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MapReduce as a monad

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==Introduction==
 
 
MapReduce is a general technique for massively parallel programming developed by Google. It takes its inspiration from ideas in functional programming, but has moved away from that paradigm to a more imperative approach.
 
I have noticed that MapReduce can be expressed naturally, using functional programming techniques, as a form of monad.
 
 
The standard implementation of MapReduce is the JAVA-based HADOOP framework, which is very complex and somewhat temperamental. Moreover, it is necessary to write HADOOP-specific code into mappers and reducers. My prototype library takes about 100 lines of code and can wrap generic mapper / reducer functions.
 
 
==Why a monad?==
 
 
What the monadic implementation lets us do is the following:
 
*Map and reduce look the same.
 
*You can write a simple wrapper function that takes a mapper / reducer and wraps it in the monad, so authors of mappers / reducers do not need to know anything about the MapReduce framework: they can concentrate on their algorithms.
 
*All of the guts of MapReduce are hidden in the monad's <hask>bind</hask> function
 
*The implementation is naturally parallel
 
*Making a MapReduce program is trivial:<br/>
 
<hask>
 
... >>= wrapMR mapper >>= wrapMR reducer >>= ...
 
</hask><br/>
 
 
==Details==
 
Full details of the implementation and sample code can be found [http://jpembeddedsolutions.wordpress.com/2011/04/02/mapreduce/ here]. I'll just give highlights here.
 
 
===Generalised mappers / reducers===
 
One can generalise MapReduce a bit, so that each stage (map, reduce, etc) becomes a function of signature<br/>
 
<hask>
 
a -> ([(s,a)] -> [(s',b)])
 
</hask><br/>
 
where <hask>s</hask> and <hask>s'</hask> are data types and <hask>a</hask> and <hask>b</hask> are key values.
 
 
===Generalised Monad===
 
Now, this is suggestive of a monad, but we can't use a monad ''per se'', because the transformation changes the key and value types, and we want to be able to access them separately. Therefore we do the following.
 
 
Let <hask>m</hask> be a <hask>Monad'</hask>, a type with four parameters: <hask>m s a s' b</hask>.
 
 
Generalise the monadic <hask>bind</hask> operation to:<br/>
 
<hask>
 
m s a s' b -> ( b -> m s' b s'' c ) -> m s a s'' c
 
</hask><br/>
 
 
See [http://blog.sigfpe.com/2009/02/beyond-monads.html Parametrized monads].
 
 
Then clearly the generalised mapper/reducer above can be written as a <hask>Monad'</hask>, meaning that we can write MapReduce as<br/>
 
<hask>
 
... >>= mapper >>= reducer >>= mapper' >>= reducer' >>= ...
 
</hask>
 
 
===Implementation details===
 
 
<hask>
 
class Monad' m where
 
return :: a -> m s x s a
 
(>>=) :: (Eq b) => m s a s' b -> ( b -> m s' b s'' c ) -> m s a s'' c
 
 
newtype MapReduce s a s' b = MR { runMR :: ([(s,a)] -> [(s',b)]) }
 
 
retMR :: a -> MapReduce s x s a
 
retMR k = MR (\ss -> [(s,k) | s <- fst <$> ss])
 
 
bindMR :: (Eq b,NFData s'',NFData c) => MapReduce s a s' b -> (b -> MapReduce s' b s'' c) -> MapReduce s a s'' c
 
bindMR f g = MR (\s ->
 
let
 
fs = runMR f s
 
gs = P.map g $ nub $ snd <$> fs
 
in
 
concat $ map (\g' -> runMR g' fs) gs)
 
</hask><br/>
 
The key point here is that <hask>P.map</hask> is a parallel version of the simple <hask>map</hask> function.
 
 
Now we can write a wrapper function<br/>
 
<hask>
 
wrapMR :: (Eq a) => ([s] -> [(s',b)]) -> (a -> MapReduce s a s' b)
 
wrapMR f = (\k -> MR (g k))
 
where
 
g k ss = f $ fst <$> filter (\s -> k == snd s) ss
 
</hask><br/>
 
which takes a conventional mapper / reducer and wraps it in the <hask>Monad'</hask>. Note that this means that the mapper / reducer functions ''do not need to know anything about the way MapReduce is implemented''. So a standard MapReduce job becomes<br/>
 
<hask>
 
mapReduce :: [String] -> [(String,Int)]
 
mapReduce state = runMapReduce mr state
 
where
 
mr = return () >>= wrapMR mapper >>= wrapMR reducer
 
</hask><br/>
 
I have tested the implementation with the standard word-counter mapper and reducer, and it works perfectly (full code is available via the link above).
 
 
==Future Directions==
 
 
*My code so far runs concurrently and in multiple threads within a single OS image. It won't work on clustered systems. This is clearly where work should go next.
 
*Currently all of the data is sent to all of the mappers / reducers at each iteration. This is okay on a single machine, but may be prohibitive on a cluster.
 
 
I would be eager for collaborative working on taking this forward.
 
 
[[User:Julianporter|julianporter]] 18:32, 2 April 2011 (UTC)
 

Revision as of 18:06, 31 October 2011