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| - | [[Category:Applications]][[Category:Monad]][[Category:Libraries]][[Category:Concurrency]][[Category:Parallel]][[Category:Research]]
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| - | ==Introduction==
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| - | 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.
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| - | I have noticed that MapReduce can be expressed naturally, using functional programming techniques, as a form of monad.
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| - | 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.
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| - | ==Why a monad?==
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| - | What the monadic implementation lets us do is the following:
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| - | *Map and reduce look the same.
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| - | *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.
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| - | *All of the guts of MapReduce are hidden in the monad's <hask>bind</hask> function
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| - | *The implementation is naturally parallel
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| - | *Making a MapReduce program is trivial:<br/>
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| - | <hask>
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| - | ... >>= wrapMR mapper >>= wrapMR reducer >>= ...
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| - | </hask><br/>
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| - | ==Details==
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| - | 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.
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| - | ===Generalised mappers / reducers===
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| - | One can generalise MapReduce a bit, so that each stage (map, reduce, etc) becomes a function of signature<br/>
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| - | <hask>
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| - | a -> ([(s,a)] -> [(s',b)])
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| - | </hask><br/>
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| - | where <hask>s</hask> and <hask>s'</hask> are data types and <hask>a</hask> and <hask>b</hask> are key values.
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| - |
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| - | ===Generalised Monad===
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| - | 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.
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| - | Let <hask>m</hask> be a <hask>Monad'</hask>, a type with four parameters: <hask>m s a s' b</hask>.
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| - | Generalise the monadic <hask>bind</hask> operation to:<br/>
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| - | <hask>
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| - | m s a s' b -> ( b -> m s' b s'' c ) -> m s a s'' c
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| - | </hask><br/>
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| - | See [http://blog.sigfpe.com/2009/02/beyond-monads.html Parametrized monads].
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| - | Then clearly the generalised mapper/reducer above can be written as a <hask>Monad'</hask>, meaning that we can write MapReduce as<br/>
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| - | <hask>
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| - | ... >>= mapper >>= reducer >>= mapper' >>= reducer' >>= ...
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| - | </hask>
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| - |
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| - | ===Implementation details===
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| - |
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| - | <hask>
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| - | class Monad' m where
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| - | return :: a -> m s x s a
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| - | (>>=) :: (Eq b) => m s a s' b -> ( b -> m s' b s'' c ) -> m s a s'' c
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| - | newtype MapReduce s a s' b = MR { runMR :: ([(s,a)] -> [(s',b)]) }
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| - | retMR :: a -> MapReduce s x s a
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| - | retMR k = MR (\ss -> [(s,k) | s <- fst <$> ss])
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| - |
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| - | bindMR :: (Eq b,NFData s'',NFData c) => MapReduce s a s' b -> (b -> MapReduce s' b s'' c) -> MapReduce s a s'' c
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| - | bindMR f g = MR (\s ->
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| - | let
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| - | fs = runMR f s
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| - | gs = P.map g $ nub $ snd <$> fs
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| - | in
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| - | concat $ map (\g' -> runMR g' fs) gs)
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| - | </hask><br/>
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| - | The key point here is that <hask>P.map</hask> is a parallel version of the simple <hask>map</hask> function.
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| - |
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| - | Now we can write a wrapper function<br/>
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| - | <hask>
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| - | wrapMR :: (Eq a) => ([s] -> [(s',b)]) -> (a -> MapReduce s a s' b)
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| - | wrapMR f = (\k -> MR (g k))
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| - | where
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| - | g k ss = f $ fst <$> filter (\s -> k == snd s) ss
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| - | </hask><br/>
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| - | 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/>
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| - | <hask>
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| - | mapReduce :: [String] -> [(String,Int)]
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| - | mapReduce state = runMapReduce mr state
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| - | where
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| - | mr = return () >>= wrapMR mapper >>= wrapMR reducer
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| - | </hask><br/>
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| - | 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).
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| - | ==Future Directions==
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| - | *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.
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| - | *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.
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| - | I would be eager for collaborative working on taking this forward.
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| - | [[User:Julianporter|julianporter]] 18:32, 2 April 2011 (UTC)
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