Data.Monoids

Documentation

type family Monoids lst :: Constraint where ...

Equations

Monoids '[] = ()

Monoids (a ': as) = (Monoid a, Monoids as)

class (Mempty a, Semigroup a) => Monoid a where

Minimal complete definition

Nothing

Methods

mconcat :: [a] -> a

Instances

(Mempty a, Semigroup a) => Monoid a

Defined in Data.Monoids

Methods

mconcat :: [a] -> a

type family Semigroups lst :: Constraint where ...

Equations

Semigroups '[] = ()

Semigroups (a ': as) = (Semigroup a, Semigroups as)

type family Mempties lst :: Constraint where ...

Equations

Mempties '[] = ()

Mempties (a ': as) = (Mempty a, Mempties as)

class Mempty a where

Minimal complete definition

Nothing

Methods

mempty :: a

mempty :: Monoid a => a

Instances

Monoid a => Mempty a

Defined in Data.Monoids

Methods

mempty :: a

Mempty [a]

Defined in Data.Monoids

Methods

mempty :: [a]

Mempty (Maybe a)

Defined in Data.Monoids

Methods

mempty :: Maybe a

Mempty (Map k a)

Defined in Data.Monoids

Methods

mempty :: Map k a

mappend :: Semigroup a => a -> a -> a

mappendWith :: Semigroup a => a -> a -> a -> a

mappendBetween :: Semigroup a => a -> a -> a -> a

mconcat' :: (Foldable t, Monoid a) => t a -> a

intersperse :: Foldable f => a -> f a -> [a]

intercalate :: (Monoid a, Foldable f) => a -> f a -> a

intercalate' :: Monoid a => a -> [a] -> a

class Semigroup a where

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

Instances should satisfy the associativity law:

• x <> (y <> z) = (x <> y) <> z

Since: base-4.9.0.0

Minimal complete definition

(<>)

Methods

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

An associative operation.

sconcat :: NonEmpty a -> a

Reduce a non-empty list with <>

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

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

Repeat a value n times.

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

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

Instances

Semigroup Ordering

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

sconcat :: NonEmpty Ordering -> Ordering

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

Semigroup ()

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

sconcat :: NonEmpty () -> ()

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

Semigroup [a]

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: [a] -> [a] -> [a]

sconcat :: NonEmpty [a] -> [a]

stimes :: Integral b => b -> [a] -> [a]

Semigroup a => Semigroup (Maybe a)

Since: base-4.9.0.0

Defined in GHC.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 (IO a)

Since: base-4.10.0.0

Defined in GHC.Base

Methods

(<>) :: IO a -> IO a -> IO a

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

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

Ord a => Semigroup (Min a)

Since: base-4.9.0.0

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

Ord a => Semigroup (Max a)

Since: base-4.9.0.0

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

Semigroup (First a)

Since: base-4.9.0.0

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

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

Monoid m => Semigroup (WrappedMonoid m)

Since: base-4.9.0.0

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 a => Semigroup (Option a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

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

Semigroup (First a)

Since: base-4.9.0.0

Defined in 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

Defined in Data.Monoid

Methods

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

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

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

Semigroup (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

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

Semigroup b => Semigroup (a -> b)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

stimes :: Integral b0 => b0 -> (a -> b) -> a -> b

Semigroup (Either a b)

Since: base-4.9.0.0

Defined in 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 a, Semigroup b) => Semigroup (a, b)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

stimes :: Integral b0 => b0 -> (a, b) -> (a, b)

Ord k => Semigroup (Map k v)

Defined in Data.Map.Internal

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)

Since: base-4.9.0.0

Defined in GHC.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)

(Applicative f, Semigroup a) => Semigroup (Ap f a)

Since: base-4.12.0.0

Defined in 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

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

Since: base-4.9.0.0

Defined in GHC.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 a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)

Since: base-4.9.0.0

Defined in GHC.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)