-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Witherable = Traversable + Filterable
--   
--   Witherable = Traversable + Filterable
@package witherable-class
@version 0


module Data.Witherable.Class

-- | Like <a>Functor</a>, but you can remove elements instead of updating
--   them.
--   
--   Formally, the class <a>Filterable</a> represents a functor from
--   <tt>Kleisli Maybe</tt> to <tt>Hask</tt>.
--   
--   A definition of <a>mapMaybe</a> must satisfy the following laws:
--   
--   <ul>
--   <li><i><i>conservation</i></i> <tt><a>mapMaybe</a> (Just . f) ≡
--   <a>fmap</a> f</tt></li>
--   <li><i><i>composition</i></i> <tt><a>mapMaybe</a> f . <a>mapMaybe</a>
--   g ≡ <a>mapMaybe</a> (f &lt;=&lt; g)</tt></li>
--   </ul>
class Functor f => Filterable f

-- | Like <a>mapMaybe</a>.
mapMaybe :: Filterable f => (a -> Maybe b) -> f a -> f b

-- | <pre>
--   <a>catMaybes</a> ≡ <a>mapMaybe</a> <a>id</a>
--   </pre>
catMaybes :: Filterable f => f (Maybe a) -> f a

-- | <pre>
--   <a>filter</a> f . <a>filter</a> g ≡ filter (<a>liftA2</a> (<a>&amp;&amp;</a>) f g)
--   </pre>
filter :: Filterable f => (a -> Bool) -> f a -> f a

-- | An enhancement of <a>Traversable</a> with <a>Filterable</a>
--   
--   A definition of <a>wither</a> must satisfy the following laws:
--   
--   <ul>
--   <li><i><i>conservation</i></i> <tt><a>wither</a> (<a>fmap</a>
--   <a>Just</a> . f) ≡ <a>traverse</a> f</tt></li>
--   <li><i><i>composition</i></i> <tt><a>Compose</a> . <a>fmap</a>
--   (<a>wither</a> f) . <a>wither</a> g ≡ <a>wither</a> (<a>Compose</a> .
--   <a>fmap</a> (<a>wither</a> f) . g)</tt></li>
--   </ul>
--   
--   Parametricity implies the naturality law:
--   
--   <pre>
--   t . <a>wither</a> f ≡ <a>wither</a> (t . f)
--   </pre>
class (Traversable t, Filterable t) => Witherable t

-- | Effectful <a>mapMaybe</a>.
--   
--   <pre>
--   <a>wither</a> (<a>pure</a> . f) ≡ <a>pure</a> . <a>mapMaybe</a> f
--   </pre>
wither :: (Witherable t, Applicative f) => (a -> f (Maybe b)) -> t a -> f (t b)

