base-4.19.1.0: Data/Semigroup/Internal.hs
{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE ScopedTypeVariables #-}
-- | Auxiliary definitions for 'Semigroup'
--
-- This module provides some @newtype@ wrappers and helpers which are
-- reexported from the "Data.Semigroup" module or imported directly
-- by some other modules.
--
-- This module also provides internal definitions related to the
-- 'Semigroup' class some.
--
-- This module exists mostly to simplify or workaround import-graph
-- issues; there is also a .hs-boot file to allow "GHC.Base" and other
-- modules to import method default implementations for 'stimes'
--
-- @since 4.11.0.0
module Data.Semigroup.Internal where
import GHC.Base hiding (Any)
import GHC.Enum
import qualified GHC.List as List
import GHC.Num
import GHC.Read
import GHC.Show
import GHC.Generics
import GHC.Real
-- | This is a valid definition of 'stimes' for an idempotent 'Semigroup'.
--
-- When @x <> x = x@, this definition should be preferred, because it
-- works in \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\).
stimesIdempotent :: Integral b => b -> a -> a
stimesIdempotent n x
| n <= 0 = errorWithoutStackTrace "stimesIdempotent: positive multiplier expected"
| otherwise = x
-- | This is a valid definition of 'stimes' for an idempotent 'Monoid'.
--
-- When @x <> x = x@, this definition should be preferred, because it
-- works in \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\)
stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a
stimesIdempotentMonoid n x = case compare n 0 of
LT -> errorWithoutStackTrace "stimesIdempotentMonoid: negative multiplier"
EQ -> mempty
GT -> x
-- | This is a valid definition of 'stimes' for a 'Monoid'.
--
-- Unlike the default definition of 'stimes', it is defined for 0
-- and so it should be preferred where possible.
stimesMonoid :: (Integral b, Monoid a) => b -> a -> a
stimesMonoid n x0 = case compare n 0 of
LT -> errorWithoutStackTrace "stimesMonoid: negative multiplier"
EQ -> mempty
GT -> f x0 n
where
f x y
| even y = f (x `mappend` x) (y `quot` 2)
| y == 1 = x
| otherwise = g (x `mappend` x) (y `quot` 2) x -- See Note [Half of y - 1]
g x y z
| even y = g (x `mappend` x) (y `quot` 2) z
| y == 1 = x `mappend` z
| otherwise = g (x `mappend` x) (y `quot` 2) (x `mappend` z) -- See Note [Half of y - 1]
-- this is used by the class definition in GHC.Base;
-- it lives here to avoid cycles
stimesDefault :: (Integral b, Semigroup a) => b -> a -> a
stimesDefault y0 x0
| y0 <= 0 = errorWithoutStackTrace "stimes: positive multiplier expected"
| otherwise = f x0 y0
where
f x y
| even y = f (x <> x) (y `quot` 2)
| y == 1 = x
| otherwise = g (x <> x) (y `quot` 2) x -- See Note [Half of y - 1]
g x y z
| even y = g (x <> x) (y `quot` 2) z
| y == 1 = x <> z
| otherwise = g (x <> x) (y `quot` 2) (x <> z) -- See Note [Half of y - 1]
{- Note [Half of y - 1]
~~~~~~~~~~~~~~~~~~~~~
Since y is guaranteed to be odd and positive here,
half of y - 1 can be computed as y `quot` 2, optimising subtraction away.
-}
stimesMaybe :: (Integral b, Semigroup a) => b -> Maybe a -> Maybe a
stimesMaybe _ Nothing = Nothing
stimesMaybe n (Just a) = case compare n 0 of
LT -> errorWithoutStackTrace "stimes: Maybe, negative multiplier"
EQ -> Nothing
GT -> Just (stimes n a)
stimesList :: Integral b => b -> [a] -> [a]
stimesList n x
| n < 0 = errorWithoutStackTrace "stimes: [], negative multiplier"
| otherwise = rep n
where
rep 0 = []
rep i = x ++ rep (i - 1)
-- | The dual of a 'Monoid', obtained by swapping the arguments of '(<>)'.
