precursor-0.1.0.0: Prelude replacement

Safe HaskellSafe
LanguageHaskell2010

Precursor.Algebra.Semigroup

Contents

Synopsis

Semigroup typeclass

class Semigroup a where #

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

Since: 4.9.0.0

Methods

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

An associative operation.

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

If a is also a Monoid we further require

(<>) = mappend

sconcat :: NonEmpty a -> a #

Reduce a non-empty list with <>

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

Instances

Semigroup Ordering 
Semigroup () 

Methods

(<>) :: () -> () -> () #

sconcat :: NonEmpty () -> () #

stimes :: Integral b => b -> () -> () #

Semigroup Void 

Methods

(<>) :: Void -> Void -> Void #

sconcat :: NonEmpty Void -> Void #

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

Semigroup All 

Methods

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

sconcat :: NonEmpty All -> All #

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

Semigroup Any 

Methods

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

sconcat :: NonEmpty Any -> Any #

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

Semigroup ByteString 
Semigroup ByteString 
Semigroup IntSet 
Semigroup Doc 

Methods

(<>) :: Doc -> Doc -> Doc #

sconcat :: NonEmpty Doc -> Doc #

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

Semigroup Builder 
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 #

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 #

Ord a => Semigroup (Min a) 

Methods

(<>) :: Min a -> Min a -> Min a #

sconcat :: NonEmpty (Min a) -> Min a #

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

Ord a => Semigroup (Max a) 

Methods

(<>) :: Max a -> Max a -> Max a #

sconcat :: NonEmpty (Max a) -> Max a #

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

Semigroup (First a) 

Methods

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

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

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

Semigroup (Last a) 

Methods

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

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

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

Monoid m => Semigroup (WrappedMonoid m) 
Semigroup a => Semigroup (Option a) 

Methods

(<>) :: Option a -> Option a -> Option a #

sconcat :: NonEmpty (Option a) -> Option a #

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

Semigroup (NonEmpty a) 

Methods

(<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a #

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

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

Semigroup a => Semigroup (Dual a) 

Methods

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

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

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

Semigroup (Endo a) 

Methods

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

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

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

Num a => Semigroup (Sum a) 

Methods

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

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

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

Num a => Semigroup (Product a) 

Methods

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

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

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

Semigroup (First a) 

Methods

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

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

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

Semigroup (Last a) 

Methods

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

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

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

Semigroup (IntMap a) 

Methods

(<>) :: IntMap a -> IntMap a -> IntMap a #

sconcat :: NonEmpty (IntMap a) -> IntMap a #

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

Semigroup (Seq a) 

Methods

(<>) :: Seq a -> Seq a -> Seq a #

sconcat :: NonEmpty (Seq a) -> Seq a #

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

Ord a => Semigroup (Set a) 

Methods

(<>) :: Set a -> Set a -> Set a #

sconcat :: NonEmpty (Set a) -> Set a #

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

Semigroup (Doc a) 

Methods

(<>) :: Doc a -> Doc a -> Doc a #

sconcat :: NonEmpty (Doc a) -> Doc a #

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

Semiring 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 #

Semiring 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 #

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 #

Ord k => Semigroup (Map k v) 

Methods

(<>) :: Map k v -> Map k v -> Map k v #

sconcat :: NonEmpty (Map k v) -> Map k v #

stimes :: Integral b => b -> Map k v -> Map k v #

(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) 

Methods

(<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) #

sconcat :: NonEmpty (a, b, c) -> (a, b, c) #

stimes :: Integral b => b -> (a, b, c) -> (a, b, c) #

Semigroup a => Semigroup (Const k a b) 

Methods

(<>) :: Const k a b -> Const k a b -> Const k a b #

sconcat :: NonEmpty (Const k a b) -> Const k a b #

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

Alternative f => Semigroup (Alt * f a) 

Methods

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

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

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

Semigroup a => Semigroup (Tagged k s a) 

Methods

(<>) :: Tagged k s a -> Tagged k s a -> Tagged k s a #

sconcat :: NonEmpty (Tagged k s a) -> Tagged k s a #

stimes :: Integral b => b -> Tagged k s a -> Tagged k s a #

(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) #

(<>) :: Semigroup a => a -> a -> a #

An associative operation.

