{-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE GeneralizedNewtypeDeriving #-} {-# LANGUAGE NoImplicitPrelude #-} {-# LANGUAGE PolyKinds #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE Trustworthy #-} ----------------------------------------------------------------------------- -- | -- Module : Data.Monoid -- Copyright : (c) Andy Gill 2001, -- (c) Oregon Graduate Institute of Science and Technology, 2001 -- License : BSD-style (see the file libraries/base/LICENSE) -- -- Maintainer : libraries@haskell.org -- Stability : stable -- Portability : portable -- -- A type @a@ is a 'Monoid' if it provides an associative function ('<>') -- that lets you combine any two values of type @a@ into one, and a neutral -- element (`mempty`) such that -- -- > a <> mempty == mempty <> a == a -- -- A 'Monoid' is a 'Semigroup' with the added requirement of a neutral element. -- Thus any 'Monoid' is a 'Semigroup', but not the other way around. -- -- ==== __Examples__ -- -- The 'Sum' monoid is defined by the numerical addition operator and `0` as neutral element: -- -- >>> mempty :: Sum Int -- Sum {getSum = 0} -- >>> Sum 1 <> Sum 2 <> Sum 3 <> Sum 4 :: Sum Int -- Sum {getSum = 10} -- -- We can combine multiple values in a list into a single value using the `mconcat` function. -- Note that we have to specify the type here since 'Int' is a monoid under several different -- operations: -- -- >>> mconcat [1,2,3,4] :: Sum Int -- Sum {getSum = 10} -- >>> mconcat [] :: Sum Int -- Sum {getSum = 0} -- -- Another valid monoid instance of 'Int' is 'Product' It is defined by multiplication -- and `1` as neutral element: -- -- >>> Product 1 <> Product 2 <> Product 3 <> Product 4 :: Product Int -- Product {getProduct = 24} -- >>> mconcat [1,2,3,4] :: Product Int -- Product {getProduct = 24} -- >>> mconcat [] :: Product Int -- Product {getProduct = 1} -- -- ----------------------------------------------------------------------------- module Data.Monoid ( -- * 'Monoid' typeclass Monoid(..), (<>), Dual(..), Endo(..), -- * 'Bool' wrappers All(..), Any(..), -- * 'Num' wrappers Sum(..), Product(..), -- * 'Maybe' wrappers -- $MaybeExamples First(..), Last(..), -- * 'Alternative' wrapper Alt(..), -- * 'Applicative' wrapper Ap(..) ) where -- Push down the module in the dependency hierarchy. import GHC.Base hiding (Any) import GHC.Enum import GHC.Generics import GHC.Num import GHC.Read import GHC.Show import Control.Monad.Fail (MonadFail) import Data.Semigroup.Internal -- $MaybeExamples -- To implement @find@ or @findLast@ on any 'Data.Foldable.Foldable': -- -- @ -- findLast :: Foldable t => (a -> Bool) -> t a -> Maybe a -- findLast pred = getLast . foldMap (\x -> if pred x -- then Last (Just x) -- else Last Nothing) -- @ -- -- Much of 'Data.Map.Lazy.Map's interface can be implemented with -- 'Data.Map.Lazy.alter'. Some of the rest can be implemented with a new -- 'Data.Map.Lazy.alterF' function and either 'First' or 'Last': -- -- > alterF :: (Functor f, Ord k) => -- > (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a) -- > -- > instance Monoid a => Functor ((,) a) -- from Data.Functor -- -- @ -- insertLookupWithKey :: Ord k => (k -> v -> v -> v) -> k -> v -- -> Map k v -> (Maybe v, Map k v) -- insertLookupWithKey combine key value = -- Arrow.first getFirst . 'Data.Map.Lazy.alterF' doChange key -- where -- doChange Nothing = (First Nothing, Just value) -- doChange (Just oldValue) = -- (First (Just oldValue), -- Just (combine key value oldValue)) -- @ -- | Maybe monoid returning the leftmost non-'Nothing' value. -- -- @'First' a@ is isomorphic to @'Alt' 'Maybe' a@, but precedes it -- historically. -- -- >>> getFirst (First (Just "hello") <> First Nothing <> First (Just "world")) -- Just "hello" -- -- Beware that @Data.Monoid.@'First' is different from -- @Data.Semigroup.