Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Semigroup.Compat

Contents

Semigroups
Re-exported monoids from Data.Monoid
Difference lists of a semigroup
ArgMin, ArgMax

Description

This backports the modern Data.Semigroup interface back to base-4.9/GHC 8.0.

Synopsis

class Semigroup a where
- (<>) :: a -> a -> a
- sconcat :: NonEmpty a -> a
- stimes :: Integral b => b -> a -> a
stimesMonoid :: (Integral b, Monoid a) => b -> a -> a
stimesIdempotent :: Integral b => b -> a -> a
stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a
mtimesDefault :: (Integral b, Monoid a) => b -> a -> a
newtype Min a = Min {
- getMin :: a
}
newtype Max a = Max {
- getMax :: a
}
newtype First a = First {
- getFirst :: a
}
newtype Last a = Last {
- getLast :: a
}
newtype WrappedMonoid m = WrapMonoid {
- unwrapMonoid :: m
}
newtype Dual a = Dual {
- getDual :: a
}
newtype Endo a = Endo {
- appEndo :: a -> a
}
newtype All = All {
- getAll :: Bool
}
newtype Any = Any {
- getAny :: Bool
}
newtype Sum a = Sum {
- getSum :: a
}
newtype Product a = Product {
- getProduct :: a
}
diff :: Semigroup m => m -> Endo m
cycle1 :: Semigroup m => m -> m
data Arg a b = Arg a b
type ArgMin a b = Min (Arg a b)
type ArgMax a b = Max (Arg a b)

Documentation

class Semigroup a where #

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

Instances should satisfy the following:

Associativity: x <> (y <> z) = (x <> y) <> z

You can alternatively define sconcat instead of (<>), in which case the laws are:

Unit: sconcat (pure x) = x
Multiplication: sconcat (join xss) = sconcat (fmap sconcat xss)

Since: base-4.9.0.0

Minimal complete definition

(<>) | sconcat

Methods

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

An associative operation.

Examples

Expand

>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]

>>> Just [1, 2, 3] <> Just [4, 5, 6]
Just [1,2,3,4,5,6]

>>> putStr "Hello, " <> putStrLn "World!"
Hello, World!

sconcat :: NonEmpty a -> a #

Reduce a non-empty list with <>

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

Examples

Expand

For the following examples, we will assume that we have:

>>> import Data.List.NonEmpty (NonEmpty (..))

>>> sconcat $ "Hello" :| [" ", "Haskell", "!"]
"Hello Haskell!"

>>> sconcat $ Just [1, 2, 3] :| [Nothing, Just [4, 5, 6]]
Just [1,2,3,4,5,6]

>>> sconcat $ Left 1 :| [Right 2, Left 3, Right 4]
Right 2

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

Repeat a value n times.

The default definition will raise an exception for a multiplier that is <= 0. This may be overridden with an implementation that is total. For monoids it is preferred to use stimesMonoid.

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

Examples

Expand

>>> stimes 4 [1]
[1,1,1,1]

>>> stimes 5 (putStr "hi!")
hi!hi!hi!hi!hi!

>>> stimes 3 (Right ":)")
Right ":)"