--
-- > Dual a <> Dual b == Dual (b <> a)
--
-- ==== __Examples__
--
-- >>> Dual "Hello" <> Dual "World"
-- Dual {getDual = "WorldHello"}
--
-- >>> Dual (Dual "Hello") <> Dual (Dual "World")
-- Dual {getDual = Dual {getDual = "HelloWorld"}}
newtype Dual a = Dual { getDual :: a }
deriving ( Eq -- ^ @since 2.01
, Ord -- ^ @since 2.01
, Read -- ^ @since 2.01
, Show -- ^ @since 2.01
, Bounded -- ^ @since 2.01
, Generic -- ^ @since 4.7.0.0
, Generic1 -- ^ @since 4.7.0.0
)
-- | @since 4.9.0.0
instance Semigroup a => Semigroup (Dual a) where
Dual a <> Dual b = Dual (b <> a)
stimes n (Dual a) = Dual (stimes n a)
-- | @since 2.01
instance Monoid a => Monoid (Dual a) where
mempty = Dual mempty
-- | @since 4.8.0.0
instance Functor Dual where
fmap = coerce
-- | @since 4.8.0.0
instance Applicative Dual where
pure = Dual
(<*>) = coerce
-- | @since 4.8.0.0
instance Monad Dual where
m >>= k = k (getDual m)
-- | The monoid of endomorphisms under composition.
--
-- > Endo f <> Endo g == Endo (f . g)
--
-- ==== __Examples__
--
-- >>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")
-- >>> appEndo computation "Haskell"
-- "Hello, Haskell!"
--
-- >>> let computation = Endo (*3) <> Endo (+1)
-- >>> appEndo computation 1
-- 6
newtype Endo a = Endo { appEndo :: a -> a }
deriving ( Generic -- ^ @since 4.7.0.0
)
-- | @since 4.9.0.0
instance Semigroup (Endo a) where
(<>) = coerce ((.) :: (a -> a) -> (a -> a) -> (a -> a))
stimes = stimesMonoid
-- | @since 2.01
instance Monoid (Endo a) where
mempty = Endo id
-- | Boolean monoid under conjunction '(&&)'.
--
-- > All x <> All y = All (x && y)
--
-- ==== __Examples__
--
-- >>> All True <> mempty <> All False)
-- All {getAll = False}
--
-- >>> mconcat (map (\x -> All (even x)) [2,4,6,7,8])
-- All {getAll = False}
--
-- >>> All True <> mempty
-- All {getAll = True}
newtype All = All { getAll :: Bool }
deriving ( Eq -- ^ @since 2.01
, Ord -- ^ @since 2.01
, Read -- ^ @since 2.01
, Show -- ^ @since 2.01
, Bounded -- ^ @since 2.01
, Generic -- ^ @since 4.7.0.0
)
-- | @since 4.9.0.0
instance Semigroup All where
(<>) = coerce (&&)
stimes = stimesIdempotentMonoid
-- | @since 2.01
instance Monoid All where
mempty = All True
-- | Boolean monoid under disjunction '(||)'.
--
-- > Any x <> Any y = Any (x || y)
--
-- ==== __Examples__
--
-- >>> Any True <> mempty <> Any False
-- Any {getAny = True}
--
-- >>> mconcat (map (\x -> Any (even x)) [2,4,6,7,8])
-- Any {getAny = True}
--
-- >>> Any False <> mempty
-- Any {getAny = False}
newtype Any = Any { getAny :: Bool }
deriving ( Eq -- ^ @since 2.01
, Ord -- ^ @since 2.01
, Read -- ^ @since 2.01
, Show -- ^ @since 2.01
, Bounded -- ^ @since 2.01
, Generic -- ^ @since 4.7.0.0
)
-- | @since 4.9.0.0
instance Semigroup Any where
(<>) = coerce (||)
stimes = stimesIdempotentMonoid
-- | @since 2.01
instance Monoid Any where
mempty = Any False
-- | Monoid under addition.