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

If a is also a Monoid we further require

(<>) = mappend

sconcat :: Semigroup a => NonEmpty a -> a #

Reduce a non-empty list with <>

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

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.

newtype First a :: * -> * #

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

Constructors

First 

Fields

Instances

Monad First 

Methods

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

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

return :: a -> First a #

fail :: String -> First a #

Functor First 

Methods

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

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

MonadFix First 

Methods

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

Applicative First 

Methods

pure :: a -> First a #

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

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

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

Foldable First 

Methods

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

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

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

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

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

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

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

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

toList :: First a -> [a] #

null :: First a -> Bool #

length :: First a -> Int #

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

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

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

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

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

Traversable First 

Methods

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

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

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

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

Generic1 First 

Associated Types

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

Methods

from1 :: First a -> Rep1 First a #

to1 :: Rep1 First a -> First a #

Bounded a => Bounded (First a) 

Methods

minBound :: First a #

maxBound :: First a #

Enum a => Enum (First a) 

Methods

succ :: First a -> First a #

pred :: First a -> First a #

toEnum :: Int -> First a #

fromEnum :: First a -> Int #

enumFrom :: First a -> [First a] #

enumFromThen :: First a -> First a -> [First a] #

enumFromTo :: First a -> First a -> [First a] #

enumFromThenTo :: First a -> First a -> First a -> [First a] #

Eq a => Eq (First a) 

Methods

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

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

Data a => Data (First a) 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a) #

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

toConstr :: First a -> Constr #

dataTypeOf :: First a -> DataType #

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (First a) 

Methods

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

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

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

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

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

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

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

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

Methods

showsPrec :: Int -> First a -> ShowS #

show :: First a -> String #

showList :: [First a] -> ShowS #

Generic (First a) 

Associated Types

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

Methods

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

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

Semigroup (First a) 

Methods

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

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

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

type Rep1 First 
type Rep1 First = D1 (MetaData "First" "Data.Semigroup" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep (First a) 
type Rep (First a) = D1 (MetaData "First" "Data.Semigroup" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

newtype Last a :: * -> * #

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

Constructors

Last 

Fields

Instances

Monad Last 

Methods

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

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

return :: a -> Last a #

fail :: String -> Last a #

Functor Last 

Methods

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

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

MonadFix Last 

Methods

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

Applicative Last 

Methods

pure :: a -> Last a #

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

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

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

Foldable Last 

Methods

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

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

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

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

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

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

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

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

toList :: Last a -> [a] #

null :: Last a -> Bool #

length :: Last a -> Int #

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

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

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

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

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

Traversable Last 

Methods

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

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

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

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

Generic1 Last 

Associated Types

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

Methods

from1 :: Last a -> Rep1 Last a #

to1 :: Rep1 Last a -> Last a #

Bounded a => Bounded (Last a) 

Methods

minBound :: Last a #

maxBound :: Last a #

Enum a => Enum (Last a) 

Methods

succ :: Last a -> Last a #

pred :: Last a -> Last a #

toEnum :: Int -> Last a #

fromEnum :: Last a -> Int #

enumFrom :: Last a -> [Last a] #

enumFromThen :: Last a -> Last a -> [Last a] #

enumFromTo :: Last a -> Last a -> [Last a] #

enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] #

Eq a => Eq (Last a) 

Methods

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

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

Data a => Data (Last a) 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a) #

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

toConstr :: Last a -> Constr #

dataTypeOf :: Last a -> DataType #

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (Last a) 

Methods

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

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

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

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

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

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

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

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

Methods

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

show :: Last a -> String #

showList :: [Last a] -> ShowS #

Generic (Last a) 

