Data.Semigroup

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

Documentation

class Semigroup a where

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

Since: 4.9.0.0

Methods

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

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

An associative operation.

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

If a is also a Monoid we further require

(<>) = mappend

sconcat :: NonEmpty a -> a

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

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

sconcat :: NonEmpty Ordering -> Ordering

stimes :: Integral b => b -> Ordering -> Ordering

Semigroup ()

Since: 4.9.0.0

Methods

(<>) :: () -> () -> ()

sconcat :: NonEmpty () -> ()

stimes :: Integral b => b -> () -> ()

Semigroup Any

Since: 4.9.0.0

Methods

(<>) :: Any -> Any -> Any

sconcat :: NonEmpty Any -> Any

stimes :: Integral b => b -> Any -> Any

Semigroup All

Since: 4.9.0.0

Methods

(<>) :: All -> All -> All

sconcat :: NonEmpty All -> All

stimes :: Integral b => b -> All -> All

Semigroup Lifetime

Since: 4.10.0.0

Methods

(<>) :: Lifetime -> Lifetime -> Lifetime

sconcat :: NonEmpty Lifetime -> Lifetime

stimes :: Integral b => b -> Lifetime -> Lifetime

Semigroup Event

Since: 4.10.0.0

Methods

(<>) :: Event -> Event -> Event

sconcat :: NonEmpty Event -> Event

stimes :: Integral b => b -> Event -> Event

Semigroup Void

Since: 4.9.0.0

Methods

(<>) :: Void -> Void -> Void

sconcat :: NonEmpty Void -> Void

stimes :: Integral b => b -> Void -> Void

Semigroup [a]

Since: 4.9.0.0

Methods

(<>) :: [a] -> [a] -> [a]

sconcat :: NonEmpty [a] -> [a]

stimes :: Integral b => b -> [a] -> [a]

Semigroup a => Semigroup (Maybe a)

Since: 4.9.0.0

Methods

(<>) :: Maybe a -> Maybe a -> Maybe a

sconcat :: NonEmpty (Maybe a) -> Maybe a

stimes :: Integral b => b -> Maybe a -> Maybe a

Semigroup a => Semigroup (IO a)

Since: 4.10.0.0

Methods

(<>) :: IO a -> IO a -> IO a

sconcat :: NonEmpty (IO a) -> IO a

stimes :: Integral b => b -> IO a -> IO a

Semigroup (Last a)

Since: 4.9.0.0

Methods

(<>) :: Last a -> Last a -> Last a

sconcat :: NonEmpty (Last a) -> Last a

stimes :: Integral b => b -> Last a -> Last a

Semigroup (First a)

Since: 4.9.0.0

Methods

(<>) :: First a -> First a -> First a

sconcat :: NonEmpty (First a) -> First a

stimes :: Integral b => b -> First a -> First a

Num a => Semigroup (Product a)

Since: 4.9.0.0

Methods

(<>) :: Product a -> Product a -> Product a

sconcat :: NonEmpty (Product a) -> Product a

stimes :: Integral b => b -> Product a -> Product a

Num a => Semigroup (Sum a)

Since: 4.9.0.0

Methods

(<>) :: Sum a -> Sum a -> Sum a

sconcat :: NonEmpty (Sum a) -> Sum a

stimes :: Integral b => b -> Sum a -> Sum a

Semigroup (Endo a)

Since: 4.9.0.0

Methods

(<>) :: Endo a -> Endo a -> Endo a

sconcat :: NonEmpty (Endo a) -> Endo a

stimes :: Integral b => b -> Endo a -> Endo a

Semigroup a => Semigroup (Dual a)

Since: 4.9.0.0

Methods

(<>) :: Dual a -> Dual a -> Dual a

sconcat :: NonEmpty (Dual a) -> Dual a

stimes :: Integral b => b -> Dual a -> Dual a

Semigroup a => Semigroup (Identity a)

Since: 4.9.0.0

Methods

(<>) :: Identity a -> Identity a -> Identity a

sconcat :: NonEmpty (Identity a) -> Identity a

stimes :: Integral b => b -> Identity a -> Identity a

Semigroup (NonEmpty a)

Since: 4.9.0.0

Methods

(<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a

sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a

stimes :: Integral b => b -> NonEmpty a -> NonEmpty a

Semigroup a => Semigroup (Option a)

Since: 4.9.0.0

Methods

(<>) :: Option a -> Option a -> Option a

sconcat :: NonEmpty (Option a) -> Option a

stimes :: Integral b => b -> Option a -> Option a

Monoid m => Semigroup (WrappedMonoid m)

Since: 4.9.0.0

Methods

(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m

stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m

Semigroup (Last a)

Since: 4.9.0.0

Methods

(<>) :: Last a -> Last a -> Last a

sconcat :: NonEmpty (Last a) -> Last a

stimes :: Integral b => b -> Last a -> Last a

Semigroup (First a)

Since: 4.9.0.0

Methods

(<>) :: First a -> First a -> First a

sconcat :: NonEmpty (First a) -> First a

stimes :: Integral b => b -> First a -> First a

Ord a => Semigroup (Max a)

Since: 4.9.0.0

Methods

(<>) :: Max a -> Max a -> Max a

sconcat :: NonEmpty (Max a) -> Max a

stimes :: Integral b => b -> Max a -> Max a

Ord a => Semigroup (Min a)

Since: 4.9.0.0

Methods

(<>) :: Min a -> Min a -> Min a

sconcat :: NonEmpty (Min a) -> Min a

stimes :: Integral b => b -> Min a -> Min a

Semigroup b => Semigroup (a -> b)

Since: 4.9.0.0

Methods

(<>) :: (a -> b) -> (a -> b) -> a -> b

sconcat :: NonEmpty (a -> b) -> a -> b

stimes :: Integral b => b -> (a -> b) -> a -> b

Semigroup (Either a b)

Since: 4.9.0.0

Methods

(<>) :: Either a b -> Either a b -> Either a b

sconcat :: NonEmpty (Either a b) -> Either a b

stimes :: Integral b => b -> Either a b -> Either a b

(Semigroup a, Semigroup b) => Semigroup (a, b)

Since: 4.9.0.0

Methods

(<>) :: (a, b) -> (a, b) -> (a, b)

sconcat :: NonEmpty (a, b) -> (a, b)

stimes :: Integral b => b -> (a, b) -> (a, b)

Semigroup (Proxy k s)

Since: 4.9.0.0

Methods

(<>) :: Proxy k s -> Proxy k s -> Proxy k s

sconcat :: NonEmpty (Proxy k s) -> Proxy k s

stimes :: Integral b => b -> Proxy k s -> Proxy k s

(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)

sconcat :: NonEmpty (a, b, c) -> (a, b, c)

stimes :: Integral b => b -> (a, b, c) -> (a, b, c)

Alternative f => Semigroup (Alt * f a)

