Provisional

This section is for patterns or techniques which are of dubious value, or which might be too niche for inclusion.

Abacus Counters

Provisional: needs a more compelling example. Although an important part of the Ook! macro, matching nested groups that are not denoted by Rust groups is sufficiently unusual that it may not merit inclusion.

Note: this section assumes understanding of push-down accumulation and incremental TT munchers.

macro_rules! abacus {
    ((- $($moves:tt)*) -> (+ $($count:tt)*)) => {
        abacus!(($($moves)*) -> ($($count)*))
    };
    ((- $($moves:tt)*) -> ($($count:tt)*)) => {
        abacus!(($($moves)*) -> (- $($count)*))
    };
    ((+ $($moves:tt)*) -> (- $($count:tt)*)) => {
        abacus!(($($moves)*) -> ($($count)*))
    };
    ((+ $($moves:tt)*) -> ($($count:tt)*)) => {
        abacus!(($($moves)*) -> (+ $($count)*))
    };

    // Check if the final result is zero.
    (() -> ()) => { true };
    (() -> ($($count:tt)+)) => { false };
}

fn main() {
    let equals_zero = abacus!((++-+-+++--++---++----+) -> ());
    assert_eq!(equals_zero, true);
}

This technique can be used in cases where you need to keep track of a varying counter that starts at or near zero, and must support the following operations:

• Increment by one.
• Decrement by one.
• Compare to zero (or any other fixed, finite value).

A value of n is represented by n instances of a specific token stored in a group. Modifications are done using recursion and push-down accumulation. Assuming the token used is x, the operations above are implemented as follows:

• Increment by one: match ($($count:tt)*), substitute (x $($count)*).
• Decrement by one: match (x $($count:tt)*), substitute ($($count)*).
• Compare to zero: match ().
• Compare to one: match (x).
• Compare to two: match (x x).
• (and so on...)

In this way, operations on the counter are like flicking tokens back and forth like an abacus.¹

This desperately thin reasoning conceals the *real* reason for this name: to avoid having *yet another* thing with "token" in the name.  Talk to your writer about avoiding [semantic satiation](https://en.wikipedia.org/wiki/Semantic_satiation) today!

In fairness, it could *also* have been called ["unary counting"](https://en.wikipedia.org/wiki/Unary_numeral_system).

In this case, the operations become slightly more complicated; increment and decrement effectively reverse their usual meanings when the counter is negative. To whit given + and - for the positive and negative tokens respectively, the operations change to:

• Increment by one:
  • match (), substitute (+).
  • match (- $($count:tt)*), substitute ($($count)*).
  • match ($($count:tt)+), substitute (+ $($count)+).
• Decrement by one:
  • match (), substitute (-).
  • match (+ $($count:tt)*), substitute ($($count)*).
  • match ($($count:tt)+), substitute (- $($count)+).
• Compare to 0: match ().
• Compare to +1: match (+).
• Compare to -1: match (-).
• Compare to +2: match (++).
• Compare to -2: match (--).
• (and so on...)

Note that the example at the top combines some of the rules together (for example, it combines increment on () and ($($count:tt)+) into an increment on ($($count:tt)*)).

If you want to extract the actual value of the counter, this can be done using a regular counter macro. For the example above, the terminal rules can be replaced with the following:

macro_rules! abacus {
    // ...

    // This extracts the counter as an integer expression.
    (() -> ()) => {0};
    (() -> (- $($count:tt)*)) => {
        {(-1i32) $(- replace_expr!($count 1i32))*}
    };
    (() -> (+ $($count:tt)*)) => {
        {(1i32) $(+ replace_expr!($count 1i32))*}
    };
}

macro_rules! replace_expr {
    ($_t:tt $sub:expr) => {$sub};
}

JFTE: strictly speaking, the above formulation of abacus! is needlessly complex. It can be implemented much more efficiently using repetition, provided you do not need to match against the counter's value in a macro:

macro_rules! abacus {
    (-) => {-1};
    (+) => {1};
    ($($moves:tt)*) => {
        0 $(+ abacus!($moves))*
    }
}