Copyright	(C) 2011-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell98

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

Synopsis

Documentation

class Semigroup a where Source

Minimal complete definition

Nothing

Methods

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

An associative operation.

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

If a is also a Monoid we further require

(<>) = mappend

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.

Since: 0.17

Instances

Semigroup Ordering Source
Methods (<>) :: Ordering -> Ordering -> Ordering Source sconcat :: NonEmpty Ordering -> Ordering Source stimes :: Integral b => b -> Ordering -> Ordering Source
Semigroup () Source
Methods (<>) :: () -> () -> () Source sconcat :: NonEmpty () -> () Source stimes :: Integral b => b -> () -> () Source
Semigroup Void Source
Methods (<>) :: Void -> Void -> Void Source sconcat :: NonEmpty Void -> Void Source stimes :: Integral b => b -> Void -> Void Source
Semigroup All Source
Methods (<>) :: All -> All -> All Source sconcat :: NonEmpty All -> All Source stimes :: Integral b => b -> All -> All Source
Semigroup Any Source
Methods (<>) :: Any -> Any -> Any Source sconcat :: NonEmpty Any -> Any Source stimes :: Integral b => b -> Any -> Any Source
Semigroup ByteString Source
Methods (<>) :: ByteString -> ByteString -> ByteString Source sconcat :: NonEmpty ByteString -> ByteString Source stimes :: Integral b => b -> ByteString -> ByteString Source
Semigroup ByteString Source
Methods (<>) :: ByteString -> ByteString -> ByteString Source sconcat :: NonEmpty ByteString -> ByteString Source stimes :: Integral b => b -> ByteString -> ByteString Source
Semigroup Builder Source
Methods (<>) :: Builder -> Builder -> Builder Source sconcat :: NonEmpty Builder -> Builder Source stimes :: Integral b => b -> Builder -> Builder Source
Semigroup Builder Source
Methods (<>) :: Builder -> Builder -> Builder Source sconcat :: NonEmpty Builder -> Builder Source stimes :: Integral b => b -> Builder -> Builder Source
Semigroup ShortByteString Source
Methods (<>) :: ShortByteString -> ShortByteString -> ShortByteString Source sconcat :: NonEmpty ShortByteString -> ShortByteString Source stimes :: Integral b => b -> ShortByteString -> ShortByteString Source
Semigroup IntSet Source
Methods (<>) :: IntSet -> IntSet -> IntSet Source sconcat :: NonEmpty IntSet -> IntSet Source stimes :: Integral b => b -> IntSet -> IntSet Source
Semigroup Builder Source
Methods (<>) :: Builder -> Builder -> Builder Source sconcat :: NonEmpty Builder -> Builder Source stimes :: Integral b => b -> Builder -> Builder Source
Semigroup Text Source
Methods (<>) :: Text -> Text -> Text Source sconcat :: NonEmpty Text -> Text Source stimes :: Integral b => b -> Text -> Text Source
Semigroup Text Source
Methods (<>) :: Text -> Text -> Text Source sconcat :: NonEmpty Text -> Text Source stimes :: Integral b => b -> Text -> Text Source
Semigroup [a] Source
Methods (<>) :: [a] -> [a] -> [a] Source sconcat :: NonEmpty [a] -> [a] Source stimes :: Integral b => b -> [a] -> [a] Source
Semigroup a => Semigroup (Identity a) Source
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 (Dual a) Source
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 (Endo a) Source
Methods (<>) :: Endo a -> Endo a -> Endo a Source sconcat :: NonEmpty (Endo a) -> Endo a Source stimes :: Integral b => b -> Endo a -> Endo a Source
Num a => Semigroup (Sum a) Source
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 => Semigroup (Product a) Source
Methods (<>) :: Product a -> Product a -> Product a Source sconcat :: NonEmpty (Product a) -> Product a Source stimes :: Integral b => b -> Product a -> Product a Source
Semigroup (First a) Source
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 (Last a) Source