Associated Types

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

Methods

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

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

Semigroup (Last a) 

Methods

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

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

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

type Rep1 Last 
type Rep1 Last = D1 (MetaData "Last" "Data.Semigroup" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just Symbol "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep (Last a) 
type Rep (Last a) = D1 (MetaData "Last" "Data.Semigroup" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just Symbol "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

Ord wrappers

newtype Min a :: * -> * #

Constructors

Min 

Fields

Instances

Monad Min 

Methods

(>>=) :: Min a -> (a -> Min b) -> Min b #

(>>) :: Min a -> Min b -> Min b #

return :: a -> Min a #

fail :: String -> Min a #

Functor Min 

Methods

fmap :: (a -> b) -> Min a -> Min b #

(<$) :: a -> Min b -> Min a #

MonadFix Min 

Methods

mfix :: (a -> Min a) -> Min a #

Applicative Min 

Methods

pure :: a -> Min a #

(<*>) :: Min (a -> b) -> Min a -> Min b #

(*>) :: Min a -> Min b -> Min b #

(<*) :: Min a -> Min b -> Min a #

Foldable Min 

Methods

fold :: Monoid m => Min m -> m #

foldMap :: Monoid m => (a -> m) -> Min a -> m #

foldr :: (a -> b -> b) -> b -> Min a -> b #

foldr' :: (a -> b -> b) -> b -> Min a -> b #

foldl :: (b -> a -> b) -> b -> Min a -> b #

foldl' :: (b -> a -> b) -> b -> Min a -> b #

foldr1 :: (a -> a -> a) -> Min a -> a #

foldl1 :: (a -> a -> a) -> Min a -> a #

toList :: Min a -> [a] #

null :: Min a -> Bool #

length :: Min a -> Int #

elem :: Eq a => a -> Min a -> Bool #

maximum :: Ord a => Min a -> a #

minimum :: Ord a => Min a -> a #

sum :: Num a => Min a -> a #

product :: Num a => Min a -> a #

Traversable Min 

Methods

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

sequenceA :: Applicative f => Min (f a) -> f (Min a) #

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

sequence :: Monad m => Min (m a) -> m (Min a) #

Generic1 Min 

Associated Types

type Rep1 (Min :: * -> *) :: * -> * #

Methods

from1 :: Min a -> Rep1 Min a #

to1 :: Rep1 Min a -> Min a #

Bounded a => Bounded (Min a) 

Methods

minBound :: Min a #

maxBound :: Min a #

Enum a => Enum (Min a) 

Methods

succ :: Min a -> Min a #

pred :: Min a -> Min a #

toEnum :: Int -> Min a #

fromEnum :: Min a -> Int #

enumFrom :: Min a -> [Min a] #

enumFromThen :: Min a -> Min a -> [Min a] #

enumFromTo :: Min a -> Min a -> [Min a] #

enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] #

Eq a => Eq (Min a) 

Methods

(==) :: Min a -> Min a -> Bool #

(/=) :: Min a -> Min a -> Bool #

Data a => Data (Min a) 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Min a -> c (Min a) #

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

toConstr :: Min a -> Constr #

dataTypeOf :: Min a -> DataType #

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

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

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

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

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

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

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

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

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

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

Num a => Num (Min a) 

Methods

(+) :: Min a -> Min a -> Min a #

(-) :: Min a -> Min a -> Min a #

(*) :: Min a -> Min a -> Min a #

negate :: Min a -> Min a #

abs :: Min a -> Min a #

signum :: Min a -> Min a #

fromInteger :: Integer -> Min a #

Ord a => Ord (Min a) 

Methods

compare :: Min a -> Min a -> Ordering #

(<) :: Min a -> Min a -> Bool #

(<=) :: Min a -> Min a -> Bool #

(>) :: Min a -> Min a -> Bool #

(>=) :: Min a -> Min a -> Bool #

max :: Min a -> Min a -> Min a #

min :: Min a -> Min a -> Min a #

Read a => Read (Min a) 
Show a => Show (Min a) 

