{-# LANGUAGE CPP #-}
{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE ExplicitForAll #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE DeriveFoldable , DeriveTraversable#-}
-- |
-- A random-access list implementation based on Chris Okasaki's approach
-- on his book \"Purely Functional Data Structures\", Cambridge University
-- Press, 1998, chapter 9.3.
--
-- 'RAList' is a replacement for ordinary finite lists.
-- 'RAList' provides the same complexity as ordinary for most the list operations.
-- Some operations take /O(log n)/ for 'RAList' where the list operation is /O(n)/,
-- notably indexing, '(!!)'.
--
module Data.RAList
(
RAList
-- * Basic functions
, empty
, cons
, uncons
-- , singleton
, (++)
, head
, last
, tail
, init
, null
, length
-- * Indexing lists
-- | These functions treat a list @xs@ as a indexed collection,
-- with indices ranging from 0 to @'length' xs - 1@.
, (!!)
,lookupWithDefault
,lookupM
,lookup
--- * KV indexing
--- | This function treats a RAList as an association list
,lookupL
-- * List transformations
, map
, reverse
{-RA
, intersperse
, intercalate
, transpose
, subsequences
, permutations
-- * Reducing lists (folds)
-}
, foldl
, foldl'
, foldl1
, foldl1'
, foldr
, foldr1
-- ** Special folds
, concat
, concatMap
, and
, or
, any
, all
, sum
, product
, maximum
, minimum
-- * Building lists
{-RA
-- ** Scans
, scanl
, scanl1
, scanr
, scanr1
-- ** Accumulating maps
, mapAccumL
, mapAccumR
-}
-- ** Repetition
, replicate
{-RA
-- ** Unfolding
, unfoldr
-}
-- * Sublists
-- ** Extracting sublists
, take
, drop
, simpleDrop
, splitAt
{-RA
, takeWhile
, dropWhile
, dropWhileEnd
, span
, break
, stripPrefix
, group
, inits
, tails
-- ** Predicates
, isPrefixOf
, isSuffixOf
, isInfixOf
-}
-- * Searching lists
-- ** Searching by equality
, elem
, notElem
{-RA
-- ** Searching with a predicate
, find
-}
, filter
, partition
{-RA
, elemIndex
, elemIndices
, findIndex
, findIndices
-}
-- * Zipping and unzipping lists
, zip
{-RA
, zip3
, zip4, zip5, zip6, zip7
-}
, zipWith
{-RA
, zipWith3
, zipWith4, zipWith5, zipWith6, zipWith7
-}
, unzip
{-RA
, unzip3
, unzip4, unzip5, unzip6, unzip7
-- * Special lists
-- ** Functions on strings
, lines
, words
, unlines
, unwords
-- ** \"Set\" operations
, nub
, delete
, (\\)
, union
, intersect
-- ** Ordered lists
, sort
, insert
-- * Generalized functions
-- ** The \"@By@\" operations
-- *** User-supplied equality (replacing an @Eq@ context)
-- | The predicate is assumed to define an equivalence.
, nubBy
, deleteBy
, deleteFirstsBy
, unionBy
, intersectBy
, groupBy
-- *** User-supplied comparison (replacing an @Ord@ context)
-- | The function is assumed to define a total ordering.
, sortBy
, insertBy
, maximumBy
, minimumBy
-- ** The \"@generic@\" operations
-- | The prefix \`@generic@\' indicates an overloaded function that
-- is a generalized version of a "Prelude" function.
, genericLength
, genericTake
, genericDrop
, genericSplitAt
, genericIndex
, genericReplicate
-}
-- * Update
, update
, adjust
-- * List conversion
, toList
, fromList
) where
import qualified Prelude
import Prelude hiding(
(++), head, last, tail, init, null, length, map, reverse,
foldl, foldl1, foldr, foldr1, concat, concatMap,
and, or, any, all, sum, product, maximum, minimum, take,
drop, elem, splitAt, notElem, lookup, replicate, (!!), filter,
zip, zipWith, unzip
)
import qualified Data.List as List
#if !MIN_VERSION_base(4,9,0) == 1
import Data.Monoid(Monoid,mappend,mempty)
#endif
import Data.Semigroup(Semigroup,(<>))
import Data.Data(Data,Typeable)
import Data.Functor.Identity(runIdentity)
import Data.Word
infixl 9 !!
infixr 5 `cons`, ++
-- A RAList is stored as a list of trees. Each tree is a full binary tree.
-- The sizes of the trees are monotonically increasing, except that the two
-- first trees may have the same size.
-- The first few tree sizes:
-- [ [], [1], [1,1], [3], [1,3], [1,1,3], [3,3], [7], [1,7], [1,1,7],
-- [3,7], [1,3,7], [1,1,3,7], [3,3,7], [7,7], [15], ...
