Copyright	(c) Artem Chirkin
License	BSD3
Maintainer	chirkin@arch.ethz.ch
Safe Haskell	None
Language	Haskell2010

Numeric.Semigroup

Contents

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

Description

Re-export most of Data.Semigroup with a few changes and new definitions.

The main initiative behind this module is to provide more strict alternatives to widely used semigroups. For example, Option has lazy (<>) implementation, which causes memory leaks in large foldMaps.

Synopsis

Documentation

class Semigroup a where #

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

Since: 4.9.0.0

Methods

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

An associative operation.

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

If a is also a Monoid we further require

(<>) = mappend

sconcat :: NonEmpty a -> a #

Reduce a non-empty list with <>

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

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

Repeat a value n times.

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

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

Instances

Semigroup Ordering
Methods (<>) :: Ordering -> Ordering -> Ordering # sconcat :: NonEmpty Ordering -> Ordering # stimes :: Integral b => b -> Ordering -> Ordering #
Semigroup ()
Methods (<>) :: () -> () -> () # sconcat :: NonEmpty () -> () # stimes :: Integral b => b -> () -> () #
Semigroup Void
Methods (<>) :: Void -> Void -> Void # sconcat :: NonEmpty Void -> Void # stimes :: Integral b => b -> Void -> Void #
Semigroup All
Methods (<>) :: All -> All -> All # sconcat :: NonEmpty All -> All # stimes :: Integral b => b -> All -> All #
Semigroup Any
Methods (<>) :: Any -> Any -> Any # sconcat :: NonEmpty Any -> Any # stimes :: Integral b => b -> Any -> Any #
Semigroup T0 #
Methods (<>) :: T0 -> T0 -> T0 # sconcat :: NonEmpty T0 -> T0 # stimes :: Integral b => b -> T0 -> T0 #
Semigroup [a]
Methods (<>) :: [a] -> [a] -> [a] # sconcat :: NonEmpty [a] -> [a] # stimes :: Integral b => b -> [a] -> [a] #
Semigroup a => Semigroup (Maybe a)
Methods (<>) :: Maybe a -> Maybe a -> Maybe a # sconcat :: NonEmpty (Maybe a) -> Maybe a # stimes :: Integral b => b -> Maybe a -> Maybe a #
Ord a => Semigroup (Min a)
Methods (<>) :: Min a -> Min a -> Min a # sconcat :: NonEmpty (Min a) -> Min a # stimes :: Integral b => b -> Min a -> Min a #
Ord a => Semigroup (Max a)
Methods (<>) :: Max a -> Max a -> Max a # sconcat :: NonEmpty (Max a) -> Max a # stimes :: Integral b => b -> Max a -> Max a #
Semigroup (First a)
Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
Semigroup (Last a)
Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
Monoid m => Semigroup (WrappedMonoid m)
Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m #
Semigroup a => Semigroup (Option a)
Methods (<>) :: Option a -> Option a -> Option a # sconcat :: NonEmpty (Option a) -> Option a # stimes :: Integral b => b -> Option a -> Option a #
Semigroup (NonEmpty a)
Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a # sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a # stimes :: Integral b => b -> NonEmpty a -> NonEmpty a #
Semigroup a => Semigroup (Dual a)
Methods (<>) :: Dual a -> Dual a -> Dual a # sconcat :: NonEmpty (Dual a) -> Dual a # stimes :: Integral b => b -> Dual a -> Dual a #
Semigroup (Endo a)
Methods (<>) :: Endo a -> Endo a -> Endo a # sconcat :: NonEmpty (Endo a) -> Endo a # stimes :: Integral b => b -> Endo a -> Endo a #
Num a => Semigroup (Sum a)
Methods (<>) :: Sum a -> Sum a -> Sum a # sconcat :: NonEmpty (Sum a) -> Sum a # stimes :: Integral b => b -> Sum a -> Sum a #
Num a => Semigroup (Product a)
Methods (<>) :: Product a -> Product a -> Product a # sconcat :: NonEmpty (Product a) -> Product a # stimes :: Integral b => b -> Product a -> Product a #
Semigroup (First a)
Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
Semigroup (Last a)
Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
Ord a => Semigroup (MinMax a) #
Methods (<>) :: MinMax a -> MinMax a -> MinMax a # sconcat :: NonEmpty (MinMax a) -> MinMax a # stimes :: Integral b => b -> MinMax a -> MinMax a #
Semigroup a => Semigroup (Option a) #
Methods (<>) :: Option a -> Option a -> Option a # sconcat :: NonEmpty (Option a) -> Option a # stimes :: Integral b => b -> Option a -> Option a #
