```{-| An implementation of a 3-way merge algorithm. -}
module Data.Algorithm.Diff3 (Hunk(..), diff3, merge) where

import Data.Algorithm.Diff
import Data.Monoid (Monoid, mempty, mappend)

--------------------------------------------------------------------------------
-- | A hunk is a collection of changes that occur in a document. A hunk can be
-- some changes only in A, only in B, in both A & B (equally), or conflicting
-- between A, B and the original document.
data Hunk a = ChangedInA [a] | ChangedInB [a] | Both [a] | Conflict [a] [a] [a]
deriving (Eq, Show)

--------------------------------------------------------------------------------
-- | Perform a 3-way diff against 2 documents and the original document.
diff3 :: Eq a => [a] -> [a] -> [a] -> [Hunk a]
diff3 a o b = step (getDiff o a) (getDiff o b)
where
step [] [] = []
step [] ob = toHunk [] ob
step oa [] = toHunk oa []
step oa ob =
let (conflictHunk, ra, rb) = shortestConflict oa ob
(matchHunk, ra', rb')  = shortestMatch ra rb
in conflictHunk ++ matchHunk ++ step ra' rb'

--------------------------------------------------------------------------------
merge :: [Hunk a] -> Either [Hunk a] [a]
merge hunks = maybe (Left hunks) Right \$ go hunks
where
go [] = Just []
go ((Conflict _ _ _):_) = Nothing
go ((ChangedInA as):t) = fmap (as ++) \$ go t
go ((ChangedInB bs):t) = fmap (bs ++) \$ go t
go ((Both xs):t) = fmap (xs ++) \$ go t

--------------------------------------------------------------------------------
toHunk :: [(DI, a)] -> [(DI, a)] -> [Hunk a]
toHunk [] [] = mempty
toHunk a  [] = return \$ ChangedInA \$ map snd a
toHunk [] b  = return \$ ChangedInB \$ map snd b
toHunk a  b
| all isB a && all isB b = return \$ Both \$ map snd \$ filter isA a
| all isB a = return \$ ChangedInB \$ map snd \$ filter isA b
| all isB b = return \$ ChangedInA \$ map snd \$ filter isA a
| otherwise = return \$ Conflict (map snd \$ filter isA a)
(map snd \$ filter isO a)
(map snd \$ filter isA b)

--------------------------------------------------------------------------------
isA :: (DI, t) -> Bool
isA (F,_) = False
isA (_,_) = True
{-# INLINE isA #-}

--------------------------------------------------------------------------------
isO :: (DI, t) -> Bool
isO (S,_) = False
isO (_,_) = True
{-# INLINE isO #-}

--------------------------------------------------------------------------------
isB :: (DI, t) -> Bool
isB (B,_) = True
isB (_,_) = False
{-# INLINE isB #-}

--------------------------------------------------------------------------------
shortestMatch :: [(DI,a)] -> [(DI,a)] -> ([Hunk a], [(DI, a)], [(DI, a)])
shortestMatch oa ob = go oa ob [] []
where
go (x@(B,_):xs) (y@(B,_):ys) accX accY = go xs ys (accX ++ [x]) (accY ++ [y])
go xs ys accX accY = (toHunk accX accY, xs, ys)

--------------------------------------------------------------------------------
shortestConflict :: [(DI,a)] -> [(DI,a)] -> ([Hunk a], [(DI, a)], [(DI, a)])
shortestConflict l r =
let (hunk, rA, rB) = go l r
in (uncurry toHunk hunk, rA, rB)
where
go [] b = (([], b), [], [])
go a [] = ((a, []), [], [])
go a b =
let (as, ta) = break isBoth a
(bs, tb) = break isBoth b
am = sum \$ map motion as
bm = sum \$ map motion bs
(as', ta') = incurMotion bm ta
(bs', tb') = incurMotion am tb
in if am == bm
then ((as, bs), ta, tb)
else ((as ++ as', bs ++ bs'), [], []) <> go ta' tb'

isBoth (B,_) = True
isBoth (_,_) = False

motion (S,_) = 0
motion _ = 1

--------------------------------------------------------------------------------
incurMotion :: Int -> [(DI, t)] -> ([(DI,t)], [(DI,t)])
incurMotion _ [] = ([], [])
incurMotion 0 as  = ([], as)
incurMotion n (a@(B,_):as) = ([a], []) <> incurMotion (pred n) as
incurMotion n (a@(S,_):as) = ([a], []) <> incurMotion (pred n) as
incurMotion n (a:as) = ([a], []) <> incurMotion n as

--------------------------------------------------------------------------------
-- This is here so we can build on GHC 7.4.
infixr 6 <>

-- | An infix synonym for 'mappend'.
(<>) :: Monoid m => m -> m -> m
(<>) = mappend
{-# INLINE (<>) #-}
```