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
}
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).

Instances should satisfy the associativity law:

```
x <> (y <> z) = (x <> y) <> z
```

Since: 4.9.0.0

Minimal complete definition

(<>)

Methods

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

An associative operation.

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
Instance details Methods (<>) :: Ordering -> Ordering -> Ordering Source # sconcat :: NonEmpty Ordering -> Ordering Source # stimes :: Integral b => b -> Ordering -> Ordering Source #
Semigroup () #	Since: 4.9.0.0
Instance details Methods (<>) :: () -> () -> () Source # sconcat :: NonEmpty () -> () Source # stimes :: Integral b => b -> () -> () Source #
Semigroup Any #	Since: 4.9.0.0
Instance details Methods (<>) :: Any -> Any -> Any Source # sconcat :: NonEmpty Any -> Any Source # stimes :: Integral b => b -> Any -> Any Source #
Semigroup All #	Since: 4.9.0.0
Instance details Methods (<>) :: All -> All -> All Source # sconcat :: NonEmpty All -> All Source # stimes :: Integral b => b -> All -> All Source #
Semigroup Lifetime #	Since: 4.10.0.0
Instance details Methods (<>) :: Lifetime -> Lifetime -> Lifetime Source # sconcat :: NonEmpty Lifetime -> Lifetime Source # stimes :: Integral b => b -> Lifetime -> Lifetime Source #
Semigroup Event #	Since: 4.10.0.0
Instance details Methods (<>) :: Event -> Event -> Event Source # sconcat :: NonEmpty Event -> Event Source # stimes :: Integral b => b -> Event -> Event Source #
Semigroup Void #	Since: 4.9.0.0
Instance details Methods (<>) :: Void -> Void -> Void Source # sconcat :: NonEmpty Void -> Void Source # stimes :: Integral b => b -> Void -> Void Source #
Semigroup [a] #	Since: 4.9.0.0
Instance details 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
Instance details 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
Instance details 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 (NonEmpty a) #	Since: 4.9.0.0
Instance details 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 (Down a) #	Since: 4.11.0.0
Instance details Methods (<>) :: Down a -> Down a -> Down a Source # sconcat :: NonEmpty (Down a) -> Down a Source # stimes :: Integral b => b -> Down a -> Down a Source #
Num a => Semigroup (Product a) #	Since: 4.9.0.0
Instance details 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
Instance details 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
Instance details 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
Instance details 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 (Last a) #	Since: 4.9.0.0
Instance details 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
Instance details Methods (<>) :: First a -> First a -> First a Source # sconcat :: NonEmpty (First a) -> First a Source # stimes :: Integral b => b -> First a -> First a Source #
Semigroup a => Semigroup (Identity a) #
Instance details 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 a => Semigroup (Option a) #	Since: 4.9.0.0
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details Methods (<>) :: (a -> b) -> (a -> b) -> a -> b Source # sconcat :: NonEmpty (a -> b) -> a -> b Source # stimes :: Integral b0 => b0 -> (a -> b) -> a -> b Source #
Semigroup (Either a b) #	Since: 4.9.0.0
Instance details Methods (<>) :: Either a b -> Either a b -> Either a b Source # sconcat :: NonEmpty (Either a b) -> Either a b Source # stimes :: Integral b0 => b0 -> Either a b -> Either a b Source #
(Semigroup a, Semigroup b) => Semigroup (a, b) #	Since: 4.9.0.0
Instance details Methods (<>) :: (a, b) -> (a, b) -> (a, b) Source # sconcat :: NonEmpty (a, b) -> (a, b) Source # stimes :: Integral b0 => b0 -> (a, b) -> (a, b) Source #
Semigroup a => Semigroup (ST s a) #	Since: 4.11.0.0
Instance details Methods (<>) :: ST s a -> ST s a -> ST s a Source # sconcat :: NonEmpty (ST s a) -> ST s a Source # stimes :: Integral b => b -> ST s a -> ST s a Source #
Semigroup (Proxy s) #	Since: 4.9.0.0
Instance details Methods (<>) :: Proxy s -> Proxy s -> Proxy s Source # sconcat :: NonEmpty (Proxy s) -> Proxy s Source # stimes :: Integral b => b -> Proxy s -> Proxy s Source #
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) #	Since: 4.9.0.0
Instance details Methods (<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # sconcat :: NonEmpty (a, b, c) -> (a, b, c) Source # stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) Source #
Alternative f => Semigroup (Alt f a) #	Since: 4.9.0.0
Instance details 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 a b) #
Instance details Methods (<>) :: Const a b -> Const a b -> Const a b Source # sconcat :: NonEmpty (Const a b) -> Const a b Source # stimes :: Integral b0 => b0 -> Const a b -> Const a b Source #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) #	Since: 4.9.0.0
Instance details 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 b0 => b0 -> (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
Instance details 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 b0 => b0 -> (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
Instance details 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
Instance details Methods fmap :: (a -> b) -> Min a -> Min b Source # (<$) :: a -> Min b -> Min a Source #
MonadFix Min #	Since: 4.9.0.0
Instance details Methods mfix :: (a -> Min a) -> Min a Source #
Applicative Min #	Since: 4.9.0.0
Instance details 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
Instance details 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
Instance details 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) #
Instance details Methods minBound :: Min a Source # maxBound :: Min a Source #
Enum a => Enum (Min a) #	Since: 4.9.0.0
Instance details 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) #
Instance details Methods (==) :: Min a -> Min a -> Bool Source # (/=) :: Min a -> Min a -> Bool Source #
Data a => Data (Min a) #
Instance details 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
Instance details 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) #
Instance details 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) #
Instance details 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) #
Instance details Methods showsPrec :: Int -> Min a -> ShowS Source # show :: Min a -> String Source # showList :: [Min a] -> ShowS Source #
Generic (Min a) #
Instance details 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
Instance details 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
Instance details Methods mempty :: Min a Source # mappend :: Min a -> Min a -> Min a Source # mconcat :: [Min a] -> Min a Source #
Generic1 Min #
Instance details Associated Types type Rep1 Min :: k -> * Source # Methods from1 :: Min a -> Rep1 Min a Source # to1 :: Rep1 Min a -> Min a Source #
type Rep (Min a) #
Instance details type Rep (Min a) = D1 (MetaData "Min" "Data.Semigroup" "base" True) (C1 (MetaCons "Min" PrefixI True) (S1 (MetaSel (Just "getMin") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Min #
Instance details type Rep1 Min = D1 (MetaData "Min" "Data.Semigroup" "base" True) (C1 (MetaCons "Min" PrefixI True) (S1 (MetaSel (Just "getMin") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Max a Source #