Semigroup a => Semigroup (T1 a) #
Methods (<>) :: T1 a -> T1 a -> T1 a # sconcat :: NonEmpty (T1 a) -> T1 a # stimes :: Integral b => b -> T1 a -> T1 a #
Semigroup b => Semigroup (a -> b)
Methods (<>) :: (a -> b) -> (a -> b) -> a -> b # sconcat :: NonEmpty (a -> b) -> a -> b # stimes :: Integral b => b -> (a -> b) -> a -> b #
Semigroup (Either a b)
Methods (<>) :: Either a b -> Either a b -> Either a b # sconcat :: NonEmpty (Either a b) -> Either a b # stimes :: Integral b => b -> Either a b -> Either a b #
(Semigroup a, Semigroup b) => Semigroup (a, b)
Methods (<>) :: (a, b) -> (a, b) -> (a, b) # sconcat :: NonEmpty (a, b) -> (a, b) # stimes :: Integral b => b -> (a, b) -> (a, b) #
Semigroup (Proxy k s)
Methods (<>) :: Proxy k s -> Proxy k s -> Proxy k s # sconcat :: NonEmpty (Proxy k s) -> Proxy k s # stimes :: Integral b => b -> Proxy k s -> Proxy k s #
(Semigroup a, Semigroup b) => Semigroup (T2 a b) #
Methods (<>) :: T2 a b -> T2 a b -> T2 a b # sconcat :: NonEmpty (T2 a b) -> T2 a b # stimes :: Integral b => b -> T2 a b -> T2 a b #
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c)
Methods (<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) # sconcat :: NonEmpty (a, b, c) -> (a, b, c) # stimes :: Integral b => b -> (a, b, c) -> (a, b, c) #
Semigroup a => Semigroup (Const k a b)
Methods (<>) :: Const k a b -> Const k a b -> Const k a b # sconcat :: NonEmpty (Const k a b) -> Const k a b # stimes :: Integral b => b -> Const k a b -> Const k a b #
Alternative f => Semigroup (Alt * f a)
Methods (<>) :: Alt * f a -> Alt * f a -> Alt * f a # sconcat :: NonEmpty (Alt * f a) -> Alt * f a # stimes :: Integral b => b -> Alt * f a -> Alt * f a #
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (T3 a b c) #
Methods (<>) :: T3 a b c -> T3 a b c -> T3 a b c # sconcat :: NonEmpty (T3 a b c) -> T3 a b c # stimes :: Integral b => b -> T3 a b c -> T3 a b c #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)
Methods (<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) # stimes :: Integral b => b -> (a, b, c, d) -> (a, b, c, d) #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (T4 a b c d) #
Methods (<>) :: T4 a b c d -> T4 a b c d -> T4 a b c d # sconcat :: NonEmpty (T4 a b c d) -> T4 a b c d # stimes :: Integral b => b -> T4 a b c d -> T4 a b c d #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)
Methods (<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) # stimes :: Integral b => b -> (a, b, c, d, e) -> (a, b, c, d, e) #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (T5 a b c d e) #
Methods (<>) :: T5 a b c d e -> T5 a b c d e -> T5 a b c d e # sconcat :: NonEmpty (T5 a b c d e) -> T5 a b c d e # stimes :: Integral b => b -> T5 a b c d e -> T5 a b c d e #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e, Semigroup f) => Semigroup (T6 a b c d e f) #
Methods (<>) :: T6 a b c d e f -> T6 a b c d e f -> T6 a b c d e f # sconcat :: NonEmpty (T6 a b c d e f) -> T6 a b c d e f # stimes :: Integral b => b -> T6 a b c d e f -> T6 a b c d e f #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e, Semigroup f, Semigroup g) => Semigroup (T7 a b c d e f g) #
Methods (<>) :: T7 a b c d e f g -> T7 a b c d e f g -> T7 a b c d e f g # sconcat :: NonEmpty (T7 a b c d e f g) -> T7 a b c d e f g # stimes :: Integral b => b -> T7 a b c d e f g -> T7 a b c d e f g #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e, Semigroup f, Semigroup g, Semigroup h) => Semigroup (T8 a b c d e f g h) #
Methods (<>) :: T8 a b c d e f g h -> T8 a b c d e f g h -> T8 a b c d e f g h # sconcat :: NonEmpty (T8 a b c d e f g h) -> T8 a b c d e f g h # stimes :: Integral b => b -> T8 a b c d e f g h -> T8 a b c d e f g h #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e, Semigroup f, Semigroup g, Semigroup h, Semigroup i) => Semigroup (T9 a b c d e f g h i) #
Methods (<>) :: T9 a b c d e f g h i -> T9 a b c d e f g h i -> T9 a b c d e f g h i # sconcat :: NonEmpty (T9 a b c d e f g h i) -> T9 a b c d e f g h i # stimes :: Integral b => b -> T9 a b c d e f g h i -> T9 a b c d e f g h i #

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

This is a valid definition of stimes for a Monoid.

