Data.Semigroup

base-4.10.1.0: Basic libraries

Copyright | (C) 2011-2015 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | libraries@haskell.org
Stability | provisional
Portability | portable
Safe Haskell | Trustworthy
Language | Haskell2010

Data.Semigroup

Contents

- Semigroups
- Re-exported monoids from Data.Monoid
- A better monoid for Maybe
- Difference lists of a semigroup
- ArgMin, ArgMax

Description

In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup generalizes a monoid in that there might not exist an identity element. It also (originally) generalized a group (a monoid with all inverses) to a type where every element did not have to have an inverse, thus the name semigroup.

The use of `(<>)` in this module conflicts with an operator with the same name that is being exported by Data.Monoid. However, this package re-exports (most of) the contents of Data.Monoid, so to use semigroups and monoids in the same package just

    import Data.Semigroup

Since: 4.9.0.0

Synopsis

- class Semigroup a where
- stimesMonoid :: (Integral b, Monoid a) => b -> a -> a
- stimesIdempotent :: Integral b => b -> a -> a
- stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a
- mtimesDefault :: (Integral b, Monoid a) => b -> a -> a
- newtype Min a = Min {
  - getMin :: a
  }
- newtype Max a = Max {
  - getMax :: a
  }
- newtype First a = First {
  - getFirst :: a
  }
- newtype Last a = Last {
  - getLast :: a
  }
- newtype WrappedMonoid m = WrapMonoid {
  - unwrapMonoid :: m
  }
- class Monoid a where
- newtype Dual a = Dual {
  - getDual :: a
  }
- newtype Endo a = Endo {
  - appEndo :: a -> a
  }
- newtype All = All {
  - getAll :: Bool
  }
- newtype Any = Any {
  - getAny :: Bool
  }
- newtype Sum a = Sum {
  - getSum :: a
  }
- newtype Product a = Product {
  - getProduct :: a
  }
- newtype Option a = Option {
  - getOption :: Maybe a
  }
- option :: b -> (a -> b) -> Option a -> b
- diff :: Semigroup m => m -> Endo m
- cycle1 :: Semigroup m => m -> m
- data Arg a b = Arg a b
- type ArgMin a b = Min (Arg a b)
- type ArgMax a b = Max (Arg a b)

# Documentation

class Semigroup a where Source #

The class of semigroups (types with an associative binary operation).

Since: 4.9.0.0

Methods

(<>) :: a -> a -> a infixr 6 Source #

An associative operation.

    (a <> b) <> c = a <> (b <> c)

If `a` is also a `Monoid` we further require

    (<>) = mappend

(<>) :: Monoid a => a -> a -> a infixr 6 Source #

An associative operation.

    (a <> b) <> c = a <> (b <> c)

If `a` is also a `Monoid` we further require

    (<>) = mappend

sconcat :: NonEmpty a -> a Source #

Reduce a non-empty list with `<>`

The default definition should be sufficient, but this can be overridden for efficiency.

stimes :: Integral b => b -> a -> a Source #

Repeat a value `n` times.

Given that this works on a `Semigroup` it is allowed to fail if you request 0 or fewer repetitions, and the default definition will do so.

By making this a member of the class, idempotent semigroups and monoids can upgrade this to execute in O(1) by picking `stimes = stimesIdempotent` or `stimes = stimesIdempotentMonoid` respectively.

Instances

Semigroup Ordering # | Since: 4.9.0.0
Methods (<>) :: Ordering -> Ordering -> Ordering Source # sconcat :: NonEmpty Ordering -> Ordering Source # stimes :: Integral b => b -> Ordering -> Ordering Source #
Semigroup () # | Since: 4.9.0.0
Methods (<>) :: () -> () -> () Source # sconcat :: NonEmpty () -> () Source # stimes :: Integral b => b -> () -> () Source #
Semigroup Any # | Since: 4.9.0.0
Methods (<>) :: Any -> Any -> Any Source # sconcat :: NonEmpty Any -> Any Source # stimes :: Integral b => b -> Any -> Any Source #
Semigroup All # | Since: 4.9.0.0
Methods (<>) :: All -> All -> All Source # sconcat :: NonEmpty All -> All Source # stimes :: Integral b => b -> All -> All Source #
Semigroup Lifetime # | Since: 4.10.0.0
Methods (<>) :: Lifetime -> Lifetime -> Lifetime Source # sconcat :: NonEmpty Lifetime -> Lifetime Source # stimes :: Integral b => b -> Lifetime -> Lifetime Source #
Semigroup Event # | Since: 4.10.0.0
Methods (<>) :: Event -> Event -> Event Source # sconcat :: NonEmpty Event -> Event Source # stimes :: Integral b => b -> Event -> Event Source #
Semigroup Void # | Since: 4.9.0.0
Methods (<>) :: Void -> Void -> Void Source # sconcat :: NonEmpty Void -> Void Source # stimes :: Integral b => b -> Void -> Void Source #
Semigroup [a] # | Since: 4.9.0.0
Methods (<>) :: [a] -> [a] -> [a] Source # sconcat :: NonEmpty [a] -> [a] Source # stimes :: Integral b => b -> [a] -> [a] Source #
Semigroup a => Semigroup (Maybe a) # | Since: 4.9.0.0
Methods (<>) :: Maybe a -> Maybe a -> Maybe a Source # sconcat :: NonEmpty (Maybe a) -> Maybe a Source # stimes :: Integral b => b -> Maybe a -> Maybe a Source #
Semigroup a => Semigroup (IO a) # | Since: 4.10.0.0
Methods (<>) :: IO a -> IO a -> IO a Source # sconcat :: NonEmpty (IO a) -> IO a Source # stimes :: Integral b => b -> IO a -> IO a Source #
Semigroup (Last a) # | Since: 4.9.0.0
Methods (<>) :: Last a -> Last a -> Last a Source # sconcat :: NonEmpty (Last a) -> Last a Source # stimes :: Integral b => b -> Last a -> Last a Source #
Semigroup (First a) # | Since: 4.9.0.0
Methods (<>) :: First a -> First a -> First a Source # sconcat :: NonEmpty (First a) -> First a Source # stimes :: Integral b => b -> First a -> First a Source #
Num a => Semigroup (Product a) # | Since: 4.9.0.0
Methods (<>) :: Product a -> Product a -> Product a Source # sconcat :: NonEmpty (Product a) -> Product a Source # stimes :: Integral b => b -> Product a -> Product a Source #
Num a => Semigroup (Sum a) # | Since: 4.9.0.0
Methods (<>) :: Sum a -> Sum a -> Sum a Source # sconcat :: NonEmpty (Sum a) -> Sum a Source # stimes :: Integral b => b -> Sum a -> Sum a Source #
Semigroup (Endo a) # | Since: 4.9.0.0
Methods (<>) :: Endo a -> Endo a -> Endo a Source # sconcat :: NonEmpty (Endo a) -> Endo a Source # stimes :: Integral b => b -> Endo a -> Endo a Source #
Semigroup a => Semigroup (Dual a) # | Since: 4.9.0.0
Methods (<>) :: Dual a -> Dual a -> Dual a Source # sconcat :: NonEmpty (Dual a) -> Dual a Source # stimes :: Integral b => b -> Dual a -> Dual a Source #
Semigroup a => Semigroup (Identity a) # | Since: 4.9.0.0
Methods (<>) :: Identity a -> Identity a -> Identity a Source # sconcat :: NonEmpty (Identity a) -> Identity a Source # stimes :: Integral b => b -> Identity a -> Identity a Source #
Semigroup (NonEmpty a) # | Since: 4.9.0.0
Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a Source # sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a Source # stimes :: Integral b => b -> NonEmpty a -> NonEmpty a Source #
Semigroup a => Semigroup (Option a) # | Since: 4.9.0.0
Methods (<>) :: Option a -> Option a -> Option a Source # sconcat :: NonEmpty (Option a) -> Option a Source # stimes :: Integral b => b -> Option a -> Option a Source #
Monoid m => Semigroup (WrappedMonoid m) # | Since: 4.9.0.0
Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source #
Semigroup (Last a) # | Since: 4.9.0.0
Methods (<>) :: Last a -> Last a -> Last a Source # sconcat :: NonEmpty (Last a) -> Last a Source # stimes :: Integral b => b -> Last a -> Last a Source #
Semigroup (First a) # | Since: 4.9.0.0
Methods (<>) :: First a -> First a -> First a Source # sconcat :: NonEmpty (First a) -> First a Source # stimes :: Integral b => b -> First a -> First a Source #
Ord a => Semigroup (Max a) # | Since: 4.9.0.0
Methods (<>) :: Max a -> Max a -> Max a Source # sconcat :: NonEmpty (Max a) -> Max a Source # stimes :: Integral b => b -> Max a -> Max a Source #
Ord a => Semigroup (Min a) # | Since: 4.9.0.0
Methods (<>) :: Min a -> Min a -> Min a Source # sconcat :: NonEmpty (Min a) -> Min a Source # stimes :: Integral b => b -> Min a -> Min a Source #
Semigroup b => Semigroup (a -> b) # | Since: 4.9.0.0
Methods (<>) :: (a -> b) -> (a -> b) -> a -> b Source # sconcat :: NonEmpty (a -> b) -> a -> b Source # stimes :: Integral b => b -> (a -> b) -> a -> b Source #
Semigroup (Either a b) # | Since: 4.9.0.0
Methods (<>) :: Either a b -> Either a b -> Either a b Source # sconcat :: NonEmpty (Either a b) -> Either a b Source # stimes :: Integral b => b -> Either a b -> Either a b Source #
(Semigroup a, Semigroup b) => Semigroup (a, b) # | Since: 4.9.0.0
Methods (<>) :: (a, b) -> (a, b) -> (a, b) Source # sconcat :: NonEmpty (a, b) -> (a, b) Source # stimes :: Integral b => b -> (a, b) -> (a, b) Source #
Semigroup (Proxy k s) # | Since: 4.9.0.0
Methods (<>) :: Proxy k s -> Proxy k s -> Proxy k s Source # sconcat :: NonEmpty (Proxy k s) -> Proxy k s Source # stimes :: Integral b => b -> Proxy k s -> Proxy k s Source #
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) # | Since: 4.9.0.0
Methods (<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # sconcat :: NonEmpty (a, b, c) -> (a, b, c) Source # stimes :: Integral b => b -> (a, b, c) -> (a, b, c) Source #
Alternative f => Semigroup (Alt * f a) # | Since: 4.9.0.0
Methods (<>) :: Alt * f a -> Alt * f a -> Alt * f a Source # sconcat :: NonEmpty (Alt * f a) -> Alt * f a Source # stimes :: Integral b => b -> Alt * f a -> Alt * f a Source #
Semigroup a => Semigroup (Const k a b) # | Since: 4.9.0.0
Methods (<>) :: Const k a b -> Const k a b -> Const k a b Source # sconcat :: NonEmpty (Const k a b) -> Const k a b Source # stimes :: Integral b => b -> Const k a b -> Const k a b Source #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) # | Since: 4.9.0.0
Methods (<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) Source # stimes :: Integral b => b -> (a, b, c, d) -> (a, b, c, d) Source #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) # | Since: 4.9.0.0
Methods (<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) Source # stimes :: Integral b => b -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

