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


-- | a 'Monus' is a commutative monoid that allows a notion of substraction.
--   
--   A <a>Monus</a> is a commutative monoid that allows a notion of
--   substraction, with the following laws:
--   
--   x &lt;&gt; (y - x) = y &lt;&gt; (x - y)
--   
--   (x - y) - z = x - (y &lt;&gt; z)
--   
--   x - x = mempty
--   
--   mempty - x = mempty
@package monus
@version 0.2.0.0


-- | A <a>commutative monoid with monus</a> is a <a>Monoid</a> equipped
--   with a subtraction operator.
module Data.Monoid.Monus

-- | A commutative monoid that supports subtraction. The following laws
--   must hold:
--   
--   <pre>
--   x &lt;&gt; (y - x) = y &lt;&gt; (x - y)
--   (x - y) - z = x - (y &lt;&gt; z)
--   x - x = mempty
--   mempty - x = mempty
--   </pre>
class Monoid a => Monus a
monus :: Monus a => a -> a -> a

-- | An infix synonym for <tt>subtraction</tt>.
(-) :: Monus a => a -> a -> a
infixl 6 -
instance GHC.Classes.Ord a => Data.Monoid.Monus.Monus (Data.Set.Internal.Set a)
instance (a ~ GHC.Natural.Natural) => Data.Monoid.Monus.Monus (Data.Semigroup.Internal.Sum a)
instance Data.Monoid.Monus.Monus Data.Semigroup.Internal.Any
instance Data.Monoid.Monus.Monus Data.Semigroup.Internal.All
instance Data.Monoid.Monus.Monus a => Data.Monoid.Monus.Monus (Data.Semigroup.Internal.Endo a)
instance Data.Monoid.Monus.Monus ()
instance (Data.Monoid.Monus.Monus a, Data.Monoid.Monus.Monus b) => Data.Monoid.Monus.Monus (a, b)
instance (Data.Monoid.Monus.Monus a, Data.Monoid.Monus.Monus b, Data.Monoid.Monus.Monus c) => Data.Monoid.Monus.Monus (a, b, c)
instance (Data.Monoid.Monus.Monus a, Data.Monoid.Monus.Monus b, Data.Monoid.Monus.Monus c, Data.Monoid.Monus.Monus d) => Data.Monoid.Monus.Monus (a, b, c, d)
instance (Data.Monoid.Monus.Monus a, Data.Monoid.Monus.Monus b, Data.Monoid.Monus.Monus c, Data.Monoid.Monus.Monus d, Data.Monoid.Monus.Monus e) => Data.Monoid.Monus.Monus (a, b, c, d, e)
instance Data.Monoid.Monus.Monus b => Data.Monoid.Monus.Monus (a -> b)
instance Data.Monoid.Monus.Monus a => Data.Monoid.Monus.Monus (GHC.Types.IO a)
instance Data.Monoid.Monus.Monus a => Data.Monoid.Monus.Monus [a]
instance Data.Monoid.Monus.Monus a => Data.Monoid.Monus.Monus (GHC.Base.Maybe a)

module Data.Map.Annihilate

-- | A <a>Map</a> that supports annihilation, i.e. it is a <a>Monus</a>,
--   where for <a>Monus</a> values, matching keys will be subtracted, and
--   keys not shared by both <a>Map</a>s will be discarded.
data Map k v

-- | Create a singleton <a>Map</a>.
singleton :: (Monoid v, Eq v) => k -> v -> Map k v

-- | Lookup a value in a <a>Map</a>. If no value is found, this returns
--   <a>mempty</a>.
lookup :: (Ord k, Monoid v) => k -> Map k v -> v
instance (GHC.Show.Show k, GHC.Show.Show v) => GHC.Show.Show (Data.Map.Annihilate.Map k v)
instance Data.Foldable.Foldable (Data.Map.Annihilate.Map k)
instance GHC.Base.Functor (Data.Map.Annihilate.Map k)
instance (GHC.Classes.Ord k, GHC.Classes.Ord v) => GHC.Classes.Ord (Data.Map.Annihilate.Map k v)
instance (GHC.Classes.Eq k, GHC.Classes.Eq v) => GHC.Classes.Eq (Data.Map.Annihilate.Map k v)
instance (GHC.Classes.Ord k, GHC.Base.Monoid v, GHC.Classes.Eq v) => GHC.Base.Semigroup (Data.Map.Annihilate.Map k v)
instance (GHC.Classes.Ord k, GHC.Base.Monoid v, GHC.Classes.Eq v) => GHC.Base.Monoid (Data.Map.Annihilate.Map k v)
instance (GHC.Classes.Ord k, Data.Monoid.Monus.Monus v, GHC.Classes.Eq v) => Data.Monoid.Monus.Monus (Data.Map.Annihilate.Map k v)


-- | This module provides generic deriving tools for monuses for
--   product-like structures.
module Data.Monoid.Monus.Generic
class GMonus f
gmonus' :: GMonus f => f a -> f a -> f a

-- | Generically generate a <a>Monus</a> <a>monus</a> operation for any
--   type implementing <a>Generic</a>. It is only defined for product
--   types.
--   
--   <pre>
--   <a>gmonus</a> a b = <a>gmonus</a> b a
--   </pre>
gmonus :: (Generic a, GMonus (Rep a)) => a -> a -> a

-- | This type is useful with -XDerivingVia.
newtype WrappedMonus a
WrappedMonus :: a -> WrappedMonus a
instance GHC.Base.Monoid a => GHC.Base.Monoid (Data.Monoid.Monus.Generic.WrappedMonus a)
instance GHC.Base.Semigroup a => GHC.Base.Semigroup (Data.Monoid.Monus.Generic.WrappedMonus a)
instance GHC.Generics.Generic (Data.Monoid.Monus.Generic.WrappedMonus a)
instance Data.Monoid.Monus.Generic.GMonus GHC.Generics.U1
instance (Data.Monoid.Monus.Generic.GMonus a, Data.Monoid.Monus.Generic.GMonus b) => Data.Monoid.Monus.Generic.GMonus (a GHC.Generics.:*: b)
instance Data.Monoid.Monus.Generic.GMonus a => Data.Monoid.Monus.Generic.GMonus (GHC.Generics.M1 i c a)
instance Data.Monoid.Monus.Monus a => Data.Monoid.Monus.Generic.GMonus (GHC.Generics.K1 i a)
instance Data.Monoid.Monus.Monus a => Data.Monoid.Monus.Monus (Data.Monoid.Monus.Generic.WrappedMonus a)