-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | Composable, streaming, and efficient left folds -- -- This library provides strict left folds that stream in constant -- memory, and you can combine folds using Applicative style to -- derive new folds. Derived folds still traverse the container just once -- and are often as efficient as hand-written folds. @package foldl @version 1.2.2 -- | This module provides efficient and streaming left folds that you can -- combine using Applicative style. -- -- Import this module qualified to avoid clashing with the Prelude: -- --
--   >>> import qualified Control.Foldl as L
--   
-- -- Use fold to apply a Fold to a list: -- --
--   >>> L.fold L.sum [1..100]
--   5050
--   
-- -- Folds are Applicatives, so you can combine them using -- Applicative combinators: -- --
--   >>> import Control.Applicative
--   
--   >>> let average = (/) <$> L.sum <*> L.genericLength
--   
-- -- Taking the sum, the sum of squares, ..., upto the sum of x^5 -- --
--   >>> import Data.Traversable
--   
--   >>> let powerSums = sequenceA [L.premap (^n) L.sum | n <- [1..5]]
--   
--   >>> L.fold powerSums [1..10]
--   [55,385,3025,25333,220825]
--   
-- -- These combined folds will still traverse the list only once, streaming -- efficiently over the list in constant space without space leaks: -- --
--   >>> L.fold average [1..10000000]
--   5000000.5
--   
--   >>> L.fold ((,) <$> L.minimum <*> L.maximum) [1..10000000]
--   (Just 1,Just 10000000)
--   
-- -- You might want to try enabling the -flate-dmd-anal flag when -- compiling executables that use this library to further improve -- performance. module Control.Foldl -- | Efficient representation of a left fold that preserves the fold's step -- function, initial accumulator, and extraction function -- -- This allows the Applicative instance to assemble derived folds -- that traverse the container only once -- -- A 'Fold a b' processes elements of type a and results in -- a value of type b. data Fold a b -- | Fold step initial extract Fold :: (x -> a -> x) -> x -> (x -> b) -> Fold a b -- | Like Fold, but monadic. -- -- A 'FoldM m a b' processes elements of type a and results -- in a monadic value of type m b. data FoldM m a b -- | FoldM step initial extract FoldM :: (x -> a -> m x) -> (m x) -> (x -> m b) -> FoldM m a b -- | Apply a strict left Fold to a Foldable container fold :: Foldable f => Fold a b -> f a -> b -- | Like fold, but monadic foldM :: (Foldable f, Monad m) => FoldM m a b -> f a -> m b -- | Convert a strict left Fold into a scan scan :: Fold a b -> [a] -> [b] -- | Fold all values within a container using mappend and -- mempty mconcat :: Monoid a => Fold a a -- | Convert a "foldMap" to a Fold foldMap :: Monoid w => (a -> w) -> (w -> b) -> Fold a b -- | Get the first element of a container or return Nothing if the -- container is empty head :: Fold a (Maybe a) -- | Get the last element of a container or return Nothing if the -- container is empty last :: Fold a (Maybe a) -- | Get the last element of a container or return a default value if the -- container is empty lastDef :: a -> Fold a a -- | Return the last N elements lastN :: Int -> Fold a [a] -- | Returns True if the container is empty, False otherwise null :: Fold a Bool -- | Return the length of the container length :: Fold a Int -- | Returns True if all elements are True, False -- otherwise and :: Fold Bool Bool -- | Returns True if any element is True, False -- otherwise or :: Fold Bool Bool -- | (all predicate) returns True if all elements satisfy -- the predicate, False otherwise all :: (a -> Bool) -> Fold a Bool -- | (any predicate) returns True if any element satisfies -- the predicate, False