Since: 4.9.0.0

Methods

(<>) :: Alt * f a -> Alt * f a -> Alt * f a

sconcat :: NonEmpty (Alt * f a) -> Alt * f a

stimes :: Integral b => b -> Alt * f a -> Alt * f a

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

sconcat :: NonEmpty (Const k a b) -> Const k a b

stimes :: Integral b => b -> Const k a b -> Const k a b

(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)

sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d)

stimes :: Integral b => b -> (a, b, c, d) -> (a, b, c, d)

(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)

sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e)

stimes :: Integral b => b -> (a, b, c, d, e) -> (a, b, c, d, e)

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

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

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

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

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

Constructors

Min

Fields

• getMin :: a

Instances

Monad Min

Since: 4.9.0.0

Methods

(>>=) :: Min a -> (a -> Min b) -> Min b

(>>) :: Min a -> Min b -> Min b

return :: a -> Min a

fail :: String -> Min a

Functor Min

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Min a -> Min b

(<$) :: a -> Min b -> Min a

MonadFix Min

Since: 4.9.0.0

Methods

mfix :: (a -> Min a) -> Min a

Applicative Min

Since: 4.9.0.0

Methods

pure :: a -> Min a

(<*>) :: Min (a -> b) -> Min a -> Min b

liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c

(*>) :: Min a -> Min b -> Min b

(<*) :: Min a -> Min b -> Min a

Foldable Min

Since: 4.9.0.0

Methods

fold :: Monoid m => Min m -> m

foldMap :: Monoid m => (a -> m) -> Min a -> m

foldr :: (a -> b -> b) -> b -> Min a -> b

foldr' :: (a -> b -> b) -> b -> Min a -> b

foldl :: (b -> a -> b) -> b -> Min a -> b

foldl' :: (b -> a -> b) -> b -> Min a -> b

foldr1 :: (a -> a -> a) -> Min a -> a

foldl1 :: (a -> a -> a) -> Min a -> a

toList :: Min a -> [a]

null :: Min a -> Bool

length :: Min a -> Int

elem :: Eq a => a -> Min a -> Bool

maximum :: Ord a => Min a -> a

minimum :: Ord a => Min a -> a

sum :: Num a => Min a -> a

product :: Num a => Min a -> a

Traversable Min

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b)

sequenceA :: Applicative f => Min (f a) -> f (Min a)

mapM :: Monad m => (a -> m b) -> Min a -> m (Min b)

sequence :: Monad m => Min (m a) -> m (Min a)

Bounded a => Bounded (Min a)

Methods

minBound :: Min a

maxBound :: Min a

Enum a => Enum (Min a)

Since: 4.9.0.0

Methods

succ :: Min a -> Min a

pred :: Min a -> Min a

toEnum :: Int -> Min a

fromEnum :: Min a -> Int

enumFrom :: Min a -> [Min a]

enumFromThen :: Min a -> Min a -> [Min a]

enumFromTo :: Min a -> Min a -> [Min a]

enumFromThenTo :: Min a -> Min a -> Min a -> [Min a]

Eq a => Eq (Min a)

Methods

(==) :: Min a -> Min a -> Bool

(/=) :: Min a -> Min a -> Bool

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)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Min a)

toConstr :: Min a -> Constr

dataTypeOf :: Min a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Min a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a))

gmapT :: (forall b. Data b => b -> b) -> Min a -> Min a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r

gmapQ :: (forall d. Data d => d -> u) -> Min a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Min a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Min a -> m (Min a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a)

Num a => Num (Min a)

Since: 4.9.0.0

Methods

(+) :: Min a -> Min a -> Min a

(-) :: Min a -> Min a -> Min a

(*) :: Min a -> Min a -> Min a

negate :: Min a -> Min a

abs :: Min a -> Min a

signum :: Min a -> Min a

fromInteger :: Integer -> Min a

Ord a => Ord (Min a)

Methods

compare :: Min a -> Min a -> Ordering

(<) :: Min a -> Min a -> Bool

(<=) :: Min a -> Min a -> Bool

(>) :: Min a -> Min a -> Bool

(>=) :: Min a -> Min a -> Bool

max :: Min a -> Min a -> Min a

min :: Min a -> Min a -> Min a

Read a => Read (Min a)

Methods

readsPrec :: Int -> ReadS (Min a)

readList :: ReadS [Min a]

readPrec :: ReadPrec (Min a)

readListPrec :: ReadPrec [Min a]

Show a => Show (Min a)

Methods

showsPrec :: Int -> Min a -> ShowS

show :: Min a -> String

showList :: [Min a] -> ShowS

Generic (Min a)

Associated Types

type Rep (Min a) :: * -> *

Methods

from :: Min a -> Rep (Min a) x

to :: Rep (Min a) x -> Min a

Ord a => Semigroup (Min a)

Since: 4.9.0.0

Methods

(<>) :: Min a -> Min a -> Min a

sconcat :: NonEmpty (Min a) -> Min a

stimes :: Integral b => b -> Min a -> Min a

(Ord a, Bounded a) => Monoid (Min a)

Since: 4.9.0.0

Methods

mempty :: Min a

mappend :: Min a -> Min a -> Min a

mconcat :: [Min a] -> Min a

Generic1 * Min

Associated Types

type Rep1 Min (f :: Min -> *) :: k -> *

Methods

from1 :: f a -> Rep1 Min f a

to1 :: Rep1 Min f a -> f a

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

Constructors

Max

Fields

• getMax :: a

Instances

Monad Max

Since: 4.9.0.0

Methods

(>>=) :: Max a -> (a -> Max b) -> Max b

(>>) :: Max a -> Max b -> Max b

return :: a -> Max a

fail :: String -> Max a

Functor Max

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Max a -> Max b

(<$) :: a -> Max b -> Max a

MonadFix Max

Since: 4.9.0.0

Methods

mfix :: (a -> Max a) -> Max a

Applicative Max

Since: 4.9.0.0

Methods

pure :: a -> Max a

(<*>) :: Max (a -> b) -> Max a -> Max b

liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c

(*>) :: Max a -> Max b -> Max b

(<*) :: Max a -> Max b -> Max a

Foldable Max

Since: 4.9.0.0

Methods

fold :: Monoid m => Max m -> m

foldMap :: Monoid m => (a -> m) -> Max a -> m

foldr :: (a -> b -> b) -> b -> Max a -> b

foldr' :: (a -> b -> b) -> b -> Max a -> b

foldl :: (b -> a -> b) -> b -> Max a -> b

foldl' :: (b -> a -> b) -> b -> Max a -> b

foldr1 :: (a -> a -> a) -> Max a -> a

foldl1 :: (a -> a -> a) -> Max a -> a

toList :: Max a -> [a]

null :: Max a -> Bool

length :: Max a -> Int

elem :: Eq a => a -> Max a -> Bool

maximum :: Ord a => Max a -> a

minimum :: Ord a => Max a -> a

sum :: Num a => Max a -> a

product :: Num a => Max a -> a

Traversable Max

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b)

sequenceA :: Applicative f => Max (f a) -> f (Max a)

mapM :: Monad m => (a -> m b) -> Max a -> m (Max b)

sequence :: Monad m => Max (m a) -> m (Max a)

Bounded a => Bounded (Max a)