Instances

Instances details

Semigroup ByteArray #	Since: base-4.17.0.0
Instance details Defined in Data.Array.Byte Methods (<>) :: ByteArray -> ByteArray -> ByteArray # sconcat :: NonEmpty ByteArray -> ByteArray # stimes :: Integral b => b -> ByteArray -> ByteArray #
Semigroup Void #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods (<>) :: Void -> Void -> Void # sconcat :: NonEmpty Void -> Void # stimes :: Integral b => b -> Void -> Void #
Semigroup All #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (<>) :: All -> All -> All # sconcat :: NonEmpty All -> All # stimes :: Integral b => b -> All -> All #
Semigroup Any #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any # sconcat :: NonEmpty Any -> Any # stimes :: Integral b => b -> Any -> Any #
Semigroup Ordering #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods (<>) :: Ordering -> Ordering -> Ordering # sconcat :: NonEmpty Ordering -> Ordering # stimes :: Integral b => b -> Ordering -> Ordering #
Semigroup () #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods (<>) :: () -> () -> () # sconcat :: NonEmpty () -> () # stimes :: Integral b => b -> () -> () #
Semigroup (FromMaybe b) #
Instance details Defined in Data.Foldable1 Methods (<>) :: FromMaybe b -> FromMaybe b -> FromMaybe b # sconcat :: NonEmpty (FromMaybe b) -> FromMaybe b # stimes :: Integral b0 => b0 -> FromMaybe b -> FromMaybe b #
Semigroup a => Semigroup (JoinWith a) #
Instance details Defined in Data.Foldable1 Methods (<>) :: JoinWith a -> JoinWith a -> JoinWith a # sconcat :: NonEmpty (JoinWith a) -> JoinWith a # stimes :: Integral b => b -> JoinWith a -> JoinWith a #
Semigroup (NonEmptyDList a) #
Instance details Defined in Data.Foldable1 Methods (<>) :: NonEmptyDList a -> NonEmptyDList a -> NonEmptyDList a # sconcat :: NonEmpty (NonEmptyDList a) -> NonEmptyDList a # stimes :: Integral b => b -> NonEmptyDList a -> NonEmptyDList a #
Semigroup (Comparison a) #	`(<>)` on comparisons combines results with `(<>) @Ordering`. Without newtypes this equals `liftA2 (liftA2 (<>))`. (<>) :: Comparison a -> Comparison a -> Comparison a Comparison cmp <> Comparison cmp' = Comparison a a' -> cmp a a' <> cmp a a'
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Comparison a -> Comparison a -> Comparison a # sconcat :: NonEmpty (Comparison a) -> Comparison a # stimes :: Integral b => b -> Comparison a -> Comparison a #
Semigroup (Equivalence a) #	`(<>)` on equivalences uses logical conjunction `(&&)` on the results. Without newtypes this equals `liftA2 (liftA2 (&&))`. (<>) :: Equivalence a -> Equivalence a -> Equivalence a Equivalence equiv <> Equivalence equiv' = Equivalence a b -> equiv a b && equiv' a b
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Equivalence a -> Equivalence a -> Equivalence a # sconcat :: NonEmpty (Equivalence a) -> Equivalence a # stimes :: Integral b => b -> Equivalence a -> Equivalence a #
Semigroup (Predicate a) #	`(<>)` on predicates uses logical conjunction `(&&)` on the results. Without newtypes this equals `liftA2 (&&)`. (<>) :: Predicate a -> Predicate a -> Predicate a Predicate pred <> Predicate pred' = Predicate a -> pred a && pred' a
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Predicate a -> Predicate a -> Predicate a # sconcat :: NonEmpty (Predicate a) -> Predicate a # stimes :: Integral b => b -> Predicate a -> Predicate a #
Semigroup (First a) #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
Semigroup (Last a) #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
Ord a => Semigroup (Max a) #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Max a -> Max a -> Max a # sconcat :: NonEmpty (Max a) -> Max a # stimes :: Integral b => b -> Max a -> Max a #
Ord a => Semigroup (Min a) #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Min a -> Min a -> Min a # sconcat :: NonEmpty (Min a) -> Min a # stimes :: Integral b => b -> Min a -> Min a #
Monoid m => Semigroup (WrappedMonoid m) #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m #
Semigroup (NonEmpty a) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a # sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a # stimes :: Integral b => b -> NonEmpty a -> NonEmpty a #
Semigroup a => Semigroup (STM a) #	Since: base-4.17.0.0
Instance details Defined in GHC.Internal.Conc.Sync Methods (<>) :: STM a -> STM a -> STM a # sconcat :: NonEmpty (STM a) -> STM a # stimes :: Integral b => b -> STM a -> STM a #
Bits a => Semigroup (And a) #	Since: base-4.16
Instance details Defined in GHC.Internal.Data.Bits Methods (<>) :: And a -> And a -> And a # sconcat :: NonEmpty (And a) -> And a # stimes :: Integral b => b -> And a -> And a #
FiniteBits a => Semigroup (Iff a) #	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in GHC.Internal.Data.Bits Methods (<>) :: Iff a -> Iff a -> Iff a # sconcat :: NonEmpty (Iff a) -> Iff a # stimes :: Integral b => b -> Iff a -> Iff a #
Bits a => Semigroup (Ior a) #	Since: base-4.16
Instance details Defined in GHC.Internal.Data.Bits Methods (<>) :: Ior a -> Ior a -> Ior a # sconcat :: NonEmpty (Ior a) -> Ior a # stimes :: Integral b => b -> Ior a -> Ior a #
Bits a => Semigroup (Xor a) #	Since: base-4.16
Instance details Defined in GHC.Internal.Data.Bits Methods (<>) :: Xor a -> Xor a -> Xor a # sconcat :: NonEmpty (Xor a) -> Xor a # stimes :: Integral b => b -> Xor a -> Xor a #
Semigroup a => Semigroup (Identity a) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Identity Methods (<>) :: Identity a -> Identity a -> Identity a # sconcat :: NonEmpty (Identity a) -> Identity a # stimes :: Integral b => b -> Identity a -> Identity a #
