module Data.Semigroup (
Semigroup(..)
, Min(..)
, Max(..)
, First(..)
, Last(..)
, WrappedMonoid(..)
, Dual(..)
, Endo(..)
, All(..)
, Any(..)
, Sum(..)
, Product(..)
, Option(..)
, option
, diff
, cycle1
) where
import Prelude hiding (foldr1)
import Data.Monoid hiding (First(..), Last(..))
import Control.Applicative
import Control.Monad
import Control.Monad.Fix
import qualified Data.Monoid as Monoid
import Data.Foldable
import Data.Traversable
import Data.List.NonEmpty
import Numeric.Natural.Internal
import Data.Sequence (Seq, (><))
import Data.Set (Set)
import Data.IntSet (IntSet)
import Data.Map (Map)
import Data.IntMap (IntMap)
#ifdef LANGUAGE_DeriveDataTypeable
import Data.Data
#endif
infixl 6 <>
class Semigroup a where
(<>) :: a -> a -> a
sconcat :: NonEmpty a -> a
sconcat (a :| as) = go a as where
go b (c:cs) = b <> go c cs
go b [] = b
replicate1p :: Whole n => n -> a -> a
replicate1p y0 x0 = f x0 (1 Prelude.+ y0)
where
f x y
| even y = f (x <> x) (y `quot` 2)
| y == 1 = x
| otherwise = g (x <> x) (unsafePred y `quot` 2) x
g x y z
| even y = g (x <> x) (y `quot` 2) z
| y == 1 = x <> z
| otherwise = g (x <> x) (unsafePred y `quot` 2) (x <> z)
cycle1 :: Semigroup m => m -> m
cycle1 xs = xs' where xs' = xs <> xs'
instance Semigroup () where
_ <> _ = ()
sconcat _ = ()
replicate1p _ _ = ()
instance Semigroup b => Semigroup (a -> b) where
f <> g = \a -> f a <> g a
replicate1p n f e = replicate1p n (f e)
instance Semigroup [a] where
(<>) = (++)
instance Semigroup a => Semigroup (Maybe a) where
Nothing <> b = b
a <> Nothing = a
Just a <> Just b = Just (a <> b)
instance Semigroup (Either a b) where
Left _ <> b = b
a <> _ = a
instance (Semigroup a, Semigroup b) => Semigroup (a, b) where
(a,b) <> (a',b') = (a<>a',b<>b')
replicate1p n (a,b) = (replicate1p n a, replicate1p n b)
instance (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) where
(a,b,c) <> (a',b',c') = (a<>a',b<>b',c<>c')
replicate1p n (a,b,c) = (replicate1p n a, replicate1p n b, replicate1p n c)
instance (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) where
(a,b,c,d) <> (a',b',c',d') = (a<>a',b<>b',c<>c',d<>d')
replicate1p n (a,b,c,d) = (replicate1p n a, replicate1p n b, replicate1p n c, replicate1p n d)
instance (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) where
(a,b,c,d,e) <> (a',b',c',d',e') = (a<>a',b<>b',c<>c',d<>d',e<>e')
replicate1p n (a,b,c,d,e) = (replicate1p n a, replicate1p n b, replicate1p n c, replicate1p n d, replicate1p n e)
instance Semigroup a => Semigroup (Dual a) where
Dual a <> Dual b = Dual (b <> a)
replicate1p n (Dual a) = Dual (replicate1p n a)
instance Semigroup (Endo a) where
Endo f <> Endo g = Endo (f . g)
instance Semigroup All where
All a <> All b = All (a && b)
replicate1p _ a = a
instance Semigroup Any where
Any a <> Any b = Any (a || b)
replicate1p _ a = a
instance Num a => Semigroup (Sum a) where
Sum a <> Sum b = Sum (a + b)
instance Num a => Semigroup (Product a) where
Product a <> Product b = Product (a * b)
instance Semigroup (Monoid.First a) where
Monoid.First Nothing <> b = b
a <> _ = a
replicate1p _ a = a
instance Semigroup (Monoid.Last a) where
a <> Monoid.Last Nothing = a
_ <> b = b
