Safe Haskell | Safe-Inferred |
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Monoid typeclass
class Monoid a where
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:
mappend mempty x = x
mappend x mempty = x
mappend x (mappend y z) = mappend (mappend x y) z
mconcat =
foldr
mappend mempty
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Minimal complete definition: mempty
and mappend
.
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
.
mempty :: a
Identity of mappend
mappend :: a -> a -> a
An associative operation
mconcat :: [a] -> a
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.
Monoid Ordering | |
Monoid () | |
Monoid All | |
Monoid Any | |
Monoid [a] | |
Monoid a => Monoid (Dual a) | |
Monoid (Endo a) | |
Num a => Monoid (Sum a) | |
Num a => Monoid (Product a) | |
Monoid (First a) | |
Monoid (Last a) | |
Monoid a => Monoid (Maybe a) | Lift a semigroup into |
Monoid b => Monoid (a -> b) | |
(Monoid a, Monoid b) => Monoid (a, b) | |
Monoid a => Monoid (Const a b) | |
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | |
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | |
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) |
newtype Endo a
The monoid of endomorphisms under composition.
Bool wrappers
newtype All
Boolean monoid under conjunction.
newtype Any
Boolean monoid under disjunction.
Num wrappers
newtype Sum a
Monoid under addition.
Maybe wrappers
newtype First a
Maybe monoid returning the leftmost non-Nothing value.