Semigroup (First a) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Monoid Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
Semigroup (Last a) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Monoid Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
Semigroup a => Semigroup (Dual a) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a # sconcat :: NonEmpty (Dual a) -> Dual a # stimes :: Integral b => b -> Dual a -> Dual a #
Semigroup (Endo a) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a # sconcat :: NonEmpty (Endo a) -> Endo a # stimes :: Integral b => b -> Endo a -> Endo a #
Num a => Semigroup (Product a) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (<>) :: Product a -> Product a -> Product a # sconcat :: NonEmpty (Product a) -> Product a # stimes :: Integral b => b -> Product a -> Product a #
Num a => Semigroup (Sum a) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (<>) :: Sum a -> Sum a -> Sum a # sconcat :: NonEmpty (Sum a) -> Sum a # stimes :: Integral b => b -> Sum a -> Sum a #
Semigroup a => Semigroup (IO a) #	Since: base-4.10.0.0
Instance details Defined in GHC.Internal.Base Methods (<>) :: IO a -> IO a -> IO a # sconcat :: NonEmpty (IO a) -> IO a # stimes :: Integral b => b -> IO a -> IO a #
Semigroup a => Semigroup (Maybe a) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods (<>) :: Maybe a -> Maybe a -> Maybe a # sconcat :: NonEmpty (Maybe a) -> Maybe a # stimes :: Integral b => b -> Maybe a -> Maybe a #
Semigroup a => Semigroup (Solo a) #	Since: base-4.15
Instance details Defined in GHC.Internal.Base Methods (<>) :: Solo a -> Solo a -> Solo a # sconcat :: NonEmpty (Solo a) -> Solo a # stimes :: Integral b => b -> Solo a -> Solo a #
Semigroup [a] #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods (<>) :: [a] -> [a] -> [a] # sconcat :: NonEmpty [a] -> [a] # stimes :: Integral b => b -> [a] -> [a] #
Semigroup a => Semigroup (Op a b) #	`(<>) @(Op a b)` without newtypes is `(<>) @(b->a)` = `liftA2 (<>)`. This lifts the `Semigroup` operation `(<>)` over the output of `a`. (<>) :: Op a b -> Op a b -> Op a b Op f <> Op g = Op a -> f a <> g a
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Op a b -> Op a b -> Op a b # sconcat :: NonEmpty (Op a b) -> Op a b # stimes :: Integral b0 => b0 -> Op a b -> Op a b #
Semigroup (Either a b) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Either Methods (<>) :: Either a b -> Either a b -> Either a b # sconcat :: NonEmpty (Either a b) -> Either a b # stimes :: Integral b0 => b0 -> Either a b -> Either a b #
Semigroup (Proxy s) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods (<>) :: Proxy s -> Proxy s -> Proxy s # sconcat :: NonEmpty (Proxy s) -> Proxy s # stimes :: Integral b => b -> Proxy s -> Proxy s #
Semigroup a => Semigroup (ST s a) #	Since: base-4.11.0.0
Instance details Defined in GHC.Internal.ST Methods (<>) :: ST s a -> ST s a -> ST s a # sconcat :: NonEmpty (ST s a) -> ST s a # stimes :: Integral b => b -> ST s a -> ST s a #
(Semigroup a, Semigroup b) => Semigroup (a, b) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods (<>) :: (a, b) -> (a, b) -> (a, b) # sconcat :: NonEmpty (a, b) -> (a, b) # stimes :: Integral b0 => b0 -> (a, b) -> (a, b) #
Semigroup b => Semigroup (a -> b) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods (<>) :: (a -> b) -> (a -> b) -> a -> b # sconcat :: NonEmpty (a -> b) -> a -> b # stimes :: Integral b0 => b0 -> (a -> b) -> a -> b #
Semigroup a => Semigroup (Const a b) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Const Methods (<>) :: Const a b -> Const a b -> Const a b # sconcat :: NonEmpty (Const a b) -> Const a b # stimes :: Integral b0 => b0 -> Const a b -> Const a b #
(Applicative f, Semigroup a) => Semigroup (Ap f a) #	Since: base-4.12.0.0
Instance details Defined in GHC.Internal.Data.Monoid Methods (<>) :: Ap f a -> Ap f a -> Ap f a # sconcat :: NonEmpty (Ap f a) -> Ap f a # stimes :: Integral b => b -> Ap f a -> Ap f a #
Alternative f => Semigroup (Alt f a) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (<>) :: Alt f a -> Alt f a -> Alt f a # sconcat :: NonEmpty (Alt f a) -> Alt f a # stimes :: Integral b => b -> Alt f a -> Alt f a #
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods (<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) # sconcat :: NonEmpty (a, b, c) -> (a, b, c) # stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) #
(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) #	Since: base-4.16.0.0
Instance details Defined in Data.Functor.Product Methods (<>) :: Product f g a -> Product f g a -> Product f g a # sconcat :: NonEmpty (Product f g a) -> Product f g a # stimes :: Integral b => b -> Product f g a -> Product f g a #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Base 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 b0 => b0 -> (a, b, c, d) -> (a, b, c, d) #
Semigroup (f (g a)) => Semigroup (Compose f g a) #	Since: base-4.16.0.0
Instance details Defined in Data.Functor.Compose Methods (<>) :: Compose f g a -> Compose f g a -> Compose f g a # sconcat :: NonEmpty (Compose f g a) -> Compose f g a # stimes :: Integral b => b -> Compose f g a -> Compose f g a #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) #	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Base 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 b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) #