Methods

minBound :: Max a

maxBound :: Max a

Enum a => Enum (Max a)

Since: 4.9.0.0

Methods

succ :: Max a -> Max a

pred :: Max a -> Max a

toEnum :: Int -> Max a

fromEnum :: Max a -> Int

enumFrom :: Max a -> [Max a]

enumFromThen :: Max a -> Max a -> [Max a]

enumFromTo :: Max a -> Max a -> [Max a]

enumFromThenTo :: Max a -> Max a -> Max a -> [Max a]

Eq a => Eq (Max a)

Methods

(==) :: Max a -> Max a -> Bool

(/=) :: Max a -> Max a -> Bool

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)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Max a)

toConstr :: Max a -> Constr

dataTypeOf :: Max a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Max a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a))

gmapT :: (forall b. Data b => b -> b) -> Max a -> Max a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r

gmapQ :: (forall d. Data d => d -> u) -> Max a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Max a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Max a -> m (Max a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a)

Num a => Num (Max a)

Since: 4.9.0.0

Methods

(+) :: Max a -> Max a -> Max a

(-) :: Max a -> Max a -> Max a

(*) :: Max a -> Max a -> Max a

negate :: Max a -> Max a

abs :: Max a -> Max a

signum :: Max a -> Max a

fromInteger :: Integer -> Max a

Ord a => Ord (Max a)

Methods

compare :: Max a -> Max a -> Ordering

(<) :: Max a -> Max a -> Bool

(<=) :: Max a -> Max a -> Bool

(>) :: Max a -> Max a -> Bool

(>=) :: Max a -> Max a -> Bool

max :: Max a -> Max a -> Max a

min :: Max a -> Max a -> Max a

Read a => Read (Max a)

Methods

readsPrec :: Int -> ReadS (Max a)

readList :: ReadS [Max a]

readPrec :: ReadPrec (Max a)

readListPrec :: ReadPrec [Max a]

Show a => Show (Max a)

Methods

showsPrec :: Int -> Max a -> ShowS

show :: Max a -> String

showList :: [Max a] -> ShowS

Generic (Max a)

Associated Types

type Rep (Max a) :: * -> *

Methods

from :: Max a -> Rep (Max a) x

to :: Rep (Max a) x -> Max a

Ord a => Semigroup (Max a)

Since: 4.9.0.0

Methods

(<>) :: Max a -> Max a -> Max a

sconcat :: NonEmpty (Max a) -> Max a

stimes :: Integral b => b -> Max a -> Max a

(Ord a, Bounded a) => Monoid (Max a)

Since: 4.9.0.0

Methods

mempty :: Max a

mappend :: Max a -> Max a -> Max a

mconcat :: [Max a] -> Max a

Generic1 * Max

Associated Types

type Rep1 Max (f :: Max -> *) :: k -> *

Methods

from1 :: f a -> Rep1 Max f a

to1 :: Rep1 Max f a -> f a

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

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

(>>) :: First a -> First b -> First b

return :: a -> First a

fail :: String -> First a

Functor First

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> First a -> First b

(<$) :: a -> First b -> First a

MonadFix First

Since: 4.9.0.0

Methods

mfix :: (a -> First a) -> First a

Applicative First

Since: 4.9.0.0

Methods

pure :: a -> First a

(<*>) :: First (a -> b) -> First a -> First b

liftA2 :: (a -> b -> c) -> First a -> First b -> First c

(*>) :: First a -> First b -> First b

(<*) :: First a -> First b -> First a

Foldable First

Since: 4.9.0.0

Methods

fold :: Monoid m => First m -> m

foldMap :: Monoid m => (a -> m) -> First a -> m

foldr :: (a -> b -> b) -> b -> First a -> b

foldr' :: (a -> b -> b) -> b -> First a -> b

foldl :: (b -> a -> b) -> b -> First a -> b

foldl' :: (b -> a -> b) -> b -> First a -> b

foldr1 :: (a -> a -> a) -> First a -> a

foldl1 :: (a -> a -> a) -> First a -> a

toList :: First a -> [a]

null :: First a -> Bool

length :: First a -> Int

elem :: Eq a => a -> First a -> Bool

maximum :: Ord a => First a -> a

minimum :: Ord a => First a -> a

sum :: Num a => First a -> a

product :: Num a => First a -> a

Traversable First

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> First a -> f (First b)

sequenceA :: Applicative f => First (f a) -> f (First a)

mapM :: Monad m => (a -> m b) -> First a -> m (First b)

sequence :: Monad m => First (m a) -> m (First a)

Bounded a => Bounded (First a)

Methods

minBound :: First a

maxBound :: First a

Enum a => Enum (First a)

Since: 4.9.0.0

Methods

succ :: First a -> First a

pred :: First a -> First a

toEnum :: Int -> First a

fromEnum :: First a -> Int

enumFrom :: First a -> [First a]

enumFromThen :: First a -> First a -> [First a]

enumFromTo :: First a -> First a -> [First a]

enumFromThenTo :: First a -> First a -> First a -> [First a]

Eq a => Eq (First a)

Methods

(==) :: First a -> First a -> Bool

(/=) :: First a -> First a -> Bool

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)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a)

toConstr :: First a -> Constr

dataTypeOf :: First a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (First a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a))

gmapT :: (forall b. Data b => b -> b) -> First a -> First a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r

gmapQ :: (forall d. Data d => d -> u) -> First a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a)

Ord a => Ord (First a)

Methods

compare :: First a -> First a -> Ordering

(<) :: First a -> First a -> Bool

(<=) :: First a -> First a -> Bool

(>) :: First a -> First a -> Bool

(>=) :: First a -> First a -> Bool

max :: First a -> First a -> First a

min :: First a -> First a -> First a

Read a => Read (First a)

Methods

readsPrec :: Int -> ReadS (First a)

readList :: ReadS [First a]

readPrec :: ReadPrec (First a)

readListPrec :: ReadPrec [First a]

Show a => Show (First a)

Methods

showsPrec :: Int -> First a -> ShowS

show :: First a -> String

showList :: [First a] -> ShowS

Generic (First a)

Associated Types

type Rep (First a) :: * -> *

Methods

from :: First a -> Rep (First a) x

to :: Rep (First a) x -> First a

Semigroup (First a)

