base-4.9.1.0: Basic libraries

Data.Semigroup

Description

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

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

import Data.Semigroup

Since: 4.9.0.0

Synopsis

# Documentation

class Semigroup a where #

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

Since: 4.9.0.0

Methods

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

An associative operation.

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


If a is also a Monoid we further require

(<>) = mappend


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

An associative operation.

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


If a is also a Monoid we further require

(<>) = mappend


sconcat :: NonEmpty a -> a #

Reduce a non-empty list with <>

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

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

Repeat a value n times.

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

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

Instances

 # Methodsstimes :: Integral b => b -> Ordering -> Ordering # # Methods(<>) :: () -> () -> () #sconcat :: NonEmpty () -> () #stimes :: Integral b => b -> () -> () # # Methods(<>) :: Any -> Any -> Any #stimes :: Integral b => b -> Any -> Any # # Methods(<>) :: All -> All -> All #stimes :: Integral b => b -> All -> All # # Methods(<>) :: Void -> Void -> Void #stimes :: Integral b => b -> Void -> Void # 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 # # Methods(<>) :: Last a -> Last a -> Last a #sconcat :: NonEmpty (Last a) -> Last a #stimes :: Integral b => b -> Last a -> Last a # # Methods(<>) :: First a -> First a -> First a #sconcat :: NonEmpty (First a) -> First a #stimes :: Integral b => b -> First a -> First a # Num a => Semigroup (Product a) # Methods(<>) :: Product a -> Product a -> Product a #sconcat :: NonEmpty (Product a) -> Product a #stimes :: Integral b => b -> Product a -> Product a # Num a => Semigroup (Sum a) # Methods(<>) :: Sum a -> Sum a -> Sum a #sconcat :: NonEmpty (Sum a) -> Sum a #stimes :: Integral b => b -> Sum a -> Sum a # # Methods(<>) :: Endo a -> Endo a -> Endo a #sconcat :: NonEmpty (Endo a) -> Endo a #stimes :: Integral b => b -> Endo a -> Endo a # Semigroup a => Semigroup (Dual a) # Methods(<>) :: Dual a -> Dual a -> Dual a #sconcat :: NonEmpty (Dual a) -> Dual a #stimes :: Integral b => b -> Dual a -> Dual 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 (Option a) # Methods(<>) :: Option a -> Option a -> Option a #sconcat :: NonEmpty (Option a) -> Option a #stimes :: Integral b => b -> Option a -> Option a # Monoid m => Semigroup (WrappedMonoid m) # Methods(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m #stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m # # Methods(<>) :: Last a -> Last a -> Last a #sconcat :: NonEmpty (Last a) -> Last a #stimes :: Integral b => b -> Last a -> Last a # # Methods(<>) :: First a -> First a -> First a #sconcat :: NonEmpty (First a) -> First a #stimes :: Integral b => b -> First a -> First a # Ord a => Semigroup (Max a) # Methods(<>) :: Max a -> Max a -> Max a #sconcat :: NonEmpty (Max a) -> Max a #stimes :: Integral b => b -> Max a -> Max a # Ord a => Semigroup (Min a) # Methods(<>) :: Min a -> Min a -> Min a #sconcat :: NonEmpty (Min a) -> Min a #stimes :: Integral b => b -> Min a -> Min a # Semigroup a => Semigroup (Identity a) # Methods(<>) :: Identity a -> Identity a -> Identity a #sconcat :: NonEmpty (Identity a) -> Identity a #stimes :: Integral b => b -> Identity a -> Identity 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 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) # 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 (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 # (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 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) #

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

This is a valid definition of stimes for a Monoid.

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

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

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

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

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

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

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

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

Repeat a value n times.

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

Implemented using stimes and mempty.