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

This is a valid definition of stimes for a Monoid.

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

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

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

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

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

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

When x <> x = x, this definition should be preferred, because it works in $\mathcal{O}(1)$ rather than $\mathcal{O}(\log n)$

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

Repeat a value n times.

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

In many cases, stimes 0 a for a Monoid will produce mempty. However, there are situations when it cannot do so. In particular, the following situation is fairly common:

data T a = ...

class Constraint1 a
class Constraint1 a => Constraint2 a

instance Constraint1 a => Semigroup (T a)
instance Constraint2 a => Monoid (T a)

Since Constraint1 is insufficient to implement mempty, stimes for T a cannot do so.

When working with such a type, or when working polymorphically with Semigroup instances, mtimesDefault should be used when the multiplier might be zero. It is implemented using stimes when the multiplier is nonzero and mempty when it is zero.

Examples

Expand

>>> mtimesDefault 0 "bark"
""

>>> mtimesDefault 3 "meow"
"meowmeowmeow"

Semigroups

newtype Min a #

The Min Monoid and Semigroup always choose the smaller element as by the Ord instance and min of the contained type.

Examples

Expand

>>> Min 42 <> Min 3
Min {getMin = 3}

>>> sconcat $ Min 1 :| [ Min n | n <- [2 .. 100]]
Min {getMin = 1}

Constructors

Min
Fields getMin :: a

Instances

Instances details

Foldable1 Min #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Min m -> m #

foldMap1 :: Semigroup m => (a -> m) -> Min a -> m #

foldMap1' :: Semigroup m => (a -> m) -> Min a -> m #

toNonEmpty :: Min a -> NonEmpty a #

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

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

head :: Min a -> a #

last :: Min a -> a #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Min a -> b #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Min a -> b #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Min a -> b #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Min a -> b #

Applicative Min #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Min a #

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

liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c #

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

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

Functor Min #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Monad Min #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> Min a #

MonadFix Min #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

Foldable Min #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 #

Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 Min = D1 ('MetaData "Min" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "Min" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMin") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Min a -> Rep1 Min a #

to1 :: Rep1 Min a -> Min a #

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Min a #

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

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

Ord a => Semigroup (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Data a => Data (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 :: forall r r'. (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) #

Bounded a => Bounded (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: Min a #

maxBound :: Min a #

Enum a => Enum (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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] #

Generic (Min a) #

Instance details

Defined in Data.Semigroup

Associated Types

type Rep (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (Min a) = D1 ('MetaData "Min" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "Min" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMin") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

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

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

Num a => Num (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 #

Read a => Read (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (Min a) #

readList :: ReadS [Min a] #

readPrec :: ReadPrec (Min a) #

readListPrec :: ReadPrec [Min a] #

Show a => Show (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

show :: Min a -> String #

showList :: [Min a] -> ShowS #

Eq a => Eq (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Ord a => Ord (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 #

type Rep1 Min #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep1 Min = D1 ('MetaData "Min" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "Min" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMin") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (Min a) = D1 ('MetaData "Min" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "Min" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMin") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Max a #

The Max Monoid and Semigroup always choose the bigger element as by the Ord instance and max of the contained type.

Examples

Expand

>>> Max 42 <> Max 3
Max {getMax = 42}

>>> sconcat $ Max 1 :| [ Max n | n <- [2 .. 100]]
Max {getMax = 100}

Constructors

Max
Fields getMax :: a

Instances

Instances details

Foldable1 Max #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Max m -> m #

foldMap1 :: Semigroup m => (a -> m) -> Max a -> m #

foldMap1' :: Semigroup m => (a -> m) -> Max a -> m #

toNonEmpty :: Max a -> NonEmpty a #

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

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

head :: Max a -> a #

last :: Max a -> a #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Max a -> b #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Max a -> b #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Max a -> b #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Max a -> b #

Applicative Max #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Max a #

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

liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c #

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

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

Functor Max #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Monad Max #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> Max a #

MonadFix Max #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

Foldable Max #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 #

Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 Max = D1 ('MetaData "Max" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "Max" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMax") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Max a -> Rep1 Max a #

to1 :: Rep1 Max a -> Max a #

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Max a #

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

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

Ord a => Semigroup (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Data a => Data (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 :: forall r r'. (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) #

Bounded a => Bounded (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: Max a #

maxBound :: Max a #

Enum a => Enum (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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] #

Generic (Max a) #

Instance details

Defined in Data.Semigroup

Associated Types

type Rep (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (Max a) = D1 ('MetaData "Max" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "Max" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMax") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

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

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

Num a => Num (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 #

Read a => Read (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (Max a) #

readList :: ReadS [Max a] #

readPrec :: ReadPrec (Max a) #

readListPrec :: ReadPrec [Max a] #

Show a => Show (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

show :: Max a -> String #

showList :: [Max a] -> ShowS #

Eq a => Eq (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Ord a => Ord (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 #

type Rep1 Max #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep1 Max = D1 ('MetaData "Max" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "Max" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMax") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (Max a) = D1 ('MetaData "Max" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "Max" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMax") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype First a #

Beware that Data.Semigroup.First is different from Data.Monoid.First. The former simply returns the first value, so Data.Semigroup.First Nothing <> x = Data.Semigroup.First Nothing. The latter returns the first non-Nothing, thus Data.Monoid.First Nothing <> x = x.

Examples

Expand

>>> First 0 <> First 10
First {getFirst = 0}

>>> sconcat $ First 1 :| [ First n | n <- [2 ..] ]
First {getFirst = 1}

Constructors

First
Fields getFirst :: a

Instances

Instances details

Foldable1 First #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => First m -> m #

foldMap1 :: Semigroup m => (a -> m) -> First a -> m #

foldMap1' :: Semigroup m => (a -> m) -> First a -> m #

toNonEmpty :: First a -> NonEmpty a #

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

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

head :: First a -> a #

last :: First a -> a #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> First a -> b #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> First a -> b #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> First a -> b #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> First a -> b #

Applicative First #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> First a #

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

liftA2 :: (a -> b -> c) -> First a -> First b -> First c #

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

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

Functor First #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Monad First #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> First a #

MonadFix First #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

Foldable First #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 #

Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 First = D1 ('MetaData "First" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: First a -> Rep1 First a #

to1 :: Rep1 First a -> First a #

Semigroup (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Data a => Data (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 :: forall r r'. (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) #

Bounded a => Bounded (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: First a #

maxBound :: First a #

Enum a => Enum (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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] #

Generic (First a) #

Instance details

Defined in Data.Semigroup

Associated Types

type Rep (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (First a) = D1 ('MetaData "First" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

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

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

Read a => Read (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (First a) #

readList :: ReadS [First a] #

readPrec :: ReadPrec (First a) #

readListPrec :: ReadPrec [First a] #

Show a => Show (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

show :: First a -> String #

showList :: [First a] -> ShowS #

Eq a => Eq (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Ord a => Ord (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 #

type Rep1 First #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep1 First = D1 ('MetaData "First" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (First a) = D1 ('MetaData "First" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Last a #

Beware that Data.Semigroup.Last is different from Data.Monoid.Last. The former simply returns the last value, so x <> Data.Semigroup.Last Nothing = Data.Semigroup.Last Nothing. The latter returns the last non-Nothing, thus x <> Data.Monoid.Last Nothing = x.