replicate1p _ a = a
instance Semigroup (NonEmpty a) where
(a :| as) <> ~(b :| bs) = a :| (as ++ b : bs)
newtype Min a = Min { getMin :: a } deriving
( Eq, Ord, Bounded, Show, Read
#ifdef LANGUAGE_DeriveDataTypeable
, Data, Typeable
#endif
)
instance Ord a => Semigroup (Min a) where
Min a <> Min b = Min (a `min` b)
replicate1p _ a = a
instance (Ord a, Bounded a) => Monoid (Min a) where
mempty = maxBound
mappend = (<>)
newtype Max a = Max { getMax :: a } deriving
( Eq, Ord, Bounded, Show, Read
#ifdef LANGUAGE_DeriveDataTypeable
, Data, Typeable
#endif
)
instance Ord a => Semigroup (Max a) where
Max a <> Max b = Max (a `max` b)
replicate1p _ a = a
instance (Ord a, Bounded a) => Monoid (Max a) where
mempty = minBound
mappend = (<>)
newtype First a = First { getFirst :: a } deriving
( Eq, Ord, Bounded, Show, Read
#ifdef LANGUAGE_DeriveDataTypeable
, Data
, Typeable
#endif
)
instance Semigroup (First a) where
a <> _ = a
replicate1p _ a = a
newtype Last a = Last { getLast :: a } deriving
( Eq, Ord, Bounded, Show, Read
#ifdef LANGUAGE_DeriveDataTypeable
, Data, Typeable
#endif
)
instance Semigroup (Last a) where
_ <> b = b
replicate1p _ a = a
newtype WrappedMonoid m = WrapMonoid
{ unwrapMonoid :: m } deriving
( Eq, Ord, Bounded, Show, Read
#ifdef LANGUAGE_DeriveDataTypeable
, Data, Typeable
#endif
)
instance Monoid m => Semigroup (WrappedMonoid m) where
WrapMonoid a <> WrapMonoid b = WrapMonoid (a `mappend` b)
instance Monoid m => Monoid (WrappedMonoid m) where
mempty = WrapMonoid mempty
WrapMonoid a `mappend` WrapMonoid b = WrapMonoid (a `mappend` b)
newtype Option a = Option
{ getOption :: Maybe a } deriving
( Eq, Ord, Show, Read
#ifdef LANGUAGE_DeriveDataTypeable
, Data, Typeable
#endif
)
instance Functor Option where
fmap f (Option a) = Option (fmap f a)
instance Applicative Option where
pure a = Option (Just a)
Option a <*> Option b = Option (a <*> b)
instance Monad Option where
return = pure
Option (Just a) >>= k = k a
_ >>= _ = Option Nothing
Option Nothing >> _ = Option Nothing
_ >> b = b
instance Alternative Option where
empty = Option Nothing
Option Nothing <|> b = b
a <|> _ = a
instance MonadPlus Option where
mzero = empty
mplus = (<|>)
instance MonadFix Option where
mfix f = Option (mfix (getOption . f))
instance Foldable Option where
foldMap f (Option (Just m)) = f m
foldMap _ (Option Nothing) = mempty
instance Traversable Option where
traverse f (Option (Just a)) = Option . Just <$> f a
traverse _ (Option Nothing) = pure (Option Nothing)
option :: b -> (a -> b) -> Option a -> b
option n j (Option m) = maybe n j m
instance Semigroup a => Semigroup (Option a) where
Option a <> Option b = Option (a <> b)
instance Semigroup a => Monoid (Option a) where
mempty = empty
Option a `mappend` Option b = Option (a <> b)
diff :: Semigroup m => m -> Endo m
diff = Endo . (<>)
instance Semigroup (Seq a) where
(<>) = (><)
instance Semigroup IntSet where
(<>) = mappend
replicate1p _ a = a
instance Ord a => Semigroup (Set a) where
(<>) = mappend
replicate1p _ a = a
instance Semigroup (IntMap v) where
(<>) = mappend
replicate1p _ a = a
instance Ord k => Semigroup (Map k v) where
(<>) = mappend
replicate1p _ a = a