--
-- * Ralf Hinze and Ross Paterson,
-- \"Finger trees: a simple general-purpose data structure\",
--- to appear in /Journal of Functional Programming/.
+-- /Journal of Functional Programming/ 16:2 (2006) pp 197-217.
-- <http://www.soi.city.ac.uk/~ross/papers/FingerTree.html>
--
-- /Note/: Many of these operations have the same names as similar
(<|), -- :: a -> Seq a -> Seq a
(|>), -- :: Seq a -> a -> Seq a
(><), -- :: Seq a -> Seq a -> Seq a
+ fromList, -- :: [a] -> Seq a
-- * Deconstruction
+ -- | Additional functions for deconstructing sequences are available
+ -- via the 'Foldable' instance of 'Seq'.
+
-- ** Queries
null, -- :: Seq a -> Bool
length, -- :: Seq a -> Int
take, -- :: Int -> Seq a -> Seq a
drop, -- :: Int -> Seq a -> Seq a
splitAt, -- :: Int -> Seq a -> (Seq a, Seq a)
- -- * Lists
- fromList, -- :: [a] -> Seq a
- toList, -- :: Seq a -> [a]
- -- * Folds
- -- ** Right associative
- foldr, -- :: (a -> b -> b) -> b -> Seq a -> b
- foldr1, -- :: (a -> a -> a) -> Seq a -> a
- foldr', -- :: (a -> b -> b) -> b -> Seq a -> b
- foldrM, -- :: Monad m => (a -> b -> m b) -> b -> Seq a -> m b
- -- ** Left associative
- foldl, -- :: (a -> b -> a) -> a -> Seq b -> a
- foldl1, -- :: (a -> a -> a) -> Seq a -> a
- foldl', -- :: (a -> b -> a) -> a -> Seq b -> a
- foldlM, -- :: Monad m => (a -> b -> m a) -> a -> Seq b -> m a
-- * Transformations
reverse, -- :: Seq a -> Seq a
#if TESTING
import Prelude hiding (
null, length, take, drop, splitAt, foldl, foldl1, foldr, foldr1,
reverse)
-import qualified Prelude (foldr)
-import qualified Data.List (foldl', intersperse)
+import qualified Data.List (foldl')
+import Control.Applicative (Applicative(..), (<$>))
import Control.Monad (MonadPlus(..))
-import Data.FunctorM
+import Data.Monoid (Monoid(..))
+import Data.Foldable
+import Data.Traversable
import Data.Typeable
#ifdef __GLASGOW_HASKELL__
-import GHC.Exts (build)
-import Text.ParserCombinators.ReadP (char, skipSpaces, between, sepBy, (+++))
-import Text.Read (readPrec, readPrec_to_P, readP_to_Prec, minPrec)
-import Control.Monad (liftM)
+import Text.Read (Lexeme(Ident), lexP, parens, prec,
+ readPrec, readListPrec, readListPrecDefault)
import Data.Generics.Basics (Data(..), Fixity(..),
constrIndex, mkConstr, mkDataType)
-#else
-import Data.Char (isSpace)
#endif
#if TESTING
-import Control.Monad (liftM, liftM2, liftM3, liftM4)
+import Control.Monad (liftM, liftM3, liftM4)
import Test.QuickCheck
#endif
instance Functor Seq where
fmap f (Seq xs) = Seq (fmap (fmap f) xs)
+instance Foldable Seq where
+ foldr f z (Seq xs) = foldr (flip (foldr f)) z xs
+ foldl f z (Seq xs) = foldl (foldl f) z xs
+
+ foldr1 f (Seq xs) = getElem (foldr1 f' xs)
+ where f' (Elem x) (Elem y) = Elem (f x y)
+
+ foldl1 f (Seq xs) = getElem (foldl1 f' xs)
+ where f' (Elem x) (Elem y) = Elem (f x y)
+
+instance Traversable Seq where
+ traverse f (Seq xs) = Seq <$> traverse (traverse f) xs
+
instance Monad Seq where
return = singleton
xs >>= f = foldl' add empty xs
mzero = empty
mplus = (><)
-instance FunctorM Seq where
- fmapM f = foldlM f' empty
- where f' ys x = do
- y <- f x
- return $! (ys |> y)
- fmapM_ f = foldlM f' ()
- where f' _ x = f x >> return ()
-
instance Eq a => Eq (Seq a) where
xs == ys = length xs == length ys && toList xs == toList ys
showsPrec p (Seq x) = showsPrec p x
#else
instance Show a => Show (Seq a) where
- showsPrec _ xs = showChar '<' .