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

# Semigroups

newtype Min a #

Constructors

 Min FieldsgetMin :: a

Instances

 # Methods(>>=) :: Min a -> (a -> Min b) -> Min b #(>>) :: Min a -> Min b -> Min b #return :: a -> Min a #fail :: String -> Min a # # Methodsfmap :: (a -> b) -> Min a -> Min b #(<$) :: a -> Min b -> Min a # # Methodsmfix :: (a -> Min a) -> Min a # # Methodspure :: a -> Min a #(<*>) :: Min (a -> b) -> Min a -> Min b #(*>) :: Min a -> Min b -> Min b #(<*) :: Min a -> Min b -> Min a # # Methodsfold :: 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 # # Methodstraverse :: 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) # # Associated Typestype Rep1 (Min :: * -> *) :: * -> * # Methodsfrom1 :: Min a -> Rep1 Min a #to1 :: Rep1 Min a -> Min a # Bounded a => Bounded (Min a) # MethodsminBound :: Min a #maxBound :: Min a # Enum a => Enum (Min a) # Methodssucc :: 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 Source #(/=) :: Min a -> Min a -> Bool Source # Data a => Data (Min a) # Methodsgfoldl :: (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 # Ord a => Ord (Min a) # Methodscompare :: Min a -> Min a -> Ordering Source #(<) :: Min a -> Min a -> Bool Source #(<=) :: Min a -> Min a -> Bool Source #(>) :: Min a -> Min a -> Bool Source #(>=) :: Min a -> Min a -> Bool Source #max :: Min a -> Min a -> Min a Source #min :: Min a -> Min a -> Min a Source # Read a => Read (Min a) # MethodsreadsPrec :: Int -> ReadS (Min a) #readList :: ReadS [Min a] #readPrec :: ReadPrec (Min a) # Show a => Show (Min a) # MethodsshowsPrec :: Int -> Min a -> ShowS #show :: Min a -> String #showList :: [Min a] -> ShowS # Generic (Min a) # Associated Typestype Rep (Min a) :: * -> * # Methodsfrom :: 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) # Methodsmempty :: 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 FieldsgetMax :: a Instances  # Methods(>>=) :: Max a -> (a -> Max b) -> Max b #(>>) :: Max a -> Max b -> Max b #return :: a -> Max a #fail :: String -> Max a # # Methodsfmap :: (a -> b) -> Max a -> Max b #(<$) :: a -> Max b -> Max a # # Methodsmfix :: (a -> Max a) -> Max a # # Methodspure :: a -> Max a #(<*>) :: Max (a -> b) -> Max a -> Max b #(*>) :: Max a -> Max b -> Max b #(<*) :: Max a -> Max b -> Max a # # Methodsfold :: 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 # # Methodstraverse :: 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) # # Associated Typestype Rep1 (Max :: * -> *) :: * -> * # Methodsfrom1 :: Max a -> Rep1 Max a #to1 :: Rep1 Max a -> Max a # Bounded a => Bounded (Max a) # MethodsminBound :: Max a #maxBound :: Max a # Enum a => Enum (Max a) # Methodssucc :: 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 Source #(/=) :: Max a -> Max a -> Bool Source # Data a => Data (Max a) # Methodsgfoldl :: (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 # Ord a => Ord (Max a) # Methodscompare :: Max a -> Max a -> Ordering Source #(<) :: Max a -> Max a -> Bool Source #(<=) :: Max a -> Max a -> Bool Source #(>) :: Max a -> Max a -> Bool Source #(>=) :: Max a -> Max a -> Bool Source #max :: Max a -> Max a -> Max a Source #min :: Max a -> Max a -> Max a Source # Read a => Read (Max a) # MethodsreadsPrec :: Int -> ReadS (Max a) #readList :: ReadS [Max a] #readPrec :: ReadPrec (Max a) # Show a => Show (Max a) # MethodsshowsPrec :: Int -> Max a -> ShowS #show :: Max a -> String #showList :: [Max a] -> ShowS # Generic (Max a) # Associated Typestype Rep (Max a) :: * -> * # Methodsfrom :: 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) # Methodsmempty :: 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 FieldsgetFirst :: a