-- (I.e., skew binary numbers.)
data RAList a = RAList {-# UNPACK #-} !Word64 !(Top a)
deriving (Eq,Data,Typeable,Foldable,Traversable)
instance (Show a) => Show (RAList a) where
showsPrec p xs = showParen (p >= 10) $ showString "fromList " . showsPrec 10 (toList xs)
instance (Read a) => Read (RAList a) where
readsPrec p = readParen (p > 10) $ \ r -> [(fromList xs, t) | ("fromList", s) <- lex r, (xs, t) <- reads s]
instance (Ord a) => Ord (RAList a) where
xs < ys = toList xs < toList ys
xs <= ys = toList xs <= toList ys
xs > ys = toList xs > toList ys
xs >= ys = toList xs >= toList ys
xs `compare` ys = toList xs `compare` toList ys
instance Monoid (RAList a) where
mempty = empty
mappend = (<>)
instance Semigroup (RAList a) where
(<>) = (++)
instance Functor RAList where
fmap f (RAList s wts) = RAList s (fmap f wts)
instance Applicative RAList where
pure = \x -> RAList 1 (Cons 1 (Leaf x) Nil)
(<*>) = zipWith ($)
instance Monad RAList where
return = pure
(>>=) = flip concatMap
-- Special list type for (Word64, Tree a), i.e., Top a ~= [(Word64, Tree a)]
data Top a = Nil | Cons {-# UNPACK #-} !Word64 !(Tree a) (Top a)
deriving (Eq,Data,Typeable,Functor,Foldable,Traversable)
--instance Functor Top where
-- fmap _ Nil = Nil
-- fmap f (Cons w t xs) = Cons w (fmap f t) (fmap f xs)
-- Complete binary tree. The completeness of the trees is an invariant that must
-- be preserved for the implementation to work.
data Tree a
= Leaf a
| Node a !(Tree a) !(Tree a)
deriving (Eq,Data,Typeable,Functor,Foldable,Traversable)
--instance Functor Tree where
-- fmap f (Leaf x) = Leaf (f x)
-- fmap f (Node x l r) = Node (f x) (fmap f l) (fmap f r)
-----
empty :: RAList a
empty = RAList 0 Nil
-- | Complexity /O(1)/.
cons :: a -> RAList a -> RAList a
cons x (RAList s wts) = RAList (s+1) $
case wts of
Cons s1 t1 (Cons s2 t2 wts') | s1 == s2 -> Cons (1 + s1 + s2) (Node x t1 t2) wts'
_ -> Cons 1 (Leaf x) wts
(++) :: RAList a -> RAList a -> RAList a
xs ++ ys | null ys = xs -- small optimization to avoid consing to empty
| otherwise = foldr cons ys xs
uncons :: RAList a -> Maybe (a, RAList a)
uncons (RAList _ Nil) = Nothing
uncons (RAList s (Cons _ (Leaf h) wts)) = Just (h,RAList (s-1) wts)
uncons (RAList s (Cons w (Node x l r) wts)) = Just (x, RAList (s-1) (Cons w2 l (Cons w2 r wts)))
where w2 = w `quot` 2
-- | Complexity /O(1)/.
head :: RAList a -> Maybe a
head = fmap fst . uncons
-- | Complexity /O(log n)/.
last :: RAList a -> a
last xs@(RAList s _) = xs !! (s-1)
half :: Word64 -> Word64
half n = n `quot` 2
-- | Complexity /O(log n)/.
(!!) :: RAList a -> Word64 -> a
RAList s wts !! n | n < 0 = error "Data.RAList.!!: negative index"
| n >= s = error "Data.RAList.!!: index too large"
| otherwise = ix n wts
where ix j (Cons w t wts') | j < w = ixt j (w `quot` 2) t
| otherwise = ix (j-w) wts'
ix _ _ = error "Data.RAList.!!: impossible"
ixt 0 0 (Leaf x) = x
ixt 0 _ (Node x _l _r) = x
ixt j w (Node _x l r) | j <= w = ixt (j-1) (w `quot` 2) l
| otherwise = ixt (j-1-w) (w `quot` 2) r
ixt _j _w _ = error "Data.RAList.!!: impossible"
lookup :: forall a. Word64 -> Top a -> a
lookup i xs = runIdentity (lookupM i xs)
lookupM :: forall (m :: * -> *) a. Monad m => Word64 -> Top a -> m a
lookupM jx zs = look zs jx
where look Nil _ = fail "RandList.lookup bad subscript"
look (Cons j t xs) i
| i < j = lookTree j t i
| otherwise = look xs (i - j)
lookTree _ (Leaf x) i
| i == 0 = return x
| otherwise = nothing
lookTree j (Node x s t) i
| i > k = lookTree k t (i - 1 - k)
| i /= 0 = lookTree k s (i - 1)
| otherwise = return x
where k = half j
nothing = fail "RandList.lookup: not found"
--- this wont fly long term
lookupWithDefault :: forall t. t -> Word64 -> Top t -> t
lookupWithDefault d jx zs = look zs jx
where look Nil _ = d
look (Cons j t xs) i
| i < j = lookTree j t i
| otherwise = look xs (i - j)
lookTree _ (Leaf x) i
| i == 0 = x
| otherwise = d
lookTree j (Node x s t) i
| i > k = lookTree k t (i - 1 - k)
| i /= 0 = lookTree k s (i - 1)
| otherwise = x
where k = half j
-- | Complexity /O(1)/.