otherwise any :: (a -> Bool) -> Fold a Bool -- | Computes the sum of all elements sum :: Num a => Fold a a -- | Computes the product of all elements product :: Num a => Fold a a -- | Compute a numerically stable arithmetic mean of all elements mean :: Fractional a => Fold a a -- | Compute a numerically stable (population) variance over all elements variance :: Fractional a => Fold a a -- | Compute a numerically stable (population) standard deviation over all -- elements std :: Floating a => Fold a a -- | Computes the maximum element maximum :: Ord a => Fold a (Maybe a) -- | Computes the maximum element with respect to the given comparison -- function maximumBy :: (a -> a -> Ordering) -> Fold a (Maybe a) -- | Computes the minimum element minimum :: Ord a => Fold a (Maybe a) -- | Computes the minimum element with respect to the given comparison -- function minimumBy :: (a -> a -> Ordering) -> Fold a (Maybe a) -- | (elem a) returns True if the container has an element -- equal to a, False otherwise elem :: Eq a => a -> Fold a Bool -- | (notElem a) returns False if the container has an -- element equal to a, True otherwise notElem :: Eq a => a -> Fold a Bool -- | (find predicate) returns the first element that satisfies the -- predicate or Nothing if no element satisfies the predicate find :: (a -> Bool) -> Fold a (Maybe a) -- | (index n) returns the nth element of the container, -- or Nothing if the container has an insufficient number of -- elements index :: Int -> Fold a (Maybe a) -- | (elemIndex a) returns the index of the first element that -- equals a, or Nothing if no element matches elemIndex :: Eq a => a -> Fold a (Maybe Int) -- | (findIndex predicate) returns the index of the first element -- that satisfies the predicate, or Nothing if no element -- satisfies the predicate findIndex :: (a -> Bool) -> Fold a (Maybe Int) -- | Pick a random element, using reservoir sampling random :: FoldM IO a (Maybe a) -- | Pick several random elements, using reservoir sampling randomN :: Vector v a => Int -> FoldM IO a (Maybe (v a)) -- | Converts an effectful function to a fold. Specialized version of -- sink. mapM_ :: Monad m => (a -> m ()) -> FoldM m a () -- | Converts an effectful function to a fold -- --
--   sink (f <> g) = sink f <> sink g -- if `(<>)` is commutative
--   sink mempty = mempty
--   
sink :: (Monoid w, Monad m) => (a -> m w) -> FoldM m a w -- | Like length, except with a more general Num return value genericLength :: Num b => Fold a b -- | Like index, except with a more general Integral argument genericIndex :: Integral i => i -> Fold a (Maybe a) -- | Fold all values into a list list :: Fold a [a] -- | Fold all values into a list, in reverse order revList :: Fold a [a] -- | O(n log n). Fold values into a list with duplicates removed, -- while preserving their first occurrences nub :: Ord a => Fold a [a] -- | O(n^2). Fold values into a list with duplicates removed, while -- preserving their first occurrences eqNub :: Eq a => Fold a [a] -- | Fold values into a set set :: Ord a => Fold a (Set a) -- | Fold all values into a vector vector :: (PrimMonad m, Vector v a) => FoldM m a (v a) -- | Upgrade a fold to accept the Fold type purely :: (forall x. (x -> a -> x) -> x -> (x -> b) -> r) -> Fold a b -> r -- | Upgrade a more traditional fold to accept the Fold type purely_ :: (forall x. (x -> a -> x) -> x -> x) -> Fold a b -> b -- | Upgrade a monadic fold to accept the FoldM type impurely :: (forall x. (x -> a -> m x) -> m x -> (x -> m b) -> r) -> FoldM m a b -> r -- | Upgrade a more traditional monadic fold to accept the FoldM -- type impurely_ :: Monad m => (forall x. (x -> a -> m x) -> m x -> m x) -> FoldM m a b -> m b -- | Generalize a Fold to a FoldM -- --
