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The + operator in Rust serves two distinct syntactic roles: as an algebraic operator that desugars to the std::ops::Add trait for arithmetic and concatenation, and as a type-system operator for specifying compound trait and lifetime bounds.

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The std::ops::Add Trait

When used as a binary operator between values (LHS + RHS), the + symbol is syntactic sugar for the add method of the std::ops::Add trait. The compiler translates a + b into a.add(b). The trait is defined in the standard library as follows: 
pub trait Add<Rhs = Self> {
    type Output;

    fn add(self, rhs: Rhs) -> Self::Output;
}
  • Rhs (Right-Hand Side): A generic type parameter that defaults to Self. This allows the right operand to be a different type than the left operand.
  • Output: An associated type defining the type returned by the addition operation.
  • Ownership: The add method takes ownership of self (the left operand) by value. Whether rhs is consumed or borrowed depends on the specific type implementation.
To enable the + operator for custom types, you must implement this trait: 
use std::ops::Add;

struct Point {
    x: i32,
    y: i32,
}

impl Add for Point {
    type Output = Self;

    fn add(self, rhs: Self) -> Self::Output {
        Self {
            x: self.x + rhs.x,
            y: self.y + rhs.y,
        }
    }
}

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String Concatenation Mechanics

When applied to strings, the + operator relies on a specific implementation of the Add trait: impl Add<&str> for String. 
let s1 = String::from("Hello, ");
let s2 = String::from("world!");
let s3 = s1 + &s2;
Mechanically, this operation:
  1. Takes ownership of s1 (self), meaning s1 is moved and can no longer be used.
  2. Takes a string slice (&str) for the right operand.
  3. Appends the contents of the right operand to the left operand’s memory buffer.
  4. Returns the reused, now-concatenated String.
If the right operand is a &String (as in &s2), Rust applies deref coercion to convert &String into &str (&s2[..]) to satisfy the trait signature.

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Compound Trait and Lifetime Bounds

In the context of the type system, the + operator acts as a logical AND (conjunction) for constraining generic types, opaque types (impl Trait), and trait objects (dyn Trait). Multiple Trait Bounds: It restricts a generic type parameter to types that implement all specified traits. 
// T must implement both Display and Clone
fn print_and_clone<T: std::fmt::Display + Clone>(item: &T) {
    // ...
}

// Equivalent syntax using a where clause
fn print_and_clone_where<T>(item: &T) 
where 
    T: std::fmt::Display + Clone 
{
    // ...
}
Lifetime Bounds: It binds a type or trait object to a specific lifetime, ensuring that any references held within the type outlive the specified lifetime. 
// The trait object must implement Debug and cannot contain 
// references that live shorter than the 'a lifetime.
fn store_debug<'a>(item: Box<dyn std::fmt::Debug + 'a>) {
    // ...
}
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