- flip (Prelude.foldr ($)) (Data.List.intersperse (showChar ',')
- (map shows (toList xs))) .
- showChar '>'
+ showsPrec p xs = showParen (p > 10) $
+ showString "fromList " . shows (toList xs)
#endif
instance Read a => Read (Seq a) where
- -- avoid lex, as < or > might be followed by symbol characters.
#ifdef __GLASGOW_HASKELL__
- readPrec = readP_to_Prec $ const $
- parens $
- between (litChar '<') (litChar '>') $
- liftM fromList $
- readPrec_to_P readPrec minPrec `sepBy` litChar ','
- where parens p = p +++ between (litChar '(') (litChar ')') (parens p)
- litChar c = skipSpaces >> char c
+ readPrec = parens $ prec 10 $ do
+ Ident "fromList" <- lexP
+ xs <- readPrec
+ return (fromList xs)
+
+ readListPrec = readListPrecDefault
#else
- readsPrec _ = readParen False $ \ r ->
- case dropWhile isSpace r of
- ('<':s) -> case dropWhile isSpace s of
- ('>':t) -> return (empty,t)
- _ -> readRest empty s
- _ -> []
- where readRest xs s = do
- (x,t) <- reads s
- let xs' = xs |> x
- case dropWhile isSpace t of
- ('>':u) -> return (xs',u)
- (',':u) -> readRest xs' u
- _ -> []
+ readsPrec p = readParen (p > 10) $ \ r -> do
+ ("fromList",s) <- lex r
+ (xs,t) <- reads s
+ return (fromList xs,t)
#endif
+instance Monoid (Seq a) where
+ mempty = empty
+ mappend = (><)
+
#include "Typeable.h"
INSTANCE_TYPEABLE1(Seq,seqTc,"Seq")
dataTypeOf _ = seqDataType
- dataCast1 = gcast1
+ dataCast1 f = gcast1 f
emptyConstr = mkConstr seqDataType "empty" [] Prefix
consConstr = mkConstr seqDataType "<|" [] Infix
size (Single x) = size x
size (Deep v _ _ _) = v
+instance Foldable FingerTree where
+ foldr _ z Empty = z
+ foldr f z (Single x) = x `f` z
+ foldr f z (Deep _ pr m sf) =
+ foldr f (foldr (flip (foldr f)) (foldr f z sf) m) pr
+
+ foldl _ z Empty = z
+ foldl f z (Single x) = z `f` x
+ foldl f z (Deep _ pr m sf) =
+ foldl f (foldl (foldl f) (foldl f z pr) m) sf
+
+ foldr1 _ Empty = error "foldr1: empty sequence"
+ foldr1 _ (Single x) = x
+ foldr1 f (Deep _ pr m sf) =
+ foldr f (foldr (flip (foldr f)) (foldr1 f sf) m) pr
+
+ foldl1 _ Empty = error "foldl1: empty sequence"
+ foldl1 _ (Single x) = x
+ foldl1 f (Deep _ pr m sf) =
+ foldl f (foldl (foldl f) (foldl1 f pr) m) sf
+
instance Functor FingerTree where
fmap _ Empty = Empty
fmap f (Single x) = Single (f x)
fmap f (Deep v pr m sf) =
Deep v (fmap f pr) (fmap (fmap f) m) (fmap f sf)
+instance Traversable FingerTree where
+ traverse _ Empty = pure Empty
+ traverse f (Single x) = Single <$> f x
+ traverse f (Deep v pr m sf) =
+ Deep v <$> traverse f pr <*> traverse (traverse f) m <*>
+ traverse f sf
+
{-# INLINE deep #-}
{-# SPECIALIZE deep :: Digit (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> FingerTree (Elem a) #-}
{-# SPECIALIZE deep :: Digit (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) -> FingerTree (Node a) #-}
deriving Show
#endif
+instance Foldable Digit where
+ foldr f z (One a) = a `f` z
+ foldr f z (Two a b) = a `f` (b `f` z)
+ foldr f z (Three a b c) = a `f` (b `f` (c `f` z))
+ foldr f z (Four a b c d) = a `f` (b `f` (c `f` (d `f` z)))
+
+ foldl f z (One a) = z `f` a
+ foldl f z (Two a b) = (z `f` a) `f` b
+ foldl f z (Three a b c) = ((z `f` a) `f` b) `f` c
