mismatched types

#![feature(no_core, lang_items)]
#![no_core]

#[lang = "sized"]
pub trait Sized {}

extern "C" {
    fn printf(format: *const i8, ...);
}

enum ast<'a> {
    num(usize),
    add(&'a ast<'a>, &'a ast<'a>),
}

fn eval(node: &ast) -> usize {
    match node {
        ast::num(n) => *n,
        ast::add(l, r) => eval(l) + eval(r),
    }
}

fn main() -> i32 {
    let a = ast::num(3);
    let b = ast::num(4);
    let c = ast::add(&a, &b);
    let d = ast::num(10);
    let e = ast::add(&c, &d);
    unsafe {
        printf("%d\n\0" as *const str as *const i8, eval(&e) as i32);
    }
    0
}

with my recusive adts work this fails with:

test.rs:31:5: error: mismatched types, expected ‘& ast’ but got ‘ast’ [E0308]
   31 |     match node {
      |     ^~~~~ ~~~~
   32 |         ast::num(n) => *n,
      |         ~~~
test.rs:31:5: error: mismatched types, expected ‘& ast’ but got ‘ast’ [E0308]
   31 |     match node {
      |     ^~~~~ ~~~~
   32 |         ast::num(n) => *n,
   33 |         ast::add(l, r) => eval(l) + eval(r),
      |         ~~~
test.rs:40:22: error: mismatched types, expected ‘ast’ but got ‘ast’ [E0308]
   27 |     add(&'a ast<'a>, &'a ast<'a>),
      |             ~~~       
......
   40 |     let c = ast::add(&a, &b);
      |                      ^~
test.rs:42:23: error: cannot find value ‘c’ in this scope [E0425]
   42 |     let e = ast::add(&c, &d);
      |                       ^
test.rs:42:22: error: failed to resolve argument type
   42 |     let e = ast::add(&c, &d);
      |                      ^
test.rs:44:60: error: cannot find value ‘e’ in this scope [E0425]
   44 |         printf("%d\n\0" as *const str as *const i8, eval(&e) as i32);
      |                                                            ^

Run the supplied test.rs reproducer first and confirm the recursive ADT mismatched-type errors. Then trace the compiler's recursive ADT and type-checking handling to determine why references are treated as mismatched types; done means the reproducer compiles without these errors.