List

module List ( 
    elemIndex, elemIndices,
    find, findIndex, findIndices,
    nub, nubBy, delete, deleteBy, (\\), 
    union, unionBy, intersect, intersectBy,
    intersperse, transpose, partition, group, groupBy,
    inits, tails, isPrefixOf, isSuffixOf,
    mapAccumL, mapAccumR,
    sort, sortBy, insert, insertBy, maximumBy, minimumBy,
    genericLength, genericTake, genericDrop,
    genericSplitAt, genericIndex, genericReplicate,
    zip4, zip5, zip6, zip7,
    zipWith4, zipWith5, zipWith6, zipWith7,
    unzip4, unzip5, unzip6, unzip7, unfoldr,

    -- ...and what the Prelude exports
    []((:), []),
    map, (++), concat, filter,
    head, last, tail, init, null, length, (!!),
    foldl, foldl1, scanl, scanl1, foldr, foldr1, scanr, scanr1,
    iterate, repeat, replicate, cycle,
    take, drop, splitAt, takeWhile, dropWhile, span, break,
    lines, words, unlines, unwords, reverse, and, or,
    any, all, elem, notElem, lookup,
    sum, product, maximum, minimum, concatMap, 
    zip, zip3, zipWith, zipWith3, unzip, unzip3
    ) where

import Maybe( listToMaybe )

infix 5 \\

elemIndex               :: Eq a => a -> [a] -> Maybe Int
elemIndex x             =  findIndex (x ==)
        
elemIndices             :: Eq a => a -> [a] -> [Int]
elemIndices x           =  findIndices (x ==)
                        
find                    :: (a -> Bool) -> [a] -> Maybe a
find p                  =  listToMaybe . filter p

findIndex               :: (a -> Bool) -> [a] -> Maybe Int
findIndex p             =  listToMaybe . findIndices p

findIndices             :: (a -> Bool) -> [a] -> [Int]
findIndices p xs        =  [ i | (x,i) <- zip xs [0..], p x ]

nub                     :: Eq a => [a] -> [a]
nub                     =  nubBy (==)

nubBy                   :: (a -> a -> Bool) -> [a] -> [a]
nubBy eq []             =  []
nubBy eq (x:xs)         =  x : nubBy eq (filter (\y -> not (eq x y)) xs)

delete                  :: Eq a => a -> [a] -> [a]
delete                  =  deleteBy (==)

deleteBy                :: (a -> a -> Bool) -> a -> [a] -> [a]
deleteBy eq x []        = []
deleteBy eq x (y:ys)    = if x `eq` y then ys else y : deleteBy eq x ys

(\\)                    :: Eq a => [a] -> [a] -> [a]
(\\)                    =  foldl (flip delete)

deleteFirstsBy          :: (a -> a -> Bool) -> [a] -> [a] -> [a]
deleteFirstsBy eq       =  foldl (flip (deleteBy eq))

union                   :: Eq a => [a] -> [a] -> [a]
union                   =  unionBy (==)    

unionBy                 :: (a -> a -> Bool) -> [a] -> [a] -> [a]
unionBy eq xs ys        =  xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs

intersect               :: Eq a => [a] -> [a] -> [a]
intersect               =  intersectBy (==)

intersectBy             :: (a -> a -> Bool) -> [a] -> [a] -> [a]
intersectBy eq xs ys    =  [x | x <- xs, any (eq x) ys]

intersperse             :: a -> [a] -> [a]
intersperse sep []      =  []
intersperse sep [x]     =  [x]
intersperse sep (x:xs)  =  x : sep : intersperse sep xs

-- transpose is lazy in both rows and columns,
--   and works for non-rectangular 'matrices'
-- For example, transpose [[1,2],[3,4,5],[]]  =  [[1,3],[2,4],[5]]
-- Note that [h | (h:t) <- xss] is not the same as (map head xss)
-- because the former discards empty sublists inside xss
transpose                :: [[a]] -> [[a]]
transpose []  = []
transpose ([]     : xss) = transpose xss
transpose ((x:xs) : xss) = (x : [h | (h:t) <- xss]) : 
   transpose (xs : [t | (h:t) <- xss])

partition               :: (a -> Bool) -> [a] -> ([a],[a])
partition p xs          =  foldr select ([],[]) xs
                           where select x (ts,fs) | p x       = (x:ts,fs)
                                                  | otherwise = (ts, x:fs)