Unlike the default definition of stimes, it is defined for 0 and so it should be preferred where possible.

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

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

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

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

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

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

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

Repeat a value n times.

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

Implemented using stimes and mempty.

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

foldMap' :: (Foldable t, Monoid m) => (a -> m) -> t a -> m Source #

Map each element of the structure to a monoid, and combine the results.

This function differs from Data.Foldable.foldMap in that uses foldl' instead of foldr inside. This makes this function suitable for Monoids with strict mappend operation. For example,

foldMap' Sum $ take 1000000000 ([1..] :: [Int])

runs in constant memory, whereas normal foldMap would cause a memory leak there.

Semigroups

newtype Min a :: * -> * #

Constructors

Min
Fields getMin :: a

Instances

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

newtype Max a :: * -> * #

Constructors

Max
Fields getMax :: a

Instances

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

newtype First a :: * -> * #

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

Constructors

First
Fields getFirst :: a

Instances

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

newtype Last a :: * -> * #

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

Constructors

Last
Fields getLast :: a

Instances

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

newtype WrappedMonoid m :: * -> * #

Provide a Semigroup for an arbitrary Monoid.

Constructors

WrapMonoid
Fields unwrapMonoid :: m

Instances

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

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 T0 #
Methods mempty :: T0 # mappend :: T0 -> T0 -> T0 # mconcat :: [T0] -> T0 #
Monoid [a]
Methods mempty :: [a] # mappend :: [a] -> [a] -> [a] # mconcat :: [[a]] -> [a] #
Monoid a => Monoid (Maybe a)	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `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 a => Monoid (IO a)
Methods mempty :: IO a # mappend :: IO a -> IO a -> IO a # mconcat :: [IO a] -> IO 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 #
(Ord a, Bounded a) => Monoid (Min a)
Methods mempty :: Min a # mappend :: Min a -> Min a -> Min a # mconcat :: [Min a] -> Min a #
(Ord a, Bounded a) => Monoid (Max a)
Methods mempty :: Max a # mappend :: Max a -> Max a -> Max a # mconcat :: [Max a] -> Max a #
Monoid m => Monoid (WrappedMonoid m)
Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m #
Semigroup a => Monoid (Option a)
Methods mempty :: Option a # mappend :: Option a -> Option a -> Option a # mconcat :: [Option a] -> Option 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 #
(Ord a, Bounded a) => Monoid (MinMax a) #
Methods mempty :: MinMax a # mappend :: MinMax a -> MinMax a -> MinMax a # mconcat :: [MinMax a] -> MinMax a #
Semigroup a => Monoid (Option a) #
Methods mempty :: Option a # mappend :: Option a -> Option a -> Option a # mconcat :: [Option a] -> Option a #
Monoid a => Monoid (T1 a) #
Methods mempty :: T1 a # mappend :: T1 a -> T1 a -> T1 a # mconcat :: [T1 a] -> T1 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 (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 #
(Monoid a, Monoid b) => Monoid (T2 a b) #
Methods mempty :: T2 a b # mappend :: T2 a b -> T2 a b -> T2 a b # mconcat :: [T2 a b] -> T2 a b #
(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) #
Monoid a => Monoid (Const k a b)
Methods mempty :: Const k a b # mappend :: Const k a b -> Const k a b -> Const k a b # mconcat :: [Const k a b] -> Const k a b #
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 b, Monoid c) => Monoid (T3 a b c) #
Methods mempty :: T3 a b c # mappend :: T3 a b c -> T3 a b c -> T3 a b c # mconcat :: [T3 a b c] -> T3 a b c #
(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 (T4 a b c d) #
Methods mempty :: T4 a b c d # mappend :: T4 a b c d -> T4 a b c d -> T4 a b c d # mconcat :: [T4 a b c d] -> T4 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) #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (T5 a b c d e) #
Methods mempty :: T5 a b c d e # mappend :: T5 a b c d e -> T5 a b c d e -> T5 a b c d e # mconcat :: [T5 a b c d e] -> T5 a b c d e #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e, Monoid f) => Monoid (T6 a b c d e f) #
Methods mempty :: T6 a b c d e f # mappend :: T6 a b c d e f -> T6 a b c d e f -> T6 a b c d e f # mconcat :: [T6 a b c d e f] -> T6 a b c d e f #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e, Monoid f, Monoid g) => Monoid (T7 a b c d e f g) #
Methods mempty :: T7 a b c d e f g # mappend :: T7 a b c d e f g -> T7 a b c d e f g -> T7 a b c d e f g # mconcat :: [T7 a b c d e f g] -> T7 a b c d e f g #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e, Monoid f, Monoid g, Monoid h) => Monoid (T8 a b c d e f g h) #
Methods mempty :: T8 a b c d e f g h # mappend :: T8 a b c d e f g h -> T8 a b c d e f g h -> T8 a b c d e f g h # mconcat :: [T8 a b c d e f g h] -> T8 a b c d e f g h #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e, Monoid f, Monoid g, Monoid h, Monoid i) => Monoid (T9 a b c d e f g h i) #
Methods mempty :: T9 a b c d e f g h i # mappend :: T9 a b c d e f g h i -> T9 a b c d e f g h i -> T9 a b c d e f g h i # mconcat :: [T9 a b c d e f g h i] -> T9 a b c d e f g h i #