+ foldl f z (Four a b c d) = (((z `f` a) `f` b) `f` c) `f` d
+
+ foldr1 f (One a) = a
+ foldr1 f (Two a b) = a `f` b
+ foldr1 f (Three a b c) = a `f` (b `f` c)
+ foldr1 f (Four a b c d) = a `f` (b `f` (c `f` d))
+
+ foldl1 f (One a) = a
+ foldl1 f (Two a b) = a `f` b
+ foldl1 f (Three a b c) = (a `f` b) `f` c
+ foldl1 f (Four a b c d) = ((a `f` b) `f` c) `f` d
+
instance Functor Digit where
- fmap f (One a) = One (f a)
- fmap f (Two a b) = Two (f a) (f b)
- fmap f (Three a b c) = Three (f a) (f b) (f c)
- fmap f (Four a b c d) = Four (f a) (f b) (f c) (f d)
+ fmap = fmapDefault
+
+instance Traversable Digit where
+ traverse f (One a) = One <$> f a
+ traverse f (Two a b) = Two <$> f a <*> f b
+ traverse f (Three a b c) = Three <$> f a <*> f b <*> f c
+ traverse f (Four a b c d) = Four <$> f a <*> f b <*> f c <*> f d
instance Sized a => Sized (Digit a) where
{-# SPECIALIZE instance Sized (Digit (Elem a)) #-}
{-# SPECIALIZE instance Sized (Digit (Node a)) #-}
- size xs = foldlDigit (\ i x -> i + size x) 0 xs
+ size xs = foldl (\ i x -> i + size x) 0 xs
{-# SPECIALIZE digitToTree :: Digit (Elem a) -> FingerTree (Elem a) #-}
{-# SPECIALIZE digitToTree :: Digit (Node a) -> FingerTree (Node a) #-}
deriving Show
#endif
-instance Functor (Node) where
- fmap f (Node2 v a b) = Node2 v (f a) (f b)
- fmap f (Node3 v a b c) = Node3 v (f a) (f b) (f c)
+instance Foldable Node where
+ foldr f z (Node2 _ a b) = a `f` (b `f` z)
+ foldr f z (Node3 _ a b c) = a `f` (b `f` (c `f` z))
+
+ foldl f z (Node2 _ a b) = (z `f` a) `f` b
+ foldl f z (Node3 _ a b c) = ((z `f` a) `f` b) `f` c
+
+instance Functor Node where
+ fmap = fmapDefault
+
+instance Traversable Node where
+ traverse f (Node2 v a b) = Node2 v <$> f a <*> f b
+ traverse f (Node3 v a b c) = Node3 v <$> f a <*> f b <*> f c
instance Sized (Node a) where
size (Node2 v _ _) = v
instance Functor Elem where
fmap f (Elem x) = Elem (f x)
+instance Foldable Elem where
+ foldr f z (Elem x) = f x z
+ foldl f z (Elem x) = f z x
+
+instance Traversable Elem where
+ traverse f (Elem x) = Elem <$> f x
+
#ifdef TESTING
instance (Show a) => Show (Elem a) where
showsPrec p (Elem x) = showsPrec p x
= EmptyL -- ^ empty sequence
| a :< Seq a -- ^ leftmost element and the rest of the sequence
#ifndef __HADDOCK__
- deriving (Eq, Show)
+# if __GLASGOW_HASKELL__
+ deriving (Eq, Ord, Show, Read, Data)
+# else
+ deriving (Eq, Ord, Show, Read)
+# endif
#else
instance Eq a => Eq (ViewL a)
+instance Ord a => Ord (ViewL a)
instance Show a => Show (ViewL a)
+instance Read a => Read (ViewL a)
+instance Data a => Data (ViewL a)
#endif
+INSTANCE_TYPEABLE1(ViewL,viewLTc,"ViewL")
instance Functor ViewL where
- fmap _ EmptyL = EmptyL
- fmap f (x :< xs) = f x :< fmap f xs
+ fmap = fmapDefault
+
+instance Foldable ViewL where
+ foldr f z EmptyL = z
+ foldr f z (x :< xs) = f x (foldr f z xs)
+
+ foldl f z EmptyL = z
+ foldl f z (x :< xs) = foldl f (f z x) xs
+
+ foldl1 f EmptyL = error "foldl1: empty view"
+ foldl1 f (x :< xs) = foldl f x xs
+
+instance Traversable ViewL where
+ traverse _ EmptyL = pure EmptyL
+ traverse f (x :< xs) = (:<) <$> f x <*> traverse f xs
-- | /O(1)/. Analyse the left end of a sequence.
