How can I merge two JSON objects with Rust?

Placing the answer suggested by Shepmaster below

#[macro_use]
extern crate serde_json;

use serde_json::Value;

fn merge(a: &mut Value, b: Value) {
    match (a, b) {
        (a @ &mut Value::Object(_), Value::Object(b)) => {
            let a = a.as_object_mut().unwrap();
            for (k, v) in b {
                merge(a.entry(k).or_insert(Value::Null), v);
            }
        }
        (a, b) => *a = b,
    }
}

fn main() {
    let mut a = json!({
        "title": "This is a title",
        "person" : {
            "firstName" : "John",
            "lastName" : "Doe"
        },
        "cities":[ "london", "paris" ]
    });

    let b = json!({
        "title": "This is another title",
        "person" : {
            "firstName" : "Jane"
        },
        "cities":[ "colombo" ]
    });

    merge(&mut a, b);
    println!("{:#}", a);
}

Since you wanted to use json-patch, I assume you were looking specifically for a JSON Merge Patch (RFC 7396) implementation which is what that crate implements. In that case, merging an object should unset those keys whose corresponding value in the patch is null, which the code samples in the other answers do not implement.

The code that accounts for that is below. I modified the patch to delete the person.lastName key by setting it to null as a demonstration. It also does not need to unwrap() the Option returned by as_object_mut().

#[macro_use]
extern crate serde_json;

use serde_json::Value;

fn merge(a: &mut Value, b: Value) {
    if let Value::Object(a) = a {
        if let Value::Object(b) = b {
            for (k, v) in b {
                if v.is_null() {
                    a.remove(&k);
                }
                else {
                    merge(a.entry(k).or_insert(Value::Null), v);
                }
            } 

            return;
        }
    }

    *a = b;
}

fn main() {
    let mut a = json!({
        "title": "This is a title",
        "person" : {
            "firstName" : "John",
            "lastName" : "Doe"
        },
        "cities":[ "london", "paris" ]
    });

    let b = json!({
        "title": "This is another title",
        "person" : {
            "firstName" : "Jane",
            "lastName": null
        },
        "cities":[ "colombo" ]
    });

    merge(&mut a, b);
    println!("{:#}", a);
}

The expected output is

{
  "cities": [
    "colombo"
  ],
  "person": {
    "firstName": "Jane"
  },
  "title": "This is a title"
}

Notice person.lastName has been unset.