Instances

 # Methods(>>=) :: First a -> (a -> First b) -> First b #(>>) :: First a -> First b -> First b #return :: a -> First a #fail :: String -> First a # # Methodsfmap :: (a -> b) -> First a -> First b #(<$) :: a -> First b -> First a # # Methodsmfix :: (a -> First a) -> First a # # Methodspure :: a -> First a #(<*>) :: First (a -> b) -> First a -> First b #(*>) :: First a -> First b -> First b #(<*) :: First a -> First b -> First a # # Methodsfold :: 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 # # Methodstraverse :: 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) # # Associated Typestype Rep1 (First :: * -> *) :: * -> * # Methodsfrom1 :: First a -> Rep1 First a #to1 :: Rep1 First a -> First a # Bounded a => Bounded (First a) # Methods Enum a => Enum (First a) # Methodssucc :: 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 Source #(/=) :: First a -> First a -> Bool Source # Data a => Data (First a) # Methodsgfoldl :: (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) # Methodscompare :: First a -> First a -> Ordering Source #(<) :: First a -> First a -> Bool Source #(<=) :: First a -> First a -> Bool Source #(>) :: First a -> First a -> Bool Source #(>=) :: First a -> First a -> Bool Source #max :: First a -> First a -> First a Source #min :: First a -> First a -> First a Source # Read a => Read (First a) # MethodsreadsPrec :: Int -> ReadS (First a) #readList :: ReadS [First a] # Show a => Show (First a) # MethodsshowsPrec :: Int -> First a -> ShowS #show :: First a -> String #showList :: [First a] -> ShowS # Generic (First a) # Associated Typestype Rep (First a) :: * -> * # Methodsfrom :: First a -> Rep (First a) x #to :: Rep (First a) x -> 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 FieldsgetLast :: a Instances  # Methods(>>=) :: Last a -> (a -> Last b) -> Last b #(>>) :: Last a -> Last b -> Last b #return :: a -> Last a #fail :: String -> Last a # # Methodsfmap :: (a -> b) -> Last a -> Last b #(<$) :: a -> Last b -> Last a # # Methodsmfix :: (a -> Last a) -> Last a # # Methodspure :: a -> Last a #(<*>) :: Last (a -> b) -> Last a -> Last b #(*>) :: Last a -> Last b -> Last b #(<*) :: Last a -> Last b -> Last a # # Methodsfold :: 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 # # Methodstraverse :: 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) # # Associated Typestype Rep1 (Last :: * -> *) :: * -> * # Methodsfrom1 :: Last a -> Rep1 Last a #to1 :: Rep1 Last a -> Last a # Bounded a => Bounded (Last a) # Methods Enum a => Enum (Last a) # Methodssucc :: 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 Source #(/=) :: Last a -> Last a -> Bool Source # Data a => Data (Last a) # Methodsgfoldl :: (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) # Methodscompare :: Last a -> Last a -> Ordering Source #(<) :: Last a -> Last a -> Bool Source #(<=) :: Last a -> Last a -> Bool Source #(>) :: Last a -> Last a -> Bool Source #(>=) :: Last a -> Last a -> Bool Source #max :: Last a -> Last a -> Last a Source #min :: Last a -> Last a -> Last a Source # Read a => Read (Last a) # MethodsreadsPrec :: Int -> ReadS (Last a) #readList :: ReadS [Last a] # Show a => Show (Last a) # MethodsshowsPrec :: Int -> Last a -> ShowS #show :: Last a -> String #showList :: [Last a] -> ShowS # Generic (Last a) # Associated Typestype Rep (Last a) :: * -> * # Methodsfrom :: Last a -> Rep (Last a) x #to :: Rep (Last a) x -> 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 FieldsunwrapMonoid :: m

Instances

 # Associated Typestype Rep1 (WrappedMonoid :: * -> *) :: * -> * # Methods Bounded a => Bounded (WrappedMonoid a) # Methods Enum a => Enum (WrappedMonoid a) # MethodsenumFrom :: 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 Data m => Data (WrappedMonoid m) # Methodsgfoldl :: (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) #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(<) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source #(>) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # Read m => Read (WrappedMonoid m) # Methods Show m => Show (WrappedMonoid m) # MethodsshowsPrec :: Int -> WrappedMonoid m -> ShowS #show :: WrappedMonoid m -> String #showList :: [WrappedMonoid m] -> ShowS # # Associated Typestype Rep (WrappedMonoid m) :: * -> * # Methodsfrom :: 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 #stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m # Monoid m => Monoid (WrappedMonoid m) # Methodsmconcat :: [WrappedMonoid m] -> WrappedMonoid m # # 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

