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


-- | Representable functors
--   
--   Representable functors
@package representable-functors
@version 0.4.3


-- | Representable endofunctors over the category of Haskell types are
--   isomorphic to the reader monad and so inherit a very large number of
--   properties for free.
module Data.Functor.Representable

-- | A <a>Functor</a> <tt>f</tt> is <a>Representable</a> if <a>tabulate</a>
--   and <a>index</a> witness an isomorphism to <tt>(-&gt;) x</tt>.
--   
--   <pre>
--   tabulate . index = id
--   index . tabulate = id
--   tabulate . return f = return f
--   </pre>
class (Indexable f, Distributive f, Keyed f, Apply f, Applicative f) => Representable f
tabulate :: Representable f => (Key f -> a) -> f a

-- | We extend lens across a representable functor, due to the preservation
--   of limits.
repLens :: Representable f => Lens a b -> Lens (f a) (f b)
fmapRep :: Representable f => (a -> b) -> f a -> f b
distributeRep :: (Representable f, Functor w) => w (f a) -> f (w a)
mapWithKeyRep :: Representable f => (Key f -> a -> b) -> f a -> f b
apRep :: Representable f => f (a -> b) -> f a -> f b
pureRep :: Representable f => a -> f a
bindRep :: Representable f => f a -> (a -> f b) -> f b
bindWithKeyRep :: Representable f => f a -> (Key f -> a -> f b) -> f b
askRep :: Representable f => f (Key f)
localRep :: Representable f => (Key f -> Key f) -> f a -> f a
duplicateRep :: (Representable f, Semigroup (Key f)) => f a -> f (f a)
extendRep :: (Representable f, Semigroup (Key f)) => (f a -> b) -> f a -> f b
extractRep :: (Indexable f, Monoid (Key f)) => f a -> a
instance (Representable f, Representable g) => Representable (Product f g)
instance Representable w => Representable (TracedT s w)
instance (Representable f, Representable g) => Representable (Compose f g)
instance Representable m => Representable (ReaderT e m)
instance Representable ((->) e)
instance Representable m => Representable (IdentityT m)
instance Representable Identity


-- | Representable functors on Hask all monads, being isomorphic to a
--   reader monad.
module Control.Monad.Representable
type Rep f = RepT f Identity
rep :: Functor f => f b -> Rep f b
runRep :: Functor f => Rep f b -> f b
newtype RepT f m b
RepT :: f (m b) -> RepT f m b
runRepT :: RepT f m b -> f (m b)
instance (Representable f, MonadWriter w m) => MonadWriter w (RepT f m)
instance (Representable f, MonadIO m) => MonadIO (RepT f m)
instance (Representable f, Representable m, Semigroup (Key f), Semigroup (Key m), Monoid (Key f), Monoid (Key m)) => Comonad (RepT f m)
instance (Representable f, Representable m, Semigroup (Key f), Semigroup (Key m)) => Extend (RepT f m)
instance (TraversableWithKey1 f, TraversableWithKey1 m) => TraversableWithKey1 (RepT f m)
instance (TraversableWithKey f, TraversableWithKey m) => TraversableWithKey (RepT f m)
instance (Traversable1 f, Traversable1 m) => Traversable1 (RepT f m)
instance (Traversable f, Traversable m) => Traversable (RepT f m)
instance (FoldableWithKey1 f, FoldableWithKey1 m) => FoldableWithKey1 (RepT f m)
instance (FoldableWithKey f, FoldableWithKey m) => FoldableWithKey (RepT f m)
instance (Foldable1 f, Foldable1 m) => Foldable1 (RepT f m)
instance (Foldable f, Foldable m) => Foldable (RepT f m)
instance (Representable f, Representable m) => Representable (RepT f m)
instance (Lookup f, Lookup m) => Lookup (RepT f m)
instance (Indexable f, Indexable m) => Indexable (RepT f m)
instance (Keyed f, Keyed m) => Keyed (RepT f m)
instance (Representable f, Distributive m) => Distributive (RepT f m)
instance Representable f => MonadTrans (RepT f)
instance (Representable f, Monad m) => Monad (RepT f m)
instance (Representable f, Bind m) => Bind (RepT f m)
instance (Representable f, Applicative m) => Applicative (RepT f m)
instance (Representable f, Apply m) => Apply (RepT f m)
instance (Functor f, Functor m) => Functor (RepT f m)


-- | Representable contravariant endofunctors over the category of Haskell
--   types are isomorphic to <tt>(_ -&gt; r)</tt> and resemble mappings to
--   a fixed range.
module Data.Functor.Corepresentable

-- | Dual to <tt>Keyed</tt>.
class Contravariant f => Valued f
contramapWithValue :: Valued f => (b -> Either a (Value f)) -> f a -> f b

-- | Dual to <tt>Indexed</tt>.
class Coindexed f
coindex :: Coindexed f => f a -> a -> Value f

-- | A <a>Functor</a> <tt>f</tt> is <a>Corepresentable</a> if <a>corep</a>
--   and <a>coindex</a> witness an isomorphism to <tt>(_ -&gt; Value
--   f)</tt>.
--   
--   <pre>
--   tabulate . index = id
--   index . tabulate = id
--   tabulate . return f = return f
--   </pre>
class (Coindexed f, Valued f) => Corepresentable f
corep :: Corepresentable f => (a -> Value f) -> f a
contramapDefault :: Corepresentable f => (a -> b) -> f b -> f a
contramapWithValueDefault :: Corepresentable f => (b -> Either a (Value f)) -> f a -> f b
instance (Coindexed f, Coindexed g) => Coindexed (Coproduct f g)
instance (Corepresentable f, Corepresentable g) => Corepresentable (Product f g)
instance (Coindexed f, Coindexed g) => Coindexed (Product f g)
instance (Valued f, Valued g) => Valued (Product f g)
instance Corepresentable Predicate
instance Coindexed Predicate
instance Valued Predicate
instance Corepresentable (Op r)
instance Coindexed (Op r)
instance Valued (Op r)