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 ;)

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

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

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

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

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 = sum.bind(null, 40);

// Invoking it with `b`
partial(2); //=> 42

The process of converting a function with multiple arity into the same function with less arity.

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

let curriedSum = (a) => (b) => a + b;

curriedSum(40)(2) // 42.

A function is said to be pure if the return value is only determined by its input values, without any side effects.

let greet = "yo";

greet.toUpperCase(); // YO;

greet // yo;

A function or expression is said to have a side effect if apart from returning a value, it modifies some state or has an observable interaction with external functions.

console.log("IO is a side effect!");

A function is said to be idempotent if it has no side-effects on multiple executions with the the same input parameters.

f(f(x)) = f(x)

Math.abs(Math.abs(10))

A function whose definition does not include information regarding its arguments.

let abs = Math.abs

Structure that can be mapped over.

Simplest functor in javascript is an Array

[2,3,4].map( n => n * 2 ); // [4,6,8]

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.

aka call-by-need is an evaluation machanism which delays the evaluation of an expression until its value is needed.

let rand = function*() {
    while(1<2) {
        yield Math.random();
    }
}

let randIter = random();
randIter.next(); // Each exectuion gives a random value, expression is evluated on need.