content: {-# LANGUAGE CPP                        #-}
  {-# LANGUAGE DefaultSignatures          #-}
  {-# LANGUAGE DeriveDataTypeable         #-}
  {-# LANGUAGE DeriveGeneric              #-}
  {-# LANGUAGE FlexibleContexts           #-}
  {-# LANGUAGE GeneralizedNewtypeDeriving #-}
  {-# LANGUAGE PolyKinds                  #-}
  {-# LANGUAGE ScopedTypeVariables        #-}
  {-# LANGUAGE Trustworthy                #-}
  {-# LANGUAGE TypeOperators              #-}
  
  -----------------------------------------------------------------------------
  -- |
  -- Module      :  Data.Semigroup
  -- Copyright   :  (C) 2011-2015 Edward Kmett
  -- License     :  BSD-style (see the file LICENSE)
  --
  -- Maintainer  :  libraries@haskell.org
  -- Stability   :  provisional
  -- Portability :  portable
  --
  -- In mathematics, a semigroup is an algebraic structure consisting of a
  -- set together with an associative binary operation. A semigroup
  -- generalizes a monoid in that there might not exist an identity
  -- element. It also (originally) generalized a group (a monoid with all
  -- inverses) to a type where every element did not have to have an inverse,
  -- thus the name semigroup.
  --
  -- The use of @(\<\>)@ in this module conflicts with an operator with the same
  -- name that is being exported by Data.Monoid. However, this package
  -- re-exports (most of) the contents of Data.Monoid, so to use semigroups
  -- and monoids in the same package just
  --
  -- > import Data.Semigroup
  --
  -- @since 4.9.0.0
  ----------------------------------------------------------------------------
  module Data.Semigroup (
      Semigroup(..)
    , stimesMonoid
    , stimesIdempotent
    , stimesIdempotentMonoid
    , mtimesDefault
    -- * Semigroups
    , Min(..)
    , Max(..)
    , First(..)
    , Last(..)
    , WrappedMonoid(..)
    -- * Re-exported monoids from Data.Monoid
    , Dual(..)
    , Endo(..)
    , All(..)
    , Any(..)
    , Sum(..)
    , Product(..)
    -- * A better monoid for Maybe
    , Option(..)
    , option
    -- * Difference lists of a semigroup
    , diff
    , cycle1
    -- * ArgMin, ArgMax
    , Arg(..)
    , ArgMin
    , ArgMax
    ) where
  
  import           Prelude             hiding (foldr1)
  
  import GHC.Base (Semigroup(..))
  
  import           Data.Semigroup.Internal
  
  import           Control.Applicative
  import           Control.Monad
  import           Control.Monad.Fix
  import           Data.Bifoldable
  import           Data.Bifunctor
  import           Data.Bitraversable
  import           Data.Coerce
  import           Data.Data
  import           Data.Monoid         (All (..), Any (..), Dual (..), Endo (..),
                                        Product (..), Sum (..))
  -- import qualified Data.Monoid         as Monoid
  import           GHC.Generics
  
  -- | A generalization of 'Data.List.cycle' to an arbitrary 'Semigroup'.
  -- May fail to terminate for some values in some semigroups.
  cycle1 :: Semigroup m => m -> m
  cycle1 xs = xs' where xs' = xs <> xs'
  
  -- | This lets you use a difference list of a 'Semigroup' as a 'Monoid'.
  diff :: Semigroup m => m -> Endo m
  diff = Endo . (<>)
  
  newtype Min a = Min { getMin :: a }
    deriving (Bounded, Eq, Ord, Show, Read, Data, Generic, Generic1)
  
  -- | @since 4.9.0.0
  instance Enum a => Enum (Min a) where
    succ (Min a) = Min (succ a)
    pred (Min a) = Min (pred a)
    toEnum = Min . toEnum
    fromEnum = fromEnum . getMin
    enumFrom (Min a) = Min <$> enumFrom a
    enumFromThen (Min a) (Min b) = Min <$> enumFromThen a b
    enumFromTo (Min a) (Min b) = Min <$> enumFromTo a b
    enumFromThenTo (Min a) (Min b) (Min c) = Min <$> enumFromThenTo a b c
  
  
  -- | @since 4.9.0.0
  instance Ord a => Semigroup (Min a) where
    (<>) = coerce (min :: a -> a -> a)
    stimes = stimesIdempotent
  
  -- | @since 4.9.0.0
  instance (Ord a, Bounded a) => Monoid (Min a) where
    mempty = maxBound
  