viewl :: Seq a -> ViewL a
| Seq a :> a -- ^ the sequence minus the rightmost element,
-- and the rightmost element
#ifndef __HADDOCK__
- deriving (Eq, Show)
+# if __GLASGOW_HASKELL__
+ deriving (Eq, Ord, Show, Read, Data)
+# else
+ deriving (Eq, Ord, Show, Read)
+# endif
#else
instance Eq a => Eq (ViewR a)
+instance Ord a => Ord (ViewR a)
instance Show a => Show (ViewR a)
+instance Read a => Read (ViewR a)
+instance Data a => Data (ViewR a)
#endif
+INSTANCE_TYPEABLE1(ViewR,viewRTc,"ViewR")
+
instance Functor ViewR where
- fmap _ EmptyR = EmptyR
- fmap f (xs :> x) = fmap f xs :> f x
+ fmap = fmapDefault
+
+instance Foldable ViewR where
+ foldr f z EmptyR = z
+ foldr f z (xs :> x) = foldr f (f x z) xs
+
+ foldl f z EmptyR = z
+ foldl f z (xs :> x) = f (foldl f z xs) x
+
+ foldr1 f EmptyR = error "foldr1: empty view"
+ foldr1 f (xs :> x) = foldr f x xs
+
+instance Traversable ViewR where
+ traverse _ EmptyR = pure EmptyR
+ traverse f (xs :> x) = (:>) <$> traverse f xs <*> f x
-- | /O(1)/. Analyse the right end of a sequence.
viewr :: Seq a -> ViewR a
-- | /O(log(min(i,n-i)))/. The element at the specified position
index :: Seq a -> Int -> a
index (Seq xs) i
- | 0 <= i && i < size xs = case lookupTree (-i) xs of
+ | 0 <= i && i < size xs = case lookupTree i xs of
Place _ (Elem x) -> x
| otherwise = error "index out of bounds"
lookupTree _ Empty = error "lookupTree of empty tree"
lookupTree i (Single x) = Place i x
lookupTree i (Deep _ pr m sf)
- | vpr > 0 = lookupDigit i pr
- | vm > 0 = case lookupTree vpr m of
+ | i < spr = lookupDigit i pr
+ | i < spm = case lookupTree (i - spr) m of
Place i' xs -> lookupNode i' xs
- | otherwise = lookupDigit vm sf
- where vpr = i + size pr
- vm = vpr + size m
+ | otherwise = lookupDigit (i - spm) sf
+ where spr = size pr
+ spm = spr + size m
{-# SPECIALIZE lookupNode :: Int -> Node (Elem a) -> Place (Elem a) #-}
{-# SPECIALIZE lookupNode :: Int -> Node (Node a) -> Place (Node a) #-}
lookupNode :: Sized a => Int -> Node a -> Place a
lookupNode i (Node2 _ a b)
- | va > 0 = Place i a
- | otherwise = Place va b
- where va = i + size a
+ | i < sa = Place i a
+ | otherwise = Place (i - sa) b
+ where sa = size a
lookupNode i (Node3 _ a b c)
- | va > 0 = Place i a
- | vab > 0 = Place va b
- | otherwise = Place vab c
- where va = i + size a
- vab = va + size b
+ | i < sa = Place i a
+ | i < sab = Place (i - sa) b
+ | otherwise = Place (i - sab) c
+ where sa = size a
+ sab = sa + size b
{-# SPECIALIZE lookupDigit :: Int -> Digit (Elem a) -> Place (Elem a) #-}
{-# SPECIALIZE lookupDigit :: Int -> Digit (Node a) -> Place (Node a) #-}
lookupDigit :: Sized a => Int -> Digit a -> Place a
lookupDigit i (One a) = Place i a
lookupDigit i (Two a b)
- | va > 0 = Place i a
- | otherwise = Place va b
- where va = i + size a
+ | i < sa = Place i a
+ | otherwise = Place (i - sa) b
+ where sa = size a
lookupDigit i (Three a b c)
- | va > 0 = Place i a
- | vab > 0 = Place va b
