base-4.9.1.0: Basic libraries

Copyright(c) Andy Gill 2001
(c) Oregon Graduate Institute of Science and Technology 2001
LicenseBSD-style (see the file libraries/base/LICENSE)
Maintainerlibraries@haskell.org
Stabilityexperimental
Portabilityportable
Safe HaskellTrustworthy
LanguageHaskell2010

Data.Monoid

Contents

Description

A class for monoids (types with an associative binary operation that has an identity) with various general-purpose instances.

Synopsis

Monoid typeclass

class Monoid a where Source #

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 Source #

Identity of mappend

mappend :: a -> a -> a Source #

An associative operation

mconcat :: [a] -> a Source #

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 # 
Monoid () # 

Methods

mempty :: () Source #

mappend :: () -> () -> () Source #

mconcat :: [()] -> () Source #

Monoid Any # 
Monoid All # 
Monoid Lifetime #

mappend == elSupremum

Monoid Event # 
Monoid [a] # 

Methods

mempty :: [a] Source #

mappend :: [a] -> [a] -> [a] Source #

mconcat :: [[a]] -> [a] Source #

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.

Methods

mempty :: Maybe a Source #

mappend :: Maybe a -> Maybe a -> Maybe a Source #

mconcat :: [Maybe a] -> Maybe a Source #

Monoid a => Monoid (IO a) # 

Methods

mempty :: IO a Source #

mappend :: IO a -> IO a -> IO a Source #

mconcat :: [IO a] -> IO a Source #

Monoid (Last a) # 

Methods

mempty :: Last a Source #

mappend :: Last a -> Last a -> Last a Source #

mconcat :: [Last a] -> Last a Source #

Monoid (First a) # 

Methods

mempty :: First a Source #

mappend :: First a -> First a -> First a Source #

mconcat :: [First a] -> First a Source #

Num a => Monoid (Product a) # 
Num a => Monoid (Sum a) # 

Methods

mempty :: Sum a Source #

mappend :: Sum a -> Sum a -> Sum a Source #

mconcat :: [Sum a] -> Sum a Source #

Monoid (Endo a) # 

Methods

mempty :: Endo a Source #

mappend :: Endo a -> Endo a -> Endo a Source #

mconcat :: [Endo a] -> Endo a Source #

Monoid a => Monoid (Dual a) # 

Methods

mempty :: Dual a Source #

mappend :: Dual a -> Dual a -> Dual a Source #

mconcat :: [Dual a] -> Dual a Source #

Semigroup a => Monoid (Option a) # 
Monoid m => Monoid (WrappedMonoid m) # 
(Ord a, Bounded a) => Monoid (Max a) # 

Methods

mempty :: Max a Source #

mappend :: Max a -> Max a -> Max a Source #

mconcat :: [Max a] -> Max a Source #

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

Methods

mempty :: Min a Source #

mappend :: Min a -> Min a -> Min a Source #

mconcat :: [Min a] -> Min a Source #

Monoid a => Monoid (Identity a) # 
Monoid b => Monoid (a -> b) # 

Methods

mempty :: a -> b Source #

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

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

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

Methods

mempty :: (a, b) Source #

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

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

Monoid (Proxy k s) # 

Methods

mempty :: Proxy k s Source #

mappend :: Proxy k s -> Proxy k s -> Proxy k s Source #

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

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

Methods

mempty :: (a, b, c) Source #

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

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

Alternative f => Monoid (Alt * f a) # 

Methods

mempty :: Alt * f a Source #

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

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

Monoid a => Monoid (Const k a b) # 

Methods

mempty :: Const k a b Source #

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

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

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

Methods

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

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

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

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

Methods

mempty :: (a, b, c, d, e) Source #

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

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

(<>) :: Monoid m => m -> m -> m infixr 6 Source #

An infix synonym for mappend.

