Okay, so I am not a Haskell programmer, but I am absolutely intrigued by a lot of the ideas behind Haskell and am looking into learning it. But I'm stuck at square one: I can't seem to wrap my head around Monads, which seem to be fairly fundamental. I know there are a million questions on SO asking to explain Monads, so I'm going to be a little more specific about what's bugging me:
I read this excellent article (an introduction in Javascript), and thought that I understood Monads completely. Then I read the Wikipedia entry on Monads, and saw this:
A binding operation of polymorphic type (M t)→(t→M u)→(M u), which Haskell represents by the infix operator >>=. Its first argument is a value in a monadic type, its second argument is a function that maps from the underlying type of the first argument to another monadic type, and its result is in that other monadic type.
Okay, in the article that I cited, bind was a function which took only one argument. Wikipedia says two. What I thought I understood about Monads was the following:
But there must be something wrong, because my concept of bind takes one argument: a function. But (according to Wikipedia) Haskell's bind actually takes two arguments! Where is my mistake?
You are not making a mistake. The key idea to understand here is currying - that a Haskell function of two arguments can be seen in two ways. The first is as simply a function of two arguments. If you have, for example, (+)
, this is usually seen as taking two arguments and adding them. The other way to see it is as a addition machine producer. (+)
is a function that takes a number, say x
, and makes a function that will add x
.
(+) x = \y -> x + y
(+) x y = (\y -> x + y) y = x + y
When dealing with monads, sometimes it is probably better, as ephemient mentioned above, to think of =<<
, the flipped version of >>=
. There are two ways to look at this:
(=<<) :: (a -> m b) -> m a -> m b
which is a function of two arguments, and
(=<<) :: (a -> m b) -> (m a -> m b)
which transforms the input function to an easily composed version as the article mentioned. These are equivalent just like (+)
as I explained before.