Since: 4.9.0.0

Methods

(<>) :: First a -> First a -> First a

sconcat :: NonEmpty (First a) -> First a

stimes :: Integral b => b -> First a -> First a

Generic1 * First

Associated Types

type Rep1 First (f :: First -> *) :: k -> *

Methods

from1 :: f a -> Rep1 First f a

to1 :: Rep1 First f a -> f a

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

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

(>>) :: Last a -> Last b -> Last b

return :: a -> Last a

fail :: String -> Last a

Functor Last

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Last a -> Last b

(<$) :: a -> Last b -> Last a

MonadFix Last

Since: 4.9.0.0

Methods

mfix :: (a -> Last a) -> Last a

Applicative Last

Since: 4.9.0.0

Methods

pure :: a -> Last a

(<*>) :: Last (a -> b) -> Last a -> Last b

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c

(*>) :: Last a -> Last b -> Last b

(<*) :: Last a -> Last b -> Last a

Foldable Last

Since: 4.9.0.0

Methods

fold :: Monoid m => Last m -> m

foldMap :: Monoid m => (a -> m) -> Last a -> m

foldr :: (a -> b -> b) -> b -> Last a -> b

foldr' :: (a -> b -> b) -> b -> Last a -> b

foldl :: (b -> a -> b) -> b -> Last a -> b

foldl' :: (b -> a -> b) -> b -> Last a -> b

foldr1 :: (a -> a -> a) -> Last a -> a

foldl1 :: (a -> a -> a) -> Last a -> a

toList :: Last a -> [a]

null :: Last a -> Bool

length :: Last a -> Int

elem :: Eq a => a -> Last a -> Bool

maximum :: Ord a => Last a -> a

minimum :: Ord a => Last a -> a

sum :: Num a => Last a -> a

product :: Num a => Last a -> a

Traversable Last

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b)

sequenceA :: Applicative f => Last (f a) -> f (Last a)

mapM :: Monad m => (a -> m b) -> Last a -> m (Last b)

sequence :: Monad m => Last (m a) -> m (Last a)

Bounded a => Bounded (Last a)

Methods

minBound :: Last a

maxBound :: Last a

Enum a => Enum (Last a)

Since: 4.9.0.0

Methods

succ :: Last a -> Last a

pred :: Last a -> Last a

toEnum :: Int -> Last a

fromEnum :: Last a -> Int

enumFrom :: Last a -> [Last a]

enumFromThen :: Last a -> Last a -> [Last a]

enumFromTo :: Last a -> Last a -> [Last a]

enumFromThenTo :: Last a -> Last a -> Last a -> [Last a]

Eq a => Eq (Last a)

Methods

(==) :: Last a -> Last a -> Bool

(/=) :: Last a -> Last a -> Bool

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)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a)

toConstr :: Last a -> Constr

dataTypeOf :: Last a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Last a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a))

gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r

gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a)

Ord a => Ord (Last a)

Methods

compare :: Last a -> Last a -> Ordering

(<) :: Last a -> Last a -> Bool

(<=) :: Last a -> Last a -> Bool

(>) :: Last a -> Last a -> Bool

(>=) :: Last a -> Last a -> Bool

max :: Last a -> Last a -> Last a

min :: Last a -> Last a -> Last a

Read a => Read (Last a)

Methods

readsPrec :: Int -> ReadS (Last a)

readList :: ReadS [Last a]

readPrec :: ReadPrec (Last a)

readListPrec :: ReadPrec [Last a]

Show a => Show (Last a)

Methods

showsPrec :: Int -> Last a -> ShowS

show :: Last a -> String

showList :: [Last a] -> ShowS

Generic (Last a)

Associated Types

type Rep (Last a) :: * -> *

Methods

from :: Last a -> Rep (Last a) x

to :: Rep (Last a) x -> Last a

Semigroup (Last a)

Since: 4.9.0.0

Methods

(<>) :: Last a -> Last a -> Last a

sconcat :: NonEmpty (Last a) -> Last a

stimes :: Integral b => b -> Last a -> Last a

Generic1 * Last

Associated Types

type Rep1 Last (f :: Last -> *) :: k -> *

Methods

from1 :: f a -> Rep1 Last f a

to1 :: Rep1 Last f a -> f a

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

Provide a Semigroup for an arbitrary Monoid.

Constructors

WrapMonoid

Fields

• unwrapMonoid :: m

Instances

Bounded m => Bounded (WrappedMonoid m)

Methods

minBound :: WrappedMonoid m

maxBound :: WrappedMonoid m

Enum a => Enum (WrappedMonoid a)

Since: 4.9.0.0

Methods

succ :: WrappedMonoid a -> WrappedMonoid a

pred :: WrappedMonoid a -> WrappedMonoid a

toEnum :: Int -> WrappedMonoid a

fromEnum :: WrappedMonoid a -> Int

enumFrom :: WrappedMonoid a -> [WrappedMonoid a]

enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a]

enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a]

enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a]

Eq m => Eq (WrappedMonoid m)

Methods

(==) :: WrappedMonoid m -> WrappedMonoid m -> Bool

(/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool

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)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonoid m)

toConstr :: WrappedMonoid m -> Constr

dataTypeOf :: WrappedMonoid m -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (WrappedMonoid m))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WrappedMonoid m))

gmapT :: (forall b. Data b => b -> b) -> WrappedMonoid m -> WrappedMonoid m

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r

gmapQ :: (forall d. Data d => d -> u) -> WrappedMonoid m -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonoid m -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m)

Ord m => Ord (WrappedMonoid m)

Methods

compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering

(<) :: WrappedMonoid m -> WrappedMonoid m -> Bool

(<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool

(>) :: WrappedMonoid m -> WrappedMonoid m -> Bool

(>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool

max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

Read m => Read (WrappedMonoid m)

Methods

readsPrec :: Int -> ReadS (WrappedMonoid m)

readList :: ReadS [WrappedMonoid m]

readPrec :: ReadPrec (WrappedMonoid m)

readListPrec :: ReadPrec [WrappedMonoid m]

Show m => Show (WrappedMonoid m)

Methods

showsPrec :: Int -> WrappedMonoid m -> ShowS

show :: WrappedMonoid m -> String

showList :: [WrappedMonoid m] -> ShowS

Generic (WrappedMonoid m)

Associated Types

type Rep (WrappedMonoid m) :: * -> *

Methods

from :: WrappedMonoid m -> Rep (WrappedMonoid m) x

to :: Rep (WrappedMonoid m) x -> WrappedMonoid m

Monoid m => Semigroup (WrappedMonoid m)

Since: 4.9.0.0

Methods

(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m

stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m

Monoid m => Monoid (WrappedMonoid m)

Since: 4.9.0.0

Methods

mempty :: WrappedMonoid m

mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

mconcat :: [WrappedMonoid m] -> WrappedMonoid m

Generic1 * WrappedMonoid

Associated Types

type Rep1 WrappedMonoid (f :: WrappedMonoid -> *) :: k -> *

Methods

from1 :: f a -> Rep1 WrappedMonoid f a

to1 :: Rep1 WrappedMonoid f a -> f a

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

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 newtypes and make those instances of Monoid, e.g. Sum and Product.

Minimal complete definition

mempty, mappend

Methods

mempty :: a

Identity of mappend

mappend :: a -> a -> a

An associative operation

mconcat :: [a] -> a

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

mappend :: Ordering -> Ordering -> Ordering

mconcat :: [Ordering] -> Ordering

Monoid ()

Since: 2.1

Methods

mempty :: ()

mappend :: () -> () -> ()

mconcat :: [()] -> ()

Monoid Any

Since: 2.1

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> Any

Monoid All

Since: 2.1

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> All

Monoid Lifetime

mappend takes the longer of two lifetimes.