-- group splits its list argument into a list of lists of equal, adjacent
-- elements.  e.g.,
-- group "Mississippi" == ["M","i","ss","i","ss","i","pp","i"]
group                   :: Eq a => [a] -> [[a]]
group                   =  groupBy (==)

groupBy                 :: (a -> a -> Bool) -> [a] -> [[a]]
groupBy eq []           =  []
groupBy eq (x:xs)       =  (x:ys) : groupBy eq zs
                           where (ys,zs) = span (eq x) xs

-- inits xs returns the list of initial segments of xs, shortest first.
-- e.g., inits "abc" == ["","a","ab","abc"]
inits                   :: [a] -> [[a]]
inits []                =  [[]]
inits (x:xs)            =  [[]] ++ map (x:) (inits xs)

-- tails xs returns the list of all final segments of xs, longest first.
-- e.g., tails "abc" == ["abc", "bc", "c",""]
tails                   :: [a] -> [[a]]
tails []                =  [[]]
tails xxs@(_:xs)        =  xxs : tails xs

isPrefixOf               :: Eq a => [a] -> [a] -> Bool
isPrefixOf []     _      =  True
isPrefixOf _      []     =  False
isPrefixOf (x:xs) (y:ys) =  x == y && isPrefixOf xs ys

isSuffixOf              :: Eq a => [a] -> [a] -> Bool
isSuffixOf x y          =  reverse x `isPrefixOf` reverse y

mapAccumL               :: (a -> b -> (a, c)) -> a -> [b] -> (a, [c])
mapAccumL f s []        =  (s, [])
mapAccumL f s (x:xs)    =  (s'',y:ys)
                           where (s', y ) = f s x
                                 (s'',ys) = mapAccumL f s' xs

mapAccumR               :: (a -> b -> (a, c)) -> a -> [b] -> (a, [c])
mapAccumR f s []        =  (s, [])
mapAccumR f s (x:xs)    =  (s'', y:ys)
                           where (s'',y ) = f s' x
                                 (s', ys) = mapAccumR f s xs

unfoldr :: (b -> Maybe (a,b)) -> b -> [a]
unfoldr f b = case f b of
Nothing    -> []
Just (a,b) -> a : unfoldr f b

sort                    :: (Ord a) => [a] -> [a]
sort                    =  sortBy compare

sortBy                  :: (a -> a -> Ordering) -> [a] -> [a]
sortBy cmp              =  foldr (insertBy cmp) []

insert :: (Ord a) => a -> [a] -> [a]
insert = insertBy compare

insertBy                :: (a -> a -> Ordering) -> a -> [a] -> [a]
insertBy cmp x []       =  [x]
insertBy cmp x ys@(y:ys')
                        =  case cmp x y of
                                GT -> y : insertBy cmp x ys'
                                _  -> x : ys

maximumBy               :: (a -> a -> a) -> [a] -> a
maximumBy max []        =  error "List.maximumBy: empty list"
maximumBy max xs        =  foldl1 max xs

minimumBy               :: (a -> a -> a) -> [a] -> a
minimumBy min []        =  error "List.minimumBy: empty list"
minimumBy min xs        =  foldl1 min xs

genericLength           :: (Integral a) => [b] -> a
genericLength []        =  0
genericLength (x:xs)    =  1 + genericLength xs

genericTake             :: (Integral a) => a -> [b] -> [b]
genericTake _ []        =  []
genericTake 0 _         =  []
genericTake n (x:xs) 
   | n > 0              =  x : genericTake (n-1) xs
   | otherwise          =  error "List.genericTake: negative argument"

genericDrop             :: (Integral a) => a -> [b] -> [b]
genericDrop 0 xs        =  xs
genericDrop _ []        =  []
genericDrop n (_:xs) 
   | n > 0              =  genericDrop (n-1) xs
   | otherwise          =  error "List.genericDrop: negative argument"