Constructors

Max
Fields getMax :: a

Instances

Monad Max #	Since: 4.9.0.0
Instance details 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
Instance details Methods fmap :: (a -> b) -> Max a -> Max b Source # (<$) :: a -> Max b -> Max a Source #
MonadFix Max #	Since: 4.9.0.0
Instance details Methods mfix :: (a -> Max a) -> Max a Source #
Applicative Max #	Since: 4.9.0.0
Instance details 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
Instance details 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
Instance details 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) #
Instance details Methods minBound :: Max a Source # maxBound :: Max a Source #
Enum a => Enum (Max a) #	Since: 4.9.0.0
Instance details 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) #
Instance details Methods (==) :: Max a -> Max a -> Bool Source # (/=) :: Max a -> Max a -> Bool Source #
Data a => Data (Max a) #
Instance details 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
Instance details 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) #
Instance details 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) #
Instance details 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) #
Instance details Methods showsPrec :: Int -> Max a -> ShowS Source # show :: Max a -> String Source # showList :: [Max a] -> ShowS Source #
Generic (Max a) #
Instance details 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
Instance details 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
Instance details Methods mempty :: Max a Source # mappend :: Max a -> Max a -> Max a Source # mconcat :: [Max a] -> Max a Source #
Generic1 Max #
Instance details Associated Types type Rep1 Max :: k -> * Source # Methods from1 :: Max a -> Rep1 Max a Source # to1 :: Rep1 Max a -> Max a Source #
type Rep (Max a) #
Instance details type Rep (Max a) = D1 (MetaData "Max" "Data.Semigroup" "base" True) (C1 (MetaCons "Max" PrefixI True) (S1 (MetaSel (Just "getMax") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Max #
Instance details type Rep1 Max = D1 (MetaData "Max" "Data.Semigroup" "base" True) (C1 (MetaCons "Max" PrefixI True) (S1 (MetaSel (Just "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
Instance details 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
Instance details Methods fmap :: (a -> b) -> First a -> First b Source # (<$) :: a -> First b -> First a Source #
MonadFix First #	Since: 4.9.0.0
Instance details Methods mfix :: (a -> First a) -> First a Source #
Applicative First #	Since: 4.9.0.0
Instance details 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
Instance details 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
Instance details 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) #
Instance details Methods minBound :: First a Source # maxBound :: First a Source #
Enum a => Enum (First a) #	Since: 4.9.0.0
Instance details 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) #
Instance details Methods (==) :: First a -> First a -> Bool Source # (/=) :: First a -> First a -> Bool Source #
Data a => Data (First a) #
Instance details 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) #
Instance details 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) #
Instance details 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) #
Instance details Methods showsPrec :: Int -> First a -> ShowS Source # show :: First a -> String Source # showList :: [First a] -> ShowS Source #
Generic (First a) #
Instance details 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
Instance details 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 #
Instance details Associated Types type Rep1 First :: k -> * Source # Methods from1 :: First a -> Rep1 First a Source # to1 :: Rep1 First a -> First a Source #
type Rep (First a) #
Instance details type Rep (First a) = D1 (MetaData "First" "Data.Semigroup" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 First #
Instance details type Rep1 First = D1 (MetaData "First" "Data.Semigroup" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just "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