tail :: RAList a -> Maybe (RAList a)
tail = fmap snd . uncons
-- XXX Is there some clever way to do this?
init :: RAList a -> RAList a
init = fromList . Prelude.init . toList
null :: RAList a -> Bool
null (RAList s _) = s == 0
-- | Complexity /O(1)/.
length :: RAList a -> Word64
length (RAList s _) = s
map :: (a->b) -> RAList a -> RAList b
map = fmap
reverse :: RAList a -> RAList a
reverse = fromList . Prelude.reverse . toList
-- XXX All the folds could be done more effiently.
foldl :: (a -> b -> a) -> a -> RAList b -> a
foldl f z xs = Prelude.foldl f z (toList xs)
foldl' :: (a -> b -> a) -> a -> RAList b -> a
foldl' f z xs = List.foldl' f z (toList xs)
foldl1 :: (a -> a -> a) -> RAList a -> a
foldl1 f xs | null xs = errorEmptyList "foldl1"
| otherwise = Prelude.foldl1 f (toList xs)
foldl1' :: (a -> a -> a) -> RAList a -> a
foldl1' f xs | null xs = errorEmptyList "foldl1'"
| otherwise = List.foldl1' f (toList xs)
-- XXX This could be deforested.
foldr :: (a -> b -> b) -> b -> RAList a -> b
foldr f z xs = Prelude.foldr f z (toList xs)
foldr1 :: (a -> a -> a) -> RAList a -> a
foldr1 f xs | null xs = errorEmptyList "foldr1"
| otherwise = Prelude.foldr1 f (toList xs)
concat :: RAList (RAList a) -> RAList a
concat = foldr (++) empty
concatMap :: (a -> RAList b) -> RAList a -> RAList b
concatMap f = concat . map f
and :: RAList Bool -> Bool
and = foldr (&&) True
or :: RAList Bool -> Bool
or = foldr (||) False
any :: (a -> Bool) -> RAList a -> Bool
any p = or . map p
all :: (a -> Bool) -> RAList a -> Bool
all p = and . map p
sum :: (Num a) => RAList a -> a
sum = foldl (+) 0
product :: (Num a) => RAList a -> a
product = foldl (*) 1
maximum :: (Ord a) => RAList a -> a
maximum xs | null xs = errorEmptyList "maximum"
| otherwise = foldl1 max xs
minimum :: (Ord a) => RAList a -> a
minimum xs | null xs = errorEmptyList "minimum"
| otherwise = foldl1 min xs
replicate :: Word64 -> a -> RAList a
replicate n v = fromList $ Prelude.replicate (fromIntegral n) v
take :: Word64 -> RAList a -> RAList a
take n ls | n < fromIntegral (maxBound :: Int) = fromList $ Prelude.take (fromIntegral n) $ toList ls
| otherwise = ls
-- | drop i l
-- @`drop` i l@ where l has length n has worst case complexity Complexity /O(log n)/, Average case
-- complexity should be /O(min(log i, log n))/.
