{-# LANGUAGE CPP #-}
{-# LANGUAGE DefaultSignatures #-}
{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE TypeOperators #-}
module Data.Semigroup (
Semigroup(..)
, stimesMonoid
, stimesIdempotent
, stimesIdempotentMonoid
, mtimesDefault
, Min(..)
, Max(..)
, First(..)
, Last(..)
, WrappedMonoid(..)
, Dual(..)
, Endo(..)
, All(..)
, Any(..)
, Sum(..)
, Product(..)
, Option(..)
, option
, diff
, cycle1
, 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 GHC.Generics
cycle1 :: Semigroup m => m -> m
cycle1 xs = xs' where xs' = xs <> xs'
diff :: Semigroup m => m -> Endo m
diff = Endo . (<>)
newtype Min a = Min { getMin :: a }
deriving (Bounded, Eq, Ord, Show, Read, Data, Generic, Generic1)
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
instance Ord a => Semigroup (Min a) where
(<>) = coerce (min :: a -> a -> a)
stimes = stimesIdempotent
instance (Ord a, Bounded a) => Monoid (Min a) where
mempty = maxBound
instance Functor Min where
fmap f (Min x) = Min (f x)
instance Foldable Min where
foldMap f (Min a) = f a
instance Traversable Min where
traverse f (Min a) = Min <$> f a
instance Applicative Min where
pure = Min
a <* _ = a
_ *> a = a
(<*>) = coerce
liftA2 = coerce
instance Monad Min where
(>>) = (*>)
Min a >>= f = f a
instance MonadFix Min where
mfix f = fix (f . getMin)
instance Num a => Num (Min a) where
(Min a) + (Min b) = Min (a + b)
(Min a) * (Min b) = Min (a * b)
(Min a) - (Min b) = Min (a - b)
negate (Min a) = Min (negate a)
abs (Min a) = Min (abs a)
signum (Min a) = Min (signum a)
fromInteger = Min . fromInteger
newtype Max a = Max { getMax :: a }
deriving (Bounded, Eq, Ord, Show, Read, Data, Generic, Generic1)
instance Enum a => Enum (Max a) where
succ (Max a) = Max (succ a)
pred (Max a) = Max (pred a)
toEnum = Max . toEnum
fromEnum = fromEnum . getMax
enumFrom (Max a) = Max <$> 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 <$> enumFromThenTo a b c
instance Ord a => Semigroup (Max a) where
(<>) = coerce (max :: a -> a -> a)
stimes = stimesIdempotent
instance (Ord a, Bounded a) => Monoid (Max a) where
mempty = minBound
instance Functor Max where
fmap f (Max x) = Max (f x)
instance Foldable Max where
foldMap f (Max a) = f a
instance Traversable Max where
traverse f (Max a) = Max <$> f a
instance Applicative Max where
pure = Max
a <* _ = a
_ *> a = a
(<*>) = coerce
liftA2 = coerce
instance Monad Max where
(>>) = (*>)
Max a >>= f = f a
instance MonadFix Max where
mfix f = fix (f . getMax)
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
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)
instance Functor (Arg a) where
fmap f (Arg x a) = Arg x (f a)
instance Foldable (Arg a) where
foldMap f (Arg _ a) = f a
instance Traversable (Arg a) where
traverse f (Arg x a) = Arg x <$> f a
instance Eq a => Eq (Arg a b) where
Arg a _ == Arg b _ = a == b
instance Ord a => Ord (Arg a b) where
Arg a _ `compare` Arg b _ = compare a b
min x@(Arg a _) y@(Arg b _)
| a <= b = x
| otherwise = y
max x@(Arg a _) y@(Arg b _)
| a >= b = x
| otherwise = y
instance Bifunctor Arg where
bimap f g (Arg a b) = Arg (f a) (g b)
instance Bifoldable Arg where
bifoldMap f g (Arg a b) = f a <> g b
instance Bitraversable Arg where
bitraverse f g (Arg a b) = Arg <$> f a <*> g b
newtype First a = First { getFirst :: a } deriving