Instance details 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
Instance details Methods fmap :: (a -> b) -> Last a -> Last b Source # (<$) :: a -> Last b -> Last a Source #
MonadFix Last #	Since: 4.9.0.0
Instance details Methods mfix :: (a -> Last a) -> Last a Source #
Applicative Last #	Since: 4.9.0.0
Instance details 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
Instance details 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
Instance details 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) #
Instance details Methods minBound :: Last a Source # maxBound :: Last a Source #
Enum a => Enum (Last a) #	Since: 4.9.0.0
Instance details 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) #
Instance details Methods (==) :: Last a -> Last a -> Bool Source # (/=) :: Last a -> Last a -> Bool Source #
Data a => Data (Last a) #
Instance details 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) #
Instance details 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) #
Instance details 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) #
Instance details Methods showsPrec :: Int -> Last a -> ShowS Source # show :: Last a -> String Source # showList :: [Last a] -> ShowS Source #
Generic (Last a) #
Instance details 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
Instance details 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 #
Instance details Associated Types type Rep1 Last :: k -> * Source # Methods from1 :: Last a -> Rep1 Last a Source # to1 :: Rep1 Last a -> Last a Source #
type Rep (Last a) #
Instance details type Rep (Last a) = D1 (MetaData "Last" "Data.Semigroup" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Last #
Instance details type Rep1 Last = D1 (MetaData "Last" "Data.Semigroup" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype WrappedMonoid m Source #

Provide a Semigroup for an arbitrary Monoid.

NOTE: This is not needed anymore since Semigroup became a superclass of Monoid in base-4.11 and this newtype be deprecated at some point in the future.

Constructors

WrapMonoid
Fields unwrapMonoid :: m

Instances

Bounded m => Bounded (WrappedMonoid m) #
Instance details Methods minBound :: WrappedMonoid m Source # maxBound :: WrappedMonoid m Source #
Enum a => Enum (WrappedMonoid a) #	Since: 4.9.0.0
Instance details 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) #
Instance details Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source #
Data m => Data (WrappedMonoid m) #
Instance details 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 m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) Source # gmapMp :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) Source # gmapMo :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) Source #
Ord m => Ord (WrappedMonoid m) #
Instance details 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) #
Instance details 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) #
Instance details Methods showsPrec :: Int -> WrappedMonoid m -> ShowS Source # show :: WrappedMonoid m -> String Source # showList :: [WrappedMonoid m] -> ShowS Source #
Generic (WrappedMonoid m) #
Instance details 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
Instance details 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
Instance details Methods mempty :: WrappedMonoid m Source # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source #
Generic1 WrappedMonoid #
Instance details Associated Types type Rep1 WrappedMonoid :: k -> * Source # Methods from1 :: WrappedMonoid a -> Rep1 WrappedMonoid a Source # to1 :: Rep1 WrappedMonoid a -> WrappedMonoid a Source #
type Rep (WrappedMonoid m) #
Instance details type Rep (WrappedMonoid m) = D1 (MetaData "WrappedMonoid" "Data.Semigroup" "base" True) (C1 (MetaCons "WrapMonoid" PrefixI True) (S1 (MetaSel (Just "unwrapMonoid") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 m)))
type Rep1 WrappedMonoid #
Instance details type Rep1 WrappedMonoid = D1 (MetaData "WrappedMonoid" "Data.Semigroup" "base" True) (C1 (MetaCons "WrapMonoid" PrefixI True) (S1 (MetaSel (Just "unwrapMonoid") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

