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:
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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
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