# Semiring

```
interface Semiring<A> {
readonly add: (x: A, y: A) => A
readonly zero: A
readonly mul: (x: A, y: A) => A
readonly one: A
}
```

Added in v1.0.0 (type class)

The `Semiring`

class is for types that support an addition and multiplication operation.

Instances must satisfy the following laws:

- Commutative monoid under addition:
- Associativity:
`(a + b) + c = a + (b + c)`

- Identity:
`zero + a = a + zero = a`

- Commutative:
`a + b = b + a`

- Associativity:
- Monoid under multiplication:
- Associativity:
`(a * b) * c = a * (b * c)`

- Identity:
`one * a = a * one = a`

- Associativity:
- Multiplication distributes over addition:
- Left distributivity:
`a * (b + c) = (a * b) + (a * c)`

- Right distributivity:
`(a + b) * c = (a * c) + (b * c)`

- Left distributivity:
- Annihilation:
`zero * a = a * zero = zero`

**Note:** The `number`

type is not fully law abiding members of this class hierarchy due to the potential
for arithmetic overflows, and the presence of `NaN`

and `Infinity`

values. The behaviour is
unspecified in these cases.

## getFunctionSemiring

```
<A, B>(S: Semiring<B>): Semiring<(a: A) => B>
```

Added in v1.0.0 (function)