Data/Monoid.hs

{-# 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 : experimental
-- 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 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"
--
-- Use of this type is discouraged. Note the following equivalence:
--
-- > Data.Monoid.First x === Maybe (Data.Semigroup.First x)
--
-- In addition to being equivalent in the structural sense, the two
-- also have 'Monoid' instances that behave the same. This type will
-- be marked deprecated in GHC 8.8, and removed in GHC 8.10.
-- Users are advised to use the variant from "Data.Semigroup" and wrap
-- it in 'Maybe'.
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"
--
-- Use of this type is discouraged. Note the following equivalence:
--
-- > Data.Monoid.Last x === Maybe (Data.Semigroup.Last x)
--
-- In addition to being equivalent in the structural sense, the two
-- also have 'Monoid' instances that behave the same. This type will
-- be marked deprecated in GHC 8.8, and removed in GHC 8.10.
-- Users are advised to use the variant from "Data.Semigroup" and wrap
-- it in 'Maybe'.
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

-- | @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