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

 # Methodsmconcat :: [Ordering] -> Ordering # Monoid () # Methodsmempty :: () #mappend :: () -> () -> () #mconcat :: [()] -> () # # Methodsmappend :: Any -> Any -> Any #mconcat :: [Any] -> Any # # Methodsmappend :: All -> All -> All #mconcat :: [All] -> All # # mappend == elSupremum Methodsmconcat :: [Lifetime] -> Lifetime # # Methodsmappend :: Event -> Event -> Event #mconcat :: [Event] -> Event # Monoid [a] # Methodsmempty :: [a] #mappend :: [a] -> [a] -> [a] #mconcat :: [[a]] -> [a] # Monoid a => Monoid (Maybe a) # Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S." Since there is no "Semigroup" typeclass providing just mappend, we use Monoid instead. Methodsmempty :: Maybe a #mappend :: Maybe a -> Maybe a -> Maybe a #mconcat :: [Maybe a] -> Maybe a # Monoid a => Monoid (IO a) # Methodsmempty :: IO a #mappend :: IO a -> IO a -> IO a #mconcat :: [IO a] -> IO a # Monoid (Last a) # Methodsmempty :: Last a #mappend :: Last a -> Last a -> Last a #mconcat :: [Last a] -> Last a # Monoid (First a) # Methodsmempty :: First a #mappend :: First a -> First a -> First a #mconcat :: [First a] -> First a # Num a => Monoid (Product a) # Methodsmappend :: Product a -> Product a -> Product a #mconcat :: [Product a] -> Product a # Num a => Monoid (Sum a) # Methodsmempty :: Sum a #mappend :: Sum a -> Sum a -> Sum a #mconcat :: [Sum a] -> Sum a # Monoid (Endo a) # Methodsmempty :: Endo a #mappend :: Endo a -> Endo a -> Endo a #mconcat :: [Endo a] -> Endo a # Monoid a => Monoid (Dual a) # Methodsmempty :: Dual a #mappend :: Dual a -> Dual a -> Dual a #mconcat :: [Dual a] -> Dual a # Semigroup a => Monoid (Option a) # Methodsmappend :: Option a -> Option a -> Option a #mconcat :: [Option a] -> Option a # Monoid m => Monoid (WrappedMonoid m) # Methodsmconcat :: [WrappedMonoid m] -> WrappedMonoid m # (Ord a, Bounded a) => Monoid (Max a) # Methodsmempty :: Max a #mappend :: Max a -> Max a -> Max a #mconcat :: [Max a] -> Max a # (Ord a, Bounded a) => Monoid (Min a) # Methodsmempty :: Min a #mappend :: Min a -> Min a -> Min a #mconcat :: [Min a] -> Min a # Monoid a => Monoid (Identity a) # Methodsmappend :: Identity a -> Identity a -> Identity a #mconcat :: [Identity a] -> Identity a # Monoid b => Monoid (a -> b) # Methodsmempty :: a -> b #mappend :: (a -> b) -> (a -> b) -> a -> b #mconcat :: [a -> b] -> a -> b # (Monoid a, Monoid b) => Monoid (a, b) # Methodsmempty :: (a, b) #mappend :: (a, b) -> (a, b) -> (a, b) #mconcat :: [(a, b)] -> (a, b) # Monoid (Proxy k s) # Methodsmempty :: Proxy k s #mappend :: Proxy k s -> Proxy k s -> Proxy k s #mconcat :: [Proxy k s] -> Proxy k s # (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) # Methodsmempty :: (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) # Methodsmempty :: Alt * f a #mappend :: Alt * f a -> Alt * f a -> Alt * f a #mconcat :: [Alt * f a] -> Alt * f a # Monoid a => Monoid (Const k a b) # Methodsmempty :: Const k a b #mappend :: Const k a b -> Const k a b -> Const k a b #mconcat :: [Const k a b] -> Const k a b # (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) # Methodsmempty :: (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) # Methodsmempty :: (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 FieldsgetDual :: a