- | otherwise = Place vab c
- where va = i + size a
- vab = va + size b
+ | i < sa = Place i a
+ | i < sab = Place (i - sa) b
+ | otherwise = Place (i - sab) c
+ where sa = size a
+ sab = sa + size b
lookupDigit i (Four a b c d)
- | va > 0 = Place i a
- | vab > 0 = Place va b
- | vabc > 0 = Place vab c
- | otherwise = Place vabc d
- where va = i + size a
- vab = va + size b
- vabc = vab + size c
+ | i < sa = Place i a
+ | i < sab = Place (i - sa) b
+ | i < sabc = Place (i - sab) c
+ | otherwise = Place (i - sabc) d
+ where sa = size a
+ sab = sa + size b
+ sabc = sab + size c
-- | /O(log(min(i,n-i)))/. Replace the element at the specified position
update :: Int -> a -> Seq a -> Seq a
-- | /O(log(min(i,n-i)))/. Update the element at the specified position
adjust :: (a -> a) -> Int -> Seq a -> Seq a
adjust f i (Seq xs)
- | 0 <= i && i < size xs = Seq (adjustTree (const (fmap f)) (-i) xs)
+ | 0 <= i && i < size xs = Seq (adjustTree (const (fmap f)) i xs)
| otherwise = Seq xs
{-# SPECIALIZE adjustTree :: (Int -> Elem a -> Elem a) -> Int -> FingerTree (Elem a) -> FingerTree (Elem a) #-}
adjustTree _ _ Empty = error "adjustTree of empty tree"
adjustTree f i (Single x) = Single (f i x)
adjustTree f i (Deep s pr m sf)
- | vpr > 0 = Deep s (adjustDigit f i pr) m sf
- | vm > 0 = Deep s pr (adjustTree (adjustNode f) vpr m) sf
- | otherwise = Deep s pr m (adjustDigit f vm sf)
- where vpr = i + size pr
- vm = vpr + size m
+ | i < spr = Deep s (adjustDigit f i pr) m sf
+ | i < spm = Deep s pr (adjustTree (adjustNode f) (i - spr) m) sf
+ | otherwise = Deep s pr m (adjustDigit f (i - spm) sf)
+ where spr = size pr
+ spm = spr + size m
{-# SPECIALIZE adjustNode :: (Int -> Elem a -> Elem a) -> Int -> Node (Elem a) -> Node (Elem a) #-}
{-# SPECIALIZE adjustNode :: (Int -> Node a -> Node a) -> Int -> Node (Node a) -> Node (Node a) #-}
adjustNode :: Sized a => (Int -> a -> a) -> Int -> Node a -> Node a
adjustNode f i (Node2 s a b)
- | va > 0 = Node2 s (f i a) b
- | otherwise = Node2 s a (f va b)
- where va = i + size a
+ | i < sa = Node2 s (f i a) b
+ | otherwise = Node2 s a (f (i - sa) b)
+ where sa = size a
adjustNode f i (Node3 s a b c)
- | va > 0 = Node3 s (f i a) b c
- | vab > 0 = Node3 s a (f va b) c
- | otherwise = Node3 s a b (f vab c)
- where va = i + size a
- vab = va + size b
+ | i < sa = Node3 s (f i a) b c
+ | i < sab = Node3 s a (f (i - sa) b) c
+ | otherwise = Node3 s a b (f (i - sab) c)
+ where sa = size a
+ sab = sa + size b
{-# SPECIALIZE adjustDigit :: (Int -> Elem a -> Elem a) -> Int -> Digit (Elem a) -> Digit (Elem a) #-}
{-# SPECIALIZE adjustDigit :: (Int -> Node a -> Node a) -> Int -> Digit (Node a) -> Digit (Node a) #-}
adjustDigit :: Sized a => (Int -> a -> a) -> Int -> Digit a -> Digit a
adjustDigit f i (One a) = One (f i a)
adjustDigit f i (Two a b)
- | va > 0 = Two (f i a) b
- | otherwise = Two a (f va b)
- where va = i + size a
+ | i < sa = Two (f i a) b
+ | otherwise = Two a (f (i - sa) b)