Examples

Expand

>>> Last 0 <> Last 10
Last {getLast = 10}

>>> sconcat $ Last 1 :| [ Last n | n <- [2..]]
* Hangs forever *

Constructors

Last
Fields getLast :: a

Instances

Instances details

Foldable1 Last #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Last m -> m #

foldMap1 :: Semigroup m => (a -> m) -> Last a -> m #

foldMap1' :: Semigroup m => (a -> m) -> Last a -> m #

toNonEmpty :: Last a -> NonEmpty a #

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

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

head :: Last a -> a #

last :: Last a -> a #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Last a -> b #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Last a -> b #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Last a -> b #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Last a -> b #

Applicative Last #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Last a #

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

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c #

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

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

Functor Last #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Monad Last #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> Last a #

MonadFix Last #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

Foldable Last #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 #

Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 Last = D1 ('MetaData "Last" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Last a -> Rep1 Last a #

to1 :: Rep1 Last a -> Last a #

Semigroup (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Data a => Data (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 :: forall r r'. (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) #

Bounded a => Bounded (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: Last a #

maxBound :: Last a #

Enum a => Enum (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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] #

Generic (Last a) #

Instance details

Defined in Data.Semigroup

Associated Types

type Rep (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (Last a) = D1 ('MetaData "Last" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

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

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

Read a => Read (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (Last a) #

readList :: ReadS [Last a] #

readPrec :: ReadPrec (Last a) #

readListPrec :: ReadPrec [Last a] #

Show a => Show (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

show :: Last a -> String #

showList :: [Last a] -> ShowS #

Eq a => Eq (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Ord a => Ord (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 #

type Rep1 Last #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep1 Last = D1 ('MetaData "Last" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (Last a) = D1 ('MetaData "Last" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype WrappedMonoid m #

Provide a Semigroup for an arbitrary Monoid.

NOTE: This is not needed anymore since Semigroup became a superclass of Monoid in base-4.11 and this newtype be deprecated at some point in the future.

Constructors

WrapMonoid
Fields unwrapMonoid :: m

Instances

Instances details

Generic1 WrappedMonoid #

Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 WrappedMonoid	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 WrappedMonoid = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: WrappedMonoid a -> Rep1 WrappedMonoid a #

to1 :: Rep1 WrappedMonoid a -> WrappedMonoid a #

Monoid m => Monoid (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: WrappedMonoid m #

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

mconcat :: [WrappedMonoid m] -> WrappedMonoid m #

Monoid m => Semigroup (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Data m => Data (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 :: forall r r'. (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 m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) #

gmapMp :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) #

gmapMo :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) #

Bounded m => Bounded (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: WrappedMonoid m #

maxBound :: WrappedMonoid m #

Enum a => Enum (WrappedMonoid a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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] #

Generic (WrappedMonoid m) #

Instance details

Defined in Data.Semigroup

Associated Types

type Rep (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (WrappedMonoid m) = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 m)))

Methods

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

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

Read m => Read (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (WrappedMonoid m) #

readList :: ReadS [WrappedMonoid m] #

readPrec :: ReadPrec (WrappedMonoid m) #

readListPrec :: ReadPrec [WrappedMonoid m] #

Show m => Show (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> WrappedMonoid m -> ShowS #

show :: WrappedMonoid m -> String #

showList :: [WrappedMonoid m] -> ShowS #

Eq m => Eq (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Ord m => Ord (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 #

type Rep1 WrappedMonoid #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep1 WrappedMonoid = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (WrappedMonoid m) = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base-4.21.0.0-a5ba" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 m)))

Re-exported monoids from Data.Monoid

newtype Dual a #

The dual of a Monoid, obtained by swapping the arguments of (<>).

Dual a <> Dual b == Dual (b <> a)

Examples

Expand

>>> Dual "Hello" <> Dual "World"
Dual {getDual = "WorldHello"}

>>> Dual (Dual "Hello") <> Dual (Dual "World")
Dual {getDual = Dual {getDual = "HelloWorld"}}

Constructors

Dual
Fields getDual :: a

Instances

Instances details

Foldable1 Dual #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Dual m -> m #

foldMap1 :: Semigroup m => (a -> m) -> Dual a -> m #

foldMap1' :: Semigroup m => (a -> m) -> Dual a -> m #

toNonEmpty :: Dual a -> NonEmpty a #

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

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

head :: Dual a -> a #

last :: Dual a -> a #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Dual a -> b #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Dual a -> b #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Dual a -> b #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Dual a -> b #

Applicative Dual #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Dual a #

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

liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c #

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

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

Functor Dual #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Monad Dual #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

return :: a -> Dual a #

Foldable Dual #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Dual a -> [a] #

null :: Dual a -> Bool #

length :: Dual a -> Int #

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

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

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

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

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

Traversable Dual #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

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

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

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

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

Generic1 Dual #

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep1 Dual	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal type Rep1 Dual = D1 ('MetaData "Dual" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Dual a -> Rep1 Dual a #

to1 :: Rep1 Dual a -> Dual a #

Monoid a => Monoid (Dual a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Dual a #

