-{-# OPTIONS -cpp #-}
+{-# OPTIONS -cpp -fglasgow-exts #-}
-----------------------------------------------------------------------------
-- |
-- Module : Data.Sequence
--
-- * Ralf Hinze and Ross Paterson,
-- \"Finger trees: a simple general-purpose data structure\",
--- submitted to /Journal of Functional Programming/.
+-- to appear in /Journal of Functional Programming/.
-- <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
-- ** Queries
null, -- :: Seq a -> Bool
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 Data.FunctorM
+import qualified Data.List (foldl')
+import Control.Applicative (Applicative(..))
+import Control.Monad (MonadPlus(..))
+import Data.Monoid (Monoid(..))
+import Data.Foldable
+import Data.Traversable
import Data.Typeable
-#if TESTING
-import Control.Monad (liftM, liftM2, liftM3, liftM4)
-import Test.QuickCheck
-#endif
-
-#if __GLASGOW_HASKELL__
+#ifdef __GLASGOW_HASKELL__
+import Text.Read (Lexeme(Ident), lexP, parens, prec,
+ readPrec, readListPrec, readListPrecDefault)
import Data.Generics.Basics (Data(..), Fixity(..),
constrIndex, mkConstr, mkDataType)
#endif
+#if TESTING
+import Control.Monad (liftM, liftM3, liftM4)
+import Test.QuickCheck
+#endif
+
infixr 5 `consTree`
infixl 5 `snocTree`
class Sized a where
size :: a -> Int
-------------------------------------------------------------------------
--- Random access sequences
-------------------------------------------------------------------------
-
-- | General-purpose finite sequences.
newtype Seq a = Seq (FingerTree (Elem a))
instance Functor Seq where
- fmap f (Seq xs) = Seq (fmap (fmap f) xs)
+ fmap = fmapDefault
+
+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 <$> traverse (traverse f) xs
+
+instance Monad Seq where
+ return = singleton
+ xs >>= f = foldl' add empty xs
+ where add ys x = ys >< f x
+
+instance MonadPlus Seq where
+ mzero = empty
+ mplus = (><)
instance Eq a => Eq (Seq a) where
xs == ys = length xs == length ys && toList xs == toList ys
showsPrec p (Seq x) = showsPrec p x
#else
instance Show a => Show (Seq a) where
- showsPrec _ xs = showChar '<' .
- flip (Prelude.foldr ($)) (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
+#ifdef __GLASGOW_HASKELL__
+ readPrec = parens $ prec 10 $ do
+ Ident "fromList" <- lexP
+ xs <- readPrec
+ return (fromList xs)
+
+ readListPrec = readListPrecDefault
+#else
+ readsPrec p = readParen (p > 10) $ \ r -> do
+ ("fromList",s) <- lex r
+ (xs,t) <- reads s
+ return (fromList xs,t)
#endif
-instance FunctorM Seq where
- fmapM f = foldlM f' empty
- where f' ys x = do
- y <- f x
- return $! (ys |> y)
- fmapM_ f = foldlM f' ()
- where f' _ x = f x >> return ()
+instance Monoid (Seq a) where
+ mempty = empty
+ mappend = (><)
#include "Typeable.h"
INSTANCE_TYPEABLE1(Seq,seqTc,"Seq")
dataTypeOf _ = seqDataType
- dataCast1 = gcast1
+ dataCast1 f = gcast1 f
emptyConstr = mkConstr seqDataType "empty" [] Prefix
consConstr = mkConstr seqDataType "<|" [] Infix
#endif
instance Sized a => Sized (FingerTree a) where
+ {-# SPECIALIZE instance Sized (FingerTree (Elem a)) #-}
+ {-# SPECIALIZE instance Sized (FingerTree (Node a)) #-}
size Empty = 0
size (Single x) = size x
size (Deep v _ _ _) = v
-instance Functor FingerTree where
- fmap _ Empty = Empty
- fmap f (Single x) = Single (f x)
- fmap f (Deep v pr m sf) =
