Rust traits: The bounds might not be implemented, and the traits I've implemented does not exist

Question

So I've been trying to implement a library for vector and matrix maths, and I created some functions that worked alright but wanted to generalize for all number primitives and add the functionality into the normal operators.

My thought was that I'd create a container for a Vec<T>, that can contain either number types (like i32) or another container for Vec, so that matrices where possible. Ergo:

#[derive(Clone, Debug)]
struct Mat<T>(Vec<T>);

Then, to add together two vecs of any number I implement Add as:

impl<'a, T> Add for &'a Mat<T>
where T: PartialEq + PartialOrd + Add<T> + Sub<T> + Mul<T> + Div<T> + Rem<T> + Clone {
    type Output = Option<Mat<<T as std::ops::Add>::Output>>;

    fn add(self, other: &Mat<T>) -> Self::Output {
        let a: &Vec<T> = self.pop();
        let b: &Vec<T> = other.pop();
        match a.len() == b.len() {
            true => {
                let mut retvec: Vec<<T as std::ops::Add>::Output> = Vec::new();
                for i in 0..a.len() {
                    retvec.push(a[i].clone() + b[i].clone());
                }
                Some(Mat(retvec))
            },
            false => None
        }
    }
}

Edit: To further clarify, Mat::pop() is just the unwrap function, though probably poorly named.

The basic scenario of adding together two vectors of any number seems to work.

#[test]
fn add_override_vectors() {
    let vec: Mat<i32> = Mat(vec![2, 2, 2]);
    let newvec = &vec + &vec;

    assert_eq!(*newvec.unwrap().pop(), vec![4,4,4]);
}

But matrices are giving me a headache. For them, the add function looks very similar, except for the let Some(x) statement:

impl<'a, T> Add for &'a Mat<Mat<T>>
where T: Add<&'a Mat<T>>{
    type Output = Option<Mat<T>>;

    fn add(self, other: &Mat<Mat<T>>) -> Self::Output {
        let a: &Vec<Mat<T>> = self.pop();
        let b: &Vec<Mat<T>> = other.pop();
        match a.len() == b.len() {
            true => {
                let mut retvec: Vec<T> = Vec::new();
                for i in 0..a.len() {
                    if let Some(x) = &a[i] + &b[i] {
                        retvec.push(x);
                    }
                }
                Some(Mat(retvec))
            },
            false => None
        }
    }
}

The error message I get is:

error[E0369]: binary operation `+` cannot be applied to type `&Mat<T>`
  --> src\main.rs:46:38
   |
46 |                     if let Some(x) = &a[i] + &b[i] {
   |                                      ^^^^^^^^^^^^^
   |
   = note: an implementation of `std::ops::Add` might be missing for `&Mat<T>`

So the compiler says that Add might not be implemented for &Mat<T>, but I thought that I've specified the bound so that it has that requirement in where T: Add<&'a Mat<T>. To me it seems that whatever is in &a[i] should have the Add trait implemented. What am I doing wrong here?

Just as extra clarification, my idea is that Add for &'a Mat<Mat<T>> should be able to be called recursively until it boils down to the Vec with an actual number type in it. Then the Add for &'a Mat<T> should be called.

Answer 1

There are two problems: the wrong associated Output type and the type of retvec

Something like that should work:

impl<'a, T> Add for &'a Mat<Mat<T>>
where
    T: PartialEq + PartialOrd + Add<T> + Clone,
{
    type Output = Option<Mat<Mat<<T as std::ops::Add>::Output>>>;

    fn add(self, other: &Mat<Mat<T>>) -> Self::Output {
        let a: &Vec<Mat<T>> = self.pop();
        let b: &Vec<Mat<T>> = other.pop();
        match a.len() == b.len() {
            true => {
                let mut retvec: Vec<Mat<<T as std::ops::Add>::Output>> = Vec::new();
                for i in 0..a.len() {
                    if let Some(x) = &a[i] + &b[i] {
                        retvec.push(x);
                    }
                }
                Some(Mat(retvec))
            }
            false => None,
        }
    }
}

A part the compilation issue I think it is not correct to implement a trait for a "recursive" struct like Mat<Mat<T>>, if you think X as type X = Mat<T> then the impl for Mat<T> suffices:

impl<'a, T> Add for &'a Mat<T>
where
    T: PartialEq + PartialOrd + Add<T> + Clone

with the additional impl for Mat<T> values:

impl<T> Add for Mat<T>
where
    T: PartialEq + PartialOrd + Add<T> + Clone

Below I post a full working code, please note that the Output type is no more an Option<Mat<T>> but a plain Mat<T> object: this avoids a lot of headaches and probably it is conceptually wrong if you want to impl some type of algebra.

use std::ops::*;
use std::vec::Vec;

#[derive(Clone, Debug, PartialEq, PartialOrd)]
struct Mat<T>(Vec<T>);

impl<T> Mat<T> {
    fn pop(&self) -> &Vec<T> {
        &self.0
    }
}

impl<T> Add for Mat<T>
where
    T: PartialEq + PartialOrd + Add<T> + Clone,
{
    type Output = Mat<<T as std::ops::Add>::Output>;

    fn add(self, other: Mat<T>) -> Self::Output {
        let a: &Vec<T> = self.pop();
        let b: &Vec<T> = other.pop();
        match a.len() == b.len() {
            true => {
                let mut retvec: Vec<<T as std::ops::Add>::Output> = Vec::new();
                for i in 0..a.len() {
                    retvec.push(a[i].clone() + b[i].clone());
                }
                Mat(retvec)
            }
            false => Mat(Vec::new()),
        }
    }
}

impl<'a, T> Add for &'a Mat<T>
where
    T: PartialEq + PartialOrd + Add<T> + Clone,
{
    type Output = Mat<<T as std::ops::Add>::Output>;

    fn add(self, other: &Mat<T>) -> Self::Output {
        let a: &Vec<T> = self.pop();
        let b: &Vec<T> = other.pop();
        match a.len() == b.len() {
            true => {
                let mut retvec: Vec<<T as std::ops::Add>::Output> = Vec::new();
                for i in 0..a.len() {
                    retvec.push(a[i].clone() + b[i].clone());
                }
                Mat(retvec)
            }
            false => Mat(Vec::new()),
        }
    }
}


#[test]
fn add_override_vectors() {
    let vec: Mat<Mat<i32>> = Mat(vec![Mat(vec![2, 2, 2]), Mat(vec![3, 3, 3])]);
    let newvec = &vec + &vec;

    assert_eq!(*newvec.pop(), vec![Mat(vec![4, 4, 4]), Mat(vec![6, 6, 6])]);
}

#[test]
fn add_wrong_vectors() {
    let vec1: Mat<Mat<i32>> = Mat(vec![Mat(vec![2, 2, 2]), Mat(vec![4, 4, 4])]);
    let vec2: Mat<Mat<i32>> = Mat(vec![Mat(vec![3, 3, 3]), Mat(vec![3, 3])]);
    let newvec = &vec1 + &vec2;

    assert_eq!(*newvec.pop(), vec![Mat(vec![5, 5, 5]), Mat(vec![])]);
}


fn main() {
    let vec: Mat<Mat<i32>> = Mat(vec![Mat(vec![1, 2, 2]), Mat(vec![3, 3, 3])]);
    let newvec = &vec + &vec;

    println!("Hello, world!: {:?}", newvec);
}

PS: Your Mat<T> type is not a matrix in the classical sense, perhaps another name should be more appropriate to avoid confusion.