-- | <pre>
--   Monadic variant of <a>wither</a>. This may have more efficient implementation.
--   </pre>
witherM :: (Witherable t, Monad m) => (a -> m (Maybe b)) -> t a -> m (t b)
filterA :: (Witherable t, Applicative f) => (a -> f Bool) -> t a -> f (t a)
instance Data.Witherable.Class.Filterable f => Data.Witherable.Class.Filterable (Control.Monad.Trans.Identity.IdentityT f)
instance Data.Witherable.Class.Filterable t => Data.Witherable.Class.Filterable (Data.Functor.Reverse.Reverse t)
instance Data.Witherable.Class.Filterable t => Data.Witherable.Class.Filterable (Control.Applicative.Backwards.Backwards t)
instance Data.Witherable.Class.Witherable GHC.Maybe.Maybe
instance Data.Witherable.Class.Witherable Data.Semigroup.Option
instance GHC.Base.Monoid e => Data.Witherable.Class.Witherable (Data.Either.Either e)
instance Data.Witherable.Class.Witherable []
instance Data.Witherable.Class.Witherable Control.Applicative.ZipList
instance Data.Witherable.Class.Witherable Data.IntMap.Internal.IntMap
instance Data.Witherable.Class.Witherable (Data.Map.Internal.Map k)
instance (GHC.Classes.Eq k, Data.Hashable.Class.Hashable k) => Data.Witherable.Class.Witherable (Data.HashMap.Base.HashMap k)
instance Data.Witherable.Class.Witherable Data.Proxy.Proxy
instance Data.Witherable.Class.Witherable (Data.Functor.Const.Const r)
instance Data.Witherable.Class.Witherable Data.Vector.Vector
instance Data.Witherable.Class.Witherable Data.Sequence.Internal.Seq
instance (Data.Traversable.Traversable f, Data.Witherable.Class.Witherable g) => Data.Witherable.Class.Witherable (Data.Functor.Compose.Compose f g)
instance (Data.Witherable.Class.Witherable f, Data.Witherable.Class.Witherable g) => Data.Witherable.Class.Witherable (Data.Functor.Product.Product f g)
instance (Data.Witherable.Class.Witherable f, Data.Witherable.Class.Witherable g) => Data.Witherable.Class.Witherable (Data.Functor.Sum.Sum f g)
instance Data.Witherable.Class.Witherable f => Data.Witherable.Class.Witherable (Control.Monad.Trans.Identity.IdentityT f)
instance Data.Traversable.Traversable t => Data.Witherable.Class.Witherable (Control.Monad.Trans.Maybe.MaybeT t)
instance Data.Witherable.Class.Witherable t => Data.Witherable.Class.Witherable (Data.Functor.Reverse.Reverse t)
instance Data.Witherable.Class.Witherable t => Data.Witherable.Class.Witherable (Control.Applicative.Backwards.Backwards t)
instance Data.Witherable.Class.Witherable GHC.Generics.V1
instance Data.Witherable.Class.Witherable GHC.Generics.U1
instance Data.Witherable.Class.Witherable f => Data.Witherable.Class.Witherable (GHC.Generics.Rec1 f)
instance Data.Witherable.Class.Witherable f => Data.Witherable.Class.Witherable (GHC.Generics.M1 i c f)
instance (Data.Witherable.Class.Witherable f, Data.Witherable.Class.Witherable g) => Data.Witherable.Class.Witherable (f GHC.Generics.:*: g)
instance (Data.Witherable.Class.Witherable f, Data.Witherable.Class.Witherable g) => Data.Witherable.Class.Witherable (f GHC.Generics.:+: g)
instance (Data.Traversable.Traversable f, Data.Witherable.Class.Witherable g) => Data.Witherable.Class.Witherable (f GHC.Generics.:.: g)
instance Data.Witherable.Class.Filterable GHC.Maybe.Maybe
instance Data.Witherable.Class.Filterable Data.Semigroup.Option
instance GHC.Base.Monoid e => Data.Witherable.Class.Filterable (Data.Either.Either e)
instance Data.Witherable.Class.Filterable []
instance Data.Witherable.Class.Filterable Control.Applicative.ZipList
instance Data.Witherable.Class.Filterable Data.IntMap.Internal.IntMap
instance Data.Witherable.Class.Filterable (Data.Map.Internal.Map k)
instance (GHC.Classes.Eq k, Data.Hashable.Class.Hashable k) => Data.Witherable.Class.Filterable (Data.HashMap.Base.HashMap k)
instance Data.Witherable.Class.Filterable Data.Proxy.Proxy
instance Data.Witherable.Class.Filterable (Data.Functor.Const.Const r)
instance Data.Witherable.Class.Filterable Data.Vector.Vector
instance Data.Witherable.Class.Filterable Data.Sequence.Internal.Seq
instance (GHC.Base.Functor f, Data.Witherable.Class.Filterable g) => Data.Witherable.Class.Filterable (Data.Functor.Compose.Compose f g)
instance (Data.Witherable.Class.Filterable f, Data.Witherable.Class.Filterable g) => Data.Witherable.Class.Filterable (Data.Functor.Product.Product f g)
instance (Data.Witherable.Class.Filterable f, Data.Witherable.Class.Filterable g) => Data.Witherable.Class.Filterable (Data.Functor.Sum.Sum f g)
instance GHC.Base.Functor f => Data.Witherable.Class.Filterable (Control.Monad.Trans.Maybe.MaybeT f)
instance Data.Witherable.Class.Filterable GHC.Generics.V1
instance Data.Witherable.Class.Filterable GHC.Generics.U1
instance Data.Witherable.Class.Filterable f => Data.Witherable.Class.Filterable (GHC.Generics.Rec1 f)
instance Data.Witherable.Class.Filterable f => Data.Witherable.Class.Filterable (GHC.Generics.M1 i c f)
instance (Data.Witherable.Class.Filterable f, Data.Witherable.Class.Filterable g) => Data.Witherable.Class.Filterable (f GHC.Generics.:*: g)
instance (Data.Witherable.Class.Filterable f, Data.Witherable.Class.Filterable g) => Data.Witherable.Class.Filterable (f GHC.Generics.:+: g)
instance (GHC.Base.Functor f, Data.Witherable.Class.Filterable g) => Data.Witherable.Class.Filterable (f GHC.Generics.:.: g)