newtype Dual a :: * -> * #

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

Constructors

Dual
Fields getDual :: a

Instances

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

newtype Endo a :: * -> * #

The monoid of endomorphisms under composition.

Constructors

Endo
Fields appEndo :: a -> a

Instances

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

newtype All :: * #

Boolean monoid under conjunction (&&).

Constructors

All
Fields getAll :: Bool

Instances

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

newtype Any :: * #

Boolean monoid under disjunction (||).

Constructors

Any
Fields getAny :: Bool

Instances

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

newtype Sum a :: * -> * #

Monoid under addition.

Constructors

Sum
Fields getSum :: a

Instances

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

newtype Product a :: * -> * #

Monoid under multiplication.

Constructors

Product
Fields getProduct :: a

Instances

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

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.

This version of Option data type is more strict than the one from Data.Semigroup.

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] #
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 => Semigroup (Option a) Source #
Methods (<>) :: Option a -> Option a -> Option a # sconcat :: NonEmpty (Option a) -> Option a # stimes :: Integral b => b -> Option a -> Option a #
Semigroup a => Monoid (Option a) Source #
Methods mempty :: Option a # mappend :: Option a -> Option a -> Option a # mconcat :: [Option a] -> Option a #
type Rep1 Option Source #
type Rep1 Option = D1 (MetaData "Option" "Numeric.Semigroup" "easytensor-0.4.0.0-Fjq1YCsNiDYFELhVj4IBRg" True) (C1 (MetaCons "Option" PrefixI True) (S1 (MetaSel (Just Symbol "getOption") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Maybe)))
type Rep (Option a) Source #
type Rep (Option a) = D1 (MetaData "Option" "Numeric.Semigroup" "easytensor-0.4.0.0-Fjq1YCsNiDYFELhVj4IBRg" True) (C1 (MetaCons "Option" PrefixI True) (S1 (MetaSel (Just Symbol "getOption") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))

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

Fold an Option case-wise, just like maybe. Eagerly evaluates the value before returning!

fromOption :: a -> Option a -> a Source #

Get value from Option with default value. Eagerly evaluates the value before returning!

toOption :: a -> Option a Source #

Wrap a value into Option container. Eagerly evaluates the value before wrapping!

Difference lists of a semigroup

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

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

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

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

ArgMin, ArgMax

data Arg a b :: * -> * -> * #

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

Constructors

Arg a b

Instances

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

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

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

data MinMax a Source #

Evaluate minimum and maximum at the same time. Arithmetics and semigroup operations are eager, functorial operations are lazy.

This data type is especially useful for calculating bounds of foldable containers with numeric data using foldMap minMax.