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 a => Semigroup (Maybe a) Source
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 (IntMap v) Source
Methods (<>) :: IntMap v -> IntMap v -> IntMap v Source sconcat :: NonEmpty (IntMap v) -> IntMap v Source stimes :: Integral b => b -> IntMap v -> IntMap v Source
Ord a => Semigroup (Set a) Source
Methods (<>) :: Set a -> Set a -> Set a Source sconcat :: NonEmpty (Set a) -> Set a Source stimes :: Integral b => b -> Set a -> Set a Source
Semigroup (Seq a) Source
Methods (<>) :: Seq a -> Seq a -> Seq a Source sconcat :: NonEmpty (Seq a) -> Seq a Source stimes :: Integral b => b -> Seq a -> Seq a Source
(Hashable a, Eq a) => Semigroup (HashSet a) Source
Methods (<>) :: HashSet a -> HashSet a -> HashSet a Source sconcat :: NonEmpty (HashSet a) -> HashSet a Source stimes :: Integral b => b -> HashSet a -> HashSet a Source
Semigroup (NonEmpty a) Source
Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a Source sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a Source stimes :: Integral b => b -> NonEmpty a -> NonEmpty a Source
Semigroup a => Semigroup (Option a) Source
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) Source
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) Source
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) Source
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) Source
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) Source
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) Source
Methods (<>) :: (a -> b) -> (a -> b) -> a -> b Source sconcat :: NonEmpty (a -> b) -> a -> b Source stimes :: Integral c => c -> (a -> b) -> a -> b Source
Semigroup (Either a b) Source
Methods (<>) :: Either a b -> Either a b -> Either a b Source sconcat :: NonEmpty (Either a b) -> Either a b Source stimes :: Integral c => c -> Either a b -> Either a b Source
(Semigroup a, Semigroup b) => Semigroup (a, b) Source
Methods (<>) :: (a, b) -> (a, b) -> (a, b) Source sconcat :: NonEmpty (a, b) -> (a, b) Source stimes :: Integral c => c -> (a, b) -> (a, b) Source
Semigroup a => Semigroup (Const a b) Source
Methods (<>) :: Const a b -> Const a b -> Const a b Source sconcat :: NonEmpty (Const a b) -> Const a b Source stimes :: Integral c => c -> Const a b -> Const a b Source
Semigroup (Proxy k s) Source
Methods (<>) :: Proxy k s -> Proxy k s -> Proxy k s Source sconcat :: NonEmpty (Proxy k s) -> Proxy k s Source stimes :: Integral b => b -> Proxy k s -> Proxy k s Source
Ord k => Semigroup (Map k v) Source
Methods (<>) :: Map k v -> Map k v -> Map k v Source sconcat :: NonEmpty (Map k v) -> Map k v Source stimes :: Integral b => b -> Map k v -> Map k v Source
(Hashable k, Eq k) => Semigroup (HashMap k a) Source
Methods (<>) :: HashMap k a -> HashMap k a -> HashMap k a Source sconcat :: NonEmpty (HashMap k a) -> HashMap k a Source stimes :: Integral b => b -> HashMap k a -> HashMap k a Source
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) Source
Methods (<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source sconcat :: NonEmpty (a, b, c) -> (a, b, c) Source stimes :: Integral d => d -> (a, b, c) -> (a, b, c) Source
Alternative f => Semigroup (Alt * f a) Source
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 (Tagged k s a) Source
Methods (<>) :: Tagged k s a -> Tagged k s a -> Tagged k s a Source sconcat :: NonEmpty (Tagged k s a) -> Tagged k s a Source stimes :: Integral b => b -> Tagged k s a -> Tagged k s a Source
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) Source
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 e => e -> (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) Source
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 f => f -> (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.