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

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

Semigroup a => Semigroup (Dual a) #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

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

Bounded a => Bounded (Dual a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Dual a #

maxBound :: Dual a #

Generic (Dual a) #

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Dual a)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal type Rep (Dual a) = D1 ('MetaData "Dual" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

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

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

Read a => Read (Dual a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Dual a) #

readList :: ReadS [Dual a] #

readPrec :: ReadPrec (Dual a) #

readListPrec :: ReadPrec [Dual a] #

Show a => Show (Dual a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

show :: Dual a -> String #

showList :: [Dual a] -> ShowS #

Eq a => Eq (Dual a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Dual a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

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

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

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

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

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

type Rep1 Dual #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Dual = D1 ('MetaData "Dual" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (Dual a) #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Dual a) = D1 ('MetaData "Dual" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Endo a #

The monoid of endomorphisms under composition.

Endo f <> Endo g == Endo (f . g)

Examples

Expand

>>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>> appEndo computation "Haskell"
"Hello, Haskell!"

>>> let computation = Endo (*3) <> Endo (+1)
>>> appEndo computation 1
6

Constructors

Endo
Fields appEndo :: a -> a

Instances

Instances details

Monoid (Endo a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Endo a #

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

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

Semigroup (Endo a) #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

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

Generic (Endo a) #

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Endo a)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal type Rep (Endo a) = D1 ('MetaData "Endo" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Endo" 'PrefixI 'True) (S1 ('MetaSel ('Just "appEndo") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a -> a))))

Methods

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

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

type Rep (Endo a) #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Endo a) = D1 ('MetaData "Endo" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Endo" 'PrefixI 'True) (S1 ('MetaSel ('Just "appEndo") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a -> a))))

newtype All #

Boolean monoid under conjunction (&&).

All x <> All y = All (x && y)

Examples

Expand

>>> All True <> mempty <> All False)
All {getAll = False}

>>> mconcat (map (\x -> All (even x)) [2,4,6,7,8])
All {getAll = False}

>>> All True <> mempty
All {getAll = True}

Constructors

All
Fields getAll :: Bool

Instances

Instances details

Monoid All #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: All #

mappend :: All -> All -> All #

mconcat :: [All] -> All #

Semigroup All #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

sconcat :: NonEmpty All -> All #

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

Bounded All #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: All #

maxBound :: All #

Generic All #

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep All	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal type Rep All = D1 ('MetaData "All" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "All" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAll") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

Methods

from :: All -> Rep All x #

to :: Rep All x -> All #

Read All #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS All #

readList :: ReadS [All] #

readPrec :: ReadPrec All #

readListPrec :: ReadPrec [All] #

Show All #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> All -> ShowS #

show :: All -> String #

showList :: [All] -> ShowS #

Eq All #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord All #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: All -> All -> Ordering #

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

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

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

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

max :: All -> All -> All #

min :: All -> All -> All #

type Rep All #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep All = D1 ('MetaData "All" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "All" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAll") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

newtype Any #

Boolean monoid under disjunction (||).

Any x <> Any y = Any (x || y)

Examples

Expand

>>> Any True <> mempty <> Any False
Any {getAny = True}

>>> mconcat (map (\x -> Any (even x)) [2,4,6,7,8])
Any {getAny = True}

>>> Any False <> mempty
Any {getAny = False}

Constructors

Any
Fields getAny :: Bool

Instances

Instances details

Monoid Any #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Any #

mappend :: Any -> Any -> Any #

mconcat :: [Any] -> Any #

Semigroup Any #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

sconcat :: NonEmpty Any -> Any #

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

Bounded Any #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Any #

maxBound :: Any #

Generic Any #

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep Any	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal type Rep Any = D1 ('MetaData "Any" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Any" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAny") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

Methods

from :: Any -> Rep Any x #

to :: Rep Any x -> Any #

Read Any #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS Any #

readList :: ReadS [Any] #

readPrec :: ReadPrec Any #

readListPrec :: ReadPrec [Any] #

Show Any #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Any -> ShowS #

show :: Any -> String #

showList :: [Any] -> ShowS #

Eq Any #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord Any #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Any -> Any -> Ordering #

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

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

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

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

max :: Any -> Any -> Any #

min :: Any -> Any -> Any #

type Rep Any #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep Any = D1 ('MetaData "Any" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Any" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAny") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

newtype Sum a #

Monoid under addition.

