Feb_19.md

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---
title: Functional design: combinators
published: true
description:
tags: functional, typescript
series: Functional design
---

In this article the term "combinator" refers to the combinator pattern

A style of organizing libraries centered around the idea of combining things. Usually there is some type T, some "primitive" values of type T, and some "combinators" which can combine values of type T in various ways to build up more complex values of type T

So the general shape of a combinator is

combinator: Thing -> Thing

The goal of a combinator is to create new "things" from previously defined "things".

Since the result can be passed back as input, you get a combinatorial explosion of possibilities, which makes this pattern very powerful.

If you mix and match several combinators together, you get an even larger combinatorial explosion.

So a design that you may often find in a functional module is

• a small set of very simple "primitives"
• a set of "combinators" for combining them into more complicated structures

Let's see some examples.

Example 1: Eq

The getEq combinator: given an instance of Eq for A, we can derive an instance of Eq for Array<A>

import { Eq } from 'fp-ts/lib/Eq'

export function getEq<A>(E: Eq<A>): Eq<Array<A>> {
  return {
    equals: (xs, ys) =>
      xs.length === ys.length &&
      xs.every((x, i) => E.equals(x, ys[i]))
  }
}

Usage

/** a primitive `Eq` instance for `number` */
export const eqNumber: Eq<number> = {
  equals: (x, y) => x === y
}

// derived
export const eqArrayOfNumber: Eq<Array<number>> = getEq(
  eqNumber
)

// derived
export const eqArrayOfArrayOfNumber: Eq<
  Array<Array<number>>
> = getEq(eqArrayOfNumber)

// derived
export const eqArrayOfArrayOfArrayOfNumber: Eq<
  Array<Array<Array<number>>>
> = getEq(eqArrayOfArrayOfNumber)

// etc...

Another combinator, contramap: given an instance of Eq for A and a function from B to A, we can derive an instance of Eq for B

export const contramap = <A, B>(f: (b: B) => A) => (
  E: Eq<A>
): Eq<B> => {
  return {
    equals: (x, y) => E.equals(f(x), f(y))
  }
}

Usage

export interface User {
  id: number
  name: string
}

export const eqUser: Eq<User> = contramap(
  (user: User) => user.id
)(eqNumber)

// mix with `getArraySetoid`
export const eqArrayOfUser: Eq<Array<User>> = getEq(eqUser)

Example 2: Monoid

The getIOMonoid combinator: given an instance of Monoid for A, we can derive an instance of Monoid for IO<A>

import { IO } from 'fp-ts/lib/IO'
import { Monoid } from 'fp-ts/lib/Monoid'

export function getIOMonoid<A>(
  M: Monoid<A>
): Monoid<IO<A>> {
  return {
    concat: (x, y) =>
      new IO(() => M.concat(x.run(), y.run())),
    empty: new IO(() => M.empty)
  }
}

We can use getIOMonoid to derive another combinator, replicateIO: given a number n and an action mv of type IO<void>, we can derive an action that performs n times mv

import { fold } from 'fp-ts/lib/Monoid'
import { replicate } from 'fp-ts/lib/Array'

/** a primitive `Monoid` instance for `void` */
export const monoidVoid: Monoid<void> = {
  concat: () => undefined,
  empty: undefined
}

export function replicateIO(
  n: number,
  mv: IO<void>
): IO<void> {
  return fold(getIOMonoid(monoidVoid))(replicate(n, mv))
}

Usage

//
// helpers
//

/** logs to the console */
export function log(message: unknown): IO<void> {
  return new IO(() => console.log(message))
}

/** returns a random integer between `low` and `high` */
export const randomInt = (
  low: number,
  high: number
): IO<number> => {
  return new IO(() =>
    Math.floor((high - low + 1) * Math.random() + low)
  )
}

//
// program
//
import { chain } from 'fp-ts/lib/IO'
import { pipe } from 'fp-ts/lib/pipeable'

function fib(n: number): number {
  return n <= 1 ? 1 : fib(n - 1) + fib(n - 2)
}

/** calculates a random fibonacci and prints the result to the console */
const printFib: IO<void> = pipe(
  randomInt(30, 35),
  chain(n => log(fib(n)))
)

replicateIO(3, printFib).run()
/*
1346269
9227465
3524578
*/

Example 3: IO

We can build many other combinators for IO, for example the time combinator mimics the analogous Unix command: given an action IO<A>, we can derive an action IO<A> that prints to the console the elapsed time

import { IO, io } from 'fp-ts/lib/IO'

/** returns the current time in millis */
export const now = new IO(() => new Date().getTime())

export function time<A>(ma: IO<A>): IO<A> {
  return io.chain(now, start =>
    io.chain(ma, a =>
      io.chain(now, end =>
        io.map(log(`Elapsed: ${end - start}`), () => a)
      )
    )
  )
}

Usage

time(replicateIO(3, printFib)).run()
/*
5702887
1346269
14930352
Elapsed: 193
*/

With partials...

time(replicateIO(3, time(printFib))).run()
/*
3524578
Elapsed: 32
14930352
Elapsed: 125
3524578
Elapsed: 32
Elapsed: 189
*/

Can we make the time combinator more general? We'll see how in the next article.