# Working with numbers

fp-ts is not a math library, but there are some good facilities we can use to work with numbers. Because the examples below use abstract concepts, e.g. Monoids, many of the examples below would work with other types of data, not just numbers.

## Min/max

import { boundedNumber } from 'fp-ts/lib/Bounded'
import { fold, getJoinMonoid, getMeetMonoid } from 'fp-ts/lib/Monoid'

const min = fold(getMeetMonoid(boundedNumber))
const max = fold(getJoinMonoid(boundedNumber))

min([5, 2, 3]) // 2
max([5, 2, 3]) // 5

## Sums and products

import { fold, monoidProduct, monoidSum } from 'fp-ts/lib/Monoid'

const sum = fold(monoidSum)
const product = fold(monoidProduct)

sum([1, 2, 3, 4]) // 10
product([1, 2, 3, 4]) // 24

## Working with nested structures

import { getStructMonoid, Monoid, monoidSum } from 'fp-ts/lib/Monoid'

type Point = {
x: number
y: number
}

const monoidPoint: Monoid<Point> = getStructMonoid({
x: monoidSum,
y: monoidSum
})

monoidPoint.concat({ x: 0, y: 3 }, { x: 2, y: 4 }) // { x: 2, y: 7 }

To check whether the resulting Point is positive, create a predicate:

import { getFunctionMonoid, Monoid, monoidAll } from 'fp-ts/lib/Monoid'

type Point = {
x: number
y: number
}

const monoidPredicate: Monoid<(p: Point) => boolean> = getFunctionMonoid(monoidAll)<Point>()

const isPositiveX = (p: Point): boolean => p.x >= 0
const isPositiveY = (p: Point): boolean => p.y >= 0

const isPositiveXY = monoidPredicate.concat(isPositiveX, isPositiveY)

isPositiveXY({ x: 1, y: 1 }) // true
isPositiveXY({ x: 1, y: -1 }) // false
isPositiveXY({ x: -1, y: 1 }) // false
isPositiveXY({ x: -1, y: -1 }) // false

## Working with optional values

import { fold, monoidProduct, monoidSum } from 'fp-ts/lib/Monoid'
import { getApplyMonoid, none, some } from 'fp-ts/lib/Option'

const sum = fold(getApplyMonoid(monoidSum))
const product = fold(getApplyMonoid(monoidProduct))

sum([some(2), none, some(4)]) // none
sum([some(2), some(3), some(4)]) // some(9)

product([some(2), none, some(4)]) // none
product([some(2), some(3), some(4)]) // some(24)

This also works for Eithers, but note that folding on Left values does not work the same way as folding on Right values.

import { getApplyMonoid, left, right } from 'fp-ts/lib/Either'
import { fold, monoidProduct, monoidSum } from 'fp-ts/lib/Monoid'

const sum = fold(getApplyMonoid(monoidSum))
const product = fold(getApplyMonoid(monoidProduct))

sum([right(2), left(3), right(4)]) // left(3)
sum([right(2), right(3), right(4)]) // right(9)
product([right(2), left(3), left(4)]) // left(3) <- it's the first left value
product([right(2), right(3), right(4)]) // right(24)