[Haskell-cafe] The Trivial Monad

[Michael Vanier]

The -> in type signatures associates to the right, so the type signatures

 > fmap :: (a -> b) -> (W a -> W b)
 > bind :: (a -> W b) -> (W a -> W b)

are the same as:

 > fmap :: (a -> b) -> W a -> W b
 > bind :: (a -> W b) -> W a -> W b

Sometimes people put in the extra parentheses because they want to 
emphasize a particular way to use the function.

I'm assuming you understand that a function that takes two arguments and 
returns a (possibly non-function) value is equivalent to a function that 
takes one argument that returns a function that takes the other argument 
and returns a value.

HTH,

Mike



Adrian Neumann wrote:
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA512
> 
> I've read this blogpost about the "trivial monad"
> http://sigfpe.blogspot.com/2007/04/trivial-monad.html, because I still
> don't understand what this monad thingy is all about.
> 
> The author defines three functions:
> 
> data W a = W a deriving Show
> 
> return :: a -> W a
> return x = W x
> 
> fmap :: (a -> b) -> (W a -> W b)
> fmap f (W x) = W (f x)
> 
> bind :: (a -> W b) -> (W a -> W b)
> bind f (W x) = f x
> 
> and asks the reader to prove the tree monad laws for them. However I
> don't understand the type signatures for bind and fmap. I'd say (and
> ghci's type inference agrees) that bind and fmap have the type
> 
> bind:: (a->W b) -> W a -> W b
> fmap:: (a->b) -> W a -> W b
> 
> They take a function f and something and return what f does to that. I
> don't see why they should return a function.
> 
> This of course makes it hard for me to prove the monad laws. The first
> however works nonetheless:
> 
> 1) bind f (return a)= f a
> 
> => bind f (return a)= bind f (W a) = f a
> 
> Can someone explain bind and fmap (and possible law 2 and 3)?
> 
> Thanks,
> 
> Adrian
> -----BEGIN PGP SIGNATURE-----
> Version: GnuPG v1.4.6 (Darwin)
> Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org
> 
> iD8DBQFGOuQS11V8mqIQMRsRCmngAJ9NwQMwXeS/PSM1NUsVA8gxPuA0KACfSLiA
> ItqRZW5a4XyQ099bhMtSWmU=
> =/8i/
> -----END PGP SIGNATURE-----
> _______________________________________________
> Haskell-Cafe mailing list
> Haskell-Cafe at haskell.org
> http://www.haskell.org/mailman/listinfo/haskell-cafe