{-# LANGUAGE PatternGuards #-} ----------------------------------------------------------------------------- -- | -- Module : Data.Stream.Infinite -- Copyright : (C) 2011 Edward Kmett, -- (C) 2007-2010 Wouter Swierstra, Bas van Dijk -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com> -- Stability : provisional -- Portability : portable (Haskell 2010) -- ---------------------------------------------------------------------------- module Data.Stream.Infinite ( -- * The type of streams Stream(..) -- * Basic functions , head -- :: Stream a -> a , tail -- :: Stream a -> Stream a , inits -- :: Stream a -> Stream [a] , tails -- :: Stream a -> Stream (Stream a) -- * Stream transformations , map -- :: (a -> b) -> Stream a -> Stream b , intersperse -- :: a -> Stream a -> Stream , interleave -- :: Stream a -> Stream a -> Stream a , scanl -- :: (b -> a -> b) -> b -> Stream a -> Stream b , scanl' -- :: (b -> a -> b) -> b -> Stream a -> Stream b , scanl1 -- :: (a -> a -> a) -> Stream a -> Stream a , scanl1' -- :: (a -> a -> a) -> Stream a -> Stream a , transpose -- :: Stream (Stream a) -> Stream (Stream a) -- * Building streams , iterate -- :: (a -> a) -> a -> Stream a , repeat -- :: a -> Stream a , cycle -- :: NonEmpty a -> Stream a , unfold -- :: (a -> (b, a)) -> a -> Stream b -- * Extracting sublists , take -- :: Int -> Stream a -> [a] , drop -- :: Int -> Stream a -> Stream a , splitAt -- :: Int -> Stream a -> ([a],Stream a) , takeWhile -- :: (a -> Bool) -> Stream a -> [a] , dropWhile -- :: (a -> Bool) -> Stream a -> Stream a , span -- :: (a -> Bool) -> Stream a -> ([a], Stream a) , break -- :: (a -> Bool) -> Stream a -> ([a], Stream a) , filter -- :: (a -> Bool) -> Stream a -> Stream a , partition -- :: (a -> Bool) -> Stream a -> (Stream a, Stream a) , group -- :: (a -> Bool) -> Stream a -> Stream (NonEmpty a) -- * Sublist predicates , isPrefixOf -- :: [a] -> Stream a -> Bool -- * Indexing streams , (!!) -- :: Int -> Stream a -> a , elemIndex -- :: Eq a => a -> Stream a -> Int , elemIndices -- :: Eq a => a -> Stream a -> Stream Int , findIndex -- :: (a -> Bool) -> Stream a -> Int , findIndices -- :: (a -> Bool) -> Stream a -> Stream Int -- * Zipping and unzipping streams , zip -- :: Stream a -> Stream b -> Stream (a, b) , zipWith -- :: (a -> b -> c) -> Stream a -> Stream b -> Stream c , unzip -- :: Functor f => f (a, b) -> (f a, f b) -- * Functions on streams of characters , words -- :: Stream Char -> Stream String , unwords -- :: Stream String -> Stream Char , lines -- :: Stream Char -> Stream String , unlines -- :: Stream String -> Stream Char -- * Converting to and from an infinite list , fromList -- :: [a] -> Stream a ) where import Prelude hiding ( head, tail, map, scanr, scanr1, scanl, scanl1 , iterate, take, drop, takeWhile , dropWhile, repeat, cycle, filter , (!!), zip, unzip, zipWith, words , unwords, lines, unlines, break, span , splitAt, foldr ) import Control.Applicative import Control.Comonad import Control.Comonad.Apply import Data.Char (isSpace) import Data.Data import Data.Functor.Apply import Data.Monoid import Data.Semigroup import Data.Foldable import Data.Traversable import Data.Distributive import Data.Semigroup.Traversable import Data.Semigroup.Foldable import Data.Stream.NonEmpty (NonEmpty(..)) data Stream a = a :> Stream a deriving ( Show #ifdef LANGUAGE_DeriveDataTypeable , Data, Typeable #endif ) infixr 5 :> -- | Map a pure function over a stream map :: (a -> b) -> Stream a -> Stream b map f (a :> as) = f a :> map f as instance Functor Stream where fmap = map b <$ _ = repeat b instance Distributive Stream where distribute w = fmap head w :> distribute (fmap tail w) -- | Extract the first element of the sequence. head :: Stream a -> a head (a :> _) = a {-# INLINE head #-} -- | Extract the sequence following the head of the stream. tail :: Stream a -> Stream a tail (_ :> as) = as {-# INLINE tail #-} -- | The 'tails' function takes a stream @xs@ and returns all the -- suffixes of @xs@. tails :: Stream a -> Stream (Stream a) tails w = w :> tails (tail w) instance Comonad Stream where extract = head duplicate = tails extend f w = f w :> extend f (tail w) instance FunctorApply Stream where (f :> fs) <.