Sum a <> Sum b = Sum (a + b)

Examples

Expand

>>> Sum 1 <> Sum 2 <> mempty
Sum {getSum = 3}

>>> mconcat [ Sum n | n <- [3 .. 9]]
Sum {getSum = 42}

Constructors

Sum
Fields getSum :: a

Instances

Instances details

Foldable1 Sum #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Sum m -> m #

foldMap1 :: Semigroup m => (a -> m) -> Sum a -> m #

foldMap1' :: Semigroup m => (a -> m) -> Sum a -> m #

toNonEmpty :: Sum a -> NonEmpty a #

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

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

head :: Sum a -> a #

last :: Sum a -> a #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Sum a -> b #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Sum a -> b #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Sum a -> b #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Sum a -> b #

Applicative Sum #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Sum a #

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

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c #

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

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

Functor Sum #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Monad Sum #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

return :: a -> Sum a #

Foldable Sum #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Sum a -> [a] #

null :: Sum a -> Bool #

length :: Sum a -> Int #

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

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

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

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

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

Traversable Sum #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

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

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

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

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

Generic1 Sum #

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep1 Sum	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal type Rep1 Sum = D1 ('MetaData "Sum" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Sum a -> Rep1 Sum a #

to1 :: Rep1 Sum a -> Sum a #

Num a => Monoid (Sum a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Sum a #

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

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

Num a => Semigroup (Sum a) #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

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

Bounded a => Bounded (Sum a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Sum a #

maxBound :: Sum a #

Generic (Sum a) #

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Sum a)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal type Rep (Sum a) = D1 ('MetaData "Sum" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

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

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

Num a => Num (Sum a) #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

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

negate :: Sum a -> Sum a #

abs :: Sum a -> Sum a #

signum :: Sum a -> Sum a #

fromInteger :: Integer -> Sum a #

Read a => Read (Sum a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Sum a) #

readList :: ReadS [Sum a] #

readPrec :: ReadPrec (Sum a) #

readListPrec :: ReadPrec [Sum a] #

Show a => Show (Sum a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

show :: Sum a -> String #

showList :: [Sum a] -> ShowS #

Eq a => Eq (Sum a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Sum a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

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

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

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

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

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

type Rep1 Sum #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Sum = D1 ('MetaData "Sum" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (Sum a) #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Sum a) = D1 ('MetaData "Sum" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Product a #

Monoid under multiplication.

Product x <> Product y == Product (x * y)

Examples

Expand

>>> Product 3 <> Product 4 <> mempty
Product {getProduct = 12}

>>> mconcat [ Product n | n <- [2 .. 10]]
Product {getProduct = 3628800}

Constructors

Product
Fields getProduct :: a

Instances

Instances details

Foldable1 Product #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Product m -> m #

foldMap1 :: Semigroup m => (a -> m) -> Product a -> m #

foldMap1' :: Semigroup m => (a -> m) -> Product a -> m #

toNonEmpty :: Product a -> NonEmpty a #

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

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

head :: Product a -> a #

last :: Product a -> a #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Product a -> b #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Product a -> b #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Product a -> b #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Product a -> b #

Applicative Product #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Product a #

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

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c #

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

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

Functor Product #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Monad Product #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

return :: a -> Product a #

Foldable Product #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Product a -> [a] #

null :: Product a -> Bool #

length :: Product a -> Int #

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

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

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

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

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

Traversable Product #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

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

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

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

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

Generic1 Product #

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep1 Product	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal type Rep1 Product = D1 ('MetaData "Product" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Product a -> Rep1 Product a #

to1 :: Rep1 Product a -> Product a #

Num a => Monoid (Product a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Product a #

mappend :: Product a -> Product a -> Product a #

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

Num a => Semigroup (Product a) #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

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

Bounded a => Bounded (Product a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Product a #

maxBound :: Product a #

Generic (Product a) #

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Product a)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal type Rep (Product a) = D1 ('MetaData "Product" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

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

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

Num a => Num (Product a) #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

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

negate :: Product a -> Product a #

abs :: Product a -> Product a #

signum :: Product a -> Product a #

fromInteger :: Integer -> Product a #

Read a => Read (Product a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Product a) #

readList :: ReadS [Product a] #

readPrec :: ReadPrec (Product a) #

readListPrec :: ReadPrec [Product a] #

Show a => Show (Product a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

show :: Product a -> String #

showList :: [Product a] -> ShowS #

Eq a => Eq (Product a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Product a) #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Product a -> Product a -> Ordering #

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

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

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

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

max :: Product a -> Product a -> Product a #

min :: Product a -> Product a -> Product a #

type Rep1 Product #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Product = D1 ('MetaData "Product" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (Product a) #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Product a) = D1 ('MetaData "Product" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Difference lists of a semigroup

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

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

Examples

Expand

>>> let hello = diff "Hello, "

>>> appEndo hello "World!"
"Hello, World!"

>>> appEndo (hello <> mempty) "World!"
"Hello, World!"

>>> appEndo (mempty <> hello) "World!"
"Hello, World!"

>>> let world = diff "World"
>>> let excl = diff "!"

>>> appEndo (hello <> (world <> excl)) mempty
"Hello, World!"

>>> appEndo ((hello <> world) <> excl) mempty
"Hello, World!"

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

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

Examples

Expand

>>> take 10 $ cycle1 [1, 2, 3]
[1,2,3,1,2,3,1,2,3,1]

>>> cycle1 (Right 1)
Right 1

>>> cycle1 (Left 1)
* Hangs forever *

ArgMin, ArgMax

data Arg a b #

Arg isn't itself a Semigroup in its own right, but it can be placed inside Min and Max to compute an arg min or arg max. In the event of ties, the leftmost qualifying Arg is chosen; contrast with the behavior of minimum and maximum for many other types, where ties are broken by considering elements to the left in the structure to be less than elements to the right.

Examples

Expand

>>> minimum [ Arg (x * x) x | x <- [-10 .. 10] ]
Arg 0 0

>>> maximum [ Arg (-0.2*x^2 + 1.5*x + 1) x | x <- [-10 .. 10] ]
Arg 3.8 4.0

>>> minimum [ Arg (-0.2*x^2 + 1.5*x + 1) x | x <- [-10 .. 10] ]
Arg (-34.0) (-10.0)

Constructors

Arg
Fields a The argument used for comparisons in `Eq` and `Ord`. b The "value" exposed via the `Functor`, `Foldable` etc. instances.

