Monoid
extends the power of Semigroup
by providing an additional empty
value.
interface Semigroup<A> {
readonly concat: (x: A, y: A) => A
}
interface Monoid<A> extends Semigroup<A> {
readonly empty: A
}
This empty
value should be an identity for the concat
operation, which means the following equalities hold for any choice of x
.
concat(x, empty) = concat(empty, x) = x
Many types that form a Semigroup
also form a Monoid
, such as number
s (with 0
) and string
s (with ''
).
import { Monoid } from 'fp-ts/Monoid'
const monoidString: Monoid<string> = {
concat: (x, y) => x + y,
empty: '',
}
Adapted from https://typelevel.org/cats
Added in v2.0.0
The dual of a Monoid
, obtained by swapping the arguments of concat
.
Signature
export declare function getDualMonoid<A>(M: Monoid<A>): Monoid<A>
Example
import { getDualMonoid, monoidString } from 'fp-ts/Monoid'
assert.deepStrictEqual(getDualMonoid(monoidString).concat('a', 'b'), 'ba')
Added in v2.0.0
Endomorphism form a monoid where the empty
value is the identity function.
Signature
export declare function getEndomorphismMonoid<A = never>(): Monoid<Endomorphism<A>>
Added in v2.0.0
Unary functions form a monoid as long as you can provide a monoid for the codomain.
Signature
export declare function getFunctionMonoid<M>(M: Monoid<M>): <A = never>() => Monoid<(a: A) => M>
Example
import { Predicate } from 'fp-ts/function'
import * as M from 'fp-ts/Monoid'
const f: Predicate<number> = (n) => n <= 2
const g: Predicate<number> = (n) => n >= 0
const M1 = M.getFunctionMonoid(M.monoidAll)<number>()
assert.deepStrictEqual(M1.concat(f, g)(1), true)
assert.deepStrictEqual(M1.concat(f, g)(3), false)
const M2 = M.getFunctionMonoid(M.monoidAny)<number>()
assert.deepStrictEqual(M2.concat(f, g)(1), true)
assert.deepStrictEqual(M2.concat(f, g)(3), true)
Added in v2.0.0
Get a monoid where concat
will return the maximum, based on the provided bounded order.
The empty
value is the bottom
value.
Signature
export declare function getJoinMonoid<A>(B: Bounded<A>): Monoid<A>
Example
import * as B from 'fp-ts/Bounded'
import * as M from 'fp-ts/Monoid'
const M1 = M.getJoinMonoid(B.boundedNumber)
assert.deepStrictEqual(M1.concat(1, 2), 2)
Added in v2.0.0
Get a monoid where concat
will return the minimum, based on the provided bounded order.
The empty
value is the top
value.
Signature
export declare function getMeetMonoid<A>(B: Bounded<A>): Monoid<A>
Example
import * as B from 'fp-ts/Bounded'
import * as M from 'fp-ts/Monoid'
const M1 = M.getMeetMonoid(B.boundedNumber)
assert.deepStrictEqual(M1.concat(1, 2), 1)
Added in v2.0.0
Given a struct of monoids returns a monoid for the struct.
Signature
export declare function getStructMonoid<O extends ReadonlyRecord<string, any>>(
monoids: { [K in keyof O]: Monoid<O[K]> }
): Monoid<O>
Example
import * as M from 'fp-ts/Monoid'
interface Point {
readonly x: number
readonly y: number
}
const monoidPoint = M.getStructMonoid<Point>({
x: M.monoidSum,
y: M.monoidSum,
})
assert.deepStrictEqual(monoidPoint.concat({ x: 1, y: 2 }, { x: 3, y: 4 }), { x: 4, y: 6 })
Added in v2.0.0
Given a tuple of monoids returns a monoid for the tuple
Signature
export declare function getTupleMonoid<T extends ReadonlyArray<Monoid<any>>>(
...monoids: T
): Monoid<{ [K in keyof T]: T[K] extends S.Semigroup<infer A> ? A : never }>
Example
import { getTupleMonoid, monoidString, monoidSum, monoidAll } from 'fp-ts/Monoid'
const M1 = getTupleMonoid(monoidString, monoidSum)
assert.deepStrictEqual(M1.concat(['a', 1], ['b', 2]), ['ab', 3])
const M2 = getTupleMonoid(monoidString, monoidSum, monoidAll)
assert.deepStrictEqual(M2.concat(['a', 1, true], ['b', 2, false]), ['ab', 3, false])
Added in v2.0.0
boolean
monoid under conjunction.
The empty
value is true
.
Signature
export declare const monoidAll: Monoid<boolean>
Example
import * as M from 'fp-ts/Monoid'
assert.deepStrictEqual(M.monoidAll.concat(true, true), true)
assert.deepStrictEqual(M.monoidAll.concat(true, false), false)
Added in v2.0.0
boolean
monoid under disjunction.
The empty
value is false
.
Signature
export declare const monoidAny: Monoid<boolean>
Example
import * as M from 'fp-ts/Monoid'
assert.deepStrictEqual(M.monoidAny.concat(true, true), true)
assert.deepStrictEqual(M.monoidAny.concat(true, false), true)
assert.deepStrictEqual(M.monoidAny.concat(false, false), false)
Added in v2.0.0
number
monoid under multiplication.
The empty
value is 1
.
Signature
export declare const monoidProduct: Monoid<number>
Example
import * as M from 'fp-ts/Monoid'
assert.deepStrictEqual(M.monoidProduct.concat(2, 3), 6)
Added in v2.0.0
string
monoid under concatenation.
The empty
value is ''
.
Signature
export declare const monoidString: Monoid<string>
Example
import * as M from 'fp-ts/Monoid'
assert.deepStrictEqual(M.monoidString.concat('a', 'b'), 'ab')
Added in v2.0.0
number
monoid under addition.
The empty
value is 0
.
Signature
export declare const monoidSum: Monoid<number>
Example
import * as M from 'fp-ts/Monoid'
assert.deepStrictEqual(M.monoidSum.concat(2, 3), 5)
Added in v2.0.0
Signature
export declare const monoidVoid: Monoid<void>
Added in v2.0.0
Signature
export interface Monoid<A> extends S.Semigroup<A> {
readonly empty: A
}
Added in v2.0.0
Given a sequence of as
, concat them and return the total.
If as
is empty, return the monoid empty
value.
Signature
export declare function fold<A>(M: Monoid<A>): (as: ReadonlyArray<A>) => A
Example
import * as M from 'fp-ts/Monoid'
assert.deepStrictEqual(M.fold(M.monoidSum)([1, 2, 3]), 6)
assert.deepStrictEqual(M.fold(M.monoidSum)([]), 0)
Added in v2.0.0