> (a :> as) = f a :> (fs <.> as) as <. _ = as _ .> bs = bs instance ComonadApply Stream -- | 'repeat' @x@ returns a constant stream, where all elements are -- equal to @x@. repeat :: a -> Stream a repeat a = as where as = a :> as instance Applicative Stream where pure = repeat (<*>) = (<.>) (<* ) = (<. ) ( *>) = ( .>) instance Foldable Stream where fold (m :> ms) = m `mappend` fold ms foldMap f (a :> as) = f a `mappend` foldMap f as foldr f0 _ = go f0 where go f (a :> as) = f a (go f as) instance Traversable Stream where traverse f ~(a :> as) = (:>) <$> f a <*> traverse f as instance Foldable1 Stream instance Traversable1 Stream where traverse1 f ~(a :> as) = (:>) <$> f a <.> traverse1 f as sequence1 ~(a :> as) = (:>) <$> a <.> sequence1 as -- | The unfold function is similar to the unfold for lists. Note -- there is no base case: all streams must be infinite. unfold :: (a -> (b, a)) -> a -> Stream b unfold f c | (x, d) <- f c = x :> unfold f d instance Monad Stream where return = repeat m >>= f = unfold (\(bs :> bss) -> (head bs, tail <$> bss)) (fmap f m) _ >> bs = bs -- | Interleave two Streams @xs@ and @ys@, alternating elements -- from each list. -- -- > [x1,x2,...] `interleave` [y1,y2,...] == [x1,y1,x2,y2,...] interleave :: Stream a -> Stream a -> Stream a interleave ~(x :> xs) ys = x :> interleave ys xs instance Semigroup (Stream a) where (<>) = interleave -- | The 'inits' function takes a stream @xs@ and returns all the -- finite prefixes of @xs@. -- -- Note that this 'inits' is lazier then @Data.List.inits@: -- -- > inits _|_ = [] ::: _|_ -- -- while for @Data.List.inits@: -- -- > inits _|_ = _|_ inits :: Stream a -> Stream [a] inits xs = [] :> ((head xs :) <$> inits (tail xs)) -- | @'intersperse' y xs@ creates an alternating stream of -- elements from @xs@ and @y@. intersperse :: a -> Stream a -> Stream a intersperse y ~(x :> xs) = x :> y :> intersperse y xs -- | 'scanl' yields a stream of successive reduced values from: -- -- > scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...] scanl :: (a -> b -> a) -> a -> Stream b -> Stream a scanl f z ~(x :> xs) = z :> scanl f (f z x) xs -- | 'scanl' yields a stream of successive reduced values from: -- -- > scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...] scanl' :: (a -> b -> a) -> a -> Stream b -> Stream a scanl' f z ~(x :> xs) = z :> (scanl' f $! f z x) xs -- | 'scanl1' is a variant of 'scanl' that has no starting value argument: -- -- > scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...] scanl1 :: (a -> a -> a) -> Stream a -> Stream a scanl1 f ~(x :> xs) = scanl f x xs -- | @scanl1'@ is a strict 'scanl' that has no starting value. scanl1' :: (a -> a -> a) -> Stream a -> Stream a scanl1' f ~(x :> xs) = scanl' f x xs -- | 'transpose' computes the transposition of a stream of streams. transpose :: Stream (Stream a) -> Stream (Stream a) transpose ~((x :> xs) :> yss) = (x :> (head <$> yss)) :> transpose (xs :> (tail <$> yss)) -- | @'iterate' f x@ produces the infinite sequence -- of repeated applications of @f@ to @x@. -- -- > iterate f x = [x, f x, f (f x), ..] iterate :: (a -> a) -> a -> Stream a iterate f x = x :> iterate f (f x) -- | @'cycle' xs@ returns the infinite repetition of @xs@: -- -- > cycle [1,2,3] = Cons 1 (Cons 2 (Cons 3 (Cons 1 (Cons 2 ... cycle :: NonEmpty a -> Stream a cycle xs = ys where ys = foldr (:>) ys xs -- | @'take' n xs@ returns the first @n@ elements