Since: 4.8.0.0

Methods

mempty :: Lifetime

mappend :: Lifetime -> Lifetime -> Lifetime

mconcat :: [Lifetime] -> Lifetime

Monoid Event

Since: 4.3.1.0

Methods

mempty :: Event

mappend :: Event -> Event -> Event

mconcat :: [Event] -> Event

Monoid [a]

Since: 2.1

Methods

mempty :: [a]

mappend :: [a] -> [a] -> [a]

mconcat :: [[a]] -> [a]

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

mappend :: Maybe a -> Maybe a -> Maybe a

mconcat :: [Maybe a] -> Maybe a

Monoid a => Monoid (IO a)

Since: 4.9.0.0

Methods

mempty :: IO a

mappend :: IO a -> IO a -> IO a

mconcat :: [IO a] -> IO a

Monoid (Last a)

Since: 2.1

Methods

mempty :: Last a

mappend :: Last a -> Last a -> Last a

mconcat :: [Last a] -> Last a

Monoid (First a)

Since: 2.1

Methods

mempty :: First a

mappend :: First a -> First a -> First a

mconcat :: [First a] -> First a

Num a => Monoid (Product a)

Since: 2.1

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product a

Num a => Monoid (Sum a)

Since: 2.1

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

Monoid (Endo a)

Since: 2.1

Methods

mempty :: Endo a

mappend :: Endo a -> Endo a -> Endo a

mconcat :: [Endo a] -> Endo a

Monoid a => Monoid (Dual a)

Since: 2.1

Methods

mempty :: Dual a

mappend :: Dual a -> Dual a -> Dual a

mconcat :: [Dual a] -> Dual a

Monoid a => Monoid (Identity a)

Methods

mempty :: Identity a

mappend :: Identity a -> Identity a -> Identity a

mconcat :: [Identity a] -> Identity a

Semigroup a => Monoid (Option a)

Since: 4.9.0.0

Methods

mempty :: Option a

mappend :: Option a -> Option a -> Option a

mconcat :: [Option a] -> Option a

Monoid m => Monoid (WrappedMonoid m)

Since: 4.9.0.0

Methods

mempty :: WrappedMonoid m

mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

mconcat :: [WrappedMonoid m] -> WrappedMonoid m

(Ord a, Bounded a) => Monoid (Max a)

Since: 4.9.0.0

Methods

mempty :: Max a

mappend :: Max a -> Max a -> Max a

mconcat :: [Max a] -> Max a

(Ord a, Bounded a) => Monoid (Min a)

Since: 4.9.0.0

Methods

mempty :: Min a

mappend :: Min a -> Min a -> Min a

mconcat :: [Min a] -> Min a

Monoid b => Monoid (a -> b)

Since: 2.1

Methods

mempty :: a -> b

mappend :: (a -> b) -> (a -> b) -> a -> b

mconcat :: [a -> b] -> a -> b

(Monoid a, Monoid b) => Monoid (a, b)

Since: 2.1

Methods

mempty :: (a, b)

mappend :: (a, b) -> (a, b) -> (a, b)

mconcat :: [(a, b)] -> (a, b)

Monoid (Proxy k s)

Since: 4.7.0.0

Methods

mempty :: Proxy k s

mappend :: Proxy k s -> Proxy k s -> Proxy k s

mconcat :: [Proxy k s] -> Proxy k s

(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)

Since: 2.1

Methods

mempty :: (a, b, c)

mappend :: (a, b, c) -> (a, b, c) -> (a, b, c)

mconcat :: [(a, b, c)] -> (a, b, c)

Alternative f => Monoid (Alt * f a)

Since: 4.8.0.0

Methods

mempty :: Alt * f a

mappend :: Alt * f a -> Alt * f a -> Alt * f a

mconcat :: [Alt * f a] -> Alt * f a

Monoid a => Monoid (Const k a b)

Methods

mempty :: Const k a b

mappend :: Const k a b -> Const k a b -> Const k a b

mconcat :: [Const k a b] -> Const k a b

(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)

Since: 2.1

Methods

mempty :: (a, b, c, d)

mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

mconcat :: [(a, b, c, d)] -> (a, b, c, d)

(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)

mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e)

newtype Dual a

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

(>>) :: Dual a -> Dual b -> Dual b

return :: a -> Dual a

fail :: String -> Dual a

Functor Dual

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Dual a -> Dual b

(<$) :: a -> Dual b -> Dual a

MonadFix Dual

Since: 4.8.0.0

Methods

mfix :: (a -> Dual a) -> Dual a

Applicative Dual

Since: 4.8.0.0

Methods

pure :: a -> Dual a

(<*>) :: Dual (a -> b) -> Dual a -> Dual b

liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c

(*>) :: Dual a -> Dual b -> Dual b

(<*) :: Dual a -> Dual b -> Dual a

Foldable Dual

Since: 4.8.0.0

Methods

fold :: Monoid m => Dual m -> m

foldMap :: Monoid m => (a -> m) -> Dual a -> m

foldr :: (a -> b -> b) -> b -> Dual a -> b

foldr' :: (a -> b -> b) -> b -> Dual a -> b

foldl :: (b -> a -> b) -> b -> Dual a -> b

foldl' :: (b -> a -> b) -> b -> Dual a -> b

foldr1 :: (a -> a -> a) -> Dual a -> a

foldl1 :: (a -> a -> a) -> Dual a -> a

toList :: Dual a -> [a]

null :: Dual a -> Bool

length :: Dual a -> Int

elem :: Eq a => a -> Dual a -> Bool

maximum :: Ord a => Dual a -> a

minimum :: Ord a => Dual a -> a

sum :: Num a => Dual a -> a

product :: Num a => Dual a -> a

Traversable Dual

Since: 4.8.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b)

sequenceA :: Applicative f => Dual (f a) -> f (Dual a)

mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b)

sequence :: Monad m => Dual (m a) -> m (Dual a)

MonadZip Dual

Since: 4.8.0.0

Methods

mzip :: Dual a -> Dual b -> Dual (a, b)

mzipWith :: (a -> b -> c) -> Dual a -> Dual b -> Dual c

munzip :: Dual (a, b) -> (Dual a, Dual b)

Bounded a => Bounded (Dual a)

Methods

minBound :: Dual a

maxBound :: Dual a

Eq a => Eq (Dual a)

Methods

(==) :: Dual a -> Dual a -> Bool

(/=) :: Dual a -> Dual a -> Bool

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)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a)

toConstr :: Dual a -> Constr

dataTypeOf :: Dual a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a))

gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r

gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a)

Ord a => Ord (Dual a)

Methods

compare :: Dual a -> Dual a -> Ordering

(<) :: Dual a -> Dual a -> Bool

(<=) :: Dual a -> Dual a -> Bool

(>) :: Dual a -> Dual a -> Bool

(>=) :: Dual a -> Dual a -> Bool

max :: Dual a -> Dual a -> Dual a

min :: Dual a -> Dual a -> Dual a

Read a => Read (Dual a)

Methods

readsPrec :: Int -> ReadS (Dual a)

readList :: ReadS [Dual a]

readPrec :: ReadPrec (Dual a)

readListPrec :: ReadPrec [Dual a]

Show a => Show (Dual a)

Methods

showsPrec :: Int -> Dual a -> ShowS

show :: Dual a -> String

showList :: [Dual a] -> ShowS

Generic (Dual a)

Associated Types

type Rep (Dual a) :: * -> *

Methods

from :: Dual a -> Rep (Dual a) x

to :: Rep (Dual a) x -> Dual a

Semigroup a => Semigroup (Dual a)

Since: 4.9.0.0

Methods

(<>) :: Dual a -> Dual a -> Dual a

sconcat :: NonEmpty (Dual a) -> Dual a

stimes :: Integral b => b -> Dual a -> Dual a

Monoid a => Monoid (Dual a)

Since: 2.1

Methods

mempty :: Dual a

mappend :: Dual a -> Dual a -> Dual a

mconcat :: [Dual a] -> Dual a

Generic1 * Dual

Associated Types

type Rep1 Dual (f :: Dual -> *) :: k -> *

Methods

from1 :: f a -> Rep1 Dual f a

to1 :: Rep1 Dual f a -> f a

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

The monoid of endomorphisms under composition.

