Jake McArthur wrote:
Generally, you can transform anything of the form:

    baz x1 = a =<< b =<< ... =<< z x1

into:

    baz = a <=< b <=< ... <=< z

I was just looking through the source for the recently announced Hyena library and decided to give a more concrete example from a real-world project. Consider this function from the project's Data.Enumerator module[1]:

    compose enum1 enum2 f initSeed = enum1 f1 (Right initSeed) >>= k
        where
          f1 (Right seed) bs = ...
          k (Right seed) = ...

First, I would flip the `(>>=)` into a `(=<<)` (and I will ignore the `where` portion of the function from now on):

    compose enum1 enum2 f initSeed = k =<< enum1 f1 (Right initSeed)

Next, transform the `(=<<)` into a `(<=<)`:

    compose enum1 enum2 f initSeed = k <=< enum1 f1 $ Right initSeed

We can "move" the `($)` to the right by using `(.)`:

    compose enum1 enum2 f initSeed = k <=< enum1 f1 . Right $ initSeed

Finally, we can drop the `initSeed` from both sides:

    compose enum1 enum2 f = k <=< enum1 f1 . Right

I didn't test that my transformation preserved the semantics of the function or even that the type is still the same, but even if it's wrong it should give you the idea.

- Jake

[1] http://github.com/tibbe/hyena/blob/9655e9e6473af1e069d22d3ee75537ad3b88a732/Data/Enumerator.hs#L117
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