Constructors

MinMax a a

Instances

Monad MinMax Source #
Methods (>>=) :: MinMax a -> (a -> MinMax b) -> MinMax b # (>>) :: MinMax a -> MinMax b -> MinMax b # return :: a -> MinMax a # fail :: String -> MinMax a #
Functor MinMax Source #
Methods fmap :: (a -> b) -> MinMax a -> MinMax b # (<$) :: a -> MinMax b -> MinMax a #
MonadFix MinMax Source #
Methods mfix :: (a -> MinMax a) -> MinMax a #
Applicative MinMax Source #
Methods pure :: a -> MinMax a # (<>) :: MinMax (a -> b) -> MinMax a -> MinMax b # (>) :: MinMax a -> MinMax b -> MinMax b # (<*) :: MinMax a -> MinMax b -> MinMax a #
Generic1 MinMax Source #
Associated Types type Rep1 (MinMax :: * -> ) :: -> * # Methods from1 :: MinMax a -> Rep1 MinMax a # to1 :: Rep1 MinMax a -> MinMax a #
Bounded a => Bounded (MinMax a) Source #
Methods minBound :: MinMax a # maxBound :: MinMax a #
Eq a => Eq (MinMax a) Source #
Methods (==) :: MinMax a -> MinMax a -> Bool # (/=) :: MinMax a -> MinMax a -> Bool #
Data a => Data (MinMax a) Source #
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> MinMax a -> c (MinMax a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (MinMax a) # toConstr :: MinMax a -> Constr # dataTypeOf :: MinMax a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (MinMax a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (MinMax a)) # gmapT :: (forall b. Data b => b -> b) -> MinMax a -> MinMax a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MinMax a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MinMax a -> r # gmapQ :: (forall d. Data d => d -> u) -> MinMax a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> MinMax a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> MinMax a -> m (MinMax a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> MinMax a -> m (MinMax a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> MinMax a -> m (MinMax a) #
(Num a, Ord a) => Num (MinMax a) Source #
Methods (+) :: MinMax a -> MinMax a -> MinMax a # (-) :: MinMax a -> MinMax a -> MinMax a # (*) :: MinMax a -> MinMax a -> MinMax a # negate :: MinMax a -> MinMax a # abs :: MinMax a -> MinMax a # signum :: MinMax a -> MinMax a # fromInteger :: Integer -> MinMax a #
Ord a => Ord (MinMax a) Source #	MinMax checks whether bounds overlap. Strict inequality means that intervals do not overlap. Non-strict inequality means non-strict inequality in both constructor arguments. `EQ` means intervals overlap
Methods compare :: MinMax a -> MinMax a -> Ordering # (<) :: MinMax a -> MinMax a -> Bool # (<=) :: MinMax a -> MinMax a -> Bool # (>) :: MinMax a -> MinMax a -> Bool # (>=) :: MinMax a -> MinMax a -> Bool # max :: MinMax a -> MinMax a -> MinMax a # min :: MinMax a -> MinMax a -> MinMax a #
Read a => Read (MinMax a) Source #
Methods readsPrec :: Int -> ReadS (MinMax a) # readList :: ReadS [MinMax a] # readPrec :: ReadPrec (MinMax a) # readListPrec :: ReadPrec [MinMax a] #
Show a => Show (MinMax a) Source #
Methods showsPrec :: Int -> MinMax a -> ShowS # show :: MinMax a -> String # showList :: [MinMax a] -> ShowS #
Generic (MinMax a) Source #
Associated Types type Rep (MinMax a) :: * -> * # Methods from :: MinMax a -> Rep (MinMax a) x # to :: Rep (MinMax a) x -> MinMax a #
Ord a => Semigroup (MinMax a) Source #
Methods (<>) :: MinMax a -> MinMax a -> MinMax a # sconcat :: NonEmpty (MinMax a) -> MinMax a # stimes :: Integral b => b -> MinMax a -> MinMax a #
(Ord a, Bounded a) => Monoid (MinMax a) Source #
Methods mempty :: MinMax a # mappend :: MinMax a -> MinMax a -> MinMax a # mconcat :: [MinMax a] -> MinMax a #
type Rep1 MinMax Source #
type Rep1 MinMax = D1 (MetaData "MinMax" "Numeric.Semigroup" "easytensor-0.4.0.0-Fjq1YCsNiDYFELhVj4IBRg" False) (C1 (MetaCons "MinMax" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)))
type Rep (MinMax a) Source #
type Rep (MinMax a) = D1 (MetaData "MinMax" "Numeric.Semigroup" "easytensor-0.4.0.0-Fjq1YCsNiDYFELhVj4IBRg" False) (C1 (MetaCons "MinMax" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))))

minMax :: a -> MinMax a Source #

mmDiff :: Num a => MinMax a -> a Source #

mmAvg :: Fractional a => MinMax a -> a Source #