Re: [Haskell-cafe] Confusion on the third monad law when using lambda abstractions

Clicking on the source code link reveals that enum2 is used in the where clause. It's not important to the transformation that Jake was performing. In essence, <=< is the monadic version of . (function composition) and as explained, it can be used to do some pointfree-like programming in the presence of monads. It's also handy in the arguments to things like mapM. E.g. f = mapM (\x -> foo x >>= bar) becomes: f = mapM (bar <=< foo) Neil. Colin Adams wrote:

What is enum2 doing in all of this - it appears to be ignored.

2009/6/18 Jake McArthur :

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Jake McArthur wrote:

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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/... _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

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