@'Data.Semigroup.First'. The former returns the first non-'Nothing', -- so @Data.Monoid.First Nothing <> x = x@. The latter simply returns the first value, -- thus @Data.Semigroup.First Nothing <> x = Data.Semigroup.First Nothing@. -- newtype First a = First { getFirst :: Maybe a } deriving ( Eq -- ^ @since 2.01 , Ord -- ^ @since 2.01 , Read -- ^ @since 2.01 , Show -- ^ @since 2.01 , Generic -- ^ @since 4.7.0.0 , Generic1 -- ^ @since 4.7.0.0 , Functor -- ^ @since 4.8.0.0 , Applicative -- ^ @since 4.8.0.0 , Monad -- ^ @since 4.8.0.0 ) -- | @since 4.9.0.0 instance Semigroup (First a) where First Nothing <> b = b a <> _ = a stimes = stimesIdempotentMonoid -- | @since 2.01 instance Monoid (First a) where mempty = First Nothing -- | Maybe monoid returning the rightmost non-'Nothing' value. -- -- @'Last' a@ is isomorphic to @'Dual' ('First' a)@, and thus to -- @'Dual' ('Alt' 'Maybe' a)@ -- -- >>> getLast (Last (Just "hello") <> Last Nothing <> Last (Just "world")) -- Just "world" -- -- Beware that @Data.Monoid.@'Last' is different from -- @Data.Semigroup.@'Data.Semigroup.Last'. The former returns the last non-'Nothing', -- so @x <> Data.Monoid.Last Nothing = x@. The latter simply returns the last value, -- thus @x <> Data.Semigroup.Last Nothing = Data.Semigroup.Last Nothing@. -- newtype Last a = Last { getLast :: Maybe a } deriving ( Eq -- ^ @since 2.01 , Ord -- ^ @since 2.01 , Read -- ^ @since 2.01 , Show -- ^ @since 2.01 , Generic -- ^ @since 4.7.0.0 , Generic1 -- ^ @since 4.7.0.0 , Functor -- ^ @since 4.8.0.0 , Applicative -- ^ @since 4.8.0.0 , Monad -- ^ @since 4.8.0.0 ) -- | @since 4.9.0.0 instance Semigroup (Last a) where a <> Last Nothing = a _ <> b = b stimes = stimesIdempotentMonoid -- | @since 2.01 instance Monoid (Last a) where mempty = Last Nothing -- | This data type witnesses the lifting of a 'Monoid' into an -- 'Applicative' pointwise. -- -- @since 4.12.0.0 newtype Ap f a = Ap { getAp :: f a } deriving ( Alternative -- ^ @since 4.12.0.0 , Applicative -- ^ @since 4.12.0.0 , Enum -- ^ @since 4.12.0.0 , Eq -- ^ @since 4.12.0.0 , Functor -- ^ @since 4.12.0.0 , Generic -- ^ @since 4.12.0.0 , Generic1 -- ^ @since 4.12.0.0 , Monad -- ^ @since 4.12.0.0 , MonadFail -- ^ @since 4.12.0.0 , MonadPlus -- ^ @since 4.12.0.0 , Ord -- ^ @since 4.12.0.0 , Read -- ^ @since 4.12.0.0 , Show -- ^ @since 4.12.0.0 ) -- | @since 4.12.0.0 instance (Applicative f, Semigroup a) => Semigroup (Ap f a) where (Ap x) <> (Ap y) = Ap $ liftA2 (<>) x y -- | @since 4.12.0.0 instance (Applicative f, Monoid a) => Monoid (Ap f a) where mempty = Ap $ pure mempty -- | @since 4.12.0.0 instance (Applicative f, Bounded a) => Bounded (Ap f a) where minBound = pure minBound maxBound = pure maxBound -- | Note that even if the underlying 'Num' and 'Applicative' instances are -- lawful, for most 'Applicative's, this instance will not be lawful. If you use -- this instance with the list 'Applicative', the following customary laws will -- not hold: -- -- Commutativity: -- -- >>> Ap [10,20] + Ap [1,2] -- Ap {getAp = [11,12,21,22]} -- >>> Ap [1,2] + Ap [10,20] -- Ap {getAp = [11,21,12,22]} -- -- Additive inverse: -- -- >>> Ap [] + negate (Ap []) -- Ap {getAp = []} -- >>> fromInteger 0 :: Ap [] Int -- Ap {getAp = [0]} -- -- Distributivity: -- -- >>> Ap [1,2] * (3 + 4) -- Ap {getAp = [7,14]} -- >>> (Ap [1,2] * 3) + (Ap [1,2] * 4) -- Ap {getAp = [7,11,10,14]} -- -- @since 4.12.0.0 instance (Applicative f, Num a) => Num (Ap f a) where (+) = liftA2 (+) (*) = liftA2 (*) negate = fmap negate fromInteger = pure . fromInteger abs = fmap abs signum = fmap signum {- {-------------------------------------------------------------------- Testing --------------------------------------------------------------------} instance Arbitrary a => Arbitrary (Maybe a) where arbitrary = oneof [return Nothing, Just `fmap` arbitrary] prop_mconcatMaybe :: [Maybe [Int]] -> Bool prop_mconcatMaybe x = fromMaybe [] (mconcat x) == mconcat (catMaybes x) prop_mconcatFirst :: [Maybe Int] -> Bool prop_mconcatFirst x = getFirst (mconcat (map First x)) == listToMaybe (catMaybes x) prop_mconcatLast :: [Maybe Int] -> Bool prop_mconcatLast x = getLast (mconcat (map Last x)) == listLastToMaybe (catMaybes x) where listLastToMaybe [] = Nothing listLastToMaybe lst = Just (last lst) -- -} -- $setup -- >>> import Prelude