Methods

showsPrec :: Int -> Min a -> ShowS #

show :: Min a -> String #

showList :: [Min a] -> ShowS #

Generic (Min a) 

Associated Types

type Rep (Min a) :: * -> * #

Methods

from :: Min a -> Rep (Min a) x #

to :: Rep (Min a) x -> Min a #

Ord a => Semigroup (Min a) 

Methods

(<>) :: Min a -> Min a -> Min a #

sconcat :: NonEmpty (Min a) -> Min a #

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

(Ord a, Bounded a) => Monoid (Min a) 

Methods

mempty :: Min a #

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

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

type Rep1 Min 
type Rep1 Min = D1 (MetaData "Min" "Data.Semigroup" "base" True) (C1 (MetaCons "Min" PrefixI True) (S1 (MetaSel (Just Symbol "getMin") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep (Min a) 
type Rep (Min a) = D1 (MetaData "Min" "Data.Semigroup" "base" True) (C1 (MetaCons "Min" PrefixI True) (S1 (MetaSel (Just Symbol "getMin") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

newtype Max a :: * -> * #

Constructors

Max 

Fields

Instances

Monad Max 

Methods

(>>=) :: Max a -> (a -> Max b) -> Max b #

(>>) :: Max a -> Max b -> Max b #

return :: a -> Max a #

fail :: String -> Max a #

Functor Max 

Methods

fmap :: (a -> b) -> Max a -> Max b #

(<$) :: a -> Max b -> Max a #

MonadFix Max 

Methods

mfix :: (a -> Max a) -> Max a #

Applicative Max 

Methods

pure :: a -> Max a #

(<*>) :: Max (a -> b) -> Max a -> Max b #

(*>) :: Max a -> Max b -> Max b #

(<*) :: Max a -> Max b -> Max a #

Foldable Max 

Methods

fold :: Monoid m => Max m -> m #

foldMap :: Monoid m => (a -> m) -> Max a -> m #

foldr :: (a -> b -> b) -> b -> Max a -> b #

foldr' :: (a -> b -> b) -> b -> Max a -> b #

foldl :: (b -> a -> b) -> b -> Max a -> b #

foldl' :: (b -> a -> b) -> b -> Max a -> b #

foldr1 :: (a -> a -> a) -> Max a -> a #

foldl1 :: (a -> a -> a) -> Max a -> a #

toList :: Max a -> [a] #

null :: Max a -> Bool #

length :: Max a -> Int #

elem :: Eq a => a -> Max a -> Bool #

maximum :: Ord a => Max a -> a #

minimum :: Ord a => Max a -> a #

sum :: Num a => Max a -> a #

product :: Num a => Max a -> a #

Traversable Max 

Methods

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

sequenceA :: Applicative f => Max (f a) -> f (Max a) #

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

sequence :: Monad m => Max (m a) -> m (Max a) #

Generic1 Max 

Associated Types

type Rep1 (Max :: * -> *) :: * -> * #

Methods

from1 :: Max a -> Rep1 Max a #

to1 :: Rep1 Max a -> Max a #

Bounded a => Bounded (Max a) 

Methods

minBound :: Max a #

maxBound :: Max a #

Enum a => Enum (Max a) 

Methods

succ :: Max a -> Max a #

pred :: Max a -> Max a #

toEnum :: Int -> Max a #

fromEnum :: Max a -> Int #

enumFrom :: Max a -> [Max a] #

enumFromThen :: Max a -> Max a -> [Max a] #

enumFromTo :: Max a -> Max a -> [Max a] #

enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] #

Eq a => Eq (Max a) 

Methods

(==) :: Max a -> Max a -> Bool #

(/=) :: Max a -> Max a -> Bool #

Data a => Data (Max a) 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Max a -> c (Max a) #