(Bounded, Eq, Ord, Show, Read, Data, Generic, Generic1)
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
instance Semigroup (First a) where
a <> _ = a
stimes = stimesIdempotent
instance Functor First where
fmap f (First x) = First (f x)
instance Foldable First where
foldMap f (First a) = f a
instance Traversable First where
traverse f (First a) = First <$> f a
instance Applicative First where
pure x = First x
a <* _ = a
_ *> a = a
(<*>) = coerce
liftA2 = coerce
instance Monad First where
(>>) = (*>)
First a >>= f = f a
instance MonadFix First where
mfix f = fix (f . getFirst)
newtype Last a = Last { getLast :: a } deriving
(Bounded, Eq, Ord, Show, Read, Data, Generic, Generic1)
instance Enum a => Enum (Last a) where
succ (Last a) = Last (succ a)
pred (Last a) = Last (pred a)
toEnum = Last . toEnum
fromEnum = fromEnum . getLast
enumFrom (Last a) = Last <$> 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 <$> enumFromThenTo a b c
instance Semigroup (Last a) where
_ <> b = b
stimes = stimesIdempotent
instance Functor Last where
fmap f (Last x) = Last (f x)
a <$ _ = Last a
instance Foldable Last where
foldMap f (Last a) = f a
instance Traversable Last where
traverse f (Last a) = Last <$> f a
instance Applicative Last where
pure = Last
a <* _ = a
_ *> a = a
(<*>) = coerce
liftA2 = coerce
instance Monad Last where
(>>) = (*>)
Last a >>= f = f a
instance MonadFix Last where
mfix f = fix (f . getLast)
newtype WrappedMonoid m = WrapMonoid { unwrapMonoid :: m }
deriving (Bounded, Eq, Ord, Show, Read, Data, Generic, Generic1)
instance Monoid m => Semigroup (WrappedMonoid m) where
(<>) = coerce (mappend :: m -> m -> m)
instance Monoid m => Monoid (WrappedMonoid m) where
mempty = WrapMonoid mempty
instance Enum a => Enum (WrappedMonoid a) where
succ (WrapMonoid a) = WrapMonoid (succ a)
pred (WrapMonoid a) = WrapMonoid (pred a)
toEnum = WrapMonoid . toEnum
fromEnum = fromEnum . unwrapMonoid
enumFrom (WrapMonoid a) = WrapMonoid <$> 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 <$> enumFromThenTo a b c
mtimesDefault :: (Integral b, Monoid a) => b -> a -> a
mtimesDefault n x
| n == 0 = mempty
| otherwise = unwrapMonoid (stimes n (WrapMonoid x))
newtype Option a = Option { getOption :: Maybe a }
deriving (Eq, Ord, Show, Read, Data, Generic, Generic1)
instance Functor Option where
fmap f (Option a) = Option (fmap f a)
instance Applicative Option where
pure a = Option (Just a)
Option a <*> Option b = Option (a <*> b)
liftA2 f (Option x) (Option y) = Option (liftA2 f x y)
Option Nothing *> _ = Option Nothing
_ *> b = b
instance Monad Option where
Option (Just a) >>= k = k a
_ >>= _ = Option Nothing
(>>) = (*>)
instance Alternative Option where
empty = Option Nothing
Option Nothing <|> b = b
a <|> _ = a
instance MonadPlus Option
instance MonadFix Option where
mfix f = Option (mfix (getOption . f))
instance Foldable Option where
foldMap f (Option (Just m)) = f m
foldMap _ (Option Nothing) = mempty
instance Traversable Option where
traverse f (Option (Just a)) = Option . Just <$> 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
(<>) = coerce ((<>) :: Maybe a -> Maybe a -> Maybe a)
#if !defined(__HADDOCK_VERSION__)
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
instance Semigroup a => Monoid (Option a) where
mempty = Option Nothing