Re-exported monoids from Data.Monoid

newtype Dual a Source #

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

>>> getDual (mappend (Dual "Hello") (Dual "World"))
"WorldHello"

Constructors

Dual
Fields getDual :: a

Instances

Monad Dual #	Since: 4.8.0.0
Instance details 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
Instance details Methods fmap :: (a -> b) -> Dual a -> Dual b Source # (<$) :: a -> Dual b -> Dual a Source #
MonadFix Dual #	Since: 4.8.0.0
Instance details Methods mfix :: (a -> Dual a) -> Dual a Source #
Applicative Dual #	Since: 4.8.0.0
Instance details 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
Instance details 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
Instance details 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
Instance details 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) #
Instance details Methods minBound :: Dual a Source # maxBound :: Dual a Source #
Eq a => Eq (Dual a) #
Instance details Methods (==) :: Dual a -> Dual a -> Bool Source # (/=) :: Dual a -> Dual a -> Bool Source #
Data a => Data (Dual a) #	Since: 4.8.0.0
Instance details 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) #
Instance details 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) #
Instance details 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) #
Instance details Methods showsPrec :: Int -> Dual a -> ShowS Source # show :: Dual a -> String Source # showList :: [Dual a] -> ShowS Source #
Generic (Dual a) #
Instance details 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
Instance details 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
Instance details Methods mempty :: Dual a Source # mappend :: Dual a -> Dual a -> Dual a Source # mconcat :: [Dual a] -> Dual a Source #
Generic1 Dual #
Instance details Associated Types type Rep1 Dual :: k -> * Source # Methods from1 :: Dual a -> Rep1 Dual a Source # to1 :: Rep1 Dual a -> Dual a Source #
type Rep (Dual a) #
Instance details type Rep (Dual a) = D1 (MetaData "Dual" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Dual" PrefixI True) (S1 (MetaSel (Just "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Dual #
Instance details type Rep1 Dual = D1 (MetaData "Dual" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Dual" PrefixI True) (S1 (MetaSel (Just "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Endo a Source #

The monoid of endomorphisms under composition.

>>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>> appEndo computation "Haskell"
"Hello, Haskell!"

Constructors

Endo
Fields appEndo :: a -> a

Instances

Generic (Endo a) #
Instance details 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
Instance details 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
Instance details Methods mempty :: Endo a Source # mappend :: Endo a -> Endo a -> Endo a Source # mconcat :: [Endo a] -> Endo a Source #
type Rep (Endo a) #
Instance details type Rep (Endo a) = D1 (MetaData "Endo" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Endo" PrefixI True) (S1 (MetaSel (Just "appEndo") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (a -> a))))

newtype All Source #

Boolean monoid under conjunction (&&).

>>> getAll (All True <> mempty <> All False)
False

>>> getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))
False

Constructors

All
Fields getAll :: Bool

Instances

Bounded All #
Instance details Methods minBound :: All Source # maxBound :: All Source #
Eq All #
Instance details Methods (==) :: All -> All -> Bool Source # (/=) :: All -> All -> Bool Source #
Data All #	Since: 4.8.0.0
Instance details 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 #
Instance details 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 #
Instance details Methods readsPrec :: Int -> ReadS All Source # readList :: ReadS [All] Source # readPrec :: ReadPrec All Source # readListPrec :: ReadPrec [All] Source #
Show All #
Instance details Methods showsPrec :: Int -> All -> ShowS Source # show :: All -> String Source # showList :: [All] -> ShowS Source #
Generic All #
Instance details 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
Instance details Methods (<>) :: All -> All -> All Source # sconcat :: NonEmpty All -> All Source # stimes :: Integral b => b -> All -> All Source #
Monoid All #	Since: 2.1
Instance details Methods mempty :: All Source # mappend :: All -> All -> All Source # mconcat :: [All] -> All Source #
type Rep All #
Instance details type Rep All = D1 (MetaData "All" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "All" PrefixI True) (S1 (MetaSel (Just "getAll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool)))

newtype Any Source #

Boolean monoid under disjunction (||).