Constructors

Endo

Fields

• appEndo :: a -> a

Instances

Generic (Endo a)

Associated Types

type Rep (Endo a) :: * -> *

Methods

from :: Endo a -> Rep (Endo a) x

to :: Rep (Endo a) x -> Endo a

Semigroup (Endo a)

Since: 4.9.0.0

Methods

(<>) :: Endo a -> Endo a -> Endo a

sconcat :: NonEmpty (Endo a) -> Endo a

stimes :: Integral b => b -> Endo a -> Endo a

Monoid (Endo a)

Since: 2.1

Methods

mempty :: Endo a

mappend :: Endo a -> Endo a -> Endo a

mconcat :: [Endo a] -> Endo a

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

Boolean monoid under conjunction (&&).

Constructors

All

Fields

• getAll :: Bool

Instances

Bounded All

Methods

minBound :: All

maxBound :: All

Eq All

Methods

(==) :: All -> All -> Bool

(/=) :: All -> All -> Bool

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

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All

toConstr :: All -> Constr

dataTypeOf :: All -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c All)

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All)

gmapT :: (forall b. Data b => b -> b) -> All -> All

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r

gmapQ :: (forall d. Data d => d -> u) -> All -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All

Ord All

Methods

compare :: All -> All -> Ordering

(<) :: All -> All -> Bool

(<=) :: All -> All -> Bool

(>) :: All -> All -> Bool

(>=) :: All -> All -> Bool

max :: All -> All -> All

min :: All -> All -> All

Read All

Methods

readsPrec :: Int -> ReadS All

readList :: ReadS [All]

readPrec :: ReadPrec All

readListPrec :: ReadPrec [All]

Show All

Methods

showsPrec :: Int -> All -> ShowS

show :: All -> String

showList :: [All] -> ShowS

Generic All

Associated Types

type Rep All :: * -> *

Methods

from :: All -> Rep All x

to :: Rep All x -> All

Semigroup All

Since: 4.9.0.0

Methods

(<>) :: All -> All -> All

sconcat :: NonEmpty All -> All

stimes :: Integral b => b -> All -> All

Monoid All

Since: 2.1

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> All

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

Boolean monoid under disjunction (||).

Constructors

Any

Fields

• getAny :: Bool

Instances

Bounded Any

Methods

minBound :: Any

maxBound :: Any

Eq Any

Methods

(==) :: Any -> Any -> Bool

(/=) :: Any -> Any -> Bool

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

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any

toConstr :: Any -> Constr

dataTypeOf :: Any -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Any)

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any)

gmapT :: (forall b. Data b => b -> b) -> Any -> Any

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r

gmapQ :: (forall d. Data d => d -> u) -> Any -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any

Ord Any

Methods

compare :: Any -> Any -> Ordering

(<) :: Any -> Any -> Bool

(<=) :: Any -> Any -> Bool

(>) :: Any -> Any -> Bool

(>=) :: Any -> Any -> Bool

max :: Any -> Any -> Any

min :: Any -> Any -> Any

Read Any

Methods

readsPrec :: Int -> ReadS Any

readList :: ReadS [Any]

readPrec :: ReadPrec Any

readListPrec :: ReadPrec [Any]

Show Any

Methods

showsPrec :: Int -> Any -> ShowS

show :: Any -> String

showList :: [Any] -> ShowS

Generic Any

Associated Types

type Rep Any :: * -> *

Methods

from :: Any -> Rep Any x

to :: Rep Any x -> Any

Semigroup Any

Since: 4.9.0.0

Methods

(<>) :: Any -> Any -> Any

sconcat :: NonEmpty Any -> Any

stimes :: Integral b => b -> Any -> Any

Monoid Any

Since: 2.1

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> Any

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

Monoid under addition.

Constructors

Sum

Fields

• getSum :: a

Instances

Monad Sum

Since: 4.8.0.0

Methods

(>>=) :: Sum a -> (a -> Sum b) -> Sum b

(>>) :: Sum a -> Sum b -> Sum b

return :: a -> Sum a

fail :: String -> Sum a

Functor Sum

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Sum a -> Sum b

(<$) :: a -> Sum b -> Sum a

MonadFix Sum

Since: 4.8.0.0

Methods

mfix :: (a -> Sum a) -> Sum a

Applicative Sum

Since: 4.8.0.0

Methods

pure :: a -> Sum a

(<*>) :: Sum (a -> b) -> Sum a -> Sum b

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c

(*>) :: Sum a -> Sum b -> Sum b

(<*) :: Sum a -> Sum b -> Sum a

Foldable Sum

Since: 4.8.0.0

Methods

fold :: Monoid m => Sum m -> m

foldMap :: Monoid m => (a -> m) -> Sum a -> m

foldr :: (a -> b -> b) -> b -> Sum a -> b

foldr' :: (a -> b -> b) -> b -> Sum a -> b

foldl :: (b -> a -> b) -> b -> Sum a -> b

foldl' :: (b -> a -> b) -> b -> Sum a -> b

foldr1 :: (a -> a -> a) -> Sum a -> a

foldl1 :: (a -> a -> a) -> Sum a -> a

toList :: Sum a -> [a]

null :: Sum a -> Bool

length :: Sum a -> Int

elem :: Eq a => a -> Sum a -> Bool

maximum :: Ord a => Sum a -> a

minimum :: Ord a => Sum a -> a

sum :: Num a => Sum a -> a

product :: Num a => Sum a -> a

Traversable Sum

Since: 4.8.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b)

sequenceA :: Applicative f => Sum (f a) -> f (Sum a)

mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b)

sequence :: Monad m => Sum (m a) -> m (Sum a)

MonadZip Sum

Since: 4.8.0.0

Methods

mzip :: Sum a -> Sum b -> Sum (a, b)

mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c

munzip :: Sum (a, b) -> (Sum a, Sum b)

Bounded a => Bounded (Sum a)

Methods

minBound :: Sum a

maxBound :: Sum a

Eq a => Eq (Sum a)