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

toConstr :: Max a -> Constr #

dataTypeOf :: Max a -> DataType #

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

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

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

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

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

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

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

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

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

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

Num a => Num (Max a) 

Methods

(+) :: Max a -> Max a -> Max a #

(-) :: Max a -> Max a -> Max a #

(*) :: Max a -> Max a -> Max a #

negate :: Max a -> Max a #

abs :: Max a -> Max a #

signum :: Max a -> Max a #

fromInteger :: Integer -> Max a #

Ord a => Ord (Max a) 

Methods

compare :: Max a -> Max a -> Ordering #

(<) :: Max a -> Max a -> Bool #

(<=) :: Max a -> Max a -> Bool #

(>) :: Max a -> Max a -> Bool #

(>=) :: Max a -> Max a -> Bool #

max :: Max a -> Max a -> Max a #

min :: Max a -> Max a -> Max a #

Read a => Read (Max a) 
Show a => Show (Max a) 

Methods

showsPrec :: Int -> Max a -> ShowS #

show :: Max a -> String #

showList :: [Max a] -> ShowS #

Generic (Max a) 

Associated Types

type Rep (Max a) :: * -> * #

Methods

from :: Max a -> Rep (Max a) x #

to :: Rep (Max a) x -> Max a #

Ord a => Semigroup (Max a) 

Methods

(<>) :: Max a -> Max a -> Max a #

sconcat :: NonEmpty (Max a) -> Max a #

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

(Ord a, Bounded a) => Monoid (Max a) 

Methods

mempty :: Max a #

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

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

type Rep1 Max 
type Rep1 Max = D1 (MetaData "Max" "Data.Semigroup" "base" True) (C1 (MetaCons "Max" PrefixI True) (S1 (MetaSel (Just Symbol "getMax") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep (Max a) 
type Rep (Max a) = D1 (MetaData "Max" "Data.Semigroup" "base" True) (C1 (MetaCons "Max" PrefixI True) (S1 (MetaSel (Just Symbol "getMax") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

Backwards compatibility

newtype WrappedMonoid m :: * -> * #

Provide a Semigroup for an arbitrary Monoid.

Constructors

WrapMonoid 

Fields

Instances

Generic1 WrappedMonoid 

Associated Types

type Rep1 (WrappedMonoid :: * -> *) :: * -> * #

Bounded a => Bounded (WrappedMonoid a) 
Enum a => Enum (WrappedMonoid a) 
Eq m => Eq (WrappedMonoid m) 
Data m => Data (WrappedMonoid m) 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> WrappedMonoid m -> c (WrappedMonoid m) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonoid m) #

toConstr :: WrappedMonoid m -> Constr #

dataTypeOf :: WrappedMonoid m -> DataType #

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

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

gmapT :: (forall b. Data b => b -> b) -> WrappedMonoid m -> WrappedMonoid m #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r #

gmapQ :: (forall d. Data d => d -> u) -> WrappedMonoid m -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonoid m -> u #

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

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

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

Ord m => Ord (WrappedMonoid m) 
Read m => Read (WrappedMonoid m) 
Show m => Show (WrappedMonoid m) 
Generic (WrappedMonoid m) 

Associated Types

type Rep (WrappedMonoid m) :: * -> * #

Monoid m => Semigroup (WrappedMonoid m) 
Monoid m => Monoid (WrappedMonoid m) 
type Rep1 WrappedMonoid 
type Rep1 WrappedMonoid = D1 (MetaData "WrappedMonoid" "Data.Semigroup" "base" True) (C1 (MetaCons "WrapMonoid" PrefixI True) (S1 (MetaSel (Just Symbol "unwrapMonoid") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep (WrappedMonoid m) 
type Rep (WrappedMonoid m) = D1 (MetaData "WrappedMonoid" "Data.Semigroup" "base" True) (C1 (MetaCons "WrapMonoid" PrefixI True) (S1 (MetaSel (Just Symbol "unwrapMonoid") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 m)))