Since: 4.5.0.0

newtype Dual a Source #

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

Constructors

Dual 

Fields

Instances

Monad Dual # 

Methods

(>>=) :: Dual a -> (a -> Dual b) -> Dual b Source #

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

return :: a -> Dual a Source #

fail :: String -> Dual a Source #

Functor Dual # 

Methods

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

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

MonadFix Dual # 

Methods

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

Applicative Dual # 

Methods

pure :: a -> Dual a Source #

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

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

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

Foldable Dual # 

Methods

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

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

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

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

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

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

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

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

toList :: Dual a -> [a] Source #

null :: Dual a -> Bool Source #

length :: Dual a -> Int Source #

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

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

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

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

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

Traversable Dual # 

Methods

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

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

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

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

Generic1 Dual # 

Associated Types

type Rep1 (Dual :: * -> *) :: * -> * Source #

Methods

from1 :: Dual a -> Rep1 Dual a Source #

to1 :: Rep1 Dual a -> Dual a Source #

MonadZip Dual # 

Methods

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

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

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

Bounded a => Bounded (Dual a) # 
Eq a => Eq (Dual a) # 

Methods

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

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

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) Source #

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

toConstr :: Dual a -> Constr Source #

dataTypeOf :: Dual a -> DataType Source #

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (Dual a) # 

Methods

compare :: Dual a -> Dual a -> Ordering Source #

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

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

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

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

max :: Dual a -> Dual a -> Dual a Source #

min :: Dual a -> Dual a -> Dual a Source #

Read a => Read (Dual a) # 
Show a => Show (Dual a) # 

Methods

showsPrec :: Int -> Dual a -> ShowS Source #

show :: Dual a -> String Source #

showList :: [Dual a] -> ShowS Source #

Generic (Dual a) # 

Associated Types

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

Methods

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

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

Semigroup a => Semigroup (Dual a) # 

Methods

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

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

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

Monoid a => Monoid (Dual a) # 

Methods

mempty :: Dual a Source #

mappend :: Dual a -> Dual a -> Dual a Source #

mconcat :: [Dual a] -> Dual a Source #

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 Source #

The monoid of endomorphisms under composition.

Constructors

Endo 

Fields

Instances

Generic (Endo a) # 

Associated Types

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

Methods

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

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

Semigroup (Endo a) # 

Methods

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

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

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

Monoid (Endo a) # 

Methods

mempty :: Endo a Source #

mappend :: Endo a -> Endo a -> Endo a Source #

mconcat :: [Endo a] -> Endo a Source #

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))))

Bool wrappers

newtype All Source #

Boolean monoid under conjunction (&&).

Constructors

All 

Fields

Instances

Bounded All # 
Eq All # 

Methods

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

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

Data All # 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> All -> c All Source #

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

toConstr :: All -> Constr Source #

dataTypeOf :: All -> DataType Source #

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

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

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

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

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

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

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

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

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

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

Ord All # 

Methods

compare :: All -> All -> Ordering Source #

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

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

(>) :: All -> All -> Bool Source #

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

max :: All -> All -> All Source #

min :: All -> All -> All Source #

Read All # 
Show All # 
Generic All # 

Associated Types

type Rep All :: * -> * Source #

Methods

from :: All -> Rep All x Source #

to :: Rep All x -> All Source #

Semigroup All # 

Methods

(<>) :: All -> All -> All Source #

sconcat :: NonEmpty All -> All Source #

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

Monoid 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 Source #

Boolean monoid under disjunction (||).

Constructors

Any 

Fields

Instances

Bounded Any # 
Eq Any # 

Methods

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

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

Data Any # 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Any -> c Any Source #

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

toConstr :: Any -> Constr Source #

dataTypeOf :: Any -> DataType Source #

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

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

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

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

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

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

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

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

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

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

Ord Any # 

Methods

compare :: Any -> Any -> Ordering Source #

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

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

(>) :: Any -> Any -> Bool Source #

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

max :: Any -> Any -> Any Source #

min :: Any -> Any -> Any Source #

Read Any # 
Show Any # 
Generic Any # 

Associated Types

type Rep Any :: * -> * Source #

Methods

from :: Any -> Rep Any x Source #

to :: Rep Any x -> Any Source #

Semigroup Any # 

Methods

(<>) :: Any -> Any -> Any Source #

sconcat :: NonEmpty Any -> Any Source #

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

Monoid 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)))

Num wrappers

newtype Sum a Source #

Monoid under addition.