Instances

 # Methods(>>=) :: Dual a -> (a -> Dual b) -> Dual b #(>>) :: Dual a -> Dual b -> Dual b #return :: a -> Dual a #fail :: String -> Dual a # # Methodsfmap :: (a -> b) -> Dual a -> Dual b #(<$) :: a -> Dual b -> Dual a # # Methodsmfix :: (a -> Dual a) -> Dual a # # Methodspure :: a -> Dual a #(<*>) :: Dual (a -> b) -> Dual a -> Dual b #(*>) :: Dual a -> Dual b -> Dual b #(<*) :: Dual a -> Dual b -> Dual a # # Methodsfold :: 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 # # Methodstraverse :: 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) # # Associated Typestype Rep1 (Dual :: * -> *) :: * -> * # Methodsfrom1 :: Dual a -> Rep1 Dual a #to1 :: Rep1 Dual a -> Dual a # # Methodsmzip :: Dual a -> Dual b -> Dual (a, b) #mzipWith :: (a -> b -> c) -> Dual a -> Dual b -> Dual c #munzip :: Dual (a, b) -> (Dual a, Dual b) # Bounded a => Bounded (Dual a) # Methods Eq a => Eq (Dual a) # Methods(==) :: Dual a -> Dual a -> Bool Source #(/=) :: Dual a -> Dual a -> Bool Source # Data a => Data (Dual a) # Methodsgfoldl :: (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) # Methodscompare :: Dual a -> Dual a -> Ordering Source #(<) :: Dual a -> Dual a -> Bool Source #(<=) :: Dual a -> Dual a -> Bool Source #(>) :: Dual a -> Dual a -> Bool Source #(>=) :: Dual a -> Dual a -> Bool Source #max :: Dual a -> Dual a -> Dual a Source #min :: Dual a -> Dual a -> Dual a Source # Read a => Read (Dual a) # MethodsreadsPrec :: Int -> ReadS (Dual a) #readList :: ReadS [Dual a] # Show a => Show (Dual a) # MethodsshowsPrec :: Int -> Dual a -> ShowS #show :: Dual a -> String #showList :: [Dual a] -> ShowS # Generic (Dual a) # Associated Typestype Rep (Dual a) :: * -> * # Methodsfrom :: 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) # Methodsmempty :: 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 FieldsappEndo :: a -> a Instances  Generic (Endo a) # Associated Typestype Rep (Endo a) :: * -> * # Methodsfrom :: Endo a -> Rep (Endo a) x #to :: Rep (Endo a) x -> 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) # Methodsmempty :: 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 FieldsgetAll :: Bool Instances  # Methods # Methods(==) :: All -> All -> Bool Source #(/=) :: All -> All -> Bool Source # # Methodsgfoldl :: (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 #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 # # Methods(<) :: All -> All -> Bool Source #(<=) :: All -> All -> Bool Source #(>) :: All -> All -> Bool Source #(>=) :: All -> All -> Bool Source #max :: All -> All -> All Source #min :: All -> All -> All Source # # Methods # MethodsshowsPrec :: Int -> All -> ShowS #show :: All -> String #showList :: [All] -> ShowS # # Associated Typestype Rep All :: * -> * # Methodsfrom :: All -> Rep All x #to :: Rep All x -> All # # Methods(<>) :: All -> All -> All #stimes :: Integral b => b -> All -> All # # Methodsmappend :: 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 FieldsgetAny :: Bool Instances  # Methods # Methods(==) :: Any -> Any -> Bool Source #(/=) :: Any -> Any -> Bool Source # # Methodsgfoldl :: (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 #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 # # Methods(<) :: Any -> Any -> Bool Source #(<=) :: Any -> Any -> Bool Source #(>) :: Any -> Any -> Bool Source #(>=) :: Any -> Any -> Bool Source #max :: Any -> Any -> Any Source #min :: Any -> Any -> Any Source # # Methods # MethodsshowsPrec :: Int -> Any -> ShowS #show :: Any -> String #showList :: [Any] -> ShowS # # Associated Typestype Rep Any :: * -> * # Methodsfrom :: Any -> Rep Any x #to :: Rep Any x -> Any # # Methods(<>) :: Any -> Any -> Any #stimes :: Integral b => b -> Any -> Any # # Methodsmappend :: 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 FieldsgetSum :: a Instances  # Methods(>>=) :: Sum a -> (a -> Sum b) -> Sum b #(>>) :: Sum a -> Sum b -> Sum b #return :: a -> Sum a #fail :: String -> Sum a # # Methodsfmap :: (a -> b) -> Sum a -> Sum b #(<$) :: a -> Sum b -> Sum a # # Methodsmfix :: (a -> Sum a) -> Sum a # # Methodspure :: a -> Sum a #(<*>) :: Sum (a -> b) -> Sum a -> Sum b #(*>) :: Sum a -> Sum b -> Sum b #(<*) :: Sum a -> Sum b -> Sum a # # Methodsfold :: 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 # # Methodstraverse :: 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) # # Associated Typestype Rep1 (Sum :: * -> *) :: * -> * # Methodsfrom1 :: Sum a -> Rep1 Sum a #to1 :: Rep1 Sum a -> Sum a # # Methodsmzip :: Sum a -> Sum b -> Sum (a, b) #mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c #munzip :: Sum (a, b) -> (Sum a, Sum b) # Bounded a => Bounded (Sum a) # MethodsminBound :: Sum a #maxBound :: Sum a # Eq a => Eq (Sum a) # Methods(==) :: Sum a -> Sum a -> Bool Source #(/=) :: Sum a -> Sum a -> Bool Source # Data a => Data (Sum a) # Methodsgfoldl :: (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 # Ord a => Ord (Sum a) # Methodscompare :: Sum a -> Sum a -> Ordering Source #(<) :: Sum a -> Sum a -> Bool Source #(<=) :: Sum a -> Sum a -> Bool Source #(>) :: Sum a -> Sum a -> Bool Source #(>=) :: Sum a -> Sum a -> Bool Source #max :: Sum a -> Sum a -> Sum a Source #min :: Sum a -> Sum a -> Sum a Source # Read a => Read (Sum a) # MethodsreadsPrec :: Int -> ReadS (Sum a) #readList :: ReadS [Sum a] #readPrec :: ReadPrec (Sum a) # Show a => Show (Sum a) # MethodsshowsPrec :: Int -> Sum a -> ShowS #show :: Sum a -> String #showList :: [Sum a] -> ShowS # Generic (Sum a) # Associated Typestype Rep (Sum a) :: * -> * # Methodsfrom :: 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) # Methodsmempty :: 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 FieldsgetProduct :: a