Since: 0.17

Semigroups

newtype Min a Source

Constructors

Min
Fields getMin :: a

Instances

Monad Min Source
Methods (>>=) :: Min a -> (a -> Min b) -> Min b (>>) :: Min a -> Min b -> Min b return :: a -> Min a fail :: String -> Min a
Functor Min Source
Methods fmap :: (a -> b) -> Min a -> Min b (<$) :: a -> Min b -> Min a
MonadFix Min Source
Methods mfix :: (a -> Min a) -> Min a
Applicative Min Source
Methods pure :: a -> Min a (<>) :: Min (a -> b) -> Min a -> Min b (>) :: Min a -> Min b -> Min b (<*) :: Min a -> Min b -> Min a
Foldable Min Source
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 Source
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)
Generic1 Min Source
Associated Types type Rep1 (Min :: * -> ) :: -> * Methods from1 :: Min a -> Rep1 Min a to1 :: Rep1 Min a -> Min a
Bounded a => Bounded (Min a) Source
Methods minBound :: Min a maxBound :: Min a
Enum a => Enum (Min a) Source
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) Source
Methods (==) :: Min a -> Min a -> Bool (/=) :: Min a -> Min a -> Bool
Data a => Data (Min a) Source
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) Source
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) Source
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) Source
Methods readsPrec :: Int -> ReadS (Min a) readList :: ReadS [Min a] readPrec :: ReadPrec (Min a) readListPrec :: ReadPrec [Min a]
Show a => Show (Min a) Source
Methods showsPrec :: Int -> Min a -> ShowS show :: Min a -> String showList :: [Min a] -> ShowS
Generic (Min a) Source
Associated Types type Rep (Min a) :: * -> * Methods from :: Min a -> Rep (Min a) x to :: Rep (Min a) x -> Min a
(Ord a, Bounded a) => Monoid (Min a) Source
Methods mempty :: Min a mappend :: Min a -> Min a -> Min a mconcat :: [Min a] -> Min a
NFData a => NFData (Min a) Source
Methods rnf :: Min a -> ()
Hashable a => Hashable (Min a) Source
Methods hashWithSalt :: Int -> Min a -> Int hash :: Min a -> Int
Ord a => Semigroup (Min a) Source
Methods (<>) :: Min a -> Min a -> Min a Source sconcat :: NonEmpty (Min a) -> Min a Source stimes :: Integral b => b -> Min a -> Min a Source
type Rep1 Min Source
type Rep (Min a) Source

newtype Max a Source

Constructors

Max
Fields getMax :: a

Instances

Monad Max Source
Methods (>>=) :: Max a -> (a -> Max b) -> Max b (>>) :: Max a -> Max b -> Max b return :: a -> Max a fail :: String -> Max a
Functor Max Source
Methods fmap :: (a -> b) -> Max a -> Max b (<$) :: a -> Max b -> Max a
MonadFix Max Source
Methods mfix :: (a -> Max a) -> Max a
Applicative Max Source
Methods pure :: a -> Max a (<>) :: Max (a -> b) -> Max a -> Max b (>) :: Max a -> Max b -> Max b (<*) :: Max a -> Max b -> Max a
Foldable Max Source
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 Source
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)
Generic1 Max Source
Associated Types type Rep1 (Max :: * -> ) :: -> * Methods from1 :: Max a -> Rep1 Max a to1 :: Rep1 Max a -> Max a
Bounded a => Bounded (Max a) Source
Methods minBound :: Max a maxBound :: Max a
Enum a => Enum (Max a) Source
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) Source
Methods (==) :: Max a -> Max a -> Bool (/=) :: Max a -> Max a -> Bool
Data a => Data (Max a) Source
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) Source
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) Source
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) Source
Methods readsPrec :: Int -> ReadS (Max a) readList :: ReadS [Max a] readPrec :: ReadPrec (Max a) readListPrec :: ReadPrec [Max a]
Show a => Show (Max a) Source
Methods showsPrec :: Int -> Max a -> ShowS show :: Max a -> String showList :: [Max a] -> ShowS
Generic (Max a) Source
Associated Types type Rep (Max a) :: * -> * Methods from :: Max a -> Rep (Max a) x to :: Rep (Max a) x -> Max a
(Ord a, Bounded a) => Monoid (Max a) Source
Methods mempty :: Max a mappend :: Max a -> Max a -> Max a mconcat :: [Max a] -> Max a
NFData a => NFData (Max a) Source
Methods rnf :: Max a -> ()
Hashable a => Hashable (Max a) Source
Methods hashWithSalt :: Int -> Max a -> Int hash :: Max a -> Int
Ord a => Semigroup (Max a) Source
Methods (<>) :: Max a -> Max a -> Max a Source sconcat :: NonEmpty (Max a) -> Max a Source stimes :: Integral b => b -> Max a -> Max a Source
type Rep1 Max Source
type Rep (Max a) Source

