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.