+ where sa = size a
adjustDigit f i (Three a b c)
- | va > 0 = Three (f i a) b c
- | vab > 0 = Three a (f va b) c
- | otherwise = Three a b (f vab c)
- where va = i + size a
- vab = va + size b
+ | i < sa = Three (f i a) b c
+ | i < sab = Three a (f (i - sa) b) c
+ | otherwise = Three a b (f (i - sab) c)
+ where sa = size a
+ sab = sa + size b
adjustDigit f i (Four a b c d)
- | va > 0 = Four (f i a) b c d
- | vab > 0 = Four a (f va b) c d
- | vabc > 0 = Four a b (f vab c) d
- | otherwise = Four a b c (f vabc d)
- where va = i + size a
- vab = va + size b
- vabc = vab + size c
+ | i < sa = Four (f i a) b c d
+ | i < sab = Four a (f (i - sa) b) c d
+ | i < sabc = Four a b (f (i - sab) c) d
+ | otherwise = Four a b c (f (i- sabc) d)
+ where sa = size a
+ sab = sa + size b
+ sabc = sab + size c
-- Splitting
split i xs
| size xs > i = (l, consTree x r)
| otherwise = (xs, Empty)
- where Split l x r = splitTree (-i) xs
+ where Split l x r = splitTree i xs
data Split t a = Split t a t
#if TESTING
splitTree _ Empty = error "splitTree of empty tree"
splitTree i (Single x) = i `seq` Split Empty x Empty
splitTree i (Deep _ pr m sf)
- | vpr > 0 = case splitDigit i pr of
+ | i < spr = case splitDigit i pr of
Split l x r -> Split (maybe Empty digitToTree l) x (deepL r m sf)
- | vm > 0 = case splitTree vpr m of
- Split ml xs mr -> case splitNode (vpr + size ml) xs of
+ | i < spm = case splitTree im m of
+ Split ml xs mr -> case splitNode (im - size ml) xs of
Split l x r -> Split (deepR pr ml l) x (deepL r mr sf)
- | otherwise = case splitDigit vm sf of
+ | otherwise = case splitDigit (i - spm) sf of
Split l x r -> Split (deepR pr m l) x (maybe Empty digitToTree r)
- where vpr = i + size pr
- vm = vpr + size m
+ where spr = size pr
+ spm = spr + size m
+ im = i - spr
{-# SPECIALIZE deepL :: Maybe (Digit (Elem a)) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> FingerTree (Elem a) #-}
{-# SPECIALIZE deepL :: Maybe (Digit (Node a)) -> FingerTree (Node (Node a)) -> Digit (Node a) -> FingerTree (Node a) #-}
{-# SPECIALIZE splitNode :: Int -> Node (Node a) -> Split (Maybe (Digit (Node a))) (Node a) #-}
splitNode :: Sized a => Int -> Node a -> Split (Maybe (Digit a)) a
splitNode i (Node2 _ a b)
- | va > 0 = Split Nothing a (Just (One b))
+ | i < sa = Split Nothing a (Just (One b))
| otherwise = Split (Just (One a)) b Nothing
- where va = i + size a
+ where sa = size a
splitNode i (Node3 _ a b c)
- | va > 0 = Split Nothing a (Just (Two b c))
- | vab > 0 = Split (Just (One a)) b (Just (One c))
+ | i < sa = Split Nothing a (Just (Two b c))
+ | i < sab = Split (Just (One a)) b (Just (One c))
| otherwise = Split (Just (Two a b)) c Nothing
- where va = i + size a
- vab = va + size b
+ where sa = size a
+ sab = sa + size b
{-# SPECIALIZE splitDigit :: Int -> Digit (Elem a) -> Split (Maybe (Digit (Elem a))) (Elem a) #-}
{-# SPECIALIZE splitDigit :: Int -> Digit (Node a) -> Split (Maybe (Digit (Node a))) (Node a) #-}
