# Push-down Accumulation

The following macro uses push-down accumulation.

#![allow(unused)]
fn main() {
macro_rules! init_array {
[$e:expr;$n:tt] => {
{
let e = $e; accum!([$n, e.clone()] -> [])
}
};
}
macro_rules! accum {
([3, $e:expr] -> [$($body:tt)*]) => { accum!([2,$e] -> [$($body)* $e,]) }; ([2,$e:expr] -> [$($body:tt)*]) => { accum!([1, $e] -> [$($body)*$e,]) };
([1, $e:expr] -> [$($body:tt)*]) => { accum!([0,$e] -> [$($body)* $e,]) }; ([0,$_:expr] -> [$($body:tt)*]) => { [$($body)*] };
}

let strings: [String; 3] = init_array![String::from("hi!"); 3];
assert_eq!(format!("{:?}", strings), "[\"hi!\", \"hi!\", \"hi!\"]");
}


All syntax extensions in Rust must result in a complete, supported syntax element (such as an expression, item, etc.). This means that it is impossible to have a syntax extension expand to a partial construct.

One might hope that the above example could be more directly expressed like so:

macro_rules! init_array {
[$e:expr;$n:tt] => {
{
let e = $e; [accum!($n, e.clone())]
}
};
}
macro_rules! accum {
(3, $e:expr) => {$e, accum!(2, $e) }; (2,$e:expr) => { $e, accum!(1,$e) };
(1, $e:expr) => {$e };
}


The expectation is that the expansion of the array literal would proceed as follows:

    [accum!(3, e.clone())]
[e.clone(), accum!(2, e.clone())]
[e.clone(), e.clone(), accum!(1, e.clone())]
[e.clone(), e.clone(), e.clone()]


However, this would require each intermediate step to expand to an incomplete expression. Even though the intermediate results will never be used outside of a macro context, it is still forbidden.

Push-down, however, allows us to incrementally build up a sequence of tokens without needing to actually have a complete construct at any point prior to completion. In the example given at the top, the sequence of invocations proceeds as follows:

init_array!(String::from("hi!"); 3)
accum!([3, e.clone()] -> [])
accum!([2, e.clone()] -> [e.clone(),])
accum!([1, e.clone()] -> [e.clone(), e.clone(),])
accum!([0, e.clone()] -> [e.clone(), e.clone(), e.clone(),])
[e.clone(), e.clone(), e.clone(),]


As you can see, each layer adds to the accumulated output until the terminating rule finally emits it as a complete construct.

The only critical part of the above formulation is the use of $($body:tt)* to preserve the output without triggering parsing. The use of ($input) -> ($output) is simply a convention adopted to help clarify the behavior of such macros.

Push-down accumulation is frequently used as part of incremental TT munchers, as it allows arbitrarily complex intermediate results to be constructed. Internal Rules were of use here as well, as they simplify creating such macros.

## Performance

Push-down accumulation is inherently quadratic. Consider a push-down accumulation rule that builds up an accumulator of 100 token trees, one token tree per invocation.

• The initial invocation will match against the empty accumulator.
• The first recursive invocation will match against the accumulator of 1 token tree.
• The next recursive invocation will match against the accumulator of 2 token trees.

And so on, up to 100. This is a classic quadratic pattern, and long inputs can cause macro expansion to blow out compile times. Furthermore, TT munchers are also inherently quadratic over their input, so a macro that uses both TT munching and push-down accumulation will be doubly quadratic!

All the performance advice about TT munchers holds for push-down accumulation. In general, avoid using them too much, and keep them as simple as possible.

Finally, make sure you put the accumulator at the end of rules, rather than the beginning. That way, if a rule fails, the compiler won't have had to match the (potentially long) accumulator before hitting the part of the rule that fails to match. This can make a large difference to compile times.