- Deep v (fmap f pr) (fmap (fmap f) m) (fmap f sf)
+instance Foldable FingerTree where
+ foldr _ z Empty = z
+ foldr f z (Single x) = x `f` z
+ foldr f z (Deep _ pr m sf) =
+ foldr f (foldr (flip (foldr f)) (foldr f z sf) m) pr
+
+ foldl _ z Empty = z
+ foldl f z (Single x) = z `f` x
+ foldl f z (Deep _ pr m sf) =
+ foldl f (foldl (foldl f) (foldl f z pr) m) sf
+
+ foldr1 _ Empty = error "foldr1: empty sequence"
+ foldr1 _ (Single x) = x
+ foldr1 f (Deep _ pr m sf) =
+ foldr f (foldr (flip (foldr f)) (foldr1 f sf) m) pr
+
+ foldl1 _ Empty = error "foldl1: empty sequence"
+ foldl1 _ (Single x) = x
+ foldl1 f (Deep _ pr m sf) =
+ foldl f (foldl (foldl f) (foldl1 f pr) m) sf
+
+instance Traversable FingerTree where
+ traverse _ Empty = pure Empty
+ traverse f (Single x) = Single <$> f x
+ traverse f (Deep v pr m sf) =
+ Deep v <$> traverse f pr <*> traverse (traverse f) m <*>
+ traverse f sf
{-# INLINE deep #-}
{-# SPECIALIZE deep :: Digit (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> FingerTree (Elem a) #-}
deriving Show
#endif
-instance Functor Digit where
- fmap f (One a) = One (f a)
- fmap f (Two a b) = Two (f a) (f b)
- fmap f (Three a b c) = Three (f a) (f b) (f c)
- fmap f (Four a b c d) = Four (f a) (f b) (f c) (f d)
+instance Foldable Digit where
+ foldr f z (One a) = a `f` z
+ foldr f z (Two a b) = a `f` (b `f` z)
+ foldr f z (Three a b c) = a `f` (b `f` (c `f` z))
+ foldr f z (Four a b c d) = a `f` (b `f` (c `f` (d `f` z)))
+
+ foldl f z (One a) = z `f` a
+ foldl f z (Two a b) = (z `f` a) `f` b
+ foldl f z (Three a b c) = ((z `f` a) `f` b) `f` c
+ foldl f z (Four a b c d) = (((z `f` a) `f` b) `f` c) `f` d
+
+ foldr1 f (One a) = a
+ foldr1 f (Two a b) = a `f` b
+ foldr1 f (Three a b c) = a `f` (b `f` c)
+ foldr1 f (Four a b c d) = a `f` (b `f` (c `f` d))
+
+ foldl1 f (One a) = a
+ foldl1 f (Two a b) = a `f` b
+ foldl1 f (Three a b c) = (a `f` b) `f` c
+ foldl1 f (Four a b c d) = ((a `f` b) `f` c) `f` d
+
+instance Traversable Digit where
+ traverse f (One a) = One <$> 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 <$> f a <*> f b <*> f c <*> f d
instance Sized a => Sized (Digit a) where
- size xs = foldlDigit (\ i x -> i + size x) 0 xs
+ {-# SPECIALIZE instance Sized (Digit (Elem a)) #-}
+ {-# SPECIALIZE instance Sized (Digit (Node a)) #-}
+ size xs = foldl (\ i x -> i + size x) 0 xs
{-# SPECIALIZE digitToTree :: Digit (Elem a) -> FingerTree (Elem a) #-}
{-# SPECIALIZE digitToTree :: Digit (Node a) -> FingerTree (Node a) #-}
deriving Show
#endif
-instance Functor (Node) where
- fmap f (Node2 v a b) = Node2 v (f a) (f b)
- fmap f (Node3 v a b c) = Node3 v (f a) (f b) (f c)
+instance Foldable Node where
+ foldr f z (Node2 _ a b) = a `f` (b `f` z)
+ foldr f z (Node3 _ a b c) = a `f` (b `f` (c `f` z))
+
+ foldl f z (Node2 _ a b) = (z `f` a) `f` b
+ foldl f z (Node3 _ a b c) = ((z `f` a) `f` b) `f` c
+
+instance Traversable Node where
+ traverse f (Node2 v a b) = Node2 v <$> 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
fromList :: [a] -> Seq a
fromList = Data.List.foldl' (|>) empty
--- | /O(n)/. List of elements of the sequence.
-toList :: Seq a -> [a]
-toList = foldr (:) []
-
-------------------------------------------------------------------------
--- 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 / ghc-base.git / blobdiff