[Haskell-cafe] Martin Odersky on "What's wrong with Monads"
wren ng thornton
wren at freegeek.org
Mon Jun 25 06:34:44 CEST 2012
On 6/24/12 5:41 AM, Anton Kholomiov wrote:
> I think monad's methods are misleading, let's rename them
> class Monad m where
> idM :: a -> m a
> (*$) :: (a -> m b) -> m a -> m b
> We can see that `return` is a monadic identity and the `bind`
> is an application in disguise. So now we have two applications.
> It's standard `($)` and monadic `(*$)`. But they are application.
> Well isn't it something like `plusInt` and `plusDouble`?
> Maybe we can devise single class for application. Let's
> imagine a special class `App`
> class App ?? where
> ($) :: ???
> As you can see it's defined so that we can fit
> monads and plain functions in this framework. Moreover
> if we redefine this class than whitespace is redefined
The class you're looking for is Applicative. The (<*>) operator handles
application of "effectful" things to "effectful" things, whereas (<$>)
handles the application of non-"effectful" things to "effectful" things.
This situation is interesting because it highlights the fact that there
is a distinction between the meaning of whitespace between function and
argument vs the meaning of whitespace between argument and argument.
The desire to invoke (<$>) and (<*>) implicitly is known as idiom
brackets. SHE provides this as syntactic sugar, and of course you can
define your own version using iI and Ii as your "brackets".
> So `($)` really means *white space* in haskell.
Not entirely so, as noted above. Though yes, ($) denotes application in
just the same way as function--argument whitespace does. However, the
presence of ($) as an operator is helpful because it allows us to
capture the syntax of our language, as in:
fmap ($x) fs
zipWith ($) fs xs
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