--
-- > Sum a <> Sum b = Sum (a + b)
--
-- ==== __Examples__
--
-- >>> Sum 1 <> Sum 2 <> mempty
-- Sum {getSum = 3}
--
-- >>> mconcat [ Sum n | n <- [3 .. 9]]
-- Sum {getSum = 42}
newtype Sum a = Sum { getSum :: a }
deriving ( Eq -- ^ @since 2.01
, Ord -- ^ @since 2.01
, Read -- ^ @since 2.01
, Show -- ^ @since 2.01
, Bounded -- ^ @since 2.01
, Generic -- ^ @since 4.7.0.0
, Generic1 -- ^ @since 4.7.0.0
, Num -- ^ @since 4.7.0.0
)
-- | @since 4.9.0.0
instance Num a => Semigroup (Sum a) where
(<>) = coerce ((+) :: a -> a -> a)
stimes n (Sum a) = Sum (fromIntegral n * a)
-- | @since 2.01
instance Num a => Monoid (Sum a) where
mempty = Sum 0
-- By default, we would get a lazy right fold. This forces the use of a strict
-- left fold instead.
mconcat = List.foldl' (<>) mempty
{-# INLINE mconcat #-}
-- | @since 4.8.0.0
instance Functor Sum where
fmap = coerce
-- | @since 4.8.0.0
instance Applicative Sum where
pure = Sum
(<*>) = coerce
-- | @since 4.8.0.0
instance Monad Sum where
m >>= k = k (getSum m)
-- | Monoid under multiplication.
--
-- > Product x <> Product y == Product (x * y)
--
-- ==== __Examples__
--
-- >>> Product 3 <> Product 4 <> mempty
-- Product {getProduct = 12}
--
-- >>> mconcat [ Product n | n <- [2 .. 10]]
-- Product {getProduct = 3628800}
newtype Product a = Product { getProduct :: a }
deriving ( Eq -- ^ @since 2.01
, Ord -- ^ @since 2.01
, Read -- ^ @since 2.01
, Show -- ^ @since 2.01
, Bounded -- ^ @since 2.01
, Generic -- ^ @since 4.7.0.0
, Generic1 -- ^ @since 4.7.0.0
, Num -- ^ @since 4.7.0.0
)
-- | @since 4.9.0.0
instance Num a => Semigroup (Product a) where
(<>) = coerce ((*) :: a -> a -> a)
stimes n (Product a) = Product (a ^ n)
-- | @since 2.01
instance Num a => Monoid (Product a) where
mempty = Product 1
-- By default, we would get a lazy right fold. This forces the use of a strict
-- left fold instead.
mconcat = List.foldl' (<>) mempty
{-# INLINE mconcat #-}
-- | @since 4.8.0.0
instance Functor Product where
fmap = coerce
-- | @since 4.8.0.0
instance Applicative Product where
pure = Product
(<*>) = coerce
-- | @since 4.8.0.0
instance Monad Product where
m >>= k = k (getProduct m)
-- | Monoid under '<|>'.
--
-- > Alt l <> Alt r == Alt (l <|> r)
--
-- ==== __Examples__
-- >>> Alt (Just 12) <> Alt (Just 24)
-- Alt {getAlt = Just 12}
--
-- >>> Alt Nothing <> Alt (Just 24)
-- Alt {getAlt = Just 24}
--
-- @since 4.8.0.0
newtype Alt f a = Alt {getAlt :: f a}
deriving ( Generic -- ^ @since 4.8.0.0
, Generic1 -- ^ @since 4.8.0.0
, Read -- ^ @since 4.8.0.0
, Show -- ^ @since 4.8.0.0
, Eq -- ^ @since 4.8.0.0
, Ord -- ^ @since 4.8.0.0
, Num -- ^ @since 4.8.0.0
, Enum -- ^ @since 4.8.0.0
, Monad -- ^ @since 4.8.0.0
, MonadPlus -- ^ @since 4.8.0.0
, Applicative -- ^ @since 4.8.0.0
, Alternative -- ^ @since 4.8.0.0
, Functor -- ^ @since 4.8.0.0
)
-- | @since 4.9.0.0
instance Alternative f => Semigroup (Alt f a) where
(<>) = coerce ((<|>) :: f a -> f a -> f a)
stimes = stimesMonoid
-- | @since 4.8.0.0
instance Alternative f => Monoid (Alt f a) where
mempty = Alt empty