Discussion on: Actually, callbacks are fine

[Ralph Fischer]

I'm not going to argue about strict definitions with you because you don't know what you're talking about and are opinionated about your misconceptions. I simply don't have the time.

They are the same - please inform yourself more thoroughly.

// pure :: a -> m a
const pure = v => Promise.resolve(v);
// (>>=) :: m a -> (a -> m b) -> m b 
const bind = ma => a2mb => ma.then(a2mb);

bind(pure(1))((v) => pure(v + 1))// == pure(2)

Not being able to implement join has nothing to do with it being a monad. It's because they're automatically flattened. You don't have to implement m (m a) -> m a if m (m a) is equivalent to m a. But again - it has nothing to do with it being a monad.

My point is that they can be used the same way as your continuation monad implementation and as such should be favoured over it because they're standard language constructs. Period.

Also, of course async function verifyUser(user, password) { ... } is a pure function. It's referentially transparent in the sense that given the same parameters the Promise returned will always be the same. How that promise is consumed doesn't matter. Again - inform yourself.

Lazy evaluation also doesn't have anything to do with purity or it being a monad. (regarding your deleteUser example. You're mixing up concepts that you don't seem to understand)

[Asad Saeeduddin]

Thanks, the definition you posted above is helpful. Try evaluating const map = f => bind(x => pure(f(x))); map(pure)(pure(5)) to understand why this is not actually a lawful implementation of bind.

Without having a join operation (which can be recovered as bind(id) from a lawful bind), it's actually meaningless to talk about a "monad". Monads are fundamentally defined by an associative join and an idempotent pure, together forming a monoid.

This isn't about lazy evaluation vs strict evaluation, but rather about pure vs impure evaluation. The term verifyUser(user, password) does not purely evaluate to a representation of an effect; instead it immediately starts performing effects in the course of its evaluation. The result of evaluating it is not dependent only on its inputs, but also on the state of the world.

This means verifyUser isn't actually a function in the functional programming sense of the word, preventing us from reasoning equationally in programs that involve it. For example the following program:

const userDetails = b ? map(just)(verifyUser(user, password)) : pure(nothing)

is not the same program as:

const verification = map(just)(verifyUser(user, password))

const default = pure(nothing)

const userDetails = b ? verification : default

when using promises. It is when using a lawful asynchronicity monad (e.g. the continuation monad above). Whether this is bad or good depends on whether you prefer an imperative or functional style of reasoning.

[Ralph Fischer]

Your definition of monads is wrong. It has nothing to do with join, their time of evaluation or 'imperative vs functional reasoning' lol.

Here are the monadic laws proven with the Promise definitions from above - in js.

// pure :: a -> m a
const pure = v => Promise.resolve(v);
// (>>=) :: m a -> (a -> m b) -> m b 
const bind = ma => a2mb => ma.then(a2mb);

// monadic laws
// 1. left identity - pure a >>= f ≡ f a
const f = v => pure(v + 1);
bind(pure(1))(f) // == f(1) ✔

// 2. right identity - m >>= pure ≡ m
const m = pure(1);
bind(m)(pure) // == m ✔

// 3. associativity - (m >>= f) >>= g ≡ m >>= (\x -> f x >>= g)
const m = pure(1);
const f = v => pure(v + 1);
const g = v => pure(v * 2);
bind(bind(m)(f))(g) // == pure(4) ✔
bind(m)(x => bind(f(x))(g)) // == pure(4) ✔

You're also wrong about the fact that the promises don't evaluate to the representation of an effect first. Of course they do. The point in time the underlying implementation decides to consume that value has no significance whatsoever. As I said - you're mixing up concepts, don't understand monads and likely don't understand Promises either.

[Asad Saeeduddin]

This is the first time I've heard that monads have nothing to do with the join operation. You should share this revolutionary insight with the mathematics community.

Regarding the "proof" of the monadic laws above, unfortunately the laws don't hold for the definitions given (the proof-by-single-example notwithstanding). In fact, the definitions are not even well-typed.

Conveniently, to disprove something requires only a single counterexample:

// Function composition
// :: a -> a
const id = x => x
// :: (b -> c) -> (a -> b) -> a -> c
const compose = f => g => x => f(g(x))

// A pair of operations witnessing that a particular type constructor forms a monad
// :: type Monad m = { pure: a -> m a, bind: m a -> (a -> m b) -> m b }

// The associativity law satisfied by any monad
// :: Monad m -> [m Int, m Int]
const testAssociativity = ({ pure, bind }) => {
  // Some selected inputs
  // :: m Int
  const mx = pure(42)
  // :: a -> m (m a)
  const f = compose(pure)(pure)
  // :: m a -> m a
  const g = ma => bind(ma)(pure)

  // associativity:
  // (mx >>= f) >>= g
  // ===
  // mx >>= \x -> f x >>= g

  // :: m Int
  const ml = bind(bind(mx)(f))(g)
  // :: m Int
  const mr = bind(mx)(x => bind(f(x))(g))

  return [ml, mr]
}

// The array monad
// :: Monad Array
const array = {
  pure: v => [v],
  bind: ma => a2mb => ma.reduce((p, a) => [...p, ...a2mb(a)], [])
}

// Is it really a monad?
const [a1, a2] = testAssociativity(array)
console.log(a1)
console.log(a2)

// The promise "monad"
// :: Monad Promise
const promise = {
  pure: v => Promise.resolve(v),
  bind: ma => a2mb => ma.then(a2mb)
}

// Is it really a monad?
const [p1, p2] = testAssociativity(promise)
p1.then(x => { console.log(x) })
p2.then(x => { console.log(x) })

I'd like to have discussed how the word "monad" refers to a particular kind of endofunctor with join and pure natural transformations, but I really have to take a break from this conversation. I don't mind discussing things with people I disagree with, but the complete lack of manners displayed in your comments goes poorly with your total ignorance of the subject.