Donald Bruce Stewart dons at cse.unsw.edu.au
Sun Nov 12 21:15:45 EST 2006

Kleisli composition of monads is a foundational feature missing from the
current Control.Monad library. A recent discussion revealed solid
support for its inclusion.

(>=>) :: (Monad m) => (a -> m b) -> (b -> m c) -> (a -> m c)
(<=<) :: (Monad m) => (b -> m c) -> (a -> m b) -> (a -> m c)

Along with the useful control combinator:

forever :: (Monad m) => m a -> m ()

Traditionally, >=> has been written as @@, however to support the
flipped version, new notation seems to be required. It should be notated
that there is overlap with the Kleisli class in Control.Arrow
(specifically >>>), however, short of a convenient unifying form for
and =<<, infixr 1 was chosen.

Proposal period: 2 weeks.

-- Don

------------------------------------------------------------------------

+    , (>=>)         -- :: (Monad m) => (a -> m b) -> (b -> m c) -> (a -> m c)
+    , (<=<)         -- :: (Monad m) => (b -> m c) -> (a -> m b) -> (a -> m c)
+    , forever       -- :: (Monad m) => m a -> m ()
+infixr 1 <=<, >=>
+
+-- | Left-to-right Kleisli composition of monads.
+(>=>)       :: Monad m => (a -> m b) -> (b -> m c) -> (a -> m c)
+f >=> g     = \x -> f x >>= g
+
+-- | Right-to-left Kleisli composition of monads. '(>=>)', with the arguments flipped
+(<=<)       :: Monad m => (b -> m c) -> (a -> m b) -> (a -> m c)
+(<=<)       = flip (>=>)
+
+-- | @'forever' act@ repeats the action infinitely.
+forever     :: (Monad m) => m a -> m ()
+forever a   = a >> forever a

------------------------------------------------------------------------