  -- | @since 4.9.0.0
  instance Functor Min where
    fmap f (Min x) = Min (f x)
  
  -- | @since 4.9.0.0
  instance Foldable Min where
    foldMap f (Min a) = f a
  
  -- | @since 4.9.0.0
  instance Traversable Min where
    traverse f (Min a) = Min <$> f a
  
  -- | @since 4.9.0.0
  instance Applicative Min where
    pure = Min
    a <* _ = a
    _ *> a = a
    (<*>) = coerce
    liftA2 = coerce
  
  -- | @since 4.9.0.0
  instance Monad Min where
    (>>) = (*>)
    Min a >>= f = f a
  
  -- | @since 4.9.0.0
  instance MonadFix Min where
    mfix f = fix (f . getMin)
  
  -- | @since 4.9.0.0
  instance Num a => Num (Min a) where
    (Min a) + (Min b) = Min (a + b)
    (Min a) * (Min b) = Min (a * b)
    (Min a) - (Min b) = Min (a - b)
    negate (Min a) = Min (negate a)
    abs    (Min a) = Min (abs a)
    signum (Min a) = Min (signum a)
    fromInteger    = Min . fromInteger
  
  newtype Max a = Max { getMax :: a }
    deriving (Bounded, Eq, Ord, Show, Read, Data, Generic, Generic1)
  
  -- | @since 4.9.0.0
  instance Enum a => Enum (Max a) where
    succ (Max a) = Max (succ a)
    pred (Max a) = Max (pred a)
    toEnum = Max . toEnum
    fromEnum = fromEnum . getMax
    enumFrom (Max a) = Max <$> enumFrom a
    enumFromThen (Max a) (Max b) = Max <$> enumFromThen a b
    enumFromTo (Max a) (Max b) = Max <$> enumFromTo a b
    enumFromThenTo (Max a) (Max b) (Max c) = Max <$> enumFromThenTo a b c
  
  -- | @since 4.9.0.0
  instance Ord a => Semigroup (Max a) where
    (<>) = coerce (max :: a -> a -> a)
    stimes = stimesIdempotent
  
  -- | @since 4.9.0.0
  instance (Ord a, Bounded a) => Monoid (Max a) where
    mempty = minBound
  
  -- | @since 4.9.0.0
  instance Functor Max where
    fmap f (Max x) = Max (f x)
  
  -- | @since 4.9.0.0
  instance Foldable Max where
    foldMap f (Max a) = f a
  
  -- | @since 4.9.0.0
  instance Traversable Max where
    traverse f (Max a) = Max <$> f a
  
  -- | @since 4.9.0.0
  instance Applicative Max where
    pure = Max
    a <* _ = a
    _ *> a = a
    (<*>) = coerce
    liftA2 = coerce
  
  -- | @since 4.9.0.0
  instance Monad Max where
    (>>) = (*>)
    Max a >>= f = f a
  
  -- | @since 4.9.0.0
  instance MonadFix Max where
    mfix f = fix (f . getMax)
  
  -- | @since 4.9.0.0
  instance Num a => Num (Max a) where
    (Max a) + (Max b) = Max (a + b)
    (Max a) * (Max b) = Max (a * b)
    (Max a) - (Max b) = Max (a - b)
    negate (Max a) = Max (negate a)
    abs    (Max a) = Max (abs a)
    signum (Max a) = Max (signum a)
    fromInteger    = Max . fromInteger
  
  -- | 'Arg' isn't itself a 'Semigroup' in its own right, but it can be
  -- placed inside 'Min' and 'Max' to compute an arg min or arg max.
  data Arg a b = Arg a b deriving
    (Show, Read, Data, Generic, Generic1)
  
  type ArgMin a b = Min (Arg a b)
  type ArgMax a b = Max (Arg a b)
  
  -- | @since 4.9.0.0
  instance Functor (Arg a) where
    fmap f (Arg x a) = Arg x (f a)
  
  -- | @since 4.9.0.0
  instance Foldable (Arg a) where
    foldMap f (Arg _ a) = f a
  
  -- | @since 4.9.0.0
  instance Traversable (Arg a) where
    traverse f (Arg x a) = Arg x <$> f a
  
  -- | @since 4.9.0.0
  instance Eq a => Eq (Arg a b) where
    Arg a _ == Arg b _ = a == b
  