drop :: Word64 -> RAList a -> RAList a
drop n xs | n <= 0 = xs
drop n _xs@(RAList s _) | n >= s = empty
drop n (RAList s wts) = RAList (s-n) (loop n wts)
where loop 0 xs = xs
loop m (Cons w _ xs) | w <= m = loop (m-w) xs -- drops full trees
loop m (Cons w tre xs) = splitTree m w tre xs -- splits tree
loop _ _ = error "Data.RAList.drop: impossible"
-- helper function for drop
-- drops the first n elements of the tree and adds them to the front
splitTree :: Word64 -> Word64 -> Tree a -> Top a -> Top a
splitTree n treeSize tree@(Node _ l r) xs =
case (compare n 1, n <= halfTreeSize) of
(LT {- n==0 -}, _ ) -> Cons treeSize tree xs
(EQ {- n==1 -}, _ ) -> Cons halfTreeSize l (Cons halfTreeSize r xs)
(_, True ) -> splitTree (n-1) halfTreeSize l (Cons halfTreeSize r xs)
(_, False) -> splitTree (n-halfTreeSize-1) halfTreeSize r xs
where halfTreeSize = treeSize `quot` 2
splitTree n treeSize nd@(Leaf _) xs =
case compare n 1 of
EQ {-1-} -> xs
LT {-0-}-> Cons treeSize nd xs
GT {- > 1-} -> error "drop invariant violated, must be smaller than current tree"
-- Old version of drop
-- worst case complexity /O(n)/
simpleDrop :: Word64 -> RAList a -> RAList a
simpleDrop n xs | n <= 0 = xs
simpleDrop n _xs@(RAList s _) | n >= s = empty
simpleDrop n (RAList s wts) = RAList (s-n) (loop n wts)
where loop 0 xs = xs
loop n1 (Cons w _ xs) | w <= n1 = loop (n1-w) xs
loop n2 (Cons w (Node _ l r) xs) = loop (n2-1) (Cons w2 l (Cons w2 r xs))
where w2 = w `quot` 2
loop _ _ = error "Data.RAList.drop: impossible"
splitAt :: Word64 -> RAList a -> (RAList a, RAList a)
splitAt n xs = (take n xs, drop n xs)
elem :: (Eq a) => a -> RAList a -> Bool
elem x = any (== x)
notElem :: (Eq a) => a -> RAList a -> Bool
notElem x = not . elem x -- aka all (/=)
-- naive list based lookup
lookupL :: (Eq a) => a -> RAList (a, b) -> Maybe b
lookupL x xys = Prelude.lookup x (toList xys)
filter :: (a->Bool) -> RAList a -> RAList a
filter p xs =
case uncons xs of
Nothing -> empty
Just(h,tl) ->
let
ys = filter p tl
in
if p h then h `cons` ys else ys
partition :: (a->Bool) -> RAList a -> (RAList a, RAList a)
partition p xs = (filter p xs, filter (not . p) xs)
zip :: RAList a -> RAList b -> RAList (a, b)
zip = zipWith (,)
zipWith :: (a->b->c) -> RAList a -> RAList b -> RAList c
zipWith f xs1@(RAList s1 wts1) xs2@(RAList s2 wts2)
| s1 == s2 = RAList s1 (zipTop wts1 wts2)
| otherwise = fromList $ Prelude.zipWith f (toList xs1) (toList xs2)
where zipTree (Leaf x1) (Leaf x2) = Leaf (f x1 x2)
zipTree (Node x1 l1 r1) (Node x2 l2 r2) = Node (f x1 x2) (zipTree l1 l2) (zipTree r1 r2)
zipTree _ _ = error "Data.RAList.zipWith: impossible"
zipTop Nil Nil = Nil
zipTop (Cons w t1 xss1) (Cons _ t2 xss2) = Cons w (zipTree t1 t2) (zipTop xss1 xss2)
zipTop _ _ = error "Data.RAList.zipWith: impossible"
unzip :: RAList (a, b) -> (RAList a, RAList b)
unzip xs = (map fst xs, map snd xs)
-- | Change element at the given index.
-- Complexity /O(log n)/.
update :: Word64 -> a -> RAList a -> RAList a
update i x = adjust (const x) i
-- | Apply a function to the value at the given index.
-- Complexity /O(log n)/.
adjust :: (a->a) -> Word64 -> RAList a -> RAList a
adjust f n (RAList s wts) | n < 0 = error "Data.RAList.adjust: negative index"
| n >= s = error "Data.RAList.adjust: index too large"
| otherwise = RAList s (adj n wts)
where adj j (Cons w t wts') | j < w = Cons w (adjt j (w `quot` 2) t) wts'
| otherwise = Cons w t (adj (j-w) wts')
adj j _ = error ("Data.RAList.adjust: impossible Nil element: " <> show j)
adjt 0 0 (Leaf x) = Leaf (f x)
adjt 0 _ (Node x l r) = Node (f x) l r
adjt j w (Node x l r) | j <= w = Node x (adjt (j-1) (w `quot` 2) l) r
| otherwise = Node x l (adjt (j-1-w) (w `quot` 2) r)
adjt _ _ _ = error "Data.RAList.adjust: impossible"
-- XXX Make this a good producer
-- | Complexity /O(n)/.
toList :: RAList a -> [a]
toList (RAList _ wts) = tops wts []
where flat (Leaf x) a = x : a
flat (Node x l r) a = x : flat l (flat r a)
tops Nil r = r
tops (Cons _ t xs) r = flat t (tops xs r)
-- XXX Use number system properties to make this more efficient.
-- | Complexity /O(n)/.
fromList :: [a] -> RAList a
fromList = Prelude.foldr cons empty
errorEmptyList :: String -> a
errorEmptyList fun =
error ("Data.RAList." Prelude.++ fun Prelude.++ ": empty list")