stimesMonoid :: (Integral b, Monoid a) => b -> a -> a Source #

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.

stimesIdempotent :: Integral b => b -> a -> a Source #

This is a valid definition of `stimes` for an idempotent `Semigroup`.

When `x <> x = x`, this definition should be preferred, because it works in O(1) rather than O(log n).

stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a Source #

This is a valid definition of `stimes` for an idempotent `Monoid`.

When `mappend x x = x`, this definition should be preferred, because it works in O(1) rather than O(log n)

mtimesDefault :: (Integral b, Monoid a) => b -> a -> a Source #

Repeat a value `n` times.

    mtimesDefault n a = a <> a <> ... <> a  -- using <> (n-1) times

Implemented using `stimes` and `mempty`.

This is a suitable definition for an `mtimes` member of `Monoid`.

# Semigroups

newtype Min a Source #

Constructors

Min |
Fields getMin :: a

Instances

Monad Min # | Since: 4.9.0.0
Methods (>>=) :: Min a -> (a -> Min b) -> Min b Source # (>>) :: Min a -> Min b -> Min b Source # return :: a -> Min a Source # fail :: String -> Min a Source #
Functor Min # | Since: 4.9.0.0
Methods fmap :: (a -> b) -> Min a -> Min b Source # (<$) :: a -> Min b -> Min a Source #
MonadFix Min # | Since: 4.9.0.0
Methods mfix :: (a -> Min a) -> Min a Source #
Applicative Min # | Since: 4.9.0.0
Methods pure :: a -> Min a Source # (<*>) :: Min (a -> b) -> Min a -> Min b Source # liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c Source # (*>) :: Min a -> Min b -> Min b Source # (<*) :: Min a -> Min b -> Min a Source #
Foldable Min # | Since: 4.9.0.0
Methods fold :: Monoid m => Min m -> m Source # foldMap :: Monoid m => (a -> m) -> Min a -> m Source # foldr :: (a -> b -> b) -> b -> Min a -> b Source # foldr' :: (a -> b -> b) -> b -> Min a -> b Source # foldl :: (b -> a -> b) -> b -> Min a -> b Source # foldl' :: (b -> a -> b) -> b -> Min a -> b Source # foldr1 :: (a -> a -> a) -> Min a -> a Source # foldl1 :: (a -> a -> a) -> Min a -> a Source # toList :: Min a -> [a] Source # null :: Min a -> Bool Source # length :: Min a -> Int Source # elem :: Eq a => a -> Min a -> Bool Source # maximum :: Ord a => Min a -> a Source # minimum :: Ord a => Min a -> a Source # sum :: Num a => Min a -> a Source # product :: Num a => Min a -> a Source #
Traversable Min # | Since: 4.9.0.0
Methods traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) Source # sequenceA :: Applicative f => Min (f a) -> f (Min a) Source # mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) Source # sequence :: Monad m => Min (m a) -> m (Min a) Source #
Bounded a => Bounded (Min a) # |
Methods minBound :: Min a Source # maxBound :: Min a Source #
Enum a => Enum (Min a) # | Since: 4.9.0.0
Methods succ :: Min a -> Min a Source # pred :: Min a -> Min a Source # toEnum :: Int -> Min a Source # fromEnum :: Min a -> Int Source # enumFrom :: Min a -> [Min a] Source # enumFromThen :: Min a -> Min a -> [Min a] Source # enumFromTo :: Min a -> Min a -> [Min a] Source # enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] Source #
Eq a => Eq (Min a) # |
Methods (==) :: Min a -> Min a -> Bool Source # (/=) :: Min a -> Min a -> Bool Source #
Data a => Data (Min a) # |
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Min a -> c (Min a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Min a) Source # toConstr :: Min a -> Constr Source # dataTypeOf :: Min a -> DataType Source # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Min a)) Source # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a)) Source # gmapT :: (forall b. Data b => b -> b) -> Min a -> Min a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Min a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Min a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source #
Num a => Num (Min a) # | Since: 4.9.0.0
Methods (+) :: Min a -> Min a -> Min a Source # (-) :: Min a -> Min a -> Min a Source # (*) :: Min a -> Min a -> Min a Source # negate :: Min a -> Min a Source # abs :: Min a -> Min a Source # signum :: Min a -> Min a Source # fromInteger :: Integer -> Min a Source #
Ord a => Ord (Min a) # |
Methods compare :: Min a -> Min a -> Ordering Source # (<) :: Min a -> Min a -> Bool Source # (<=) :: Min a -> Min a -> Bool Source # (>) :: Min a -> Min a -> Bool Source # (>=) :: Min a -> Min a -> Bool Source # max :: Min a -> Min a -> Min a Source # min :: Min a -> Min a -> Min a Source #
Read a => Read (Min a) # |
Methods readsPrec :: Int -> ReadS (Min a) Source # readList :: ReadS [Min a] Source # readPrec :: ReadPrec (Min a) Source # readListPrec :: ReadPrec [Min a] Source #
Show a => Show (Min a) # |
Methods showsPrec :: Int -> Min a -> ShowS Source # show :: Min a -> String Source # showList :: [Min a] -> ShowS Source #
Generic (Min a) # |
Associated Types type Rep (Min a) :: * -> * Source # Methods from :: Min a -> Rep (Min a) x Source # to :: Rep (Min a) x -> Min a Source #
Ord a => Semigroup (Min a) # | Since: 4.9.0.0
Methods (<>) :: Min a -> Min a -> Min a Source # sconcat :: NonEmpty (Min a) -> Min a Source # stimes :: Integral b => b -> Min a -> Min a Source #
(Ord a, Bounded a) => Monoid (Min a) # | Since: 4.9.0.0
Methods mempty :: Min a Source # mappend :: Min a -> Min a -> Min a Source # mconcat :: [Min a] -> Min a Source #
Generic1 * Min # |
Associated Types type Rep1 Min (f :: Min -> *) :: k -> * Source # Methods from1 :: f a -> Rep1 Min f a Source # to1 :: Rep1 Min f a -> f a Source #
type Rep (Min a) # |
type Rep (Min a) = D1 * (MetaData "Min" "Data.Semigroup" "base" True) (C1 * (MetaCons "Min" PrefixI True) (S1 * (MetaSel (Just Symbol "getMin") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Min # |
type Rep1 * Min = D1 * (MetaData "Min" "Data.Semigroup" "base" True) (C1 * (MetaCons "Min" PrefixI True) (S1 * (MetaSel (Just Symbol "getMin") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Max a Source #