Constructors

Sum 

Fields

Instances

Monad Sum # 

Methods

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

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

return :: a -> Sum a Source #

fail :: String -> Sum a Source #

Functor Sum # 

Methods

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

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

MonadFix Sum # 

Methods

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

Applicative Sum # 

Methods

pure :: a -> Sum a Source #

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

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

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

Foldable Sum # 

Methods

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

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

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

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

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

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

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

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

toList :: Sum a -> [a] Source #

null :: Sum a -> Bool Source #

length :: Sum a -> Int Source #

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

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

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

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

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

Traversable Sum # 

Methods

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

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

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

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

Generic1 Sum # 

Associated Types

type Rep1 (Sum :: * -> *) :: * -> * Source #

Methods

from1 :: Sum a -> Rep1 Sum a Source #

to1 :: Rep1 Sum a -> Sum a Source #

MonadZip Sum # 

Methods

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

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

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

Bounded a => Bounded (Sum a) # 
Eq a => Eq (Sum a) # 

Methods

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

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

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) Source #

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

toConstr :: Sum a -> Constr Source #

dataTypeOf :: Sum a -> DataType Source #

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

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

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

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

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

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

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

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

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

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

Num a => Num (Sum a) # 

Methods

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

(-) :: Sum a -> Sum a -> Sum a Source #

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

negate :: Sum a -> Sum a Source #

abs :: Sum a -> Sum a Source #

signum :: Sum a -> Sum a Source #

fromInteger :: Integer -> Sum a Source #

Ord a => Ord (Sum a) # 

Methods

compare :: Sum a -> Sum a -> Ordering Source #

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

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

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

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

max :: Sum a -> Sum a -> Sum a Source #

min :: Sum a -> Sum a -> Sum a Source #

Read a => Read (Sum a) # 
Show a => Show (Sum a) # 

Methods

showsPrec :: Int -> Sum a -> ShowS Source #

show :: Sum a -> String Source #

showList :: [Sum a] -> ShowS Source #

Generic (Sum a) # 

Associated Types

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

Methods

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

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

Num a => Semigroup (Sum a) # 

Methods

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

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

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

Num a => Monoid (Sum a) # 

Methods

mempty :: Sum a Source #

mappend :: Sum a -> Sum a -> Sum a Source #

mconcat :: [Sum a] -> Sum a Source #

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 Source #

Monoid under multiplication.

Constructors

Product 

Fields

Instances

Monad Product # 

Methods

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

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

return :: a -> Product a Source #

fail :: String -> Product a Source #

Functor Product # 

Methods

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

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

MonadFix Product # 

Methods

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

Applicative Product # 

Methods

pure :: a -> Product a Source #

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

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

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

Foldable Product # 

Methods

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

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

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

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

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

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

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

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

toList :: Product a -> [a] Source #

null :: Product a -> Bool Source #

length :: Product a -> Int Source #

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

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

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

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

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

Traversable Product # 

Methods

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

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

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

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

Generic1 Product # 

Associated Types

type Rep1 (Product :: * -> *) :: * -> * Source #

MonadZip Product # 

Methods

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

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

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

Bounded a => Bounded (Product a) # 
Eq a => Eq (Product a) # 

Methods

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

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

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) Source #

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

toConstr :: Product a -> Constr Source #

dataTypeOf :: Product a -> DataType Source #

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

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

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

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

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

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

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

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

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

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

Num a => Num (Product a) # 
Ord a => Ord (Product a) # 
Read a => Read (Product a) # 
Show a => Show (Product a) # 
Generic (Product a) # 