Methods

(==) :: Sum a -> Sum a -> Bool

(/=) :: Sum a -> Sum a -> Bool

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)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a)

toConstr :: Sum a -> Constr

dataTypeOf :: Sum a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a))

gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r

gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a)

Num a => Num (Sum a)

Methods

(+) :: Sum a -> Sum a -> Sum a

(-) :: Sum a -> Sum a -> Sum a

(*) :: Sum a -> Sum a -> Sum a

negate :: Sum a -> Sum a

abs :: Sum a -> Sum a

signum :: Sum a -> Sum a

fromInteger :: Integer -> Sum a

Ord a => Ord (Sum a)

Methods

compare :: Sum a -> Sum a -> Ordering

(<) :: Sum a -> Sum a -> Bool

(<=) :: Sum a -> Sum a -> Bool

(>) :: Sum a -> Sum a -> Bool

(>=) :: Sum a -> Sum a -> Bool

max :: Sum a -> Sum a -> Sum a

min :: Sum a -> Sum a -> Sum a

Read a => Read (Sum a)

Methods

readsPrec :: Int -> ReadS (Sum a)

readList :: ReadS [Sum a]

readPrec :: ReadPrec (Sum a)

readListPrec :: ReadPrec [Sum a]

Show a => Show (Sum a)

Methods

showsPrec :: Int -> Sum a -> ShowS

show :: Sum a -> String

showList :: [Sum a] -> ShowS

Generic (Sum a)

Associated Types

type Rep (Sum a) :: * -> *

Methods

from :: Sum a -> Rep (Sum a) x

to :: Rep (Sum a) x -> Sum a

Num a => Semigroup (Sum a)

Since: 4.9.0.0

Methods

(<>) :: Sum a -> Sum a -> Sum a

sconcat :: NonEmpty (Sum a) -> Sum a

stimes :: Integral b => b -> Sum a -> Sum a

Num a => Monoid (Sum a)

Since: 2.1

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

Generic1 * Sum

Associated Types

type Rep1 Sum (f :: Sum -> *) :: k -> *

Methods

from1 :: f a -> Rep1 Sum f a

to1 :: Rep1 Sum f a -> f a

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

Monoid under multiplication.

Constructors

Product

Fields

• getProduct :: a

Instances

Monad Product

Since: 4.8.0.0

Methods

(>>=) :: Product a -> (a -> Product b) -> Product b

(>>) :: Product a -> Product b -> Product b

return :: a -> Product a

fail :: String -> Product a

Functor Product

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Product a -> Product b

(<$) :: a -> Product b -> Product a

MonadFix Product

Since: 4.8.0.0

Methods

mfix :: (a -> Product a) -> Product a

Applicative Product

Since: 4.8.0.0

Methods

pure :: a -> Product a

(<*>) :: Product (a -> b) -> Product a -> Product b

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c

(*>) :: Product a -> Product b -> Product b

(<*) :: Product a -> Product b -> Product a

Foldable Product

Since: 4.8.0.0

Methods

fold :: Monoid m => Product m -> m

foldMap :: Monoid m => (a -> m) -> Product a -> m

foldr :: (a -> b -> b) -> b -> Product a -> b

foldr' :: (a -> b -> b) -> b -> Product a -> b

foldl :: (b -> a -> b) -> b -> Product a -> b

foldl' :: (b -> a -> b) -> b -> Product a -> b

foldr1 :: (a -> a -> a) -> Product a -> a

foldl1 :: (a -> a -> a) -> Product a -> a

toList :: Product a -> [a]

null :: Product a -> Bool

length :: Product a -> Int

elem :: Eq a => a -> Product a -> Bool

maximum :: Ord a => Product a -> a

minimum :: Ord a => Product a -> a

sum :: Num a => Product a -> a

product :: Num a => Product a -> a

Traversable Product

Since: 4.8.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b)

sequenceA :: Applicative f => Product (f a) -> f (Product a)

mapM :: Monad m => (a -> m b) -> Product a -> m (Product b)

sequence :: Monad m => Product (m a) -> m (Product a)

MonadZip Product

Since: 4.8.0.0

Methods

mzip :: Product a -> Product b -> Product (a, b)

mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c

munzip :: Product (a, b) -> (Product a, Product b)

Bounded a => Bounded (Product a)

Methods

minBound :: Product a

maxBound :: Product a

Eq a => Eq (Product a)

Methods

(==) :: Product a -> Product a -> Bool

(/=) :: Product a -> Product a -> Bool

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)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a)

toConstr :: Product a -> Constr

dataTypeOf :: Product a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Product a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a))

gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r

gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a)

Num a => Num (Product a)

Methods

(+) :: Product a -> Product a -> Product a

(-) :: Product a -> Product a -> Product a

(*) :: Product a -> Product a -> Product a

negate :: Product a -> Product a

abs :: Product a -> Product a

signum :: Product a -> Product a

fromInteger :: Integer -> Product a

Ord a => Ord (Product a)

Methods

compare :: Product a -> Product a -> Ordering

(<) :: Product a -> Product a -> Bool

(<=) :: Product a -> Product a -> Bool

(>) :: Product a -> Product a -> Bool

(>=) :: Product a -> Product a -> Bool

max :: Product a -> Product a -> Product a

min :: Product a -> Product a -> Product a

Read a => Read (Product a)

Methods

readsPrec :: Int -> ReadS (Product a)

readList :: ReadS [Product a]

readPrec :: ReadPrec (Product a)

readListPrec :: ReadPrec [Product a]

Show a => Show (Product a)

Methods

showsPrec :: Int -> Product a -> ShowS

show :: Product a -> String

showList :: [Product a] -> ShowS

Generic (Product a)

Associated Types

type Rep (Product a) :: * -> *

Methods

from :: Product a -> Rep (Product a) x

to :: Rep (Product a) x -> Product a

Num a => Semigroup (Product a)

Since: 4.9.0.0

Methods

(<>) :: Product a -> Product a -> Product a

sconcat :: NonEmpty (Product a) -> Product a

stimes :: Integral b => b -> Product a -> Product a

Num a => Monoid (Product a)

Since: 2.1

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product a

Generic1 * Product

Associated Types

type Rep1 Product (f :: Product -> *) :: k -> *

Methods

from1 :: f a -> Rep1 Product f a

to1 :: Rep1 Product f a -> f a

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

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

(>>) :: Option a -> Option b -> Option b

return :: a -> Option a

fail :: String -> Option a

Functor Option

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Option a -> Option b

(<$) :: a -> Option b -> Option a

MonadFix Option

Since: 4.9.0.0

Methods

mfix :: (a -> Option a) -> Option a

Applicative Option

Since: 4.9.0.0

Methods

pure :: a -> Option a

(<*>) :: Option (a -> b) -> Option a -> Option b

liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c

(*>) :: Option a -> Option b -> Option b

(<*) :: Option a -> Option b -> Option a

Foldable Option

Since: 4.9.0.0

Methods

fold :: Monoid m => Option m -> m

foldMap :: Monoid m => (a -> m) -> Option a -> m

foldr :: (a -> b -> b) -> b -> Option a -> b

foldr' :: (a -> b -> b) -> b -> Option a -> b

foldl :: (b -> a -> b) -> b -> Option a -> b

foldl' :: (b -> a -> b) -> b -> Option a -> b

foldr1 :: (a -> a -> a) -> Option a -> a

foldl1 :: (a -> a -> a) -> Option a -> a

toList :: Option a -> [a]

null :: Option a -> Bool

length :: Option a -> Int

elem :: Eq a => a -> Option a -> Bool

maximum :: Ord a => Option a -> a

minimum :: Ord a => Option a -> a

sum :: Num a => Option a -> a

product :: Num a => Option a -> a

Traversable Option

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Option a -> f (Option b)

sequenceA :: Applicative f => Option (f a) -> f (Option a)

mapM :: Monad m => (a -> m b) -> Option a -> m (Option b)

sequence :: Monad m => Option (m a) -> m (Option a)