Constructors

Max |
Fields getMax :: a

Instances

Monad Max # | Since: 4.9.0.0
Methods (>>=) :: Max a -> (a -> Max b) -> Max b Source # (>>) :: Max a -> Max b -> Max b Source # return :: a -> Max a Source # fail :: String -> Max a Source #
Functor Max # | Since: 4.9.0.0
Methods fmap :: (a -> b) -> Max a -> Max b Source # (<$) :: a -> Max b -> Max a Source #
MonadFix Max # | Since: 4.9.0.0
Methods mfix :: (a -> Max a) -> Max a Source #
Applicative Max # | Since: 4.9.0.0
Methods pure :: a -> Max a Source # (<*>) :: Max (a -> b) -> Max a -> Max b Source # liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c Source # (*>) :: Max a -> Max b -> Max b Source # (<*) :: Max a -> Max b -> Max a Source #
Foldable Max # | Since: 4.9.0.0
Methods fold :: Monoid m => Max m -> m Source # foldMap :: Monoid m => (a -> m) -> Max a -> m Source # foldr :: (a -> b -> b) -> b -> Max a -> b Source # foldr' :: (a -> b -> b) -> b -> Max a -> b Source # foldl :: (b -> a -> b) -> b -> Max a -> b Source # foldl' :: (b -> a -> b) -> b -> Max a -> b Source # foldr1 :: (a -> a -> a) -> Max a -> a Source # foldl1 :: (a -> a -> a) -> Max a -> a Source # toList :: Max a -> [a] Source # null :: Max a -> Bool Source # length :: Max a -> Int Source # elem :: Eq a => a -> Max a -> Bool Source # maximum :: Ord a => Max a -> a Source # minimum :: Ord a => Max a -> a Source # sum :: Num a => Max a -> a Source # product :: Num a => Max a -> a Source #
Traversable Max # | Since: 4.9.0.0
Methods traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) Source # sequenceA :: Applicative f => Max (f a) -> f (Max a) Source # mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) Source # sequence :: Monad m => Max (m a) -> m (Max a) Source #
Bounded a => Bounded (Max a) # |
Methods minBound :: Max a Source # maxBound :: Max a Source #
Enum a => Enum (Max a) # | Since: 4.9.0.0
Methods succ :: Max a -> Max a Source # pred :: Max a -> Max a Source # toEnum :: Int -> Max a Source # fromEnum :: Max a -> Int Source # enumFrom :: Max a -> [Max a] Source # enumFromThen :: Max a -> Max a -> [Max a] Source # enumFromTo :: Max a -> Max a -> [Max a] Source # enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] Source #
Eq a => Eq (Max a) # |
Methods (==) :: Max a -> Max a -> Bool Source # (/=) :: Max a -> Max a -> Bool Source #
Data a => Data (Max a) # |
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Max a -> c (Max a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Max a) Source # toConstr :: Max a -> Constr Source # dataTypeOf :: Max a -> DataType Source # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Max a)) Source # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a)) Source # gmapT :: (forall b. Data b => b -> b) -> Max a -> Max a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Max a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Max a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source #
Num a => Num (Max a) # | Since: 4.9.0.0
Methods (+) :: Max a -> Max a -> Max a Source # (-) :: Max a -> Max a -> Max a Source # (*) :: Max a -> Max a -> Max a Source # negate :: Max a -> Max a Source # abs :: Max a -> Max a Source # signum :: Max a -> Max a Source # fromInteger :: Integer -> Max a Source #
Ord a => Ord (Max a) # |
Methods compare :: Max a -> Max a -> Ordering Source # (<) :: Max a -> Max a -> Bool Source # (<=) :: Max a -> Max a -> Bool Source # (>) :: Max a -> Max a -> Bool Source # (>=) :: Max a -> Max a -> Bool Source # max :: Max a -> Max a -> Max a Source # min :: Max a -> Max a -> Max a Source #
Read a => Read (Max a) # |
Methods readsPrec :: Int -> ReadS (Max a) Source # readList :: ReadS [Max a] Source # readPrec :: ReadPrec (Max a) Source # readListPrec :: ReadPrec [Max a] Source #
Show a => Show (Max a) # |
Methods showsPrec :: Int -> Max a -> ShowS Source # show :: Max a -> String Source # showList :: [Max a] -> ShowS Source #
Generic (Max a) # |
Associated Types type Rep (Max a) :: * -> * Source # Methods from :: Max a -> Rep (Max a) x Source # to :: Rep (Max a) x -> Max a Source #
Ord a => Semigroup (Max a) # | Since: 4.9.0.0
Methods (<>) :: Max a -> Max a -> Max a Source # sconcat :: NonEmpty (Max a) -> Max a Source # stimes :: Integral b => b -> Max a -> Max a Source #
(Ord a, Bounded a) => Monoid (Max a) # | Since: 4.9.0.0
Methods mempty :: Max a Source # mappend :: Max a -> Max a -> Max a Source # mconcat :: [Max a] -> Max a Source #
Generic1 * Max # |
Associated Types type Rep1 Max (f :: Max -> *) :: k -> * Source # Methods from1 :: f a -> Rep1 Max f a Source # to1 :: Rep1 Max f a -> f a Source #
type Rep (Max a) # |
type Rep (Max a) = D1 * (MetaData "Max" "Data.Semigroup" "base" True) (C1 * (MetaCons "Max" PrefixI True) (S1 * (MetaSel (Just Symbol "getMax") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Max # |
type Rep1 * Max = D1 * (MetaData "Max" "Data.Semigroup" "base" True) (C1 * (MetaCons "Max" PrefixI True) (S1 * (MetaSel (Just Symbol "getMax") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype First a Source #

Use ``Option` (`First` a)` to get the behavior of `First` from Data.Monoid.

Constructors

First |
Fields getFirst :: a

Instances

Monad First # | Since: 4.9.0.0
Methods (>>=) :: First a -> (a -> First b) -> First b Source # (>>) :: First a -> First b -> First b Source # return :: a -> First a Source # fail :: String -> First a Source #
Functor First # | Since: 4.9.0.0
Methods fmap :: (a -> b) -> First a -> First b Source # (<$) :: a -> First b -> First a Source #
MonadFix First # | Since: 4.9.0.0
Methods mfix :: (a -> First a) -> First a Source #
Applicative First # | Since: 4.9.0.0
Methods pure :: a -> First a Source # (<*>) :: First (a -> b) -> First a -> First b Source # liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source # (*>) :: First a -> First b -> First b Source # (<*) :: First a -> First b -> First a Source #
Foldable First # | Since: 4.9.0.0
Methods fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # sum :: Num a => First a -> a Source # product :: Num a => First a -> a Source #
Traversable First # | Since: 4.9.0.0
Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) Source # sequenceA :: Applicative f => First (f a) -> f (First a) Source # mapM :: Monad m => (a -> m b) -> First a -> m (First b) Source # sequence :: Monad m => First (m a) -> m (First a) Source #
Bounded a => Bounded (First a) # |
Methods minBound :: First a Source # maxBound :: First a Source #
Enum a => Enum (First a) # | Since: 4.9.0.0
Methods succ :: First a -> First a Source # pred :: First a -> First a Source # toEnum :: Int -> First a Source # fromEnum :: First a -> Int Source # enumFrom :: First a -> [First a] Source # enumFromThen :: First a -> First a -> [First a] Source # enumFromTo :: First a -> First a -> [First a] Source # enumFromThenTo :: First a -> First a -> First a -> [First a] Source #
Eq a => Eq (First a) # |
Methods (==) :: First a -> First a -> Bool Source # (/=) :: First a -> First a -> Bool Source #
Data a => Data (First a) # |
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) Source # toConstr :: First a -> Constr Source # dataTypeOf :: First a -> DataType Source # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) Source # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) Source # gmapT :: (forall b. Data b => b -> b) -> First a -> First a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source #
Ord a => Ord (First a) # |
Methods compare :: First a -> First a -> Ordering Source # (<) :: First a -> First a -> Bool Source # (<=) :: First a -> First a -> Bool Source # (>) :: First a -> First a -> Bool Source # (>=) :: First a -> First a -> Bool Source # max :: First a -> First a -> First a Source # min :: First a -> First a -> First a Source #
Read a => Read (First a) # |
Methods readsPrec :: Int -> ReadS (First a) Source # readList :: ReadS [First a] Source # readPrec :: ReadPrec (First a) Source # readListPrec :: ReadPrec [First a] Source #
Show a => Show (First a) # |
Methods showsPrec :: Int -> First a -> ShowS Source # show :: First a -> String Source # showList :: [First a] -> ShowS Source #
Generic (First a) # |
Associated Types type Rep (First a) :: * -> * Source # Methods from :: First a -> Rep (First a) x Source # to :: Rep (First a) x -> First a Source #
Semigroup (First a) # | Since: 4.9.0.0
Methods (<>) :: First a -> First a -> First a Source # sconcat :: NonEmpty (First a) -> First a Source # stimes :: Integral b => b -> First a -> First a Source #
Generic1 * First # |
Associated Types type Rep1 First (f :: First -> *) :: k -> * Source # Methods from1 :: f a -> Rep1 First f a Source # to1 :: Rep1 First f a -> f a Source #
type Rep (First a) # |
type Rep (First a) = D1 * (MetaData "First" "Data.Semigroup" "base" True) (C1 * (MetaCons "First" PrefixI True) (S1 * (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * First # |
type Rep1 * First = D1 * (MetaData "First" "Data.Semigroup" "base" True) (C1 * (MetaCons "First" PrefixI True) (S1 * (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Last a Source #

