Functional Programming Jargons

The whole idea of this repos is to try and define jargons from combinatorics and category theory jargons that are used in functional programming in a easier fashion.

Let's try and define these with examples, this is a WIP please feel free to send PR ;)

Arity

The number of arguments a function takes.

const sum = (a, b) => a + b;

const arity = sum.length;
console.log(arity);
// => 2
// The arity of sum is 2

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Higher Order Functions (HOF)

A function for which both the input and the output are functions.

let greet = (name) => () => `Hello ${name}!`;

greet("HOF")(); // Hello HOF!

Partial Application

The process of getting a function with lesser arity compared to the original function by fixing the number of arguments is known as partial application.

let sum = (a, b) => a + b;

// partially applying `a` to `40`
let partial = add.bind(null, 40);

// Invoking it with `b`
partial(40); //=> 42

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Currying

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Purity

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Side effects

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Idempotency

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Contracts

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Guarded Functions

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Categories

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Functor

Structure that can be mapped over.

Simplest functor in javascript is an Array

[2,3,4].map( function(n) {
  return n + 2;
}); // [4,6,8]

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Referential Transparency

An expression that can be replaced with its value without changing the behaviour of the program is said to be referential transparent.

Say we have function greet:

let greet = () => "Hello World!";

Any invocation of greet() can be replaced with Hello World! hence greet is referential transparent.

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Monoid

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Monad

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Applicative Functor

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Morphism

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