Precursor.Algebra.Semigroup

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

Methods

(<>) :: Ordering -> Ordering -> Ordering

sconcat :: NonEmpty Ordering -> Ordering

stimes :: Integral b => b -> Ordering -> Ordering

Semigroup ()

Methods

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

sconcat :: NonEmpty () -> ()

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

Semigroup Void

Methods

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

sconcat :: NonEmpty Void -> Void

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

Semigroup All

Methods

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

sconcat :: NonEmpty All -> All

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

Semigroup Any

Methods

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

sconcat :: NonEmpty Any -> Any

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

Semigroup ByteString

Methods

(<>) :: ByteString -> ByteString -> ByteString

sconcat :: NonEmpty ByteString -> ByteString

stimes :: Integral b => b -> ByteString -> ByteString

Semigroup ByteString

Methods

(<>) :: ByteString -> ByteString -> ByteString

sconcat :: NonEmpty ByteString -> ByteString

stimes :: Integral b => b -> ByteString -> ByteString

Semigroup IntSet

Methods

(<>) :: IntSet -> IntSet -> IntSet

sconcat :: NonEmpty IntSet -> IntSet

stimes :: Integral b => b -> IntSet -> IntSet

Semigroup Doc

Methods

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

sconcat :: NonEmpty Doc -> Doc

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

Semigroup Builder

Methods

(<>) :: Builder -> Builder -> Builder

sconcat :: NonEmpty Builder -> Builder

stimes :: Integral b => b -> Builder -> 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)

Methods

(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m

stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m

Semigroup a => Semigroup (Option a)

Methods

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

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

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

Semigroup (NonEmpty a)

Methods

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

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

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

Semigroup a => Semigroup (Dual a)

Methods

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

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

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

Semigroup (Endo a)

Methods

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

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

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

Num a => Semigroup (Sum a)

Methods

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

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

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

Num a => Semigroup (Product a)

Methods

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

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

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

Semigroup (First a)

Methods

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

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

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

Semigroup (Last a)

Methods

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

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

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

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

• getFirst :: a

Instances

Monad First

Methods

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

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

return :: a -> First a

fail :: String -> First a

Functor First

Methods

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

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

MonadFix First

Methods

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

Applicative First

Methods

pure :: a -> First a

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

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

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

Foldable First

Methods

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

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

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

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

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

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

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

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

toList :: First a -> [a]

null :: First a -> Bool

length :: First a -> Int

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

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

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

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

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

Traversable First

Methods

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

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

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

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

Generic1 First

Associated Types

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

Methods

from1 :: First a -> Rep1 First a

to1 :: Rep1 First a -> First a

Bounded a => Bounded (First a)

Methods

minBound :: First a

maxBound :: First a

Enum a => Enum (First a)

Methods

succ :: First a -> First a

pred :: First a -> First a

toEnum :: Int -> First a

fromEnum :: First a -> Int

enumFrom :: First a -> [First a]

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

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

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

Eq a => Eq (First a)

Methods

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

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

Data a => Data (First a)

Methods

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

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

toConstr :: First a -> Constr

dataTypeOf :: First a -> DataType

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (First a)

Methods

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

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

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

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

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

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

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

Read a => Read (First a)

Methods

readsPrec :: Int -> ReadS (First a)

readList :: ReadS [First a]

readPrec :: ReadPrec (First a)

readListPrec :: ReadPrec [First a]

Show a => Show (First a)

Methods

showsPrec :: Int -> First a -> ShowS

show :: First a -> String

showList :: [First a] -> ShowS

Generic (First a)

Associated Types

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

Methods

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

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

Semigroup (First a)

Methods

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

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

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

type Rep1 First

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

type Rep (First a)

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

newtype Last a :: * -> *

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

Constructors

Last

Fields

• getLast :: a

Instances

Monad Last

Methods

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

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

return :: a -> Last a

fail :: String -> Last a

Functor Last

Methods

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

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

MonadFix Last

Methods

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

Applicative Last

Methods

pure :: a -> Last a

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

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

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

Foldable Last

Methods

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

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

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

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

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

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

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

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

toList :: Last a -> [a]

null :: Last a -> Bool

length :: Last a -> Int

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

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

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

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

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

Traversable Last

Methods

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

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

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

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

Generic1 Last

Associated Types

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

Methods

from1 :: Last a -> Rep1 Last a

to1 :: Rep1 Last a -> Last a

Bounded a => Bounded (Last a)