Use ``Option` (`Last` a)` to get the behavior of `Last` from Data.Monoid

Constructors

Last |
Fields getLast :: a

Instances

Monad Last # | Since: 4.9.0.0
Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source # (>>) :: Last a -> Last b -> Last b Source # return :: a -> Last a Source # fail :: String -> Last a Source #
Functor Last # | Since: 4.9.0.0
Methods fmap :: (a -> b) -> Last a -> Last b Source # (<$) :: a -> Last b -> Last a Source #
MonadFix Last # | Since: 4.9.0.0
Methods mfix :: (a -> Last a) -> Last a Source #
Applicative Last # | Since: 4.9.0.0
Methods pure :: a -> Last a Source # (<*>) :: Last (a -> b) -> Last a -> Last b Source # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source # (*>) :: Last a -> Last b -> Last b Source # (<*) :: Last a -> Last b -> Last a Source #
Foldable Last # | Since: 4.9.0.0
Methods fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # sum :: Num a => Last a -> a Source # product :: Num a => Last a -> a Source #
Traversable Last # | Since: 4.9.0.0
Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) Source # sequenceA :: Applicative f => Last (f a) -> f (Last a) Source # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) Source # sequence :: Monad m => Last (m a) -> m (Last a) Source #
Bounded a => Bounded (Last a) # |
Methods minBound :: Last a Source # maxBound :: Last a Source #
Enum a => Enum (Last a) # | Since: 4.9.0.0
Methods succ :: Last a -> Last a Source # pred :: Last a -> Last a Source # toEnum :: Int -> Last a Source # fromEnum :: Last a -> Int Source # enumFrom :: Last a -> [Last a] Source # enumFromThen :: Last a -> Last a -> [Last a] Source # enumFromTo :: Last a -> Last a -> [Last a] Source # enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] Source #
Eq a => Eq (Last a) # |
Methods (==) :: Last a -> Last a -> Bool Source # (/=) :: Last a -> Last a -> Bool Source #
Data a => Data (Last a) # |
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) Source # toConstr :: Last a -> Constr Source # dataTypeOf :: Last a -> DataType Source # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) Source # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) Source # gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source #
Ord a => Ord (Last a) # |
Methods compare :: Last a -> Last a -> Ordering Source # (<) :: Last a -> Last a -> Bool Source # (<=) :: Last a -> Last a -> Bool Source # (>) :: Last a -> Last a -> Bool Source # (>=) :: Last a -> Last a -> Bool Source # max :: Last a -> Last a -> Last a Source # min :: Last a -> Last a -> Last a Source #
Read a => Read (Last a) # |
Methods readsPrec :: Int -> ReadS (Last a) Source # readList :: ReadS [Last a] Source # readPrec :: ReadPrec (Last a) Source # readListPrec :: ReadPrec [Last a] Source #
Show a => Show (Last a) # |
Methods showsPrec :: Int -> Last a -> ShowS Source # show :: Last a -> String Source # showList :: [Last a] -> ShowS Source #
Generic (Last a) # |
Associated Types type Rep (Last a) :: * -> * Source # Methods from :: Last a -> Rep (Last a) x Source # to :: Rep (Last a) x -> Last a Source #
Semigroup (Last a) # | Since: 4.9.0.0
Methods (<>) :: Last a -> Last a -> Last a Source # sconcat :: NonEmpty (Last a) -> Last a Source # stimes :: Integral b => b -> Last a -> Last a Source #
Generic1 * Last # |
Associated Types type Rep1 Last (f :: Last -> *) :: k -> * Source # Methods from1 :: f a -> Rep1 Last f a Source # to1 :: Rep1 Last f a -> f a Source #
type Rep (Last a) # |
type Rep (Last a) = D1 * (MetaData "Last" "Data.Semigroup" "base" True) (C1 * (MetaCons "Last" PrefixI True) (S1 * (MetaSel (Just Symbol "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Last # |
type Rep1 * Last = D1 * (MetaData "Last" "Data.Semigroup" "base" True) (C1 * (MetaCons "Last" PrefixI True) (S1 * (MetaSel (Just Symbol "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype WrappedMonoid m Source #

Provide a Semigroup for an arbitrary Monoid.

Constructors

WrapMonoid |
Fields unwrapMonoid :: m

Instances

Bounded m => Bounded (WrappedMonoid m) # |
Methods minBound :: WrappedMonoid m Source # maxBound :: WrappedMonoid m Source #
Enum a => Enum (WrappedMonoid a) # | Since: 4.9.0.0
Methods succ :: WrappedMonoid a -> WrappedMonoid a Source # pred :: WrappedMonoid a -> WrappedMonoid a Source # toEnum :: Int -> WrappedMonoid a Source # fromEnum :: WrappedMonoid a -> Int Source # enumFrom :: WrappedMonoid a -> [WrappedMonoid a] Source # enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source # enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source # enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source #
Eq m => Eq (WrappedMonoid m) # |
Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source #
Data m => Data (WrappedMonoid m) # |
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> WrappedMonoid m -> c (WrappedMonoid m) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonoid m) Source # toConstr :: WrappedMonoid m -> Constr Source # dataTypeOf :: WrappedMonoid m -> DataType Source # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (WrappedMonoid m)) Source # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WrappedMonoid m)) Source # gmapT :: (forall b. Data b => b -> b) -> WrappedMonoid m -> WrappedMonoid m Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r Source # gmapQ :: (forall d. Data d => d -> u) -> WrappedMonoid m -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonoid m -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m) Source #
Ord m => Ord (WrappedMonoid m) # |
Methods compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering Source # (<) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (>) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source #
Read m => Read (WrappedMonoid m) # |
Methods readsPrec :: Int -> ReadS (WrappedMonoid m) Source # readList :: ReadS [WrappedMonoid m] Source # readPrec :: ReadPrec (WrappedMonoid m) Source # readListPrec :: ReadPrec [WrappedMonoid m] Source #
Show m => Show (WrappedMonoid m) # |
Methods showsPrec :: Int -> WrappedMonoid m -> ShowS Source # show :: WrappedMonoid m -> String Source # showList :: [WrappedMonoid m] -> ShowS Source #
Generic (WrappedMonoid m) # |
Associated Types type Rep (WrappedMonoid m) :: * -> * Source # Methods from :: WrappedMonoid m -> Rep (WrappedMonoid m) x Source # to :: Rep (WrappedMonoid m) x -> WrappedMonoid m Source #
Monoid m => Semigroup (WrappedMonoid m) # | Since: 4.9.0.0
Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source #
Monoid m => Monoid (WrappedMonoid m) # | Since: 4.9.0.0
Methods mempty :: WrappedMonoid m Source # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source #
Generic1 * WrappedMonoid # |
Associated Types type Rep1 WrappedMonoid (f :: WrappedMonoid -> *) :: k -> * Source # Methods from1 :: f a -> Rep1 WrappedMonoid f a Source # to1 :: Rep1 WrappedMonoid f a -> f a Source #
type Rep (WrappedMonoid m) # |
type Rep (WrappedMonoid m) = D1 * (MetaData "WrappedMonoid" "Data.Semigroup" "base" True) (C1 * (MetaCons "WrapMonoid" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapMonoid") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * m)))
type Rep1 * WrappedMonoid # |
type Rep1 * WrappedMonoid = D1 * (MetaData "WrappedMonoid" "Data.Semigroup" "base" True) (C1 * (MetaCons "WrapMonoid" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapMonoid") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

# Re-exported monoids from Data.Monoid

class Monoid a where Source #

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:

-     mappend mempty x = x

-     mappend x mempty = x

-     mappend x (mappend y z) = mappend (mappend x y) z

-     mconcat = foldr mappend mempty

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define `newtype`s and make those instances of `Monoid`, e.g. `Sum` and `Product`.