--   generalize (pure r) = pure r
--   
--   generalize (f <*> x) = generalize f <*> generalize x
--   
generalize :: Monad m => Fold a b -> FoldM m a b -- | Simplify a pure FoldM to a Fold -- --
--   simplify (pure r) = pure r
--   
--   simplify (f <*> x) = simplify f <*> simplify x
--   
simplify :: FoldM Identity a b -> Fold a b -- | Shift a FoldM from one monad to another with a morphism such as -- lift or liftIO; the effect is the same as -- hoist. hoists :: (forall x. m x -> n x) -> FoldM m a b -> FoldM n a b -- | Allows to continue feeding a FoldM even after passing it to a -- function that closes it. -- -- For pure Folds, this is provided by the Comonad -- instance. duplicateM :: Applicative m => FoldM m a b -> FoldM m a (FoldM m a b) -- | _Fold1 step returns a new Fold using just a step -- function that has the same type for the accumulator and the element. -- The result type is the accumulator type wrapped in Maybe. The -- initial accumulator is retrieved from the Foldable, the result -- is None for empty containers. _Fold1 :: (a -> a -> a) -> Fold a (Maybe a) -- | (premap f folder) returns a new Fold where f is -- applied at each step -- --
--   fold (premap f folder) list = fold folder (map f list)
--   
-- --
--   >>> fold (premap Sum mconcat) [1..10]
--   Sum {getSum = 55}
--   
-- --
--   >>> fold mconcat (map Sum [1..10])
--   Sum {getSum = 55}
--   
-- --
--   premap id = id
--   
--   premap (f . g) = premap g . premap f
--   
-- --
--   premap k (pure r) = pure r
--   
--   premap k (f <*> x) = premap k f <*> premap k x
--   
premap :: (a -> b) -> Fold b r -> Fold a r -- | (premapM f folder) returns a new FoldM where f is -- applied to each input element -- --
--   foldM (premapM f folder) list = foldM folder (map f list)
--   
-- --
--   premapM id = id
--   
--   premapM (f . g) = premap g . premap f
--   
-- --
--   premapM k (pure r) = pure r
--   
--   premapM k (f <*> x) = premapM k f <*> premapM k x
--   
premapM :: (a -> b) -> FoldM m b r -> FoldM m a r -- | A handler for the upstream input of a Fold -- -- Any lens, traversal, or prism will type-check as a Handler type Handler a b = forall x. (b -> Const (Dual (Endo x)) b) -> a -> Const (Dual (Endo x)) a -- | (handles t folder) transforms the input of a Fold -- using a lens, traversal, or prism: -- --
--   handles _1       :: Fold a r -> Fold (a, b) r
--   handles _Left    :: Fold a r -> Fold (Either a b) r
--   handles traverse :: Traversable t => Fold a r -> Fold (t a) r
--   handles folded   :: Foldable    t => Fold a r -> Fold (t a) r
--   
-- --
--   >>> fold (handles traverse sum) [[1..5],[6..10]]
--   55
--   
-- --
--   >>> fold (handles (traverse.traverse) sum) [[Nothing, Just 2, Just 7],[Just 13, Nothing, Just 20]]
--   42
--   
-- --
--   >>> fold (handles (filtered even) sum) [1..10]
--   30
--   
-- --
--   >>> fold (handles _2 mconcat) [(1,"Hello "),(2,"World"),(3,"!")]
--   "Hello World!"
--   
-- --
--   handles id = id
--   
--   handles (f . g) = handles f . handles g
--   
-- --
--   handles t (pure r) = pure r
--   
--   handles t (f <*> x) = handles t f <*> handles t x
--   
handles :: Handler a b -> Fold b r -> Fold a r -- | @{foldOver f folder xs} folds all values from a Lens, Traversal, Prism -- or Fold with the given folder -- --
--   >>> foldOver (_Just . both) L.sum (Just (2, 3))
--   5
--   
-- --
--   >>> foldOver (_Just . both) L.sum Nothing
--   0
--   
-- --
--   L.foldOver f folder xs == L.fold folder (xs^..f)
--   
-- --
--   L.foldOver (folded.f) folder == L.fold (handles f folder)
--   
-- --
--   L.foldOver folded == L.fold
--   
foldOver :: Handler s a -> Fold a b -> s -> b -- |