Methods

minBound :: Last a

maxBound :: Last a

Enum a => Enum (Last a)

Methods

succ :: Last a -> Last a

pred :: Last a -> Last a

toEnum :: Int -> Last a

fromEnum :: Last a -> Int

enumFrom :: Last a -> [Last a]

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

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

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

Eq a => Eq (Last a)

Methods

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

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

Data a => Data (Last a)

Methods

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

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

toConstr :: Last a -> Constr

dataTypeOf :: Last a -> DataType

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (Last a)

Methods

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

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

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

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

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

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

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

Read a => Read (Last a)

Methods

readsPrec :: Int -> ReadS (Last a)

readList :: ReadS [Last a]

readPrec :: ReadPrec (Last a)

readListPrec :: ReadPrec [Last a]

Show a => Show (Last a)

Methods

showsPrec :: Int -> Last a -> ShowS

show :: Last a -> String

showList :: [Last a] -> ShowS

Generic (Last a)

Associated Types

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

Methods

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

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

Semigroup (Last a)

Methods

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

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

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

type Rep1 Last

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

type Rep (Last a)

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

Ord wrappers

newtype Min a :: * -> *

Constructors

Min

Fields

• getMin :: a

Instances

Monad Min

Methods

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

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

return :: a -> Min a

fail :: String -> Min a

Functor Min

Methods

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

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

MonadFix Min

Methods

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

Applicative Min

Methods

pure :: a -> Min a

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

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

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

Foldable Min

Methods

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

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

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

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

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

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

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

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

toList :: Min a -> [a]

null :: Min a -> Bool

length :: Min a -> Int

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

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

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

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

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

Traversable Min

Methods

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

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

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

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

Generic1 Min

Associated Types

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

Methods

from1 :: Min a -> Rep1 Min a

to1 :: Rep1 Min a -> Min a

Bounded a => Bounded (Min a)

Methods

minBound :: Min a

maxBound :: Min a

Enum a => Enum (Min a)

Methods

succ :: Min a -> Min a

pred :: Min a -> Min a

toEnum :: Int -> Min a

fromEnum :: Min a -> Int

enumFrom :: Min a -> [Min a]

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

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

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

Eq a => Eq (Min a)

Methods

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

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

Data a => Data (Min a)

Methods

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

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

toConstr :: Min a -> Constr

dataTypeOf :: Min a -> DataType

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

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

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

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

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

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

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

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

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

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

Num a => Num (Min a)

Methods

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

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

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

negate :: Min a -> Min a

abs :: Min a -> Min a

signum :: Min a -> Min a

fromInteger :: Integer -> Min a

Ord a => Ord (Min a)

Methods

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

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

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

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

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

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

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

Read a => Read (Min a)

Methods

readsPrec :: Int -> ReadS (Min a)

readList :: ReadS [Min a]

readPrec :: ReadPrec (Min a)

readListPrec :: ReadPrec [Min a]

Show a => Show (Min a)

Methods

showsPrec :: Int -> Min a -> ShowS

show :: Min a -> String

showList :: [Min a] -> ShowS

Generic (Min a)

Associated Types

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

Methods

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

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

Ord a => Semigroup (Min a)

Methods

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

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

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

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

Methods

mempty :: Min a

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

mconcat :: [Min a] -> Min a

type Rep1 Min

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

type Rep (Min a)

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

newtype Max a :: * -> *

Constructors

Max

Fields

• getMax :: a

Instances

Monad Max

Methods

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

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

return :: a -> Max a

fail :: String -> Max a

Functor Max

Methods

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

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

MonadFix Max

Methods

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

Applicative Max

Methods

pure :: a -> Max a

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

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

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

Foldable Max

Methods

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

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

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

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

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

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

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

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

toList :: Max a -> [a]

null :: Max a -> Bool

length :: Max a -> Int

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

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

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

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

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

Traversable Max

Methods

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

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

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

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

Generic1 Max

Associated Types

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

Methods

from1 :: Max a -> Rep1 Max a

to1 :: Rep1 Max a -> Max a

Bounded a => Bounded (Max a)