Minimal complete definition

mempty, mappend

Methods

mempty :: a Source #

Identity of `mappend`

mappend :: a -> a -> a Source #

An associative operation

mconcat :: [a] -> a Source #

Fold a list using the monoid. For most types, the default definition for `mconcat` will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

Instances

Monoid Ordering # | Since: 2.1
Methods mempty :: Ordering Source # mappend :: Ordering -> Ordering -> Ordering Source # mconcat :: [Ordering] -> Ordering Source #
Monoid () # | Since: 2.1
Methods mempty :: () Source # mappend :: () -> () -> () Source # mconcat :: [()] -> () Source #
Monoid Any # | Since: 2.1
Methods mempty :: Any Source # mappend :: Any -> Any -> Any Source # mconcat :: [Any] -> Any Source #
Monoid All # | Since: 2.1
Methods mempty :: All Source # mappend :: All -> All -> All Source # mconcat :: [All] -> All Source #
Monoid Lifetime # | `mappend` takes the longer of two lifetimes. Since: 4.8.0.0
Methods mempty :: Lifetime Source # mappend :: Lifetime -> Lifetime -> Lifetime Source # mconcat :: [Lifetime] -> Lifetime Source #
Monoid Event # | Since: 4.3.1.0
Methods mempty :: Event Source # mappend :: Event -> Event -> Event Source # mconcat :: [Event] -> Event Source #
Monoid [a] # | Since: 2.1
Methods mempty :: [a] Source # mappend :: [a] -> [a] -> [a] Source # mconcat :: [[a]] -> [a] Source #
Monoid a => Monoid (Maybe a) # | Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `e*e = e` and `e*s = s = s*e` for all `s ∈ S`." Since there used to be no "Semigroup" typeclass providing just `mappend`, we use `Monoid` instead. Since: 2.1
Methods mempty :: Maybe a Source # mappend :: Maybe a -> Maybe a -> Maybe a Source # mconcat :: [Maybe a] -> Maybe a Source #
Monoid a => Monoid (IO a) # | Since: 4.9.0.0
Methods mempty :: IO a Source # mappend :: IO a -> IO a -> IO a Source # mconcat :: [IO a] -> IO a Source #
Monoid (Last a) # | Since: 2.1
Methods mempty :: Last a Source # mappend :: Last a -> Last a -> Last a Source # mconcat :: [Last a] -> Last a Source #
Monoid (First a) # | Since: 2.1
Methods mempty :: First a Source # mappend :: First a -> First a -> First a Source # mconcat :: [First a] -> First a Source #
Num a => Monoid (Product a) # | Since: 2.1
Methods mempty :: Product a Source # mappend :: Product a -> Product a -> Product a Source # mconcat :: [Product a] -> Product a Source #
Num a => Monoid (Sum a) # | Since: 2.1
Methods mempty :: Sum a Source # mappend :: Sum a -> Sum a -> Sum a Source # mconcat :: [Sum a] -> Sum a Source #
Monoid (Endo a) # | Since: 2.1
Methods mempty :: Endo a Source # mappend :: Endo a -> Endo a -> Endo a Source # mconcat :: [Endo a] -> Endo a Source #
Monoid a => Monoid (Dual a) # | Since: 2.1
Methods mempty :: Dual a Source # mappend :: Dual a -> Dual a -> Dual a Source # mconcat :: [Dual a] -> Dual a Source #
Monoid a => Monoid (Identity a) # |
Methods mempty :: Identity a Source # mappend :: Identity a -> Identity a -> Identity a Source # mconcat :: [Identity a] -> Identity a Source #
Semigroup a => Monoid (Option a) # | Since: 4.9.0.0
Methods mempty :: Option a Source # mappend :: Option a -> Option a -> Option a Source # mconcat :: [Option a] -> Option a Source #
Monoid m => Monoid (WrappedMonoid m) # | Since: 4.9.0.0
Methods mempty :: WrappedMonoid m Source # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source #
(Ord a, Bounded a) => Monoid (Max a) # | Since: 4.9.0.0
Methods mempty :: Max a Source # mappend :: Max a -> Max a -> Max a Source # mconcat :: [Max a] -> Max a Source #
(Ord a, Bounded a) => Monoid (Min a) # | Since: 4.9.0.0
Methods mempty :: Min a Source # mappend :: Min a -> Min a -> Min a Source # mconcat :: [Min a] -> Min a Source #
Monoid b => Monoid (a -> b) # | Since: 2.1
Methods mempty :: a -> b Source # mappend :: (a -> b) -> (a -> b) -> a -> b Source # mconcat :: [a -> b] -> a -> b Source #
(Monoid a, Monoid b) => Monoid (a, b) # | Since: 2.1
Methods mempty :: (a, b) Source # mappend :: (a, b) -> (a, b) -> (a, b) Source # mconcat :: [(a, b)] -> (a, b) Source #
Monoid (Proxy k s) # | Since: 4.7.0.0
Methods mempty :: Proxy k s Source # mappend :: Proxy k s -> Proxy k s -> Proxy k s Source # mconcat :: [Proxy k s] -> Proxy k s Source #
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) # | Since: 2.1
Methods mempty :: (a, b, c) Source # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # mconcat :: [(a, b, c)] -> (a, b, c) Source #
Alternative f => Monoid (Alt * f a) # | Since: 4.8.0.0
Methods mempty :: Alt * f a Source # mappend :: Alt * f a -> Alt * f a -> Alt * f a Source # mconcat :: [Alt * f a] -> Alt * f a Source #
Monoid a => Monoid (Const k a b) # |
Methods mempty :: Const k a b Source # mappend :: Const k a b -> Const k a b -> Const k a b Source # mconcat :: [Const k a b] -> Const k a b Source #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) # | Since: 2.1
Methods mempty :: (a, b, c, d) Source # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # mconcat :: [(a, b, c, d)] -> (a, b, c, d) Source #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) # | Since: 2.1
Methods mempty :: (a, b, c, d, e) Source # mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) Source #

newtype Dual a Source #

The dual of a `Monoid`, obtained by swapping the arguments of `mappend`.

Constructors

Dual |
Fields getDual :: a

Instances

Monad Dual # | Since: 4.8.0.0
Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b Source # (>>) :: Dual a -> Dual b -> Dual b Source # return :: a -> Dual a Source # fail :: String -> Dual a Source #
Functor Dual # | Since: 4.8.0.0
Methods fmap :: (a -> b) -> Dual a -> Dual b Source # (<$) :: a -> Dual b -> Dual a Source #
MonadFix Dual # | Since: 4.8.0.0
Methods mfix :: (a -> Dual a) -> Dual a Source #
Applicative Dual # | Since: 4.8.0.0
Methods pure :: a -> Dual a Source # (<*>) :: Dual (a -> b) -> Dual a -> Dual b Source # liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source # (*>) :: Dual a -> Dual b -> Dual b Source # (<*) :: Dual a -> Dual b -> Dual a Source #
Foldable Dual # | Since: 4.8.0.0
Methods fold :: Monoid m => Dual m -> m Source # foldMap :: Monoid m => (a -> m) -> Dual a -> m Source # foldr :: (a -> b -> b) -> b -> Dual a -> b Source # foldr' :: (a -> b -> b) -> b -> Dual a -> b Source # foldl :: (b -> a -> b) -> b -> Dual a -> b Source # foldl' :: (b -> a -> b) -> b -> Dual a -> b Source # foldr1 :: (a -> a -> a) -> Dual a -> a Source # foldl1 :: (a -> a -> a) -> Dual a -> a Source # toList :: Dual a -> [a] Source # null :: Dual a -> Bool Source # length :: Dual a -> Int Source # elem :: Eq a => a -> Dual a -> Bool Source # maximum :: Ord a => Dual a -> a Source # minimum :: Ord a => Dual a -> a Source # sum :: Num a => Dual a -> a Source # product :: Num a => Dual a -> a Source #
Traversable Dual # | Since: 4.8.0.0
Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) Source # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) Source # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) Source # sequence :: Monad m => Dual (m a) -> m (Dual a) Source #
MonadZip Dual # | Since: 4.8.0.0
Methods mzip :: Dual a -> Dual b -> Dual (a, b) Source # mzipWith :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source # munzip :: Dual (a, b) -> (Dual a, Dual b) Source #
Bounded a => Bounded (Dual a) # |
Methods minBound :: Dual a Source # maxBound :: Dual a Source #
Eq a => Eq (Dual a) # |
Methods (==) :: Dual a -> Dual a -> Bool Source # (/=) :: Dual a -> Dual a -> Bool Source #
Data a => Data (Dual a) # | Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dual a -> c (Dual a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) Source # toConstr :: Dual a -> Constr Source # dataTypeOf :: Dual a -> DataType Source # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) Source # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) Source # gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source #
Ord a => Ord (Dual a) # |
Methods compare :: Dual a -> Dual a -> Ordering Source # (<) :: Dual a -> Dual a -> Bool Source # (<=) :: Dual a -> Dual a -> Bool Source # (>) :: Dual a -> Dual a -> Bool Source # (>=) :: Dual a -> Dual a -> Bool Source # max :: Dual a -> Dual a -> Dual a Source # min :: Dual a -> Dual a -> Dual a Source #
Read a => Read (Dual a) # |
Methods readsPrec :: Int -> ReadS (Dual a) Source # readList :: ReadS [Dual a] Source # readPrec :: ReadPrec (Dual a) Source # readListPrec :: ReadPrec [Dual a] Source #
Show a => Show (Dual a) # |
Methods showsPrec :: Int -> Dual a -> ShowS Source # show :: Dual a -> String Source # showList :: [Dual a] -> ShowS Source #
Generic (Dual a) # |
Associated Types type Rep (Dual a) :: * -> * Source # Methods from :: Dual a -> Rep (Dual a) x Source # to :: Rep (Dual a) x -> Dual a Source #
Semigroup a => Semigroup (Dual a) # | Since: 4.9.0.0
Methods (<>) :: Dual a -> Dual a -> Dual a Source # sconcat :: NonEmpty (Dual a) -> Dual a Source # stimes :: Integral b => b -> Dual a -> Dual a Source #
Monoid a => Monoid (Dual a) # | Since: 2.1
Methods mempty :: Dual a Source # mappend :: Dual a -> Dual a -> Dual a Source # mconcat :: [Dual a] -> Dual a Source #
Generic1 * Dual # |
Associated Types type Rep1 Dual (f :: Dual -> *) :: k -> * Source # Methods from1 :: f a -> Rep1 Dual f a Source # to1 :: Rep1 Dual f a -> f a Source #
type Rep (Dual a) # |
type Rep (Dual a) = D1 * (MetaData "Dual" "Data.Monoid" "base" True) (C1 * (MetaCons "Dual" PrefixI True) (S1 * (MetaSel (Just Symbol "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Dual # |
type Rep1 * Dual = D1 * (MetaData "Dual" "Data.Monoid" "base" True) (C1 * (MetaCons "Dual" PrefixI True) (S1 * (MetaSel (Just Symbol "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Endo a Source #

The monoid of endomorphisms under composition.