MonadPlus Option

Since: 4.9.0.0

Methods

mzero :: Option a

mplus :: Option a -> Option a -> Option a

Alternative Option

Since: 4.9.0.0

Methods

empty :: Option a

(<|>) :: Option a -> Option a -> Option a

some :: Option a -> Option [a]

many :: Option a -> Option [a]

Eq a => Eq (Option a)

Methods

(==) :: Option a -> Option a -> Bool

(/=) :: Option a -> Option a -> Bool

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)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Option a)

toConstr :: Option a -> Constr

dataTypeOf :: Option a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Option a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Option a))

gmapT :: (forall b. Data b => b -> b) -> Option a -> Option a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r

gmapQ :: (forall d. Data d => d -> u) -> Option a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Option a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Option a -> m (Option a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a)

Ord a => Ord (Option a)

Methods

compare :: Option a -> Option a -> Ordering

(<) :: Option a -> Option a -> Bool

(<=) :: Option a -> Option a -> Bool

(>) :: Option a -> Option a -> Bool

(>=) :: Option a -> Option a -> Bool

max :: Option a -> Option a -> Option a

min :: Option a -> Option a -> Option a

Read a => Read (Option a)

Methods

readsPrec :: Int -> ReadS (Option a)

readList :: ReadS [Option a]

readPrec :: ReadPrec (Option a)

readListPrec :: ReadPrec [Option a]

Show a => Show (Option a)

Methods

showsPrec :: Int -> Option a -> ShowS

show :: Option a -> String

showList :: [Option a] -> ShowS

Generic (Option a)

Associated Types

type Rep (Option a) :: * -> *

Methods

from :: Option a -> Rep (Option a) x

to :: Rep (Option a) x -> Option a

Semigroup a => Semigroup (Option a)

Since: 4.9.0.0

Methods

(<>) :: Option a -> Option a -> Option a

sconcat :: NonEmpty (Option a) -> Option a

stimes :: Integral b => b -> Option a -> Option a

Semigroup a => Monoid (Option a)

Since: 4.9.0.0

Methods

mempty :: Option a

mappend :: Option a -> Option a -> Option a

mconcat :: [Option a] -> Option a

Generic1 * Option

Associated Types

type Rep1 Option (f :: Option -> *) :: k -> *

Methods

from1 :: f a -> Rep1 Option f a

to1 :: Rep1 Option f a -> f a

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

Fold an Option case-wise, just like maybe.

Difference lists of a semigroup

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

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

cycle1 :: Semigroup m => m -> m

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

ArgMin, ArgMax

data Arg a b

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

first :: (a -> b) -> Arg a c -> Arg b c

second :: (b -> c) -> Arg a b -> Arg a c

Bifoldable Arg

Since: 4.10.0.0

Methods

bifold :: Monoid m => Arg m m -> m

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c

Bitraversable Arg

Since: 4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d)

Functor (Arg a)

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Arg a a -> Arg a b

(<$) :: a -> Arg a b -> Arg a a

Foldable (Arg a)

Since: 4.9.0.0

Methods

fold :: Monoid m => Arg a m -> m

foldMap :: Monoid m => (a -> m) -> Arg a a -> m

foldr :: (a -> b -> b) -> b -> Arg a a -> b

foldr' :: (a -> b -> b) -> b -> Arg a a -> b

foldl :: (b -> a -> b) -> b -> Arg a a -> b

foldl' :: (b -> a -> b) -> b -> Arg a a -> b

foldr1 :: (a -> a -> a) -> Arg a a -> a

foldl1 :: (a -> a -> a) -> Arg a a -> a

toList :: Arg a a -> [a]

null :: Arg a a -> Bool

length :: Arg a a -> Int

elem :: Eq a => a -> Arg a a -> Bool

maximum :: Ord a => Arg a a -> a

minimum :: Ord a => Arg a a -> a

sum :: Num a => Arg a a -> a

product :: Num a => Arg a a -> a

Traversable (Arg a)

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Arg a a -> f (Arg a b)

sequenceA :: Applicative f => Arg a (f a) -> f (Arg a a)

mapM :: Monad m => (a -> m b) -> Arg a a -> m (Arg a b)

sequence :: Monad m => Arg a (m a) -> m (Arg a a)

Generic1 * (Arg a)

Associated Types

type Rep1 (Arg a) (f :: Arg a -> *) :: k -> *

Methods

from1 :: f a -> Rep1 (Arg a) f a

to1 :: Rep1 (Arg a) f a -> f a

Eq a => Eq (Arg a b)

Since: 4.9.0.0

Methods

(==) :: Arg a b -> Arg a b -> Bool

(/=) :: Arg a b -> Arg a b -> Bool

(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)

gunfold :: (forall c r. Data c => c (c -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b)

toConstr :: Arg a b -> Constr

dataTypeOf :: Arg a b -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Arg a b))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Arg a b))

gmapT :: (forall c. Data c => c -> c) -> Arg a b -> Arg a b

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r

gmapQ :: (forall d. Data d => d -> u) -> Arg a b -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Arg a b -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b)

Ord a => Ord (Arg a b)

Since: 4.9.0.0

Methods

compare :: Arg a b -> Arg a b -> Ordering

(<) :: Arg a b -> Arg a b -> Bool

(<=) :: Arg a b -> Arg a b -> Bool

(>) :: Arg a b -> Arg a b -> Bool

(>=) :: Arg a b -> Arg a b -> Bool

max :: Arg a b -> Arg a b -> Arg a b

min :: Arg a b -> Arg a b -> Arg a b

(Read b, Read a) => Read (Arg a b)

Methods

readsPrec :: Int -> ReadS (Arg a b)

readList :: ReadS [Arg a b]

readPrec :: ReadPrec (Arg a b)

readListPrec :: ReadPrec [Arg a b]

(Show b, Show a) => Show (Arg a b)

Methods

showsPrec :: Int -> Arg a b -> ShowS

show :: Arg a b -> String

showList :: [Arg a b] -> ShowS

Generic (Arg a b)

Associated Types

type Rep (Arg a b) :: * -> *

Methods

from :: Arg a b -> Rep (Arg a b) x

to :: Rep (Arg a b) x -> Arg a b

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)

type ArgMax a b = Max (Arg a b)