Module rust2fun::monad

source ·
Expand description

Monad.

A monad is a monoid in the category of endofunctors, what these means is that there must be two operations, pure and flat_map, and these two operations must satisfy three laws:

  1. Left identity: pure(x).flat_map(f) == f(x)
  2. Right identity: m.flat_map(pure) == m
  3. Associativity: m.flat_map(f).flat_map(g) == m.flat_map(|x| f(x).flat_map(g))

The first law says that if we take a value, put it in a default context with pure and then flat_map it with a function, we get the same result as just taking the value and applying the function to it.

The second law says that if we have a monad, we can flat_map it with the pure function and the result is our original monad.

The third law says that flat_map is associative. This may not be so obvious, but what it’s saying is that it doesn’t matter how we nest our flat_maps, the result is the same. In other words, the following two expressions are equivalent:

ⓘ
m.flat_map(f).flat_map(g)
ⓘ
m.flat_map(|x| f(x).flat_map(g))

The first law is sometimes called the “unit law” and the second law is sometimes called the “morphism law”. The third law is sometimes called the “associativity law”.

Examples

use rust2fun::prelude::*;

fn get_user(id: u32) -> Option<User> {
    todo!("Get a user from a storage by id if it exists")
}

fn get_credit_card(user: User) -> Option<CreditCard> {
    todo!("Get a credit card of the user if it has one")
}

fn charge_credit_card(amount: u32, card: CreditCard) -> Option<Transaction> {
    todo!("Charge a credit card if it has enough money")
}

fn charge_user_card(amount: u32, user_id: u32) -> Option<Transaction> {
    get_user(user_id)
        .flat_map(get_credit_card)
        .flat_map(|card| charge_credit_card(amount, card))
}

// Or using the `bind!` macro:
fn charge_user_card_alt(amount: u32, user_id: u32) -> Option<Transaction> {
    bind! {
        for user in get_user(user_id);
        for card in get_credit_card(user);
        return charge_credit_card(amount, card);
    }
}

Traits