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 Source
Methods (>>=) :: First a -> (a -> First b) -> First b (>>) :: First a -> First b -> First b return :: a -> First a fail :: String -> First a
Functor First Source
Methods fmap :: (a -> b) -> First a -> First b (<$) :: a -> First b -> First a
MonadFix First Source
Methods mfix :: (a -> First a) -> First a
Applicative First Source
Methods pure :: a -> First a (<>) :: First (a -> b) -> First a -> First b (>) :: First a -> First b -> First b (<*) :: First a -> First b -> First a
Foldable First Source
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 Source
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)
Generic1 First Source
Associated Types type Rep1 (First :: * -> ) :: -> * Methods from1 :: First a -> Rep1 First a to1 :: Rep1 First a -> First a
Bounded a => Bounded (First a) Source
Methods minBound :: First a maxBound :: First a
Enum a => Enum (First a) Source
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) Source
Methods (==) :: First a -> First a -> Bool (/=) :: First a -> First a -> Bool
Data a => Data (First a) Source
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) Source
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) Source
Methods readsPrec :: Int -> ReadS (First a) readList :: ReadS [First a] readPrec :: ReadPrec (First a) readListPrec :: ReadPrec [First a]
Show a => Show (First a) Source
Methods showsPrec :: Int -> First a -> ShowS show :: First a -> String showList :: [First a] -> ShowS
Generic (First a) Source
Associated Types type Rep (First a) :: * -> * Methods from :: First a -> Rep (First a) x to :: Rep (First a) x -> First a
NFData a => NFData (First a) Source
Methods rnf :: First a -> ()
Hashable a => Hashable (First a) Source
Methods hashWithSalt :: Int -> First a -> Int hash :: First a -> Int
Semigroup (First a) Source
Methods (<>) :: First a -> First a -> First a Source sconcat :: NonEmpty (First a) -> First a Source stimes :: Integral b => b -> First a -> First a Source
type Rep1 First Source
type Rep (First a) Source

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 Source
Methods (>>=) :: Last a -> (a -> Last b) -> Last b (>>) :: Last a -> Last b -> Last b return :: a -> Last a fail :: String -> Last a
Functor Last Source
Methods fmap :: (a -> b) -> Last a -> Last b (<$) :: a -> Last b -> Last a
MonadFix Last Source
Methods mfix :: (a -> Last a) -> Last a
Applicative Last Source
Methods pure :: a -> Last a (<>) :: Last (a -> b) -> Last a -> Last b (>) :: Last a -> Last b -> Last b (<*) :: Last a -> Last b -> Last a
Foldable Last Source
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 Source
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)
Generic1 Last Source
Associated Types type Rep1 (Last :: * -> ) :: -> * Methods from1 :: Last a -> Rep1 Last a to1 :: Rep1 Last a -> Last a
Bounded a => Bounded (Last a) Source
Methods minBound :: Last a maxBound :: Last a
Enum a => Enum (Last a) Source
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) Source
Methods (==) :: Last a -> Last a -> Bool (/=) :: Last a -> Last a -> Bool
Data a => Data (Last a) Source
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) Source
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) Source
Methods readsPrec :: Int -> ReadS (Last a) readList :: ReadS [Last a] readPrec :: ReadPrec (Last a) readListPrec :: ReadPrec [Last a]
Show a => Show (Last a) Source
Methods showsPrec :: Int -> Last a -> ShowS show :: Last a -> String showList :: [Last a] -> ShowS
Generic (Last a) Source
Associated Types type Rep (Last a) :: * -> * Methods from :: Last a -> Rep (Last a) x to :: Rep (Last a) x -> Last a
NFData a => NFData (Last a) Source
Methods rnf :: Last a -> ()
Hashable a => Hashable (Last a) Source
Methods hashWithSalt :: Int -> Last a -> Int hash :: Last a -> Int
Semigroup (Last a) Source
Methods (<>) :: Last a -> Last a -> Last a Source sconcat :: NonEmpty (Last a) -> Last a Source stimes :: Integral b => b -> Last a -> Last a Source
type Rep1 Last Source
type Rep (Last a) Source

newtype WrappedMonoid m Source

Provide a Semigroup for an arbitrary Monoid.