Associated Types

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

Methods

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

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

Num a => Semigroup (Product a) # 

Methods

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

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

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

Num a => Monoid (Product a) # 
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)))

Maybe wrappers

To implement find or findLast on any Foldable:

findLast :: Foldable t => (a -> Bool) -> t a -> Maybe a
findLast pred = getLast . foldMap (x -> if pred x
                                           then Last (Just x)
                                           else Last Nothing)

Much of Data.Map's interface can be implemented with Data.Map.alter. Some of the rest can be implemented with a new alterA function and either First or Last:

alterA :: (Applicative f, Ord k) =>
          (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a)

instance Monoid a => Applicative ((,) a)  -- from Control.Applicative
insertLookupWithKey :: Ord k => (k -> v -> v -> v) -> k -> v
                    -> Map k v -> (Maybe v, Map k v)
insertLookupWithKey combine key value =
  Arrow.first getFirst . alterA doChange key
  where
  doChange Nothing = (First Nothing, Just value)
  doChange (Just oldValue) =
    (First (Just oldValue),
     Just (combine key value oldValue))

newtype First a Source #

Maybe monoid returning the leftmost non-Nothing value.

First a is isomorphic to Alt Maybe a, but precedes it historically.

Constructors

First 

Fields

Instances

Monad First # 

Methods

(>>=) :: First a -> (a -> First b) -> First b Source #

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

return :: a -> First a Source #

fail :: String -> First a Source #

Functor First # 

Methods

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

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

MonadFix First # 

Methods

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

Applicative First # 

Methods

pure :: a -> First a Source #

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

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

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

Foldable First # 

Methods

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

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

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

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

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

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

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

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

toList :: First a -> [a] Source #

null :: First a -> Bool Source #

length :: First a -> Int Source #

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

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

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

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

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

Traversable First # 

Methods

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

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

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

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

Generic1 First # 

Associated Types

type Rep1 (First :: * -> *) :: * -> * Source #

Methods

from1 :: First a -> Rep1 First a Source #

to1 :: Rep1 First a -> First a Source #

MonadZip First # 

Methods

mzip :: First a -> First b -> First (a, b) Source #

mzipWith :: (a -> b -> c) -> First a -> First b -> First c Source #

munzip :: First (a, b) -> (First a, First b) Source #

Eq a => Eq (First a) # 

Methods

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

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

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) Source #

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

toConstr :: First a -> Constr Source #

dataTypeOf :: First a -> DataType Source #

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (First a) # 

Methods

compare :: First a -> First a -> Ordering Source #

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

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

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

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

max :: First a -> First a -> First a Source #

min :: First a -> First a -> First a Source #

Read a => Read (First a) # 
Show a => Show (First a) # 
Generic (First a) # 

Associated Types

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

Methods

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

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

Semigroup (First a) # 

Methods

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

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

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

Monoid (First a) # 

Methods

mempty :: First a Source #

mappend :: First a -> First a -> First a Source #

mconcat :: [First a] -> First a Source #

type Rep1 First # 
type Rep1 First = D1 (MetaData "First" "Data.Monoid" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Maybe)))
type Rep (First a) # 
type Rep (First a) = D1 (MetaData "First" "Data.Monoid" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))

newtype Last a Source #

Maybe monoid returning the rightmost non-Nothing value.

Last a is isomorphic to Dual (First a), and thus to Dual (Alt Maybe a)

