Implementing a Generic Specialization Algorithm in Rust

This challenge focuses on implementing a flexible specialization mechanism in Rust. You'll create a system that allows defining a generic function and then providing specific implementations (specializations) for particular types. This is useful for optimizing performance, handling specific data types differently, or providing tailored behavior without resorting to complex if/else chains or a multitude of separate functions.

Problem Description

Your task is to implement a core part of a specialization algorithm in Rust. You need to design and implement a system that allows a generic function process to have different implementations based on the type of its input argument. This means that when process is called with a specific type (e.g., i32, String, a custom struct), the compiler should, in a sense, choose the most appropriate pre-defined implementation for that type.

Key Requirements:

Generic process function: You'll define a generic function process<T> that takes a value of type T as input.
Type-specific specializations: You must provide separate, distinct implementations of process for at least two specific types: i32 and String.
Dispatching mechanism: The challenge is to make Rust's type system (or a simulated version of it) select the correct specialized implementation when process is called.
Return type: The specialized functions should return a descriptive String indicating which specialization was executed.

Expected Behavior:

Calling process(10) (where 10 is an i32) should execute the i32 specialization and return "Processed as i32".
Calling process("hello".to_string()) should execute the String specialization and return "Processed as String".
If you choose to implement it, calling process(5.5) (a f64) might have a default generic behavior or a specific specialization.

Edge Cases to Consider:

What happens if process is called with a type for which no explicit specialization is provided? The generic implementation should gracefully handle this, perhaps by returning a default message.

Examples

Example 1:

Input: process(42)
Output: "Processed as i32"
Explanation: The input `42` is of type `i32`, so the `i32` specific implementation of `process` is invoked.

Example 2:

Input: process(String::from("Rust"))
Output: "Processed as String"
Explanation: The input is a `String`, triggering the `String` specific implementation of `process`.

Example 3:

Input: process(vec![1, 2, 3])
Output: "Processed as a generic type"
Explanation: If no specialization is provided for `Vec<i32>`, the generic `process` function will be called.

Constraints

Your solution must be written entirely in Rust.
You should define at least two explicit specializations: one for i32 and one for String.
The generic process<T> function must be defined.
There are no strict performance constraints, but efficient dispatching is encouraged.
Input values will adhere to standard Rust types.

Notes

Rust's trait system and generic programming are powerful tools for achieving this kind of specialization. Consider how you can use traits and their implementations to define default behavior and then override or extend that behavior for specific types. Think about how you might signal to the compiler or your runtime which specific implementation to use. You can approach this by:

Defining a trait with a process method.
Implementing this trait for i32 and String.
Creating a generic function that calls the process method on its input.

However, Rust's standard library doesn't offer a direct "compile-time specialization" in the way some other languages do for arbitrary functions. You'll be implementing a pattern that mimics specialization. Be creative in how you achieve the dispatch.