Constructors

WrapMonoid
Fields unwrapMonoid :: m

Instances

Generic1 WrappedMonoid Source
Associated Types type Rep1 (WrappedMonoid :: * -> ) :: -> * Methods from1 :: WrappedMonoid a -> Rep1 WrappedMonoid a to1 :: Rep1 WrappedMonoid a -> WrappedMonoid a
Bounded a => Bounded (WrappedMonoid a) Source
Methods minBound :: WrappedMonoid a maxBound :: WrappedMonoid a
Enum a => Enum (WrappedMonoid a) Source
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) Source
Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool
Data m => Data (WrappedMonoid m) Source
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 a => (forall d. Data d => d -> a d) -> WrappedMonoid m -> a (WrappedMonoid m) gmapMp :: MonadPlus a => (forall d. Data d => d -> a d) -> WrappedMonoid m -> a (WrappedMonoid m) gmapMo :: MonadPlus a => (forall d. Data d => d -> a d) -> WrappedMonoid m -> a (WrappedMonoid m)
Ord m => Ord (WrappedMonoid m) Source
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) Source
Methods readsPrec :: Int -> ReadS (WrappedMonoid m) readList :: ReadS [WrappedMonoid m] readPrec :: ReadPrec (WrappedMonoid m) readListPrec :: ReadPrec [WrappedMonoid m]
Show m => Show (WrappedMonoid m) Source
Methods showsPrec :: Int -> WrappedMonoid m -> ShowS show :: WrappedMonoid m -> String showList :: [WrappedMonoid m] -> ShowS
Generic (WrappedMonoid m) Source
Associated Types type Rep (WrappedMonoid m) :: * -> * Methods from :: WrappedMonoid m -> Rep (WrappedMonoid m) x to :: Rep (WrappedMonoid m) x -> WrappedMonoid m
Monoid m => Monoid (WrappedMonoid m) Source
Methods mempty :: WrappedMonoid m mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m mconcat :: [WrappedMonoid m] -> WrappedMonoid m
NFData m => NFData (WrappedMonoid m) Source
Methods rnf :: WrappedMonoid m -> ()
Hashable a => Hashable (WrappedMonoid a) Source
Methods hashWithSalt :: Int -> WrappedMonoid a -> Int hash :: WrappedMonoid a -> Int
Monoid m => Semigroup (WrappedMonoid m) Source
Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source
type Rep1 WrappedMonoid Source
type Rep (WrappedMonoid m) Source