Constructors

Last 

Fields

Instances

Monad Last # 

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b Source #

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

return :: a -> Last a Source #

fail :: String -> Last a Source #

Functor Last # 

Methods

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

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

MonadFix Last # 

Methods

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

Applicative Last # 

Methods

pure :: a -> Last a Source #

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

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

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

Foldable Last # 

Methods

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

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

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

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

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

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

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

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

toList :: Last a -> [a] Source #

null :: Last a -> Bool Source #

length :: Last a -> Int Source #

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

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

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

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

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

Traversable Last # 

Methods

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

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

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

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

Generic1 Last # 

Associated Types

type Rep1 (Last :: * -> *) :: * -> * Source #

Methods

from1 :: Last a -> Rep1 Last a Source #

to1 :: Rep1 Last a -> Last a Source #

MonadZip Last # 

Methods

mzip :: Last a -> Last b -> Last (a, b) Source #

mzipWith :: (a -> b -> c) -> Last a -> Last b -> Last c Source #

munzip :: Last (a, b) -> (Last a, Last b) Source #

Eq a => Eq (Last a) # 

Methods

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

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

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) Source #

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

toConstr :: Last a -> Constr Source #

dataTypeOf :: Last a -> DataType Source #

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (Last a) # 

Methods

compare :: Last a -> Last a -> Ordering Source #

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

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

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

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

max :: Last a -> Last a -> Last a Source #

min :: Last a -> Last a -> Last a Source #

Read a => Read (Last a) # 
Show a => Show (Last a) # 

Methods

showsPrec :: Int -> Last a -> ShowS Source #

show :: Last a -> String Source #

showList :: [Last a] -> ShowS Source #

Generic (Last a) # 

Associated Types

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

Methods

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

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

Semigroup (Last a) # 

Methods

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

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

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

Monoid (Last a) # 

Methods

mempty :: Last a Source #

mappend :: Last a -> Last a -> Last a Source #

mconcat :: [Last a] -> Last a Source #

type Rep1 Last # 
type Rep1 Last = D1 (MetaData "Last" "Data.Monoid" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just Symbol "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Maybe)))
type Rep (Last a) # 
type Rep (Last a) = D1 (MetaData "Last" "Data.Monoid" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just Symbol "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))

Alternative wrapper

newtype Alt f a Source #

Monoid under <|>.