--   instance Monad m => Monoid (EndoM m a) where
--       mempty = EndoM return
--       mappend (EndoM f) (EndoM g) = EndoM (f <=< g)
--   
newtype EndoM m a EndoM :: (a -> m a) -> EndoM m a [appEndoM] :: EndoM m a -> a -> m a -- | A Handler for the upstream input of FoldM -- -- Any lens, traversal, or prism will type-check as a HandlerM type HandlerM m a b = forall x. (b -> Const (Dual (EndoM m x)) b) -> a -> Const (Dual (EndoM m x)) a -- | (handlesM t folder) transforms the input of a FoldM -- using a lens, traversal, or prism: -- --
--   handlesM _1       :: FoldM m a r -> FoldM (a, b) r
--   handlesM _Left    :: FoldM m a r -> FoldM (Either a b) r
--   handlesM traverse :: Traversable t => FoldM m a r -> FoldM m (t a) r
--   handlesM folded   :: Foldable    t => FoldM m a r -> FoldM m (t a) r
--   
-- -- handlesM obeys these laws: -- --
--   handlesM id = id
--   
--   handlesM (f . g) = handlesM f . handlesM g
--   
-- --
--   handlesM t (pure r) = pure r
--   
--   handlesM t (f <*> x) = handlesM t f <*> handlesM t x
--   
handlesM :: HandlerM m a b -> FoldM m b r -> FoldM m a r -- | @{foldOverM f folder xs} folds all values from a Lens, Traversal, -- Prism or Fold monadically with the given folder -- --
--   L.foldOverM (folded.f) folder == L.foldM (handlesM f folder)
--   
-- --
--   L.foldOverM folded == L.foldM
--   
foldOverM :: Monad m => HandlerM m s a -> FoldM m a b -> s -> m b -- |
--   folded :: Foldable t => Fold (t a) a
--   
--   handles folded :: Foldable t => Fold a r -> Fold (t a) r
--   
folded :: (Contravariant f, Applicative f, Foldable t) => (a -> f a) -> (t a -> f (t a)) -- |
--   >>> fold (handles (filtered even) sum) [1..10]
--   30
--   
-- --
--   >>> foldM (handlesM (filtered even) (mapM_ print)) [1..10]
--   2
--   4
--   6
--   8
--   10
--   
filtered :: Monoid m => (a -> Bool) -> (a -> m) -> a -> m instance GHC.Base.Functor (Control.Foldl.Fold a) instance Data.Profunctor.Unsafe.Profunctor Control.Foldl.Fold instance Control.Comonad.Comonad (Control.Foldl.Fold a) instance GHC.Base.Applicative (Control.Foldl.Fold a) instance GHC.Base.Monoid b => GHC.Base.Monoid (Control.Foldl.Fold a b) instance GHC.Num.Num b => GHC.Num.Num (Control.Foldl.Fold a b) instance GHC.Real.Fractional b => GHC.Real.Fractional (Control.Foldl.Fold a b) instance GHC.Float.Floating b => GHC.Float.Floating (Control.Foldl.Fold a b) instance GHC.Base.Monad m => GHC.Base.Functor (Control.Foldl.FoldM m a) instance GHC.Base.Monad m => GHC.Base.Applicative (Control.Foldl.FoldM m a) instance GHC.Base.Monad m => Data.Profunctor.Unsafe.Profunctor (Control.Foldl.FoldM m) instance (GHC.Base.Monoid b, GHC.Base.Monad m) => GHC.Base.Monoid (Control.Foldl.FoldM m a b) instance (GHC.Base.Monad m, GHC.Num.Num b) => GHC.Num.Num (Control.Foldl.FoldM m a b) instance (GHC.Base.Monad m, GHC.Real.Fractional b) => GHC.Real.Fractional (Control.Foldl.FoldM m a b) instance (GHC.Base.Monad m, GHC.Float.Floating b) => GHC.Float.Floating (Control.Foldl.FoldM m a b) instance GHC.Base.Monad m => GHC.Base.Monoid (Control.Foldl.EndoM m a) -- | Folds for byte streams module Control.Foldl.ByteString -- | Apply a strict left Fold to a lazy bytestring fold :: Fold ByteString a -> ByteString -> a -- | Apply a strict monadic left FoldM to a lazy bytestring foldM :: Monad m => FoldM m ByteString a -> ByteString -> m a -- | Get the first byte of a byte stream or return Nothing if the -- stream is empty head :: Fold ByteString (Maybe Word8) -- | Get the last byte of a byte stream or return Nothing if the -- byte stream is empty last :: Fold ByteString (Maybe Word8) -- | Returns True if the byte stream is empty, False -- otherwise null :: Fold ByteString Bool -- | Return the length of the byte stream