splitDigit :: Sized a => Int -> Digit a -> Split (Maybe (Digit a)) a
splitDigit i (One a) = i `seq` Split Nothing a Nothing
splitDigit i (Two a b)
- | va > 0 = Split Nothing a (Just (One b))
+ | i < sa = Split Nothing a (Just (One b))
| otherwise = Split (Just (One a)) b Nothing
- where va = i + size a
+ where sa = size a
splitDigit i (Three a b c)
- | va > 0 = Split Nothing a (Just (Two b c))
- | vab > 0 = Split (Just (One a)) b (Just (One c))
+ | i < sa = Split Nothing a (Just (Two b c))
+ | i < sab = Split (Just (One a)) b (Just (One c))
| otherwise = Split (Just (Two a b)) c Nothing
- where va = i + size a
- vab = va + size b
+ where sa = size a
+ sab = sa + size b
splitDigit i (Four a b c d)
- | va > 0 = Split Nothing a (Just (Three b c d))
- | vab > 0 = Split (Just (One a)) b (Just (Two c d))
- | vabc > 0 = Split (Just (Two a b)) c (Just (One d))
+ | i < sa = Split Nothing a (Just (Three b c d))
+ | i < sab = Split (Just (One a)) b (Just (Two c d))
+ | i < sabc = Split (Just (Two a b)) c (Just (One d))
| otherwise = Split (Just (Three a b c)) d Nothing
- where va = i + size a
- vab = va + size b
- vabc = vab + size c
+ where sa = size a
+ sab = sa + size b
+ sabc = sab + size c
------------------------------------------------------------------------
-- Lists
------------------------------------------------------------------------
-- | /O(n)/. Create a sequence from a finite list of elements.
+-- There is a function 'toList' in the opposite direction for all
+-- instances of the 'Foldable' class, including 'Seq'.
fromList :: [a] -> Seq a
fromList = Data.List.foldl' (|>) empty
--- | /O(n)/. List of elements of the sequence.
-toList :: Seq a -> [a]
-#ifdef __GLASGOW_HASKELL__
-{-# INLINE toList #-}
-toList xs = build (\ c n -> foldr c n xs)
-#else
-toList = foldr (:) []
-#endif
-
-------------------------------------------------------------------------
--- Folds
-------------------------------------------------------------------------
-
--- | /O(n*t)/. Fold over the elements of a sequence,
--- associating to the right.
-foldr :: (a -> b -> b) -> b -> Seq a -> b
-foldr f z (Seq xs) = foldrTree f' z xs
- where f' (Elem x) y = f x y
-
-foldrTree :: (a -> b -> b) -> b -> FingerTree a -> b
-foldrTree _ z Empty = z
-foldrTree f z (Single x) = x `f` z
-foldrTree f z (Deep _ pr m sf) =
- foldrDigit f (foldrTree (flip (foldrNode f)) (foldrDigit f z sf) m) pr
-
-foldrDigit :: (a -> b -> b) -> b -> Digit a -> b
-foldrDigit f z (One a) = a `f` z
-foldrDigit f z (Two a b) = a `f` (b `f` z)
-foldrDigit f z (Three a b c) = a `f` (b `f` (c `f` z))
-foldrDigit f z (Four a b c d) = a `f` (b `f` (c `f` (d `f` z)))
-
-foldrNode :: (a -> b -> b) -> b -> Node a -> b
-foldrNode f z (Node2 _ a b) = a `f` (b `f` z)
-foldrNode f z (Node3 _ a b c) = a `f` (b `f` (c `f` z))
-
--- | /O(n*t)/. A variant of 'foldr' that has no base case,
--- and thus may only be applied to non-empty sequences.