Since: 4.8.0.0

Constructors

Alt 

Fields

Instances

Monad f => Monad (Alt * f) # 

Methods

(>>=) :: Alt * f a -> (a -> Alt * f b) -> Alt * f b Source #

(>>) :: Alt * f a -> Alt * f b -> Alt * f b Source #

return :: a -> Alt * f a Source #

fail :: String -> Alt * f a Source #

Functor f => Functor (Alt * f) # 

Methods

fmap :: (a -> b) -> Alt * f a -> Alt * f b Source #

(<$) :: a -> Alt * f b -> Alt * f a Source #

MonadFix f => MonadFix (Alt * f) # 

Methods

mfix :: (a -> Alt * f a) -> Alt * f a Source #

Applicative f => Applicative (Alt * f) # 

Methods

pure :: a -> Alt * f a Source #

(<*>) :: Alt * f (a -> b) -> Alt * f a -> Alt * f b Source #

(*>) :: Alt * f a -> Alt * f b -> Alt * f b Source #

(<*) :: Alt * f a -> Alt * f b -> Alt * f a Source #

Generic1 (Alt * f) # 

Associated Types

type Rep1 (Alt * f :: * -> *) :: * -> * Source #

Methods

from1 :: Alt * f a -> Rep1 (Alt * f) a Source #

to1 :: Rep1 (Alt * f) a -> Alt * f a Source #

MonadPlus f => MonadPlus (Alt * f) # 

Methods

mzero :: Alt * f a Source #

mplus :: Alt * f a -> Alt * f a -> Alt * f a Source #

Alternative f => Alternative (Alt * f) # 

Methods

empty :: Alt * f a Source #

(<|>) :: Alt * f a -> Alt * f a -> Alt * f a Source #

some :: Alt * f a -> Alt * f [a] Source #

many :: Alt * f a -> Alt * f [a] Source #

MonadZip f => MonadZip (Alt * f) # 

Methods

mzip :: Alt * f a -> Alt * f b -> Alt * f (a, b) Source #

mzipWith :: (a -> b -> c) -> Alt * f a -> Alt * f b -> Alt * f c Source #

munzip :: Alt * f (a, b) -> (Alt * f a, Alt * f b) Source #

Enum (f a) => Enum (Alt k f a) # 

Methods

succ :: Alt k f a -> Alt k f a Source #

pred :: Alt k f a -> Alt k f a Source #

toEnum :: Int -> Alt k f a Source #

fromEnum :: Alt k f a -> Int Source #

enumFrom :: Alt k f a -> [Alt k f a] Source #

enumFromThen :: Alt k f a -> Alt k f a -> [Alt k f a] Source #

enumFromTo :: Alt k f a -> Alt k f a -> [Alt k f a] Source #

enumFromThenTo :: Alt k f a -> Alt k f a -> Alt k f a -> [Alt k f a] Source #

Eq (f a) => Eq (Alt k f a) # 

Methods

(==) :: Alt k f a -> Alt k f a -> Bool Source #

(/=) :: Alt k f a -> Alt k f a -> Bool Source #

(Data (f a), Data a, Typeable (* -> *) f) => Data (Alt * f a) # 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Alt * f a -> c (Alt * f a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Alt * f a) Source #

toConstr :: Alt * f a -> Constr Source #

dataTypeOf :: Alt * f a -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Alt * f a)) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Alt * f a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Alt * f a -> Alt * f a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Alt * f a -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Alt * f a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Alt * f a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Alt * f a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Alt * f a -> m (Alt * f a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt * f a -> m (Alt * f a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt * f a -> m (Alt * f a) Source #

Num (f a) => Num (Alt k f a) # 

Methods

(+) :: Alt k f a -> Alt k f a -> Alt k f a Source #

(-) :: Alt k f a -> Alt k f a -> Alt k f a Source #

(*) :: Alt k f a -> Alt k f a -> Alt k f a Source #

negate :: Alt k f a -> Alt k f a Source #

abs :: Alt k f a -> Alt k f a Source #

signum :: Alt k f a -> Alt k f a Source #

fromInteger :: Integer -> Alt k f a Source #

Ord (f a) => Ord (Alt k f a) # 

Methods

compare :: Alt k f a -> Alt k f a -> Ordering Source #

(<) :: Alt k f a -> Alt k f a -> Bool Source #

(<=) :: Alt k f a -> Alt k f a -> Bool Source #

(>) :: Alt k f a -> Alt k f a -> Bool Source #

(>=) :: Alt k f a -> Alt k f a -> Bool Source #

max :: Alt k f a -> Alt k f a -> Alt k f a Source #

min :: Alt k f a -> Alt k f a -> Alt k f a Source #

Read (f a) => Read (Alt k f a) # 

Methods

readsPrec :: Int -> ReadS (Alt k f a) Source #

readList :: ReadS [Alt k f a] Source #

readPrec :: ReadPrec (Alt k f a) Source #

readListPrec :: ReadPrec [Alt k f a] Source #

Show (f a) => Show (Alt k f a) # 

Methods

showsPrec :: Int -> Alt k f a -> ShowS Source #

show :: Alt k f a -> String Source #

showList :: [Alt k f a] -> ShowS Source #

Generic (Alt k f a) # 

Associated Types

type Rep (Alt k f a) :: * -> * Source #

Methods

from :: Alt k f a -> Rep (Alt k f a) x Source #

to :: Rep (Alt k f a) x -> Alt k f a Source #

Alternative f => Semigroup (Alt * f a) # 

Methods

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

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

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

Alternative f => Monoid (Alt * f a) # 

Methods

mempty :: Alt * f a Source #

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

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

type Rep1 (Alt * f) # 
type Rep1 (Alt * f) = D1 (MetaData "Alt" "Data.Monoid" "base" True) (C1 (MetaCons "Alt" PrefixI True) (S1 (MetaSel (Just Symbol "getAlt") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f)))
type Rep (Alt k f a) # 
type Rep (Alt k f a) = D1 (MetaData "Alt" "Data.Monoid" "base" True) (C1 (MetaCons "Alt" PrefixI True) (S1 (MetaSel (Just Symbol "getAlt") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a))))