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> You should also understand that a list itself can be a monad.

A list is not a monad — it’s just a container of values, ie. a functor. A monad is a data structure defines a computation in a specific context, and allows composing these in a sequential manner. For example, the Haskell IO monad is a computational context in which you can do input/output, and all of these IO operations are represented using a data structure of the type “IO <return_value>”.

For example, the function “readLine” has the type “IO String”, and represents a computation that reads a line from standard input and returns it as a string. At runtime, evaluating this value will result in the runtime system asking the user for some input, and at compile-time this is represented as the string (that the user enters at runtime) inside the IO monad.



> A list is not a monad

Huh? List is very much a monad.


You're completely right. I had no idea.

But I can't make sense of the definition of >>= for the list in Haskell, which is:

    xs >>= f = [y | x <- xs, y <- f x]
It seems to imply that I get a list in return when I do xs >>= f, but I need to do the following in order for it to work:

    [1,2,3] >>= return . (+1)


You're probably use to Monads that wrap a single object, like the maybe monad. Monads can wrap multiple objects or anything. This is the case for a list.


Perhaps this might help (or perhaps not!)

    > [1,-2,3] >>= (\x -> replicate (abs x) x)
    [1,-2,-2,3,3,3]




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