of @xs@. -- -- /Beware/: passing a negative integer as the first argument will -- cause an error. take :: Int -> Stream a -> [a] take n ~(x :> xs) | n == 0 = [] | n > 0 = x : take (n - 1) xs | otherwise = error "Stream.take: negative argument" -- | @'drop' n xs@ drops the first @n@ elements off the front of -- the sequence @xs@. -- -- /Beware/: passing a negative integer as the first argument will -- cause an error. drop :: Int -> Stream a -> Stream a drop n xs | n == 0 = xs | n > 0 = drop (n - 1) (tail xs) | otherwise = error "Stream.drop: negative argument" -- | @'splitAt' n xs@ returns a pair consisting of the prefix of -- @xs@ of length @n@ and the remaining stream immediately following -- this prefix. -- -- /Beware/: passing a negative integer as the first argument will -- cause an error. splitAt :: Int -> Stream a -> ([a],Stream a) splitAt n xs | n == 0 = ([],xs) | n > 0, (prefix, rest) <- splitAt (n - 1) (tail xs) = (head xs : prefix, rest) | otherwise = error "Stream.splitAt: negative argument" -- | @'takeWhile' p xs@ returns the longest prefix of the stream -- @xs@ for which the predicate @p@ holds. takeWhile :: (a -> Bool) -> Stream a -> [a] takeWhile p (x :> xs) | p x = x : takeWhile p xs | otherwise = [] -- | @'dropWhile' p xs@ returns the suffix remaining after -- @'takeWhile' p xs@. -- -- /Beware/: this function may diverge if every element of @xs@ -- satisfies @p@, e.g. @dropWhile even (repeat 0)@ will loop. dropWhile :: (a -> Bool) -> Stream a -> Stream a dropWhile p ~(x :> xs) | p x = dropWhile p xs | otherwise = x :> xs -- | @'span' p xs@ returns the longest prefix of @xs@ that satisfies -- @p@, together with the remainder of the stream. span :: (a -> Bool) -> Stream a -> ([a], Stream a) span p xxs@(x :> xs) | p x, (ts, fs) <- span p xs = (x : ts, fs) | otherwise = ([], xxs) -- | The 'break' @p@ function is equivalent to 'span' @not . p@. break :: (a -> Bool) -> Stream a -> ([a], Stream a) break p = span (not . p) -- | @'filter' p xs@, removes any elements from @xs@ that do not satisfy @p@. -- -- /Beware/: this function may diverge if there is no element of -- @xs@ that satisfies @p@, e.g. @filter odd (repeat 0)@ will loop. filter :: (a -> Bool) -> Stream a -> Stream a filter p ~(x :> xs) | p x = x :> filter p xs | otherwise = filter p xs -- | The 'partition' function takes a predicate @p@ and a stream -- @xs@, and returns a pair of streams. The first stream corresponds -- to the elements of @xs@ for which @p@ holds; the second stream -- corresponds to the elements of @xs@ for which @p@ does not hold. -- -- /Beware/: One of the elements of the tuple may be undefined. For -- example, @fst (partition even (repeat 0)) == repeat 0@; on the -- other hand @snd (partition even (repeat 0))@ is undefined. partition :: (a -> Bool) -> Stream a -> (Stream a, Stream a) partition p ~(x :> xs) | p x = (x :> ts, fs) | otherwise = (ts, x :> fs) where (ts, fs) = partition p xs -- | The 'group' function takes a stream and returns a stream of -- lists such that flattening the resulting stream is equal to the -- argument. Moreover, each sublist in the resulting stream -- contains only equal elements. For example, -- -- > group $ cycle "Mississippi" = "M" ::: "i" ::: "ss" ::: "i" ::: "ss" ::: "i" ::: "pp" ::: "i" ::: "M" ::: "i" ::: ... group :: Eq a => Stream a -> Stream (NonEmpty a) group = groupBy (==) groupBy :: (a -> a -> Bool) -> Stream a -> Stream (NonEmpty a) groupBy eq ~(x :> ys) | (xs, zs) <- span (eq x) ys = (x :| xs) :> groupBy eq zs -- | The 'isPrefix' function returns @True@ if the first argument is -- a prefix of the second. isPrefixOf :: Eq a => [a] -> Stream a -> Bool isPrefixOf [] _ = True isPrefixOf (y:ys) (x :> xs) | y == x = isPrefixOf ys xs | otherwise = False -- | @xs !! n@ returns the element of the stream @xs@ at