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

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 = sum.bind(null, 40);

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

// Partial application with curried functions (R = Ramda)
let addOne = R.map(R.add(1))

//Invoking with number array
addOne([1,2,3]) //=> [2,3,4]

Currying

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.

Curried functions can be called with 1 to all parameters. Each call returns a new function until all parameters are satisfied.

let addThreeNumbers = (a,b,c) => a+b+c;
// R = Ramda
let curriedAddThreeNumbers = R.curry(addThreeNumbers);

curriedAddThreeNumbers(1)(2)(3) // 6.
curriedAddThreeNumbers(1,2,3) // 6.

let twoNumbers = curriedAddThreeNumbers(1,2);
twoNumbers(3) // 6.

Purity

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;

Side effects

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!");

Idempotency

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))

Point Free

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

let abs = Math.abs
//R = Ramda
let makeAllUpper = R.map(R.toUpper)
makeAllUpper(['joe', 'frank']) //['JOE', 'FRANK']

Contracts

Guarded Functions

Functor

Structure that can be mapped over.

Simplest functor in javascript is an Array

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

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.

Equational Reasoning

Lazy evalution

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.

btroncone / functional-programming-jargons

Functional Programming Jargons

Arity

Higher Order Functions (HOF)

Partial Application

Currying

Purity

Side effects

Idempotency

Point Free

Contracts

Guarded Functions

Categories

Functor

Referential Transparency

Equational Reasoning

Lazy evalution

Monoid

Monad

##Comonad

Applicative Functor

Morphism

Setoid

Semigroup

Chain

References

Functional Utility Libraries

Exercises

Articles

Videos

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