in bytes length :: Num n => Fold ByteString n -- | (any predicate) returns True if any byte satisfies the -- predicate, False otherwise any :: (Word8 -> Bool) -> Fold ByteString Bool -- | (all predicate) returns True if all bytes satisfy the -- predicate, False otherwise all :: (Word8 -> Bool) -> Fold ByteString Bool -- | Computes the maximum byte maximum :: Fold ByteString (Maybe Word8) -- | Computes the minimum byte minimum :: Fold ByteString (Maybe Word8) -- | (elem w8) returns True if the byte stream has a byte -- equal to w8, False otherwise elem :: Word8 -> Fold ByteString Bool -- | (notElem w8) returns False if the byte stream has a -- byte equal to w8, True otherwise notElem :: Word8 -> Fold ByteString Bool -- | (find predicate) returns the first byte that satisfies the -- predicate or Nothing if no byte satisfies the predicate find :: (Word8 -> Bool) -> Fold ByteString (Maybe Word8) -- | (index n) returns the nth byte of the byte stream, -- or Nothing if the stream has an insufficient number of bytes index :: Integral n => n -> Fold ByteString (Maybe Word8) -- | (elemIndex w8) returns the index of the first byte that -- equals w8, or Nothing if no byte matches elemIndex :: Num n => Word8 -> Fold ByteString (Maybe n) -- | (findIndex predicate) returns the index of the first byte -- that satisfies the predicate, or Nothing if no byte satisfies -- the predicate findIndex :: Num n => (Word8 -> Bool) -> Fold ByteString (Maybe n) -- | count w8 returns the number of times w8 appears count :: Num n => Word8 -> Fold ByteString n -- | Folds for text streams module Control.Foldl.Text -- | Apply a strict left Fold to lazy text fold :: Fold Text a -> Text -> a -- | Apply a strict monadic left FoldM to lazy text foldM :: Monad m => FoldM m Text a -> Text -> m a -- | Get the first character of a text stream or return Nothing if -- the stream is empty head :: Fold Text (Maybe Char) -- | Get the last character of a text stream or return Nothing if -- the text stream is empty last :: Fold Text (Maybe Char) -- | Returns True if the text stream is empty, False -- otherwise null :: Fold Text Bool -- | Return the length of the text stream in characters length :: Num n => Fold Text n -- | (any predicate) returns True if any character -- satisfies the predicate, False otherwise any :: (Char -> Bool) -> Fold Text Bool -- | (all predicate) returns True if all characters satisfy -- the predicate, False otherwise all :: (Char -> Bool) -> Fold Text Bool -- | Computes the maximum character maximum :: Fold Text (Maybe Char) -- | Computes the minimum character minimum :: Fold Text (Maybe Char) -- | (elem c) returns True if the text stream has a -- character equal to c, False otherwise elem :: Char -> Fold Text Bool -- | (notElem c) returns False if the text stream has a -- character equal to c, True otherwise notElem :: Char -> Fold Text Bool -- | (find predicate) returns the first character that satisfies -- the predicate or Nothing if no character satisfies the -- predicate find :: (Char -> Bool) -> Fold Text (Maybe Char) -- | (index n) returns the nth character of the text -- stream, or Nothing if the stream has an insufficient number of -- characters index :: Integral n => n -> Fold Text (Maybe Char) -- | (elemIndex c) returns the index of the first character that -- equals c, or Nothing if no character matches elemIndex :: Num n => Char -> Fold Text (Maybe n) -- | (findIndex predicate) returns the index of the first -- character that satisfies the predicate, or Nothing if no -- character satisfies the predicate findIndex :: Num n => (Char -> Bool) -> Fold Text (Maybe n) -- | (count c) returns the number of times c appears count :: Num n => Char -> Fold Text n