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
Methods mempty :: Ordering mappend :: Ordering -> Ordering -> Ordering mconcat :: [Ordering] -> Ordering
Monoid ()
Methods mempty :: () mappend :: () -> () -> () mconcat :: [()] -> ()
Monoid All
Methods mempty :: All mappend :: All -> All -> All mconcat :: [All] -> All
Monoid Any
Methods mempty :: Any mappend :: Any -> Any -> Any mconcat :: [Any] -> Any
Monoid ByteString
Methods mempty :: ByteString mappend :: ByteString -> ByteString -> ByteString mconcat :: [ByteString] -> ByteString
Monoid ByteString
Methods mempty :: ByteString mappend :: ByteString -> ByteString -> ByteString mconcat :: [ByteString] -> ByteString
Monoid Builder
Methods mempty :: Builder mappend :: Builder -> Builder -> Builder mconcat :: [Builder] -> Builder
Monoid Builder
Methods mempty :: Builder mappend :: Builder -> Builder -> Builder mconcat :: [Builder] -> Builder
Monoid ShortByteString
Methods mempty :: ShortByteString mappend :: ShortByteString -> ShortByteString -> ShortByteString mconcat :: [ShortByteString] -> ShortByteString
Monoid IntSet
Methods mempty :: IntSet mappend :: IntSet -> IntSet -> IntSet mconcat :: [IntSet] -> IntSet
Monoid Builder
Methods mempty :: Builder mappend :: Builder -> Builder -> Builder mconcat :: [Builder] -> Builder
Monoid [a]
Methods mempty :: [a] mappend :: [a] -> [a] -> [a] mconcat :: [[a]] -> [a]
Ord a => Monoid (Max a)
Methods mempty :: Max a mappend :: Max a -> Max a -> Max a mconcat :: [Max a] -> Max a
Ord a => Monoid (Min a)
Methods mempty :: Min a mappend :: Min a -> Min a -> Min a mconcat :: [Min a] -> Min a
Monoid a => Monoid (Dual a)
Methods mempty :: Dual a mappend :: Dual a -> Dual a -> Dual a mconcat :: [Dual a] -> Dual a
Monoid (Endo a)
Methods mempty :: Endo a mappend :: Endo a -> Endo a -> Endo a mconcat :: [Endo a] -> Endo a
Num a => Monoid (Sum a)
Methods mempty :: Sum a mappend :: Sum a -> Sum a -> Sum a mconcat :: [Sum a] -> Sum a
Num a => Monoid (Product a)
Methods mempty :: Product a mappend :: Product a -> Product a -> Product a mconcat :: [Product a] -> Product a
Monoid (First a)
Methods mempty :: First a mappend :: First a -> First a -> First a mconcat :: [First a] -> First a
Monoid (Last a)
Methods mempty :: Last a mappend :: Last a -> Last a -> Last a mconcat :: [Last a] -> Last 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 `ee = e` and `es = s = s*e` for all `s ∈ S`." Since there is no "Semigroup" typeclass providing just `mappend`, we use `Monoid` instead.
Methods mempty :: Maybe a mappend :: Maybe a -> Maybe a -> Maybe a mconcat :: [Maybe a] -> Maybe a
Monoid (IntMap a)
Methods mempty :: IntMap a mappend :: IntMap a -> IntMap a -> IntMap a mconcat :: [IntMap a] -> IntMap a
Ord a => Monoid (Set a)
Methods mempty :: Set a mappend :: Set a -> Set a -> Set a mconcat :: [Set a] -> Set a
Monoid (Seq a)
Methods mempty :: Seq a mappend :: Seq a -> Seq a -> Seq a mconcat :: [Seq a] -> Seq a
(Hashable a, Eq a) => Monoid (HashSet a)
Methods mempty :: HashSet a mappend :: HashSet a -> HashSet a -> HashSet a mconcat :: [HashSet a] -> HashSet a
Semigroup a => Monoid (Option a)
Methods mempty :: Option a mappend :: Option a -> Option a -> Option a mconcat :: [Option a] -> Option a
Monoid m => Monoid (WrappedMonoid m)
Methods mempty :: WrappedMonoid m mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m mconcat :: [WrappedMonoid m] -> WrappedMonoid m
(Ord a, Bounded a) => Monoid (Max a)
Methods mempty :: Max a mappend :: Max a -> Max a -> Max a mconcat :: [Max a] -> Max a
(Ord a, Bounded a) => Monoid (Min a)
Methods mempty :: Min a mappend :: Min a -> Min a -> Min a mconcat :: [Min a] -> Min a
Monoid b => Monoid (a -> b)
Methods mempty :: a -> b mappend :: (a -> b) -> (a -> b) -> a -> b mconcat :: [a -> b] -> a -> b
(Monoid a, Monoid b) => Monoid (a, b)
Methods mempty :: (a, b) mappend :: (a, b) -> (a, b) -> (a, b) mconcat :: [(a, b)] -> (a, b)
Monoid a => Monoid (Const a b)
Methods mempty :: Const a b mappend :: Const a b -> Const a b -> Const a b mconcat :: [Const a b] -> Const a b
Monoid (Proxy k s)
Methods mempty :: Proxy k s mappend :: Proxy k s -> Proxy k s -> Proxy k s mconcat :: [Proxy k s] -> Proxy k s
Ord k => Monoid (Map k v)
Methods mempty :: Map k v mappend :: Map k v -> Map k v -> Map k v mconcat :: [Map k v] -> Map k v
(Eq k, Hashable k) => Monoid (HashMap k v)
Methods mempty :: HashMap k v mappend :: HashMap k v -> HashMap k v -> HashMap k v mconcat :: [HashMap k v] -> HashMap k v
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)
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)
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 (Tagged k s a)
Methods mempty :: Tagged k s a mappend :: Tagged k s a -> Tagged k s a -> Tagged k s a mconcat :: [Tagged k s a] -> Tagged k s a
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)
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)
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

Generic1 Dual
Associated Types type Rep1 (Dual :: * -> ) :: -> * Methods from1 :: Dual a -> Rep1 Dual a to1 :: Rep1 Dual a -> Dual a
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
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
Monoid a => Monoid (Dual a)
Methods mempty :: Dual a mappend :: Dual a -> Dual a -> Dual a mconcat :: [Dual a] -> Dual a
NFData a => NFData (Dual a)	Since: 1.4.0.0
Methods rnf :: Dual a -> ()
Semigroup a => Semigroup (Dual a) Source
Methods (<>) :: Dual a -> Dual a -> Dual a Source sconcat :: NonEmpty (Dual a) -> Dual a Source stimes :: Integral b => b -> Dual a -> Dual a Source
type Rep1 Dual = D1 D1Dual (C1 C1_0Dual (S1 S1_0_0Dual Par1))
type Rep (Dual a) = D1 D1Dual (C1 C1_0Dual (S1 S1_0_0Dual (Rec0 a)))