Constructors

Endo |
Fields appEndo :: a -> a

Instances

Generic (Endo a) # |
Associated Types type Rep (Endo a) :: * -> * Source # Methods from :: Endo a -> Rep (Endo a) x Source # to :: Rep (Endo a) x -> Endo a Source #
Semigroup (Endo a) # | Since: 4.9.0.0
Methods (<>) :: Endo a -> Endo a -> Endo a Source # sconcat :: NonEmpty (Endo a) -> Endo a Source # stimes :: Integral b => b -> Endo a -> Endo a Source #
Monoid (Endo a) # | Since: 2.1
Methods mempty :: Endo a Source # mappend :: Endo a -> Endo a -> Endo a Source # mconcat :: [Endo a] -> Endo a Source #
type Rep (Endo a) # |
type Rep (Endo a) = D1 * (MetaData "Endo" "Data.Monoid" "base" True) (C1 * (MetaCons "Endo" PrefixI True) (S1 * (MetaSel (Just Symbol "appEndo") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (a -> a))))

newtype All Source #

Boolean monoid under conjunction (`&&`).

Constructors

All |
Fields getAll :: Bool

Instances

Bounded All # |
Methods minBound :: All Source # maxBound :: All Source #
Eq All # |
Methods (==) :: All -> All -> Bool Source # (/=) :: All -> All -> Bool Source #
Data All # | Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> All -> c All Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All Source # toConstr :: All -> Constr Source # dataTypeOf :: All -> DataType Source # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c All) Source # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All) Source # gmapT :: (forall b. Data b => b -> b) -> All -> All Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source # gmapQ :: (forall d. Data d => d -> u) -> All -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source #
Ord All # |
Methods compare :: All -> All -> Ordering Source # (<) :: All -> All -> Bool Source # (<=) :: All -> All -> Bool Source # (>) :: All -> All -> Bool Source # (>=) :: All -> All -> Bool Source # max :: All -> All -> All Source # min :: All -> All -> All Source #
Read All # |
Methods readsPrec :: Int -> ReadS All Source # readList :: ReadS [All] Source # readPrec :: ReadPrec All Source # readListPrec :: ReadPrec [All] Source #
Show All # |
Methods showsPrec :: Int -> All -> ShowS Source # show :: All -> String Source # showList :: [All] -> ShowS Source #
Generic All # |
Associated Types type Rep All :: * -> * Source # Methods from :: All -> Rep All x Source # to :: Rep All x -> All Source #
Semigroup All # | Since: 4.9.0.0
Methods (<>) :: All -> All -> All Source # sconcat :: NonEmpty All -> All Source # stimes :: Integral b => b -> All -> All Source #
Monoid All # | Since: 2.1
Methods mempty :: All Source # mappend :: All -> All -> All Source # mconcat :: [All] -> All Source #
type Rep All # |
type Rep All = D1 * (MetaData "All" "Data.Monoid" "base" True) (C1 * (MetaCons "All" PrefixI True) (S1 * (MetaSel (Just Symbol "getAll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool)))

newtype Any Source #

Boolean monoid under disjunction (`||`).

Constructors

Any |
Fields getAny :: Bool

Instances

Bounded Any # |
Methods minBound :: Any Source # maxBound :: Any Source #
Eq Any # |
Methods (==) :: Any -> Any -> Bool Source # (/=) :: Any -> Any -> Bool Source #
Data Any # | Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Any -> c Any Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any Source # toConstr :: Any -> Constr Source # dataTypeOf :: Any -> DataType Source # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Any) Source # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any) Source # gmapT :: (forall b. Data b => b -> b) -> Any -> Any Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source #
Ord Any # |
Methods compare :: Any -> Any -> Ordering Source # (<) :: Any -> Any -> Bool Source # (<=) :: Any -> Any -> Bool Source # (>) :: Any -> Any -> Bool Source # (>=) :: Any -> Any -> Bool Source # max :: Any -> Any -> Any Source # min :: Any -> Any -> Any Source #
Read Any # |
Methods readsPrec :: Int -> ReadS Any Source # readList :: ReadS [Any] Source # readPrec :: ReadPrec Any Source # readListPrec :: ReadPrec [Any] Source #
Show Any # |
Methods showsPrec :: Int -> Any -> ShowS Source # show :: Any -> String Source # showList :: [Any] -> ShowS Source #
Generic Any # |
Associated Types type Rep Any :: * -> * Source # Methods from :: Any -> Rep Any x Source # to :: Rep Any x -> Any Source #
Semigroup Any # | Since: 4.9.0.0
Methods (<>) :: Any -> Any -> Any Source # sconcat :: NonEmpty Any -> Any Source # stimes :: Integral b => b -> Any -> Any Source #
Monoid Any # | Since: 2.1
Methods mempty :: Any Source # mappend :: Any -> Any -> Any Source # mconcat :: [Any] -> Any Source #
type Rep Any # |
type Rep Any = D1 * (MetaData "Any" "Data.Monoid" "base" True) (C1 * (MetaCons "Any" PrefixI True) (S1 * (MetaSel (Just Symbol "getAny") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool)))

newtype Sum a Source #

Monoid under addition.

Constructors

Sum |
Fields getSum :: a

Instances

Monad Sum # | Since: 4.8.0.0
Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b Source # (>>) :: Sum a -> Sum b -> Sum b Source # return :: a -> Sum a Source # fail :: String -> Sum a Source #
Functor Sum # | Since: 4.8.0.0
Methods fmap :: (a -> b) -> Sum a -> Sum b Source # (<$) :: a -> Sum b -> Sum a Source #
MonadFix Sum # | Since: 4.8.0.0
Methods mfix :: (a -> Sum a) -> Sum a Source #
Applicative Sum # | Since: 4.8.0.0
Methods pure :: a -> Sum a Source # (<*>) :: Sum (a -> b) -> Sum a -> Sum b Source # liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source # (*>) :: Sum a -> Sum b -> Sum b Source # (<*) :: Sum a -> Sum b -> Sum a Source #
Foldable Sum # | Since: 4.8.0.0
Methods fold :: Monoid m => Sum m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum a -> m Source # foldr :: (a -> b -> b) -> b -> Sum a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum a -> b Source # foldl :: (b -> a -> b) -> b -> Sum a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum a -> b Source # foldr1 :: (a -> a -> a) -> Sum a -> a Source # foldl1 :: (a -> a -> a) -> Sum a -> a Source # toList :: Sum a -> [a] Source # null :: Sum a -> Bool Source # length :: Sum a -> Int Source # elem :: Eq a => a -> Sum a -> Bool Source # maximum :: Ord a => Sum a -> a Source # minimum :: Ord a => Sum a -> a Source # sum :: Num a => Sum a -> a Source # product :: Num a => Sum a -> a Source #
Traversable Sum # | Since: 4.8.0.0
Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) Source # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) Source # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) Source # sequence :: Monad m => Sum (m a) -> m (Sum a) Source #
MonadZip Sum # | Since: 4.8.0.0
Methods mzip :: Sum a -> Sum b -> Sum (a, b) Source # mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source # munzip :: Sum (a, b) -> (Sum a, Sum b) Source #
Bounded a => Bounded (Sum a) # |
Methods minBound :: Sum a Source # maxBound :: Sum a Source #
Eq a => Eq (Sum a) # |
Methods (==) :: Sum a -> Sum a -> Bool Source # (/=) :: Sum a -> Sum a -> Bool Source #
Data a => Data (Sum a) # | Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Sum a -> c (Sum a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a) Source # toConstr :: Sum a -> Constr Source # dataTypeOf :: Sum a -> DataType Source # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a)) Source # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a)) Source # gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source #
Num a => Num (Sum a) # |
Methods (+) :: Sum a -> Sum a -> Sum a Source # (-) :: Sum a -> Sum a -> Sum a Source # (*) :: Sum a -> Sum a -> Sum a Source # negate :: Sum a -> Sum a Source # abs :: Sum a -> Sum a Source # signum :: Sum a -> Sum a Source # fromInteger :: Integer -> Sum a Source #
Ord a => Ord (Sum a) # |
Methods compare :: Sum a -> Sum a -> Ordering Source # (<) :: Sum a -> Sum a -> Bool Source # (<=) :: Sum a -> Sum a -> Bool Source # (>) :: Sum a -> Sum a -> Bool Source # (>=) :: Sum a -> Sum a -> Bool Source # max :: Sum a -> Sum a -> Sum a Source # min :: Sum a -> Sum a -> Sum a Source #
Read a => Read (Sum a) # |
Methods readsPrec :: Int -> ReadS (Sum a) Source # readList :: ReadS [Sum a] Source # readPrec :: ReadPrec (Sum a) Source # readListPrec :: ReadPrec [Sum a] Source #
Show a => Show (Sum a) # |
Methods showsPrec :: Int -> Sum a -> ShowS Source # show :: Sum a -> String Source # showList :: [Sum a] -> ShowS Source #
Generic (Sum a) # |
Associated Types type Rep (Sum a) :: * -> * Source # Methods from :: Sum a -> Rep (Sum a) x Source # to :: Rep (Sum a) x -> Sum a Source #
Num a => Semigroup (Sum a) # | Since: 4.9.0.0
Methods (<>) :: Sum a -> Sum a -> Sum a Source # sconcat :: NonEmpty (Sum a) -> Sum a Source # stimes :: Integral b => b -> Sum a -> Sum a Source #
Num a => Monoid (Sum a) # | Since: 2.1
Methods mempty :: Sum a Source # mappend :: Sum a -> Sum a -> Sum a Source # mconcat :: [Sum a] -> Sum a Source #
Generic1 * Sum # |
Associated Types type Rep1 Sum (f :: Sum -> *) :: k -> * Source # Methods from1 :: f a -> Rep1 Sum f a Source # to1 :: Rep1 Sum f a -> f a Source #
type Rep (Sum a) # |
type Rep (Sum a) = D1 * (MetaData "Sum" "Data.Monoid" "base" True) (C1 * (MetaCons "Sum" PrefixI True) (S1 * (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Sum # |
type Rep1 * Sum = D1 * (MetaData "Sum" "Data.Monoid" "base" True) (C1 * (MetaCons "Sum" PrefixI True) (S1 * (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Product a Source #