index -- @n@. Note that the head of the stream has index 0. -- -- /Beware/: passing a negative integer as the first argument will cause -- an error. (!!) :: Stream a -> Int -> a (!!) (x :> xs) n | n == 0 = x | n > 0 = xs !! (n - 1) | otherwise = error "Stream.!! negative argument" -- | The 'elemIndex' function returns the index of the first element -- in the given stream which is equal (by '==') to the query element, -- -- /Beware/: @'elemIndex' x xs@ will diverge if none of the elements -- of @xs@ equal @x@. elemIndex :: Eq a => a -> Stream a -> Int elemIndex x = findIndex (\y -> x == y) -- | The 'elemIndices' function extends 'elemIndex', by returning the -- indices of all elements equal to the query element, in ascending order. -- -- /Beware/: 'elemIndices' @x@ @xs@ will diverge if any suffix of -- @xs@ does not contain @x@. elemIndices :: Eq a => a -> Stream a -> Stream Int elemIndices x = findIndices (x==) -- | The 'findIndex' function takes a predicate and a stream and returns -- the index of the first element in the stream that satisfies the predicate, -- -- /Beware/: 'findIndex' @p@ @xs@ will diverge if none of the elements of -- @xs@ satisfy @p@. findIndex :: (a -> Bool) -> Stream a -> Int findIndex p = indexFrom 0 where indexFrom ix (x :> xs) | p x = ix | otherwise = (indexFrom $! (ix + 1)) xs -- | The 'findIndices' function extends 'findIndex', by returning the -- indices of all elements satisfying the predicate, in ascending -- order. -- -- /Beware/: 'findIndices' @p@ @xs@ will diverge if all the elements -- of any suffix of @xs@ fails to satisfy @p@. findIndices :: (a -> Bool) -> Stream a -> Stream Int findIndices p = indicesFrom 0 where indicesFrom ix (x :> xs) | p x = ix :> ixs | otherwise = ixs where ixs = (indicesFrom $! (ix+1)) xs -- | The 'zip' function takes two streams and returns a list of -- corresponding pairs. zip :: Stream a -> Stream b -> Stream (a,b) zip ~(x :> xs) ~(y :> ys) = (x,y) :> zip xs ys -- | The 'zipWith' function generalizes 'zip'. Rather than tupling -- the functions, the elements are combined using the function -- passed as the first argument to 'zipWith'. zipWith :: (a -> b -> c) -> Stream a -> Stream b -> Stream c zipWith f ~(x :> xs) ~(y :> ys) = f x y :> zipWith f xs ys -- | The 'unzip' function is the inverse of the 'zip' function. unzip :: Stream (a,b) -> (Stream a, Stream b) unzip xs = (fst <$> xs, snd <$> xs) -- | The 'words' function breaks a stream of characters into a -- stream of words, which were delimited by white space. -- -- /Beware/: if the stream of characters @xs@ does not contain white -- space, accessing the tail of @words xs@ will loop. words :: Stream Char -> Stream String words xs | (w, ys) <- break isSpace xs = w :> words ys -- | The 'unwords' function is an inverse operation to 'words'. It -- joins words with separating spaces. unwords :: Stream String -> Stream Char unwords ~(x :> xs) = foldr (:>) (' ' :> unwords xs) x -- | The 'lines' function breaks a stream of characters into a list -- of strings at newline characters. The resulting strings do not -- contain newlines. -- -- /Beware/: if the stream of characters @xs@ does not contain -- newline characters, accessing the tail of @lines xs@ will loop. lines :: Stream Char -> Stream String lines xs | (l, ys) <- break (== '\n') xs = l :> lines (tail ys) -- | The 'unlines' function is an inverse operation to 'lines'. It -- joins lines, after appending a terminating newline to each. unlines :: Stream String -> Stream Char unlines ~(x :> xs) = foldr (:>) ('\n' :> unlines xs) x -- | The 'fromList' converts an infinite list to a -- stream. -- -- /Beware/: Passing a finite list, will cause an error. fromList :: [a] -> Stream a fromList (x:xs) = x :> fromList xs fromList [] = error "Stream.listToStream applied to finite list"