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
Monoid (Endo a)
Methods mempty :: Endo a mappend :: Endo a -> Endo a -> Endo a mconcat :: [Endo a] -> Endo a
Semigroup (Endo a) Source
Methods (<>) :: Endo a -> Endo a -> Endo a Source sconcat :: NonEmpty (Endo a) -> Endo a Source stimes :: Integral b => b -> Endo a -> Endo a Source
type Rep (Endo a) = D1 D1Endo (C1 C1_0Endo (S1 S1_0_0Endo (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
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
Monoid All
Methods mempty :: All mappend :: All -> All -> All mconcat :: [All] -> All
NFData All	Since: 1.4.0.0
Methods rnf :: All -> ()
Semigroup All Source
Methods (<>) :: All -> All -> All Source sconcat :: NonEmpty All -> All Source stimes :: Integral b => b -> All -> All Source
type Rep All = D1 D1All (C1 C1_0All (S1 S1_0_0All (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
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
Monoid Any
Methods mempty :: Any mappend :: Any -> Any -> Any mconcat :: [Any] -> Any
NFData Any	Since: 1.4.0.0
Methods rnf :: Any -> ()
Semigroup Any Source
Methods (<>) :: Any -> Any -> Any Source sconcat :: NonEmpty Any -> Any Source stimes :: Integral b => b -> Any -> Any Source
type Rep Any = D1 D1Any (C1 C1_0Any (S1 S1_0_0Any (Rec0 Bool)))

newtype Sum a :: * -> *

Monoid under addition.

Constructors

Sum
Fields getSum :: a

Instances

Generic1 Sum
Associated Types type Rep1 (Sum :: * -> ) :: -> * Methods from1 :: Sum a -> Rep1 Sum a to1 :: Rep1 Sum a -> Sum a
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
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 => Monoid (Sum a)
Methods mempty :: Sum a mappend :: Sum a -> Sum a -> Sum a mconcat :: [Sum a] -> Sum a
NFData a => NFData (Sum a)	Since: 1.4.0.0
Methods rnf :: Sum a -> ()
Num a => Semigroup (Sum a) Source
Methods (<>) :: Sum a -> Sum a -> Sum a Source sconcat :: NonEmpty (Sum a) -> Sum a Source stimes :: Integral b => b -> Sum a -> Sum a Source
type Rep1 Sum = D1 D1Sum (C1 C1_0Sum (S1 S1_0_0Sum Par1))
type Rep (Sum a) = D1 D1Sum (C1 C1_0Sum (S1 S1_0_0Sum (Rec0 a)))

newtype Product a :: * -> *

Monoid under multiplication.

Constructors

Product
Fields getProduct :: a

Instances

Generic1 Product
Associated Types type Rep1 (Product :: * -> ) :: -> * Methods from1 :: Product a -> Rep1 Product a to1 :: Rep1 Product a -> Product a
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
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 => Monoid (Product a)
Methods mempty :: Product a mappend :: Product a -> Product a -> Product a mconcat :: [Product a] -> Product a
NFData a => NFData (Product a)	Since: 1.4.0.0
Methods rnf :: Product a -> ()
Num a => Semigroup (Product a) Source
Methods (<>) :: Product a -> Product a -> Product a Source sconcat :: NonEmpty (Product a) -> Product a Source stimes :: Integral b => b -> Product a -> Product a Source
type Rep1 Product = D1 D1Product (C1 C1_0Product (S1 S1_0_0Product Par1))
type Rep (Product a) = D1 D1Product (C1 C1_0Product (S1 S1_0_0Product (Rec0 a)))