Monoid under multiplication.

Constructors

Product |
Fields getProduct :: a

Instances

Monad Product # | Since: 4.8.0.0
Methods (>>=) :: Product a -> (a -> Product b) -> Product b Source # (>>) :: Product a -> Product b -> Product b Source # return :: a -> Product a Source # fail :: String -> Product a Source #
Functor Product # | Since: 4.8.0.0
Methods fmap :: (a -> b) -> Product a -> Product b Source # (<$) :: a -> Product b -> Product a Source #
MonadFix Product # | Since: 4.8.0.0
Methods mfix :: (a -> Product a) -> Product a Source #
Applicative Product # | Since: 4.8.0.0
Methods pure :: a -> Product a Source # (<*>) :: Product (a -> b) -> Product a -> Product b Source # liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source # (*>) :: Product a -> Product b -> Product b Source # (<*) :: Product a -> Product b -> Product a Source #
Foldable Product # | Since: 4.8.0.0
Methods fold :: Monoid m => Product m -> m Source # foldMap :: Monoid m => (a -> m) -> Product a -> m Source # foldr :: (a -> b -> b) -> b -> Product a -> b Source # foldr' :: (a -> b -> b) -> b -> Product a -> b Source # foldl :: (b -> a -> b) -> b -> Product a -> b Source # foldl' :: (b -> a -> b) -> b -> Product a -> b Source # foldr1 :: (a -> a -> a) -> Product a -> a Source # foldl1 :: (a -> a -> a) -> Product a -> a Source # toList :: Product a -> [a] Source # null :: Product a -> Bool Source # length :: Product a -> Int Source # elem :: Eq a => a -> Product a -> Bool Source # maximum :: Ord a => Product a -> a Source # minimum :: Ord a => Product a -> a Source # sum :: Num a => Product a -> a Source # product :: Num a => Product a -> a Source #
Traversable Product # | Since: 4.8.0.0
Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) Source # sequenceA :: Applicative f => Product (f a) -> f (Product a) Source # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) Source # sequence :: Monad m => Product (m a) -> m (Product a) Source #
MonadZip Product # | Since: 4.8.0.0
Methods mzip :: Product a -> Product b -> Product (a, b) Source # mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c Source # munzip :: Product (a, b) -> (Product a, Product b) Source #
Bounded a => Bounded (Product a) # |
Methods minBound :: Product a Source # maxBound :: Product a Source #
Eq a => Eq (Product a) # |
Methods (==) :: Product a -> Product a -> Bool Source # (/=) :: Product a -> Product a -> Bool Source #
Data a => Data (Product a) # | Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Product a -> c (Product a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) Source # toConstr :: Product a -> Constr Source # dataTypeOf :: Product a -> DataType Source # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) Source # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) Source # gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source #
Num a => Num (Product a) # |
Methods (+) :: Product a -> Product a -> Product a Source # (-) :: Product a -> Product a -> Product a Source # (*) :: Product a -> Product a -> Product a Source # negate :: Product a -> Product a Source # abs :: Product a -> Product a Source # signum :: Product a -> Product a Source # fromInteger :: Integer -> Product a Source #
Ord a => Ord (Product a) # |
Methods compare :: Product a -> Product a -> Ordering Source # (<) :: Product a -> Product a -> Bool Source # (<=) :: Product a -> Product a -> Bool Source # (>) :: Product a -> Product a -> Bool Source # (>=) :: Product a -> Product a -> Bool Source # max :: Product a -> Product a -> Product a Source # min :: Product a -> Product a -> Product a Source #
Read a => Read (Product a) # |
Methods readsPrec :: Int -> ReadS (Product a) Source # readList :: ReadS [Product a] Source # readPrec :: ReadPrec (Product a) Source # readListPrec :: ReadPrec [Product a] Source #
Show a => Show (Product a) # |
Methods showsPrec :: Int -> Product a -> ShowS Source # show :: Product a -> String Source # showList :: [Product a] -> ShowS Source #
Generic (Product a) # |
Associated Types type Rep (Product a) :: * -> * Source # Methods from :: Product a -> Rep (Product a) x Source # to :: Rep (Product a) x -> Product a Source #
Num a => Semigroup (Product a) # | Since: 4.9.0.0
Methods (<>) :: Product a -> Product a -> Product a Source # sconcat :: NonEmpty (Product a) -> Product a Source # stimes :: Integral b => b -> Product a -> Product a Source #
Num a => Monoid (Product a) # | Since: 2.1
Methods mempty :: Product a Source # mappend :: Product a -> Product a -> Product a Source # mconcat :: [Product a] -> Product a Source #
Generic1 * Product # |
Associated Types type Rep1 Product (f :: Product -> *) :: k -> * Source # Methods from1 :: f a -> Rep1 Product f a Source # to1 :: Rep1 Product f a -> f a Source #
type Rep (Product a) # |
type Rep (Product a) = D1 * (MetaData "Product" "Data.Monoid" "base" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Product # |
type Rep1 * Product = D1 * (MetaData "Product" "Data.Monoid" "base" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

# A better monoid for Maybe

newtype Option a Source #

`Option` is effectively `Maybe` with a better instance of `Monoid`, built off of an underlying `Semigroup` instead of an underlying `Monoid`.

Ideally, this type would not exist at all and we would just fix the `Monoid` instance of `Maybe`