  -- | @since 4.9.0.0
  instance Ord a => Ord (Arg a b) where
    Arg a _ `compare` Arg b _ = compare a b
    min x@(Arg a _) y@(Arg b _)
      | a <= b    = x
      | otherwise = y
    max x@(Arg a _) y@(Arg b _)
      | a >= b    = x
      | otherwise = y
  
  -- | @since 4.9.0.0
  instance Bifunctor Arg where
    bimap f g (Arg a b) = Arg (f a) (g b)
  
  -- | @since 4.10.0.0
  instance Bifoldable Arg where
    bifoldMap f g (Arg a b) = f a <> g b
  
  -- | @since 4.10.0.0
  instance Bitraversable Arg where
    bitraverse f g (Arg a b) = Arg <$> f a <*> g b
  
  -- | Use @'Option' ('First' a)@ to get the behavior of
  -- 'Data.Monoid.First' from "Data.Monoid".
  newtype First a = First { getFirst :: a } deriving
    (Bounded, Eq, Ord, Show, Read, Data, Generic, Generic1)
  
  -- | @since 4.9.0.0
  instance Enum a => Enum (First a) where
    succ (First a) = First (succ a)
    pred (First a) = First (pred a)
    toEnum = First . toEnum
    fromEnum = fromEnum . getFirst
    enumFrom (First a) = First <$> enumFrom a
    enumFromThen (First a) (First b) = First <$> enumFromThen a b
    enumFromTo (First a) (First b) = First <$> enumFromTo a b
    enumFromThenTo (First a) (First b) (First c) = First <$> enumFromThenTo a b c
  
  -- | @since 4.9.0.0
  instance Semigroup (First a) where
    a <> _ = a
    stimes = stimesIdempotent
  
  -- | @since 4.9.0.0
  instance Functor First where
    fmap f (First x) = First (f x)
  
  -- | @since 4.9.0.0
  instance Foldable First where
    foldMap f (First a) = f a
  
  -- | @since 4.9.0.0
  instance Traversable First where
    traverse f (First a) = First <$> f a
  
  -- | @since 4.9.0.0
  instance Applicative First where
    pure x = First x
    a <* _ = a
    _ *> a = a
    (<*>) = coerce
    liftA2 = coerce
  
  -- | @since 4.9.0.0
  instance Monad First where
    (>>) = (*>)
    First a >>= f = f a
  
  -- | @since 4.9.0.0
  instance MonadFix First where
    mfix f = fix (f . getFirst)
  
  -- | Use @'Option' ('Last' a)@ to get the behavior of
  -- 'Data.Monoid.Last' from "Data.Monoid"
  newtype Last a = Last { getLast :: a } deriving
    (Bounded, Eq, Ord, Show, Read, Data, Generic, Generic1)
  
  -- | @since 4.9.0.0
  instance Enum a => Enum (Last a) where
    succ (Last a) = Last (succ a)
    pred (Last a) = Last (pred a)
    toEnum = Last . toEnum
    fromEnum = fromEnum . getLast
    enumFrom (Last a) = Last <$> enumFrom a
    enumFromThen (Last a) (Last b) = Last <$> enumFromThen a b
    enumFromTo (Last a) (Last b) = Last <$> enumFromTo a b
    enumFromThenTo (Last a) (Last b) (Last c) = Last <$> enumFromThenTo a b c
  
  -- | @since 4.9.0.0
  instance Semigroup (Last a) where
    _ <> b = b
    stimes = stimesIdempotent
  
  -- | @since 4.9.0.0
  instance Functor Last where
    fmap f (Last x) = Last (f x)
    a <$ _ = Last a
  
  -- | @since 4.9.0.0
  instance Foldable Last where
    foldMap f (Last a) = f a
  
  -- | @since 4.9.0.0
  instance Traversable Last where
    traverse f (Last a) = Last <$> f a
  
  -- | @since 4.9.0.0
  instance Applicative Last where
    pure = Last
    a <* _ = a
    _ *> a = a
    (<*>) = coerce
    liftA2 = coerce
  
  -- | @since 4.9.0.0
  instance Monad Last where
    (>>) = (*>)
    Last a >>= f = f a
  
  -- | @since 4.9.0.0
  instance MonadFix Last where
    mfix f = fix (f . getLast)
  
  -- | Provide a Semigroup for an arbitrary Monoid.
  --
  -- __NOTE__: This is not needed anymore since 'Semigroup' became a superclass of
  -- 'Monoid' in /base-4.11/ and this newtype be deprecated at some point in the future.
  newtype WrappedMonoid m = WrapMonoid { unwrapMonoid :: m }
    deriving (Bounded, Eq, Ord, Show, Read, Data, Generic, Generic1)
  