>>> getAny (Any True <> mempty <> Any False)
True

>>> getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))
True

Constructors

Any
Fields getAny :: Bool

Instances

Bounded Any #
Instance details Methods minBound :: Any Source # maxBound :: Any Source #
Eq Any #
Instance details Methods (==) :: Any -> Any -> Bool Source # (/=) :: Any -> Any -> Bool Source #
Data Any #	Since: 4.8.0.0
Instance details 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 #
Instance details 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 #
Instance details Methods readsPrec :: Int -> ReadS Any Source # readList :: ReadS [Any] Source # readPrec :: ReadPrec Any Source # readListPrec :: ReadPrec [Any] Source #
Show Any #
Instance details Methods showsPrec :: Int -> Any -> ShowS Source # show :: Any -> String Source # showList :: [Any] -> ShowS Source #
Generic Any #
Instance details 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
Instance details Methods (<>) :: Any -> Any -> Any Source # sconcat :: NonEmpty Any -> Any Source # stimes :: Integral b => b -> Any -> Any Source #
Monoid Any #	Since: 2.1
Instance details Methods mempty :: Any Source # mappend :: Any -> Any -> Any Source # mconcat :: [Any] -> Any Source #
type Rep Any #
Instance details type Rep Any = D1 (MetaData "Any" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Any" PrefixI True) (S1 (MetaSel (Just "getAny") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool)))

newtype Sum a Source #

Monoid under addition.

>>> getSum (Sum 1 <> Sum 2 <> mempty)
3

Constructors

Sum
Fields getSum :: a

Instances

Monad Sum #	Since: 4.8.0.0
Instance details 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
Instance details Methods fmap :: (a -> b) -> Sum a -> Sum b Source # (<$) :: a -> Sum b -> Sum a Source #
MonadFix Sum #	Since: 4.8.0.0
Instance details Methods mfix :: (a -> Sum a) -> Sum a Source #
Applicative Sum #	Since: 4.8.0.0
Instance details 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
Instance details 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
Instance details 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
Instance details 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) #
Instance details Methods minBound :: Sum a Source # maxBound :: Sum a Source #
Eq a => Eq (Sum a) #
Instance details Methods (==) :: Sum a -> Sum a -> Bool Source # (/=) :: Sum a -> Sum a -> Bool Source #
Data a => Data (Sum a) #	Since: 4.8.0.0
Instance details 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) #
Instance details 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) #
Instance details 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) #
Instance details 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) #
Instance details Methods showsPrec :: Int -> Sum a -> ShowS Source # show :: Sum a -> String Source # showList :: [Sum a] -> ShowS Source #
Generic (Sum a) #
Instance details 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
Instance details 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
Instance details Methods mempty :: Sum a Source # mappend :: Sum a -> Sum a -> Sum a Source # mconcat :: [Sum a] -> Sum a Source #
Generic1 Sum #
Instance details Associated Types type Rep1 Sum :: k -> * Source # Methods from1 :: Sum a -> Rep1 Sum a Source # to1 :: Rep1 Sum a -> Sum a Source #
type Rep (Sum a) #
Instance details type Rep (Sum a) = D1 (MetaData "Sum" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Sum #
Instance details type Rep1 Sum = D1 (MetaData "Sum" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Product a Source #

Monoid under multiplication.

