How to compose functions in Rust?

Question

I'm trying to write a function that composes two functions. The initial design is pretty simple: a function that takes two functions and returns a composed function which I can then compose with other functions, since Rust doesn't have rest parameters. I've run into a wall built with frustrating non-helpful compiler errors.

My compose function:

fn compose<'a, A, B, C, G, F>(f: F, g: G) -> Box<Fn(A) -> C + 'a>
where
    F: 'a + Fn(A) -> B + Sized,
    G: 'a + Fn(B) -> C + Sized,
{
    Box::new(move |x| g(f(x)))
}

How I would like to use it:

fn main() {
    let addAndMultiply = compose(|x| x * 2, |x| x + 2);
    let divideAndSubtract = compose(|x| x / 2, |x| x - 2);

    let finally = compose(*addAndMultiply, *divideAndSubtract);
    println!("Result is {}", finally(10));
}

The compiler doesn't like that, no matter what I try, the trait bounds are never satisfied. The error is:

error[E0277]: the size for values of type `dyn std::ops::Fn(_) -> _` cannot be known at compilation time
  --> src/main.rs:13:19
   |
13 |     let finally = compose(*addAndMultiply, *divideAndSubtract);
   |                   ^^^^^^^ doesn't have a size known at compile-time
   |
   = help: the trait `std::marker::Sized` is not implemented for `dyn std::ops::Fn(_) -> _`
   = note: to learn more, visit <https://doc.rust-lang.org/book/ch19-04-advanced-types.html#dynamically-sized-types-and-the-sized-trait>
note: required by `compose`
  --> src/main.rs:1:1
   |
1  | / fn compose<'a, A, B, C, G, F>(f: F, g: G) -> Box<Fn(A) -> C + 'a>
2  | | where
3  | |     F: 'a + Fn(A) -> B + Sized,
4  | |     G: 'a + Fn(B) -> C + Sized,
5  | | {
6  | |     Box::new(move |x| g(f(x)))
7  | | }
   | |_^

Answer 1

As @ljedrz points out, to make it work you only need to reference the composed functions again:

let finally = compose(&*multiply_and_add, &*divide_and_subtract);

(Note that in Rust, convention dictates that variable names should be in snake_case)

---

However, we can make this better!

Since Rust 1.26, we can use abstract return types (previously featured gated as #![feature(conservative_impl_trait)]). This can help you simplify your example greatly, as it allows you to skip the lifetimes, references, Sized constraints and Boxes:

fn compose<A, B, C, G, F>(f: F, g: G) -> impl Fn(A) -> C
where
    F: Fn(A) -> B,
    G: Fn(B) -> C,
{
    move |x| g(f(x))
}

fn main() {
    let multiply_and_add = compose(|x| x * 2, |x| x + 2);
    let divide_and_subtract = compose(|x| x / 2, |x| x - 2);

    let finally = compose(multiply_and_add, divide_and_subtract);
    println!("Result is {}", finally(10));
}

---

Finally, since you mention rest parameters, I suspect that what you actually want is to have a way to chain-compose as many functions as you want in a flexible manner. I wrote this macro for this purpose:

macro_rules! compose {
    ( $last:expr ) => { $last };
    ( $head:expr, $($tail:expr), +) => {
        compose_two($head, compose!($($tail),+))
    };
}

fn compose_two<A, B, C, G, F>(f: F, g: G) -> impl Fn(A) -> C
where
    F: Fn(A) -> B,
    G: Fn(B) -> C,
{
    move |x| g(f(x))
}

fn main() {
    let add = |x| x + 2;
    let multiply = |x| x * 2;
    let divide = |x| x / 2;
    let intermediate = compose!(add, multiply, divide);

    let subtract = |x| x - 2;
    let finally = compose!(intermediate, subtract);

    println!("Result is {}", finally(10));
}

Answer 2

Just add references in finally and it will work:

fn main() {
    let addAndMultiply = compose(|x| x * 2, |x| x + 2);
    let divideAndSubtract = compose(|x| x / 2, |x| x - 2);

    let finally = compose(&*addAndMultiply, &*divideAndSubtract);
    println!("Result is {}", finally(10));
}

Dereferencing addAndMultiply or divideAndSubtract uncovers a trait object which is not Sized; it needs to either be wrapped in a Box or referenced in order for it to be passed to a function with a Sized constraint.

Answer 3

macro_rules! comp {
    ($f: expr) => {
        move |g: fn(_) -> _| move |x: _| $f(g(x))
    };
}

fn main() {
    let add1 = |x| x + 1;
    let add2 = |x| x + 2;
    let add3 = comp!(add1)(add2);
    println!("{}", add3(3));
}

https://play.rust-lang.org/?version=stable&mode=debug&edition=2018&gist=1c6915d94f7e1e35cf93fb21daceb9ef