Data.Monoid

class (Semigroup m) <= Monoid m  where

A Monoid is a Semigroup with a value mempty, which is both a left and right unit for the associative operation <>:

forall x. mempty <> x = x <> mempty = x

Monoids are commonly used as the result of fold operations, where <> is used to combine individual results, and mempty gives the result of folding an empty collection of elements.

Members

• mempty :: m

Instances

• Monoid Unit
• Monoid Ordering
• (Monoid b) => Monoid (a -> b)
• Monoid String
• Monoid (Array a)

power :: forall m. Monoid m => m -> Int -> m

Append a value to itself a certain number of times. For the Multiplicative type, and for a non-negative power, this is the same as normal number exponentiation.

If the second argument is negative this function will return mempty (unlike normal number exponentiation). The Monoid constraint alone is not enough to write a power function with the property that power x n cancels with power x (-n), i.e. power x n <> power x (-n) = mempty. For that, we would additionally need the ability to invert elements, i.e. a Group.

class Semigroup a  where

The Semigroup type class identifies an associative operation on a type.

Instances are required to satisfy the following law:

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

One example of a Semigroup is String, with (<>) defined as string concatenation.

Members

• append :: a -> a -> a

Instances

• Semigroup String
• Semigroup Unit
• Semigroup Void
• (Semigroup s') => Semigroup (s -> s')
• Semigroup (Array a)

Operator alias for Data.Semigroup.append (right-associative / precedence 5)