Instances

Instances details

Bifoldable Arg #

Since: base-4.10.0.0

Instance details

Defined in Data.Semigroup

Methods

bifold :: Monoid m => Arg m m -> m #

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m #

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c #

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c #

Bifoldable1 Arg #

Instance details

Defined in Data.Bifoldable1

Methods

bifold1 :: Semigroup m => Arg m m -> m #

bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Arg a b -> m #

Bifunctor Arg #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d #

first :: (a -> b) -> Arg a c -> Arg b c #

second :: (b -> c) -> Arg a b -> Arg a c #

Bitraversable Arg #

Since: base-4.10.0.0

Instance details

Defined in Data.Semigroup

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) #

Generic1 (Arg a :: Type -> Type) #

Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 (Arg a :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 (Arg a :: Type -> Type) = D1 ('MetaData "Arg" "Data.Semigroup" "base-4.21.0.0-a5ba" 'False) (C1 ('MetaCons "Arg" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Arg a a0 -> Rep1 (Arg a) a0 #

to1 :: Rep1 (Arg a) a0 -> Arg a a0 #

Functor (Arg a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a0 -> b) -> Arg a a0 -> Arg a b #

(<$) :: a0 -> Arg a b -> Arg a a0 #

Foldable (Arg a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => Arg a m -> m #

foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m #

foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m #

foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b #

foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b #

foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b #

foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b #

foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 #

foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 #

toList :: Arg a a0 -> [a0] #

null :: Arg a a0 -> Bool #

length :: Arg a a0 -> Int #

elem :: Eq a0 => a0 -> Arg a a0 -> Bool #

maximum :: Ord a0 => Arg a a0 -> a0 #

minimum :: Ord a0 => Arg a a0 -> a0 #

sum :: Num a0 => Arg a a0 -> a0 #

product :: Num a0 => Arg a a0 -> a0 #

Traversable (Arg a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

traverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) #

sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) #

mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) #

sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) #

(Data a, Data b) => Data (Arg a b) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Arg a b -> c (Arg a b) #

gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b) #

toConstr :: Arg a b -> Constr #

dataTypeOf :: Arg a b -> DataType #

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

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

gmapT :: (forall b0. Data b0 => b0 -> b0) -> Arg a b -> Arg a b #

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

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

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

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

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

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

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

Generic (Arg a b) #

Instance details

Defined in Data.Semigroup

Associated Types

type Rep (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (Arg a b) = D1 ('MetaData "Arg" "Data.Semigroup" "base-4.21.0.0-a5ba" 'False) (C1 ('MetaCons "Arg" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b)))

Methods

from :: Arg a b -> Rep (Arg a b) x #

to :: Rep (Arg a b) x -> Arg a b #

(Read a, Read b) => Read (Arg a b) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (Arg a b) #

readList :: ReadS [Arg a b] #

readPrec :: ReadPrec (Arg a b) #

readListPrec :: ReadPrec [Arg a b] #

(Show a, Show b) => Show (Arg a b) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Arg a b -> ShowS #

show :: Arg a b -> String #

showList :: [Arg a b] -> ShowS #

Eq a => Eq (Arg a b) #

Note that Arg's Eq instance does not satisfy extensionality:

>>> Arg 0 0 == Arg 0 1
True
>>> let f (Arg _ x) = x in f (Arg 0 0) == f (Arg 0 1)
False

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: Arg a b -> Arg a b -> Bool #

(/=) :: Arg a b -> Arg a b -> Bool #

Ord a => Ord (Arg a b) #

Note that Arg's Ord instance has min and max implementations that differ from the tie-breaking conventions of the default implementation of min and max in class Ord; Arg breaks ties by favoring the first argument in both functions.

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: Arg a b -> Arg a b -> Ordering #

(<) :: Arg a b -> Arg a b -> Bool #

(<=) :: Arg a b -> Arg a b -> Bool #

(>) :: Arg a b -> Arg a b -> Bool #

(>=) :: Arg a b -> Arg a b -> Bool #

max :: Arg a b -> Arg a b -> Arg a b #

min :: Arg a b -> Arg a b -> Arg a b #

type Rep1 (Arg a :: Type -> Type) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep1 (Arg a :: Type -> Type) = D1 ('MetaData "Arg" "Data.Semigroup" "base-4.21.0.0-a5ba" 'False) (C1 ('MetaCons "Arg" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (Arg a b) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (Arg a b) = D1 ('MetaData "Arg" "Data.Semigroup" "base-4.21.0.0-a5ba" 'False) (C1 ('MetaCons "Arg" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b)))

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

Examples

Expand

>>> Min (Arg 0 ()) <> Min (Arg 1 ())
Min {getMin = Arg 0 ()}

>>> minimum [ Arg (length name) name | name <- ["violencia", "lea", "pixie"]]
Arg 3 "lea"

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

Examples

Expand

>>> Max (Arg 0 ()) <> Max (Arg 1 ())
Max {getMax = Arg 1 ()}

>>> maximum [ Arg (length name) name | name <- ["violencia", "lea", "pixie"]]
Arg 9 "violencia"