# Data.Monoid

- Package
- prelude
- Repository
- purerl/purescript-prelude

### #Monoid Source

`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
```

`Monoid`

s 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

### #power Source

`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.

### #MonoidRecord Source

`class (SemigroupRecord rowlist row subrow) <= MonoidRecord rowlist row subrow | rowlist -> row subrow where`

A class for records where all fields have `Monoid`

instances, used to
implement the `Monoid`

instance for records.

#### Members

`memptyRecord :: RLProxy rowlist -> Record subrow`

#### Instances

`MonoidRecord Nil row ()`

`(IsSymbol key, Monoid focus, Cons key focus subrowTail subrow, MonoidRecord rowlistTail row subrowTail) => MonoidRecord (Cons key focus rowlistTail) row subrow`

## Re-exports from **Data.**Semigroup

### #Semigroup Source

`class Semigroup a `

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.

#### Instances

### #SemigroupRecord Source

`class SemigroupRecord rowlist row subrow | rowlist -> subrow`

A class for records where all fields have `Semigroup`

instances, used to
implement the `Semigroup`

instance for records.

#### Instances

`SemigroupRecord Nil row ()`

`(IsSymbol key, Cons key focus subrowTail subrow, SemigroupRecord rowlistTail row subrowTail, Semigroup focus) => SemigroupRecord (Cons key focus rowlistTail) row subrow`

- Modules
- Control.
Applicative - Control.
Apply - Control.
Bind - Control.
Category - Control.
Monad - Control.
Semigroupoid - Data.
Boolean - Data.
BooleanAlgebra - Data.
Bounded - Data.
CommutativeRing - Data.
DivisionRing - Data.
Eq - Data.
EuclideanRing - Data.
Field - Data.
Function - Data.
Functor - Data.
HeytingAlgebra - Data.
Monoid - Data.
Monoid. Additive - Data.
Monoid. Conj - Data.
Monoid. Disj - Data.
Monoid. Dual - Data.
Monoid. Endo - Data.
Monoid. Multiplicative - Data.
NaturalTransformation - Data.
Ord - Data.
Ord. Unsafe - Data.
Ordering - Data.
Ring - Data.
Semigroup - Data.
Semigroup. First - Data.
Semigroup. Last - Data.
Semiring - Data.
Show - Data.
Symbol - Data.
Unit - Data.
Void - Prelude
- Record.
Unsafe - Type.
Data. Row - Type.
Data. RowList