all cases (Nothing and Just).
>> >>>
>> >>> fmap f Nothing = Nothing
>> >>>
>> >>>so here we need to return something of type 'Maybe b'.  Well, we don't
>> >>>have any values of type b, so the only thing we can do is return
>> >>>Nothing.
>> >>>
>> >>> fmap f (Just x) = ?
>> >>>
>> >>>The reason we need the parentheses around (Just x) is simply that
>> >>>otherwise the compiler thinks we are writing a definition of fmap that
>> >>>takes three arguments: f, Just, and x, but that doesn't make sense.
>> >>>
>> >>>Now, here f has type (a -> b), and (Just x) has type (Maybe a), hence
>> >>>x has type a.  If we apply f to x we get something of type b, so we
>> >>>can define
>> >>>
>> >>> fmap f (Just x) = Just (f x)
>> >>>
>> >>>Does that make sense?
>> >>>
>> >>>-Brent
>> >>
>>