Instances

 # Methods(>>=) :: Product a -> (a -> Product b) -> Product b #(>>) :: Product a -> Product b -> Product b #return :: a -> Product a #fail :: String -> Product a # # Methodsfmap :: (a -> b) -> Product a -> Product b #(<$) :: a -> Product b -> Product a # # Methodsmfix :: (a -> Product a) -> Product a # # Methodspure :: a -> Product a #(<*>) :: Product (a -> b) -> Product a -> Product b #(*>) :: Product a -> Product b -> Product b #(<*) :: Product a -> Product b -> Product a # # Methodsfold :: 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 # # Methodstraverse :: 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) # # Associated Typestype Rep1 (Product :: * -> *) :: * -> * # Methodsfrom1 :: Product a -> Rep1 Product a #to1 :: Rep1 Product a -> Product a # # Methodsmzip :: Product a -> Product b -> Product (a, b) #mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c #munzip :: Product (a, b) -> (Product a, Product b) # Bounded a => Bounded (Product a) # Methods Eq a => Eq (Product a) # Methods(==) :: Product a -> Product a -> Bool Source #(/=) :: Product a -> Product a -> Bool Source # Data a => Data (Product a) # Methodsgfoldl :: (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 #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 # Ord a => Ord (Product a) # Methodscompare :: Product a -> Product a -> Ordering Source #(<) :: Product a -> Product a -> Bool Source #(<=) :: Product a -> Product a -> Bool Source #(>) :: Product a -> Product a -> Bool Source #(>=) :: Product a -> Product a -> Bool Source #max :: Product a -> Product a -> Product a Source #min :: Product a -> Product a -> Product a Source # Read a => Read (Product a) # MethodsreadsPrec :: Int -> ReadS (Product a) # Show a => Show (Product a) # MethodsshowsPrec :: Int -> Product a -> ShowS #show :: Product a -> String #showList :: [Product a] -> ShowS # # Associated Typestype Rep (Product a) :: * -> * # Methodsfrom :: 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) # Methodsmappend :: 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 # 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 FieldsgetOption :: Maybe a Instances  # Methods(>>=) :: Option a -> (a -> Option b) -> Option b #(>>) :: Option a -> Option b -> Option b #return :: a -> Option a #fail :: String -> Option a # # Methodsfmap :: (a -> b) -> Option a -> Option b #(<$) :: a -> Option b -> Option a # # Methodsmfix :: (a -> Option a) -> Option a # # Methodspure :: a -> Option a #(<*>) :: Option (a -> b) -> Option a -> Option b #(*>) :: Option a -> Option b -> Option b #(<*) :: Option a -> Option b -> Option a # # Methodsfold :: 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 # # Methodstraverse :: 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) # # Associated Typestype Rep1 (Option :: * -> *) :: * -> * # Methodsfrom1 :: Option a -> Rep1 Option a #to1 :: Rep1 Option a -> Option a # # Methodsmzero :: Option a #mplus :: Option a -> Option a -> Option a # # Methodsempty :: Option a #(<|>) :: Option a -> Option a -> Option a #some :: Option a -> Option [a] #many :: Option a -> Option [a] # Eq a => Eq (Option a) # Methods(==) :: Option a -> Option a -> Bool Source #(/=) :: Option a -> Option a -> Bool Source # Data a => Data (Option a) # Methodsgfoldl :: (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 #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) # Methodscompare :: Option a -> Option a -> Ordering Source #(<) :: Option a -> Option a -> Bool Source #(<=) :: Option a -> Option a -> Bool Source #(>) :: Option a -> Option a -> Bool Source #(>=) :: Option a -> Option a -> Bool Source #max :: Option a -> Option a -> Option a Source #min :: Option a -> Option a -> Option a Source # Read a => Read (Option a) # MethodsreadsPrec :: Int -> ReadS (Option a) #readList :: ReadS [Option a] # Show a => Show (Option a) # MethodsshowsPrec :: Int -> Option a -> ShowS #show :: Option a -> String #showList :: [Option a] -> ShowS # # Associated Typestype Rep (Option a) :: * -> * # Methodsfrom :: Option a -> Rep (Option a) x #to :: Rep (Option a) x -> Option 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 => Monoid (Option a) # Methodsmappend :: Option a -> Option a -> Option a #mconcat :: [Option a] -> Option a # type Rep1 Option # type Rep1 Option = D1 (MetaData "Option" "Data.Semigroup" "base" True) (C1 (MetaCons "Option" PrefixI True) (S1 (MetaSel (Just Symbol "getOption") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Maybe))) type Rep (Option a) # type Rep (Option a) = D1 (MetaData "Option" "Data.Semigroup" "base" True) (C1 (MetaCons "Option" PrefixI True) (S1 (MetaSel (Just Symbol "getOption") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))

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

Fold an Option case-wise, just like maybe.

# Difference lists of a semigroup

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

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

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

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

# ArgMin, ArgMax

data Arg a b #

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

Constructors

 Arg a b

Instances

 # Methodsbimap :: (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) # Methodsfmap :: (a -> b) -> Arg a a -> Arg a b #(<\$) :: a -> Arg a b -> Arg a a # Foldable (Arg a) # Methodsfold :: 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 # # Methodstraverse :: 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 Typestype Rep1 (Arg a :: * -> *) :: * -> * # Methodsfrom1 :: 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 Source #(/=) :: Arg a b -> Arg a b -> Bool Source # (Data b, Data a) => Data (Arg a b) # Methodsgfoldl :: (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) # Methodscompare :: Arg a b -> Arg a b -> Ordering Source #(<) :: Arg a b -> Arg a b -> Bool Source #(<=) :: Arg a b -> Arg a b -> Bool Source #(>) :: Arg a b -> Arg a b -> Bool Source #(>=) :: Arg a b -> Arg a b -> Bool Source #max :: Arg a b -> Arg a b -> Arg a b Source #min :: Arg a b -> Arg a b -> Arg a b Source # (Read b, Read a) => Read (Arg a b) # MethodsreadsPrec :: 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) # MethodsshowsPrec :: Int -> Arg a b -> ShowS #show :: Arg a b -> String #showList :: [Arg a b] -> ShowS # Generic (Arg a b) # Associated Typestype Rep (Arg a b) :: * -> * # Methodsfrom :: 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) #