>>> getProduct (Product 3 <> Product 4 <> mempty)
12

Constructors

Product
Fields getProduct :: a

Instances

Monad Product #	Since: 4.8.0.0
Instance details 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
Instance details Methods fmap :: (a -> b) -> Product a -> Product b Source # (<$) :: a -> Product b -> Product a Source #
MonadFix Product #	Since: 4.8.0.0
Instance details Methods mfix :: (a -> Product a) -> Product a Source #
Applicative Product #	Since: 4.8.0.0
Instance details 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
Instance details 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
Instance details 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
Instance details 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) #
Instance details Methods minBound :: Product a Source # maxBound :: Product a Source #
Eq a => Eq (Product a) #
Instance details Methods (==) :: Product a -> Product a -> Bool Source # (/=) :: Product a -> Product a -> Bool Source #
Data a => Data (Product a) #	Since: 4.8.0.0
Instance details 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) #
Instance details 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) #
Instance details 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) #
Instance details 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) #
Instance details Methods showsPrec :: Int -> Product a -> ShowS Source # show :: Product a -> String Source # showList :: [Product a] -> ShowS Source #
Generic (Product a) #
Instance details 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
Instance details 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
Instance details Methods mempty :: Product a Source # mappend :: Product a -> Product a -> Product a Source # mconcat :: [Product a] -> Product a Source #
Generic1 Product #
Instance details Associated Types type Rep1 Product :: k -> * Source # Methods from1 :: Product a -> Rep1 Product a Source # to1 :: Rep1 Product a -> Product a Source #
type Rep (Product a) #
Instance details type Rep (Product a) = D1 (MetaData "Product" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Product" PrefixI True) (S1 (MetaSel (Just "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Product #
Instance details type Rep1 Product = D1 (MetaData "Product" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Product" PrefixI True) (S1 (MetaSel (Just "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
Instance details 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
Instance details Methods fmap :: (a -> b) -> Option a -> Option b Source # (<$) :: a -> Option b -> Option a Source #
MonadFix Option #	Since: 4.9.0.0
Instance details Methods mfix :: (a -> Option a) -> Option a Source #
Applicative Option #	Since: 4.9.0.0
Instance details 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
Instance details 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
Instance details 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
Instance details Methods mzero :: Option a Source # mplus :: Option a -> Option a -> Option a Source #
Alternative Option #	Since: 4.9.0.0
Instance details 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) #
Instance details Methods (==) :: Option a -> Option a -> Bool Source # (/=) :: Option a -> Option a -> Bool Source #
Data a => Data (Option a) #
Instance details 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) #
Instance details 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) #
Instance details 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) #
Instance details Methods showsPrec :: Int -> Option a -> ShowS Source # show :: Option a -> String Source # showList :: [Option a] -> ShowS Source #
Generic (Option a) #
Instance details 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
Instance details 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
Instance details Methods mempty :: Option a Source # mappend :: Option a -> Option a -> Option a Source # mconcat :: [Option a] -> Option a Source #
Generic1 Option #
Instance details Associated Types type Rep1 Option :: k -> * Source # Methods from1 :: Option a -> Rep1 Option a Source # to1 :: Rep1 Option a -> Option a Source #
type Rep (Option a) #
Instance details type Rep (Option a) = D1 (MetaData "Option" "Data.Semigroup" "base" True) (C1 (MetaCons "Option" PrefixI True) (S1 (MetaSel (Just "getOption") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))
type Rep1 Option #
Instance details type Rep1 Option = D1 (MetaData "Option" "Data.Semigroup" "base" True) (C1 (MetaCons "Option" PrefixI True) (S1 (MetaSel (Just "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
Instance details 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
Instance details 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
Instance details 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
Instance details Methods fmap :: (a0 -> b) -> Arg a a0 -> Arg a b Source # (<$) :: a0 -> Arg a b -> Arg a a0 Source #
Foldable (Arg a) #	Since: 4.9.0.0
Instance details Methods fold :: Monoid m => Arg a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # toList :: Arg a a0 -> [a0] Source # null :: Arg a a0 -> Bool Source # length :: Arg a a0 -> Int Source # elem :: Eq a0 => a0 -> Arg a a0 -> Bool Source # maximum :: Ord a0 => Arg a a0 -> a0 Source # minimum :: Ord a0 => Arg a a0 -> a0 Source # sum :: Num a0 => Arg a a0 -> a0 Source # product :: Num a0 => Arg a a0 -> a0 Source #
Traversable (Arg a) #	Since: 4.9.0.0
Instance details Methods traverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) Source # sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) Source # mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) Source # sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) Source #
Generic1 (Arg a :: * -> *) #
Instance details Associated Types type Rep1 (Arg a) :: k -> * Source # Methods from1 :: Arg a a0 -> Rep1 (Arg a) a0 Source # to1 :: Rep1 (Arg a) a0 -> Arg a a0 Source #
Eq a => Eq (Arg a b) #	Since: 4.9.0.0
Instance details Methods (==) :: Arg a b -> Arg a b -> Bool Source # (/=) :: Arg a b -> Arg a b -> Bool Source #
(Data a, Data b) => Data (Arg a b) #
Instance details Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Arg a b -> c (Arg a b) Source # gunfold :: (forall b0 r. Data b0 => c (b0 -> 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 b0. Data b0 => b0 -> b0) -> 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
Instance details 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 a, Read b) => Read (Arg a b) #
Instance details 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 a, Show b) => Show (Arg a b) #
Instance details Methods showsPrec :: Int -> Arg a b -> ShowS Source # show :: Arg a b -> String Source # showList :: [Arg a b] -> ShowS Source #
Generic (Arg a b) #
Instance details 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 :: * -> *) #
Instance details type Rep1 (Arg a :: * -> ) = D1 (MetaData "Arg" "Data.Semigroup" "base" False) (C1 (MetaCons "Arg" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep (Arg a b) #
Instance details type Rep (Arg a b) = D1 (MetaData "Arg" "Data.Semigroup" "base" False) (C1 (MetaCons "Arg" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 b)))

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

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