  -- | @since 4.9.0.0
  instance Monoid m => Semigroup (WrappedMonoid m) where
    (<>) = coerce (mappend :: m -> m -> m)
  
  -- | @since 4.9.0.0
  instance Monoid m => Monoid (WrappedMonoid m) where
    mempty = WrapMonoid mempty
  
  -- | @since 4.9.0.0
  instance Enum a => Enum (WrappedMonoid a) where
    succ (WrapMonoid a) = WrapMonoid (succ a)
    pred (WrapMonoid a) = WrapMonoid (pred a)
    toEnum = WrapMonoid . toEnum
    fromEnum = fromEnum . unwrapMonoid
    enumFrom (WrapMonoid a) = WrapMonoid <$> enumFrom a
    enumFromThen (WrapMonoid a) (WrapMonoid b) = WrapMonoid <$> enumFromThen a b
    enumFromTo (WrapMonoid a) (WrapMonoid b) = WrapMonoid <$> enumFromTo a b
    enumFromThenTo (WrapMonoid a) (WrapMonoid b) (WrapMonoid c) =
        WrapMonoid <$> enumFromThenTo a b c
  
  -- | Repeat a value @n@ times.
  --
  -- > mtimesDefault n a = a <> a <> ... <> a  -- using <> (n-1) times
  --
  -- Implemented using 'stimes' and 'mempty'.
  --
  -- This is a suitable definition for an 'mtimes' member of 'Monoid'.
  mtimesDefault :: (Integral b, Monoid a) => b -> a -> a
  mtimesDefault n x
    | n == 0    = mempty
    | otherwise = unwrapMonoid (stimes n (WrapMonoid x))
  
  -- | 'Option' is effectively 'Maybe' with a better instance of
  -- 'Monoid', built off of an underlying 'Semigroup' instead of an
  -- underlying 'Monoid'.
  --
  -- Ideally, this type would not exist at all and we would just fix the
  -- 'Monoid' instance of 'Maybe'
  newtype Option a = Option { getOption :: Maybe a }
    deriving (Eq, Ord, Show, Read, Data, Generic, Generic1)
  
  -- | @since 4.9.0.0
  instance Functor Option where
    fmap f (Option a) = Option (fmap f a)
  
  -- | @since 4.9.0.0
  instance Applicative Option where
    pure a = Option (Just a)
    Option a <*> Option b = Option (a <*> b)
    liftA2 f (Option x) (Option y) = Option (liftA2 f x y)
  
    Option Nothing  *>  _ = Option Nothing
    _               *>  b = b
  
  -- | @since 4.9.0.0
  instance Monad Option where
    Option (Just a) >>= k = k a
    _               >>= _ = Option Nothing
    (>>) = (*>)
  
  -- | @since 4.9.0.0
  instance Alternative Option where
    empty = Option Nothing
    Option Nothing <|> b = b
    a <|> _ = a
  
  -- | @since 4.9.0.0
  instance MonadPlus Option
  
  -- | @since 4.9.0.0
  instance MonadFix Option where
    mfix f = Option (mfix (getOption . f))
  
  -- | @since 4.9.0.0
  instance Foldable Option where
    foldMap f (Option (Just m)) = f m
    foldMap _ (Option Nothing)  = mempty
  
  -- | @since 4.9.0.0
  instance Traversable Option where
    traverse f (Option (Just a)) = Option . Just <$> f a
    traverse _ (Option Nothing)  = pure (Option Nothing)
  
  -- | Fold an 'Option' case-wise, just like 'maybe'.
  option :: b -> (a -> b) -> Option a -> b
  option n j (Option m) = maybe n j m
  
  -- | @since 4.9.0.0
  instance Semigroup a => Semigroup (Option a) where
    (<>) = coerce ((<>) :: Maybe a -> Maybe a -> Maybe a)
  #if !defined(__HADDOCK_VERSION__)
      -- workaround https://github.com/haskell/haddock/issues/680
    stimes _ (Option Nothing) = Option Nothing
    stimes n (Option (Just a)) = case compare n 0 of
      LT -> errorWithoutStackTrace "stimes: Option, negative multiplier"
      EQ -> Option Nothing
      GT -> Option (Just (stimes n a))
  #endif
  
  -- | @since 4.9.0.0
  instance Semigroup a => Monoid (Option a) where
    mempty = Option Nothing
  