Constructors

Option |
Fields getOption :: Maybe a

Instances

Monad Option # | Since: 4.9.0.0
Methods (>>=) :: Option a -> (a -> Option b) -> Option b Source # (>>) :: Option a -> Option b -> Option b Source # return :: a -> Option a Source # fail :: String -> Option a Source #
Functor Option # | Since: 4.9.0.0
Methods fmap :: (a -> b) -> Option a -> Option b Source # (<$) :: a -> Option b -> Option a Source #
MonadFix Option # | Since: 4.9.0.0
Methods mfix :: (a -> Option a) -> Option a Source #
Applicative Option # | Since: 4.9.0.0
Methods pure :: a -> Option a Source # (<*>) :: Option (a -> b) -> Option a -> Option b Source # liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c Source # (*>) :: Option a -> Option b -> Option b Source # (<*) :: Option a -> Option b -> Option a Source #
Foldable Option # | Since: 4.9.0.0
Methods fold :: Monoid m => Option m -> m Source # foldMap :: Monoid m => (a -> m) -> Option a -> m Source # foldr :: (a -> b -> b) -> b -> Option a -> b Source # foldr' :: (a -> b -> b) -> b -> Option a -> b Source # foldl :: (b -> a -> b) -> b -> Option a -> b Source # foldl' :: (b -> a -> b) -> b -> Option a -> b Source # foldr1 :: (a -> a -> a) -> Option a -> a Source # foldl1 :: (a -> a -> a) -> Option a -> a Source # toList :: Option a -> [a] Source # null :: Option a -> Bool Source # length :: Option a -> Int Source # elem :: Eq a => a -> Option a -> Bool Source # maximum :: Ord a => Option a -> a Source # minimum :: Ord a => Option a -> a Source # sum :: Num a => Option a -> a Source # product :: Num a => Option a -> a Source #
Traversable Option # | Since: 4.9.0.0
Methods traverse :: Applicative f => (a -> f b) -> Option a -> f (Option b) Source # sequenceA :: Applicative f => Option (f a) -> f (Option a) Source # mapM :: Monad m => (a -> m b) -> Option a -> m (Option b) Source # sequence :: Monad m => Option (m a) -> m (Option a) Source #
MonadPlus Option # | Since: 4.9.0.0
Methods mzero :: Option a Source # mplus :: Option a -> Option a -> Option a Source #
Alternative Option # | Since: 4.9.0.0
Methods empty :: Option a Source # (<|>) :: Option a -> Option a -> Option a Source # some :: Option a -> Option [a] Source # many :: Option a -> Option [a] Source #
Eq a => Eq (Option a) # |
Methods (==) :: Option a -> Option a -> Bool Source # (/=) :: Option a -> Option a -> Bool Source #
Data a => Data (Option a) # |
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Option a -> c (Option a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Option a) Source # toConstr :: Option a -> Constr Source # dataTypeOf :: Option a -> DataType Source # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Option a)) Source # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Option a)) Source # gmapT :: (forall b. Data b => b -> b) -> Option a -> Option a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Option a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Option a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) Source #
Ord a => Ord (Option a) # |
Methods compare :: Option a -> Option a -> Ordering Source # (<) :: Option a -> Option a -> Bool Source # (<=) :: Option a -> Option a -> Bool Source # (>) :: Option a -> Option a -> Bool Source # (>=) :: Option a -> Option a -> Bool Source # max :: Option a -> Option a -> Option a Source # min :: Option a -> Option a -> Option a Source #
Read a => Read (Option a) # |
Methods readsPrec :: Int -> ReadS (Option a) Source # readList :: ReadS [Option a] Source # readPrec :: ReadPrec (Option a) Source # readListPrec :: ReadPrec [Option a] Source #
Show a => Show (Option a) # |
Methods showsPrec :: Int -> Option a -> ShowS Source # show :: Option a -> String Source # showList :: [Option a] -> ShowS Source #
Generic (Option a) # |
Associated Types type Rep (Option a) :: * -> * Source # Methods from :: Option a -> Rep (Option a) x Source # to :: Rep (Option a) x -> Option a Source #
Semigroup a => Semigroup (Option a) # | Since: 4.9.0.0
Methods (<>) :: Option a -> Option a -> Option a Source # sconcat :: NonEmpty (Option a) -> Option a Source # stimes :: Integral b => b -> Option a -> Option a Source #
Semigroup a => Monoid (Option a) # | Since: 4.9.0.0
Methods mempty :: Option a Source # mappend :: Option a -> Option a -> Option a Source # mconcat :: [Option a] -> Option a Source #
Generic1 * Option # |
Associated Types type Rep1 Option (f :: Option -> *) :: k -> * Source # Methods from1 :: f a -> Rep1 Option f a Source # to1 :: Rep1 Option f a -> f a Source #
type Rep (Option a) # |
type Rep (Option a) = D1 * (MetaData "Option" "Data.Semigroup" "base" True) (C1 * (MetaCons "Option" PrefixI True) (S1 * (MetaSel (Just Symbol "getOption") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (Maybe a))))
type Rep1 * Option # |
type Rep1 * Option = D1 * (MetaData "Option" "Data.Semigroup" "base" True) (C1 * (MetaCons "Option" PrefixI True) (S1 * (MetaSel (Just Symbol "getOption") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 * Maybe)))

option :: b -> (a -> b) -> Option a -> b Source #

Fold an `Option` case-wise, just like `maybe`.

# Difference lists of a semigroup

diff :: Semigroup m => m -> Endo m Source #

This lets you use a difference list of a `Semigroup` as a `Monoid`.

cycle1 :: Semigroup m => m -> m Source #

A generalization of `cycle` to an arbitrary `Semigroup`. May fail to terminate for some values in some semigroups.

# ArgMin, ArgMax

data Arg a b Source #

`Arg` isn't itself a `Semigroup` in its own right, but it can be placed inside `Min` and `Max` to compute an arg min or arg max.

Constructors

Arg a b |

Instances

Bifunctor Arg # | Since: 4.9.0.0
Methods bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d Source # first :: (a -> b) -> Arg a c -> Arg b c Source # second :: (b -> c) -> Arg a b -> Arg a c Source #
Bifoldable Arg # | Since: 4.10.0.0
Methods bifold :: Monoid m => Arg m m -> m Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c Source #
Bitraversable Arg # | Since: 4.10.0.0
Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) Source #
Functor (Arg a) # | Since: 4.9.0.0
Methods fmap :: (a -> b) -> Arg a a -> Arg a b Source # (<$) :: a -> Arg a b -> Arg a a Source #
Foldable (Arg a) # | Since: 4.9.0.0
Methods fold :: Monoid m => Arg a m -> m Source # foldMap :: Monoid m => (a -> m) -> Arg a a -> m Source # foldr :: (a -> b -> b) -> b -> Arg a a -> b Source # foldr' :: (a -> b -> b) -> b -> Arg a a -> b Source # foldl :: (b -> a -> b) -> b -> Arg a a -> b Source # foldl' :: (b -> a -> b) -> b -> Arg a a -> b Source # foldr1 :: (a -> a -> a) -> Arg a a -> a Source # foldl1 :: (a -> a -> a) -> Arg a a -> a Source # toList :: Arg a a -> [a] Source # null :: Arg a a -> Bool Source # length :: Arg a a -> Int Source # elem :: Eq a => a -> Arg a a -> Bool Source # maximum :: Ord a => Arg a a -> a Source # minimum :: Ord a => Arg a a -> a Source # sum :: Num a => Arg a a -> a Source # product :: Num a => Arg a a -> a Source #
Traversable (Arg a) # | Since: 4.9.0.0
Methods traverse :: Applicative f => (a -> f b) -> Arg a a -> f (Arg a b) Source # sequenceA :: Applicative f => Arg a (f a) -> f (Arg a a) Source # mapM :: Monad m => (a -> m b) -> Arg a a -> m (Arg a b) Source # sequence :: Monad m => Arg a (m a) -> m (Arg a a) Source #
Generic1 * (Arg a) # |
Associated Types type Rep1 (Arg a) (f :: Arg a -> *) :: k -> * Source # Methods from1 :: f a -> Rep1 (Arg a) f a Source # to1 :: Rep1 (Arg a) f a -> f a Source #
Eq a => Eq (Arg a b) # | Since: 4.9.0.0
Methods (==) :: Arg a b -> Arg a b -> Bool Source # (/=) :: Arg a b -> Arg a b -> Bool Source #
(Data b, Data a) => Data (Arg a b) # |
Methods gfoldl :: (forall d c. Data d => c (d -> c) -> d -> c c) -> (forall g. g -> c g) -> Arg a b -> c (Arg a b) Source # gunfold :: (forall c r. Data c => c (c -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b) Source # toConstr :: Arg a b -> Constr Source # dataTypeOf :: Arg a b -> DataType Source # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Arg a b)) Source # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Arg a b)) Source # gmapT :: (forall c. Data c => c -> c) -> Arg a b -> Arg a b Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Arg a b -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Arg a b -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source #
Ord a => Ord (Arg a b) # | Since: 4.9.0.0
Methods compare :: Arg a b -> Arg a b -> Ordering Source # (<) :: Arg a b -> Arg a b -> Bool Source # (<=) :: Arg a b -> Arg a b -> Bool Source # (>) :: Arg a b -> Arg a b -> Bool Source # (>=) :: Arg a b -> Arg a b -> Bool Source # max :: Arg a b -> Arg a b -> Arg a b Source # min :: Arg a b -> Arg a b -> Arg a b Source #
(Read b, Read a) => Read (Arg a b) # |
Methods readsPrec :: Int -> ReadS (Arg a b) Source # readList :: ReadS [Arg a b] Source # readPrec :: ReadPrec (Arg a b) Source # readListPrec :: ReadPrec [Arg a b] Source #
(Show b, Show a) => Show (Arg a b) # |
Methods showsPrec :: Int -> Arg a b -> ShowS Source # show :: Arg a b -> String Source # showList :: [Arg a b] -> ShowS Source #
Generic (Arg a b) # |
Associated Types type Rep (Arg a b) :: * -> * Source # Methods from :: Arg a b -> Rep (Arg a b) x Source # to :: Rep (Arg a b) x -> Arg a b Source #
type Rep1 * (Arg a) # |
type Rep1 * (Arg a) = D1 * (MetaData "Arg" "Data.Semigroup" "base" False) (C1 * (MetaCons "Arg" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)))
type Rep (Arg a b) # |
type Rep (Arg a b) = D1 * (MetaData "Arg" "Data.Semigroup" "base" False) (C1 * (MetaCons "Arg" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * b))))

type ArgMin a b = Min (Arg a b) Source #

type ArgMax a b = Max (Arg a b) Source #