I'm learning about the Map Reduce computation frequently used with big data. For the fun of it, I decided to write a very high-level spec of Map Reduce. Here is what I came up with. Enjoy. John
module MapReduce where import Data.List (nub)
A high-level specification of Map Reduce as a Haskell program. The program uses lists to represent multisets. As multisets have no implied ordering, the ordering implied by lists in this specification should be ignored. The database is a multiset of key-value pairs.
type Key = String type Value = String type Datum = (Key, Value) type Data = [Datum]
A mapper maps a datum to a finite multiset of key-value pairs.
type Mapper = Datum -> Data
A reducer takes a key and a multiset of values and produces a finite multiset of values.
type Reducer = (Key, [Value]) -> [Value]
A step is a mapper followed by a reducer
type Step = (Mapper, Reducer)
A program is a finite sequence of steps
type Program = [Step]
The semantics of a program is provided by the run function.
run :: Program -> Data -> Data run [] d = d run (s : p) d = run p (step s d)
The three parts of a step are mapping, shuffling, and reducing.
step :: Step -> Data -> Data step (m, r) d = let mapped = transform m d shuffled = shuffle mapped in reduce r shuffled
The first part of a step is to transform the data by applying the mapper to each datum and collecting the results.
transform :: Mapper -> Data -> Data transform m d = [p | u <- d, p <- m u]
Next, values with common keys are collected. Keys are unique after shuffling.
shuffle :: Data -> [(Key, [Value])] shuffle d = [(k, vs) | k <- nub (map fst d), -- nub eliminates duplicate keys let vs = [v | (k', v) <- d, k' == k]]
A reducer is applied to the data associated with one key, and always produces data with that key.
reduce :: Reducer -> [(Key, [Value])] -> Data reduce r rs = [(k, v) | (k, vs) <- rs, v <- r (k, vs)]