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

[Neil Brown]

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 <jake.mcarthur at gmail.com>:
>   
>> 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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