Is it possible to make a recursive closure in Rust?

As of Rust 1.62 (July 2022), there's still no direct way to recurse in a closure. As the other answers have pointed out, you need at least a bit of indirection, like passing the closure to itself as an argument, or moving it into a cell after creating it. These things can work, but in my opinion they're kind of gross, and they're definitely hard for Rust beginners to follow. If you want to use recursion but you have to have a closure, for example because you need something that implements FnOnce() to use with thread::spawn, then I think the cleanest approach is to use a regular fn function for the recursive part and to wrap it in a non-recursive closure that captures the environment. Here's an example:

let x = 5;
let fact = || {
    fn helper(arg: u64) -> u64 {
        match arg {
            0 => 1,
            _ => arg * helper(arg - 1),
        }
    }
    helper(x)
};
assert_eq!(120, fact());

Here's a really ugly and verbose solution I came up with:

use std::{
    cell::RefCell,
    rc::{Rc, Weak},
};

fn main() {
    let weak_holder: Rc<RefCell<Weak<dyn Fn(u32) -> u32>>> =
        Rc::new(RefCell::new(Weak::<fn(u32) -> u32>::new()));
    let weak_holder2 = weak_holder.clone();
    let fact: Rc<dyn Fn(u32) -> u32> = Rc::new(move |x| {
        let fact = weak_holder2.borrow().upgrade().unwrap();
        if x == 0 {
            1
        } else {
            x * fact(x - 1)
        }
    });
    weak_holder.replace(Rc::downgrade(&fact));

    println!("{}", fact(5)); // prints "120"
    println!("{}", fact(6)); // prints "720"
}

The advantages of this are that you call the function with the expected signature (no extra arguments needed), it's a closure that can capture variables (by move), it doesn't require defining any new structs, and the closure can be returned from the function or otherwise stored in a place that outlives the scope where it was created (as an Rc<Fn...>) and it still works.

There are a few ways to do this.

You can put closures into a struct and pass this struct to the closure. You can even define structs inline in a function:

fn main() {
    struct Fact<'s> { f: &'s dyn Fn(&Fact, u32) -> u32 }
    let fact = Fact {
        f: &|fact, x| if x == 0 {1} else {x * (fact.f)(fact, x - 1)}
    };

    println!("{}", (fact.f)(&fact, 5));
}

This gets around the problem of having an infinite type (a function that takes itself as an argument) and the problem that fact isn't yet defined inside the closure itself when one writes let fact = |x| {...} and so one can't refer to it there.

---

Another option is to just write a recursive function as a fn item, which can also be defined inline in a function:

fn main() {
    fn fact(x: u32) -> u32 { if x == 0 {1} else {x * fact(x - 1)} }

    println!("{}", fact(5));
}

This works fine if you don't need to capture anything from the environment.

---

One more option is to use the fn item solution but explicitly pass the args/environment you want.

fn main() {
    struct FactEnv { base_case: u32 }
    fn fact(env: &FactEnv, x: u32) -> u32 {
        if x == 0 {env.base_case} else {x * fact(env, x - 1)}
    }

    let env =  FactEnv { base_case: 1 };
    println!("{}", fact(&env, 5));
}

All of these work with Rust 1.17 and have probably worked since version 0.6. The fn's defined inside fns are no different to those defined at the top level, except they are only accessible within the fn they are defined inside.