{-# LANGUAGE Safe #-} -- | -- -- 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: -- -- >>> import Data.Int -- >>> 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 import GHC.Internal.Data.Monoid