Safe Haskell | Safe |
---|---|
Language | Haskell2010 |
Synopsis
- class (Loop a, Monoid a) => Group a where
- inv :: a -> a
- greplicate :: Integer -> a -> a
- class Quasigroup a => Loop a where
- lempty :: a
- lreplicate :: Natural -> a -> a
- class Magma a => Quasigroup a where
- class Semigroup a => Monoid a where
- mreplicate :: Monoid a => Natural -> a -> a
- class Semigroup a where
- class Magma a where
- (<<) :: a -> a -> a
Documentation
class Quasigroup a => Loop a where Source #
Nothing
class Magma a => Quasigroup a where Source #
Nothing
class Semigroup a => Monoid a where #
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:
x
<>
mempty
= xmempty
<>
x = xx
(<>
(y<>
z) = (x<>
y)<>
zSemigroup
law)mconcat
=foldr
'(<>)'mempty
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define newtype
s and make those instances
of Monoid
, e.g. Sum
and Product
.
NOTE: Semigroup
is a superclass of Monoid
since base-4.11.0.0.
Identity of mappend
An associative operation
NOTE: This method is redundant and has the default
implementation
since base-4.11.0.0.mappend
= '(<>)'
Fold a list using the monoid.
For most types, the default definition for mconcat
will be
used, but the function is included in the class definition so
that an optimized version can be provided for specific types.
Instances
Monoid Ordering | Since: base-2.1 |
Monoid () | Since: base-2.1 |
Monoid All | Since: base-2.1 |
Monoid Any | Since: base-2.1 |
Monoid [a] | Since: base-2.1 |
Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
(Ord a, Bounded a) => Monoid (Min a) | Since: base-4.9.0.0 |
(Ord a, Bounded a) => Monoid (Max a) | Since: base-4.9.0.0 |
Monoid m => Monoid (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m # | |
Semigroup a => Monoid (Option a) | Since: base-4.9.0.0 |
Monoid a => Monoid (Dual a) | Since: base-2.1 |
Monoid (Endo a) | Since: base-2.1 |
Num a => Monoid (Sum a) | Since: base-2.1 |
Num a => Monoid (Product a) | Since: base-2.1 |
Monoid b => Monoid (a -> b) | Since: base-2.1 |
(Monoid a, Monoid b) => Monoid (a, b) | Since: base-2.1 |
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | Since: base-2.1 |
Alternative f => Monoid (Alt f a) | Since: base-4.8.0.0 |
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | Since: base-2.1 |
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | Since: base-2.1 |
mreplicate :: Monoid a => Natural -> a -> a Source #
A generalization of replicate
to an arbitrary Monoid
.
Adapted from http://augustss.blogspot.com/2008/07/lost-and-found-if-i-write-108-in.html.
The class of semigroups (types with an associative binary operation).
Instances should satisfy the associativity law:
Since: base-4.9.0.0
(<>) :: a -> a -> a infixr 6 #
An associative operation.
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 =
or stimesIdempotent
stimes =
respectively.stimesIdempotentMonoid
Instances
Semigroup Ordering | Since: base-4.9.0.0 |
Semigroup () | Since: base-4.9.0.0 |
Semigroup All | Since: base-4.9.0.0 |
Semigroup Any | Since: base-4.9.0.0 |
Semigroup [a] | Since: base-4.9.0.0 |
Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0 |
Ord a => Semigroup (Min a) | Since: base-4.9.0.0 |
Ord a => Semigroup (Max a) | Since: base-4.9.0.0 |
Semigroup (First a) | Since: base-4.9.0.0 |
Semigroup (Last a) | Since: base-4.9.0.0 |
Monoid m => Semigroup (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup (<>) :: 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 |
Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0 |
Semigroup (Endo a) | Since: base-4.9.0.0 |
Num a => Semigroup (Sum a) | Since: base-4.9.0.0 |
Num a => Semigroup (Product a) | Since: base-4.9.0.0 |
Semigroup (NonEmpty a) | Since: base-4.9.0.0 |
Semigroup b => Semigroup (a -> b) | Since: base-4.9.0.0 |
Semigroup (Either a b) | Since: base-4.9.0.0 |
(Semigroup a, Semigroup b) => Semigroup (a, b) | Since: base-4.9.0.0 |
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) | Since: base-4.9.0.0 |
Alternative f => Semigroup (Alt f a) | Since: base-4.9.0.0 |
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) | Since: base-4.9.0.0 |
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) | Since: base-4.9.0.0 |