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 Source
Methods (>>=) :: Option a -> (a -> Option b) -> Option b (>>) :: Option a -> Option b -> Option b return :: a -> Option a fail :: String -> Option a
Functor Option Source
Methods fmap :: (a -> b) -> Option a -> Option b (<$) :: a -> Option b -> Option a
MonadFix Option Source
Methods mfix :: (a -> Option a) -> Option a
Applicative Option Source
Methods pure :: a -> Option a (<>) :: Option (a -> b) -> Option a -> Option b (>) :: Option a -> Option b -> Option b (<*) :: Option a -> Option b -> Option a
Foldable Option Source
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 Source
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)
Generic1 Option Source
Associated Types type Rep1 (Option :: * -> ) :: -> * Methods from1 :: Option a -> Rep1 Option a to1 :: Rep1 Option a -> Option a
Alternative Option Source
Methods empty :: Option a (<\|>) :: Option a -> Option a -> Option a some :: Option a -> Option [a] many :: Option a -> Option [a]
MonadPlus Option Source
Methods mzero :: Option a mplus :: Option a -> Option a -> Option a
Eq a => Eq (Option a) Source
Methods (==) :: Option a -> Option a -> Bool (/=) :: Option a -> Option a -> Bool
Data a => Data (Option a) Source
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) Source
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) Source
Methods readsPrec :: Int -> ReadS (Option a) readList :: ReadS [Option a] readPrec :: ReadPrec (Option a) readListPrec :: ReadPrec [Option a]
Show a => Show (Option a) Source
Methods showsPrec :: Int -> Option a -> ShowS show :: Option a -> String showList :: [Option a] -> ShowS
Generic (Option a) Source
Associated Types type Rep (Option a) :: * -> * Methods from :: Option a -> Rep (Option a) x to :: Rep (Option a) x -> Option a
Semigroup a => Monoid (Option a) Source
Methods mempty :: Option a mappend :: Option a -> Option a -> Option a mconcat :: [Option a] -> Option a
NFData a => NFData (Option a) Source
Methods rnf :: Option a -> ()
Hashable a => Hashable (Option a) Source
Methods hashWithSalt :: Int -> Option a -> Int hash :: Option a -> Int
Semigroup a => Semigroup (Option a) Source
Methods (<>) :: Option a -> Option a -> Option a Source sconcat :: NonEmpty (Option a) -> Option a Source stimes :: Integral b => b -> Option a -> Option a Source
type Rep1 Option Source
type Rep (Option a) Source

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 Source
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
Functor (Arg a) Source
Methods fmap :: (b -> c) -> Arg a b -> Arg a c (<$) :: b -> Arg a c -> Arg a b
Foldable (Arg a) Source
Methods fold :: Monoid m => Arg a m -> m foldMap :: Monoid m => (b -> m) -> Arg a b -> m foldr :: (b -> c -> c) -> c -> Arg a b -> c foldr' :: (b -> c -> c) -> c -> Arg a b -> c foldl :: (b -> c -> b) -> b -> Arg a c -> b foldl' :: (b -> c -> b) -> b -> Arg a c -> b foldr1 :: (b -> b -> b) -> Arg a b -> b foldl1 :: (b -> b -> b) -> Arg a b -> b toList :: Arg a b -> [b] null :: Arg a b -> Bool length :: Arg a b -> Int elem :: Eq b => b -> Arg a b -> Bool maximum :: Ord b => Arg a b -> b minimum :: Ord b => Arg a b -> b sum :: Num b => Arg a b -> b product :: Num b => Arg a b -> b
Traversable (Arg a) Source
Methods traverse :: Applicative f => (b -> f c) -> Arg a b -> f (Arg a c) sequenceA :: Applicative f => Arg a (f b) -> f (Arg a b) mapM :: Monad m => (b -> m c) -> Arg a b -> m (Arg a c) sequence :: Monad m => Arg a (m b) -> m (Arg a b)
Generic1 (Arg a) Source
Associated Types type Rep1 (Arg a :: * -> ) :: -> * Methods from1 :: Arg a b -> Rep1 (Arg a) b to1 :: Rep1 (Arg a) b -> Arg a b
Eq a => Eq (Arg a b) Source
Methods (==) :: Arg a b -> Arg a b -> Bool (/=) :: Arg a b -> Arg a b -> Bool
(Data a, Data b) => Data (Arg a b) Source
Methods gfoldl :: (forall d e. Data d => c (d -> e) -> d -> c e) -> (forall g. g -> c g) -> Arg a b -> c (Arg a b) gunfold :: (forall d r. Data d => c (d -> 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) Source
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 a, Read b) => Read (Arg a b) Source
Methods readsPrec :: Int -> ReadS (Arg a b) readList :: ReadS [Arg a b] readPrec :: ReadPrec (Arg a b) readListPrec :: ReadPrec [Arg a b]
(Show a, Show b) => Show (Arg a b) Source
Methods showsPrec :: Int -> Arg a b -> ShowS show :: Arg a b -> String showList :: [Arg a b] -> ShowS
Generic (Arg a b) Source
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
(NFData a, NFData b) => NFData (Arg a b) Source
Methods rnf :: Arg a b -> ()
(Hashable a, Hashable b) => Hashable (Arg a b) Source
Methods hashWithSalt :: Int -> Arg a b -> Int hash :: Arg a b -> Int
type Rep1 (Arg a) Source
type Rep (Arg a b) Source

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

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