monadsjs

Installation

npm install --save monadsjs

Monads

Don't forget to check tests.

Identity

It's the most basic monad implementation which only wraps a value. It doesn't make much sense to use this monad as is. Understanding Identity monad is quite crucial to move forward. It can be a starting point for any new monad.

// Identity.unit :: a -> M a
// Identity.bind :: (a -> M b) -> M b
// Identity.map  :: (a -> b) -> M b
 
Identity.unit("Monads are awesome!")
  .bind(str => Identity.unit(str.split(" ")))
  .map(words => words.length);
 
// Identity(3)

Maybe (Just | Nothing)

Maybe monad represents a value (Just) or monadic zero (Nothing). It's very convinient way to literally, let your code fail. Instead of writing multiple checks and try-catches just check type of the value at the end of transformations chain. In this particular implementation Maybe is just a union type which exists only if you are using TypeScript.

Just wraps actual value.

// Just.unit :: a -> Just a
// Just.bind :: (a -> Just b | Nothing) -> Just b | Nothing
// Just.map  :: (a -> b) -> Just b | Nothing
 
Just.unit("Monads are awesome!")
  .bind(str => Just.unit(str.split(" ")))
  .map((words: string[]) => words.length);
 
  // Just(3)

At that point it's really similar to Identity monad. Things looks different when Nothing comes in. Nothing can be explicity returned from function passed to bind or when error occures. Further execution is stopped. In the following example double is not going to be called due to TypeError throwed in firstWordLength when empty array is passed.

// Nothing.unit :: () -> Nothing
// Nothing.bind :: (a -> Just b | Nothing) -> Nothing
// Nothing.map  :: (a -> b) -> Nothing
 
const firstWordLength = words => words[0].length;
const double = n => n * 2;
 
Just.unit([])
  .bind(strs => Just.unit(firstWordLength(strs)));
  .map(double);
 
  // Nothing()

Either (Left | Right)

Either monad is almost like a Maybe monad. Right and Just are basically the same. Either unlike Maybe doesn't have monadic zero. Left is supposed to wrap Error. Left can be explicity returned from function passed to bind or when error occures. In this particular implementation Either is just a union type which exists only if you are using TypeScript. In the following example double is not going to be called due to TypeError throwed in firstWordLength when empty array is passed.

// Right.unit :: a -> Right a
// Right.bind :: (a -> Right b | Left b) -> Right b | Left b
// Right.map  :: (a -> b) -> Right b | Left b
 
Right.unit("Monads are awesome!")
  .bind(str => Right.unit(str.split(" ")))
  .map((words: string[]) => words.length);
 
  // Right(3)

// Left.unit :: a -> Left a
// Left.bind :: (a -> Right b | Left b) -> Left a
// Left.map  :: (a -> b) -> Left a
 
const firstWordLength = words => words[0].length;
const double = n => n * 2;
 
Right.unit([])
  .bind(strs => Right.unit(firstWordLength(strs)))
  .map(double);
 
  // Left(TypeError: Cannot read property 'length' of undefined)

IO

IO monad was invented to make it possible to perform side effects in pure functional languages (here I have Haskell in mind). In JavaScript we can take an advantage of IO monads to change unpure functions into pure which makes them easy to test. This implementation is also a Setoid. IO.equals makes it easy to deeply compare two IO monads.

// IO.unit :: (a, ...) -> IO a, [...]
// IO.bind :: ((a, ...) -> IO) -> IO a, [...]
// IO.run  :: () -> void
 
function sayHello(name) {
  return IO.unit(alert, `Hello ${name}!`);
}
 
const m = sayHello("World"); // IO(sayHello, ["World"])
 
assert(m.equals(IO.unit(alert, "Hello World!"))); // passes
 
m.run(); // alerts: Hello World!

Continuation (Promise)

Promise out of the box is a great Continuation monad implementation! Promise.resolve corresponds to unit and Promise.then corresponds to bind. Provided Continuation implementation is a minimal wrapper for Promise with methods you know from other monads (bind and unit). Don't use it, use Promise.

// Continuation.unit :: a -> Continuation a
// Continuation.bind :: (a -> b) -> Continuation b
 
Continuation.unit(fetch("https://api.github.com/users/octocat"))
  .bind(response => response.json());
 
  // Continuation(<Promise>{ "login": "octocat", "id": ... })

List

List monad is a clever one. List constructor accepts Iterable and allows for lazy transformations. It is achieved using generators. What is more, List implements Symbol.iterator so you can iterate through it like any regular iterator.

// List.unit    :: a -> List a
// List.bind    :: (a -> List b) -> List b
// List.map     :: (a -> b) -> List b
// List.forEach :: (a -> void) -> void
 
const lazySpy = sinon.spy();
const nextLazySpy = sinon.spy();
 
const m = List.of([1, 2, 3])
  .map(x => {
    lazySpy();
    return x + 1;
  }).map(x => {
    nextLazySpy();
    return x + 1;
  });
 
  // List([object Generator])
 
const asIterable = m[Symbol.iterator]();
 
// no computation was done so far
 
assert(lazySpy.notCalled);
assert(nextLazySpy.notCalled);
 
assert(asIterable.next().value === 3);
 
// only first value was computed
 
assert(lazySpy.calledOnce);
assert(nextLazySpy.calledOnce);
 
assert(asIterable.next().value === 4);
assert(lazySpy.calledTwice);
assert(nextLazySpy.calledTwice);
 
assert(asIterable.next().value === 5);
assert(lazySpy.calledThrice);
assert(nextLazySpy.calledThrice);

Monads next

Monad next is a bit different approach to implementing monads in JavaScript. It requires :: bind operator wich is not yet supported in TypeScript (shame on you TypeScript, ave Babel!) and having types when implemening monads is more important for me at this very moment.

const List = {
  *unit(iterable) {
    yield* iterable;
  },
 
  *bind(fn) {
    for (let x of this) {
      yield fn(x);
    }
  }
};
 
const m = List.unit([1, 2, 3])::List.bind(x => x + 1)::List.bind(x => x + 1);

Check it live.