Methods

minBound :: Max a

maxBound :: Max a

Enum a => Enum (Max a)

Methods

succ :: Max a -> Max a

pred :: Max a -> Max a

toEnum :: Int -> Max a

fromEnum :: Max a -> Int

enumFrom :: Max a -> [Max a]

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

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

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

Eq a => Eq (Max a)

Methods

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

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

Data a => Data (Max a)

Methods

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

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

toConstr :: Max a -> Constr

dataTypeOf :: Max a -> DataType

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

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

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

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

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

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

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

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

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

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

Num a => Num (Max a)

Methods

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

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

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

negate :: Max a -> Max a

abs :: Max a -> Max a

signum :: Max a -> Max a

fromInteger :: Integer -> Max a

Ord a => Ord (Max a)

Methods

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

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

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

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

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

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

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

Read a => Read (Max a)

Methods

readsPrec :: Int -> ReadS (Max a)

readList :: ReadS [Max a]

readPrec :: ReadPrec (Max a)

readListPrec :: ReadPrec [Max a]

Show a => Show (Max a)

Methods

showsPrec :: Int -> Max a -> ShowS

show :: Max a -> String

showList :: [Max a] -> ShowS

Generic (Max a)

Associated Types

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

Methods

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

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

Ord a => Semigroup (Max a)

Methods

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

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

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

(Ord a, Bounded a) => Monoid (Max a)

Methods

mempty :: Max a

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

mconcat :: [Max a] -> Max a

type Rep1 Max

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

type Rep (Max a)

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

Backwards compatibility

newtype WrappedMonoid m :: * -> *

Provide a Semigroup for an arbitrary Monoid.

Constructors

WrapMonoid

Fields

• unwrapMonoid :: m

Instances

Generic1 WrappedMonoid

Associated Types

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

Methods

from1 :: WrappedMonoid a -> Rep1 WrappedMonoid a

to1 :: Rep1 WrappedMonoid a -> WrappedMonoid a

Bounded a => Bounded (WrappedMonoid a)

Methods

minBound :: WrappedMonoid a

maxBound :: WrappedMonoid a

Enum a => Enum (WrappedMonoid a)

Methods

succ :: WrappedMonoid a -> WrappedMonoid a

pred :: WrappedMonoid a -> WrappedMonoid a

toEnum :: Int -> WrappedMonoid a

fromEnum :: WrappedMonoid a -> Int

enumFrom :: WrappedMonoid a -> [WrappedMonoid a]

enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a]

enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a]

enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a]

Eq m => Eq (WrappedMonoid m)

Methods

(==) :: WrappedMonoid m -> WrappedMonoid m -> Bool

(/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool

Data m => Data (WrappedMonoid m)

Methods

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

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

toConstr :: WrappedMonoid m -> Constr

dataTypeOf :: WrappedMonoid m -> DataType

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

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

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

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

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

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

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

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

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

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

Ord m => Ord (WrappedMonoid m)

Methods

compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering

(<) :: WrappedMonoid m -> WrappedMonoid m -> Bool

(<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool

(>) :: WrappedMonoid m -> WrappedMonoid m -> Bool

(>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool

max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

Read m => Read (WrappedMonoid m)

Methods

readsPrec :: Int -> ReadS (WrappedMonoid m)

readList :: ReadS [WrappedMonoid m]

readPrec :: ReadPrec (WrappedMonoid m)

readListPrec :: ReadPrec [WrappedMonoid m]

Show m => Show (WrappedMonoid m)

Methods

showsPrec :: Int -> WrappedMonoid m -> ShowS

show :: WrappedMonoid m -> String

showList :: [WrappedMonoid m] -> ShowS

Generic (WrappedMonoid m)

Associated Types

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

Methods

from :: WrappedMonoid m -> Rep (WrappedMonoid m) x

to :: Rep (WrappedMonoid m) x -> WrappedMonoid m

Monoid m => Semigroup (WrappedMonoid m)

Methods

(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m

stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m

Monoid m => Monoid (WrappedMonoid m)

Methods

mempty :: WrappedMonoid m

mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

mconcat :: [WrappedMonoid m] -> WrappedMonoid m

type Rep1 WrappedMonoid

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

type Rep (WrappedMonoid m)

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