-foldr1 :: (a -> a -> a) -> Seq a -> a
-foldr1 f (Seq xs) = getElem (foldr1Tree f' xs)
- where f' (Elem x) (Elem y) = Elem (f x y)
-
-foldr1Tree :: (a -> a -> a) -> FingerTree a -> a
-foldr1Tree _ Empty = error "foldr1: empty sequence"
-foldr1Tree _ (Single x) = x
-foldr1Tree f (Deep _ pr m sf) =
- foldrDigit f (foldrTree (flip (foldrNode f)) (foldr1Digit f sf) m) pr
-
-foldr1Digit :: (a -> a -> a) -> Digit a -> a
-foldr1Digit f (One a) = a
-foldr1Digit f (Two a b) = a `f` b
-foldr1Digit f (Three a b c) = a `f` (b `f` c)
-foldr1Digit f (Four a b c d) = a `f` (b `f` (c `f` d))
-
--- | /O(n*t)/. Fold over the elements of a sequence,
--- associating to the left.
-foldl :: (a -> b -> a) -> a -> Seq b -> a
-foldl f z (Seq xs) = foldlTree f' z xs
- where f' x (Elem y) = f x y
-
-foldlTree :: (a -> b -> a) -> a -> FingerTree b -> a
-foldlTree _ z Empty = z
-foldlTree f z (Single x) = z `f` x
-foldlTree f z (Deep _ pr m sf) =
- foldlDigit f (foldlTree (foldlNode f) (foldlDigit f z pr) m) sf
-
-foldlDigit :: (a -> b -> a) -> a -> Digit b -> a
-foldlDigit f z (One a) = z `f` a
-foldlDigit f z (Two a b) = (z `f` a) `f` b
-foldlDigit f z (Three a b c) = ((z `f` a) `f` b) `f` c
-foldlDigit f z (Four a b c d) = (((z `f` a) `f` b) `f` c) `f` d
-
-foldlNode :: (a -> b -> a) -> a -> Node b -> a
-foldlNode f z (Node2 _ a b) = (z `f` a) `f` b
-foldlNode f z (Node3 _ a b c) = ((z `f` a) `f` b) `f` c
-
--- | /O(n*t)/. A variant of 'foldl' that has no base case,
--- and thus may only be applied to non-empty sequences.
-foldl1 :: (a -> a -> a) -> Seq a -> a
-foldl1 f (Seq xs) = getElem (foldl1Tree f' xs)
- where f' (Elem x) (Elem y) = Elem (f x y)
-
-foldl1Tree :: (a -> a -> a) -> FingerTree a -> a
-foldl1Tree _ Empty = error "foldl1: empty sequence"
-foldl1Tree _ (Single x) = x
-foldl1Tree f (Deep _ pr m sf) =
- foldlDigit f (foldlTree (foldlNode f) (foldl1Digit f pr) m) sf
-
-foldl1Digit :: (a -> a -> a) -> Digit a -> a
-foldl1Digit f (One a) = a
-foldl1Digit f (Two a b) = a `f` b
-foldl1Digit f (Three a b c) = (a `f` b) `f` c
-foldl1Digit f (Four a b c d) = ((a `f` b) `f` c) `f` d
-
-------------------------------------------------------------------------
--- Derived folds
-------------------------------------------------------------------------
-
--- | /O(n*t)/. Fold over the elements of a sequence,
--- associating to the right, but strictly.
-foldr' :: (a -> b -> b) -> b -> Seq a -> b
-foldr' f z xs = foldl f' id xs z
- where f' k x z = k $! f x z
-
--- | /O(n*t)/. Monadic fold over the elements of a sequence,
--- associating to the right, i.e. from right to left.
-foldrM :: Monad m => (a -> b -> m b) -> b -> Seq a -> m b
-foldrM f z xs = foldl f' return xs z
- where f' k x z = f x z >>= k
-
--- | /O(n*t)/. Fold over the elements of a sequence,
--- associating to the left, but strictly.
-foldl' :: (a -> b -> a) -> a -> Seq b -> a
-foldl' f z xs = foldr f' id xs z
- where f' x k z = k $! f z x
-
--- | /O(n*t)/. Monadic fold over the elements of a sequence,
--- associating to the left, i.e. from left to right.
-foldlM :: Monad m => (a -> b -> m a) -> a -> Seq b -> m a
-foldlM f z xs = foldr f' return xs z
- where f' x k z = f z x >>= k
-
------------------------------------------------------------------------
-- Reverse
------------------------------------------------------------------------
projects / haskell-directory.git / blobdiff