[Haskell-cafe] left to right pipeline of functions

Csongor Kiss kiss.csongor.kiss at gmail.com
Sun Jun 12 06:07:08 UTC 2016

```Hi,

(>>=) :: Monad m => m a -> (a -> m b) -> m b, and if I understand correctly, what you need is a ‘generic’ version, that works without the returns?

'return :: a -> m a' for some monad m. This m comes from the monad instance you use, but if we want a generic one, it’s only possible by fixing a specific m. The obvious choice is to use the Identity monad and have a specialised (>>=‘) :: Identity a -> (a -> Identity b) -> Identity b.

For all `a`, `Identity a` is isomorphic to `a`, so with a bit of cheating, you could rewrite the above to (>>=‘’) :: a -> (a -> b) -> b,
which starts to look really familiar, in fact, it’s just the function composition (.) with its arguments flipped, and is actually defined
as (&) in Data.Function.

g' = 2 & \n -> (n + 1) & \n -> (n + 3)

This was obviously a really roundabout way of arriving at the result, but I think the analogy with function composition is really nice, as we can think of (a -> b) as a special case of (a -> m b), the so-called Kleisli arrow. What monads do is they compose these Kleisli arrows.

--
Csongor
On 12 June 2016 at 06:47:13, Christopher Howard (ch.howard at zoho.com) wrote:

Hi, I am learning about monads, and this question came to mind: is there
a way to have a sequence of functions left to right like so:

g = return 2 >>= \n -> return (n + 1) >>= \n -> return (n + 3)

Either: some kind of generic monad that makes this legal, or some way to
do this without monad (i.e., without the "returns").

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