genericSplitAt          :: (Integral a) => a -> [b] -> ([b],[b])
genericSplitAt 0 xs     =  ([],xs)
genericSplitAt _ []     =  ([],[])
genericSplitAt n (x:xs) 
   | n > 0              =  (x:xs',xs'')
   | otherwise          =  error "List.genericSplitAt: negative argument"
       where (xs',xs'') =  genericSplitAt (n-1) xs

genericIndex            :: (Integral a) => [b] -> a -> b
genericIndex (x:_)  0   =  x
genericIndex (_:xs) n 
        | n > 0         =  genericIndex xs (n-1)
        | otherwise     =  error "List.genericIndex: negative argument"
genericIndex _ _        =  error "List.genericIndex: index too large"

genericReplicate        :: (Integral a) => a -> b -> [b]
genericReplicate n x    =  genericTake n (repeat x)
 
zip4                    :: [a] -> [b] -> [c] -> [d] -> [(a,b,c,d)]
zip4                    =  zipWith4 (,,,)

zip5                    :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a,b,c,d,e)]
zip5                    =  zipWith5 (,,,,)

zip6                    :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> 
                              [(a,b,c,d,e,f)]
zip6                    =  zipWith6 (,,,,,)

zip7                    :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] ->
                              [g] -> [(a,b,c,d,e,f,g)]
zip7                    =  zipWith7 (,,,,,,)

zipWith4                :: (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]
zipWith4 z (a:as) (b:bs) (c:cs) (d:ds)
                        =  z a b c d : zipWith4 z as bs cs ds
zipWith4 _ _ _ _ _      =  []

zipWith5                :: (a->b->c->d->e->f) -> 
                           [a]->[b]->[c]->[d]->[e]->[f]
zipWith5 z (a:as) (b:bs) (c:cs) (d:ds) (e:es)
                        =  z a b c d e : zipWith5 z as bs cs ds es
zipWith5 _ _ _ _ _ _    =  []

zipWith6                :: (a->b->c->d->e->f->g) ->
                           [a]->[b]->[c]->[d]->[e]->[f]->[g]
zipWith6 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs)
                        =  z a b c d e f : zipWith6 z as bs cs ds es fs
zipWith6 _ _ _ _ _ _ _  =  []

zipWith7                :: (a->b->c->d->e->f->g->h) ->
                           [a]->[b]->[c]->[d]->[e]->[f]->[g]->[h]
zipWith7 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs) (g:gs)
                   =  z a b c d e f g : zipWith7 z as bs cs ds es fs gs
zipWith7 _ _ _ _ _ _ _ _ = []

unzip4                  :: [(a,b,c,d)] -> ([a],[b],[c],[d])
unzip4                  =  foldr (\(a,b,c,d) ~(as,bs,cs,ds) ->
                                        (a:as,b:bs,c:cs,d:ds))
                                 ([],[],[],[])

unzip5                  :: [(a,b,c,d,e)] -> ([a],[b],[c],[d],[e])
unzip5                  =  foldr (\(a,b,c,d,e) ~(as,bs,cs,ds,es) ->
                                        (a:as,b:bs,c:cs,d:ds,e:es))
                                 ([],[],[],[],[])

unzip6                  :: [(a,b,c,d,e,f)] -> ([a],[b],[c],[d],[e],[f])
unzip6                  =  foldr (\(a,b,c,d,e,f) ~(as,bs,cs,ds,es,fs) ->
                                        (a:as,b:bs,c:cs,d:ds,e:es,f:fs))
                                 ([],[],[],[],[],[])

unzip7          :: [(a,b,c,d,e,f,g)] -> ([a],[b],[c],[d],[e],[f],[g])
unzip7          =  foldr (\(a,b,c,d,e,f,g) ~(as,bs,cs,ds,es,fs,gs) ->
                                (a:as,b:bs,c:cs,d:ds,e:es,f:fs,g:gs))
                         ([],[],[],[],[],[],[])

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