Macro vstd::calc

macro_rules! calc {
    ($($tt:tt)*) => { ... };
}

The calc! macro supports structured proofs through calculations.

In particular, one can show a_1 R a_n for some transitive relation R by performing a series of steps a_1 R a_2, a_2 R a_3, … a_{n-1} R a_n. The calc macro provides both convenient syntax sugar to perform such a proof conveniently, without repeating oneself too often, or exposing the internal steps to the outside context.

The expected usage looks like:

calc! {
  (R)
  a_1; { /* proof that a_1 R a_2 */ }
  a_2; { /* proof that a_2 R a_3 */ }
   ...
  a_n;
}

Currently, the calc! macro supports common transitive relations for R, and this set of relations may be extended in the future.

Note that calc! also supports stating intermediate relations, as long as they are consistent with the main relation R. If consistency cannot be immediately shown, Verus will give a helpful message about this. Intermediate relations can be specified by placing them right before the proof block of that step.

A simple example of using intermediate relations looks like:

let x: int = 2;
let y: int = 5;
calc! {
  (<=)
  x; (==) {}
  5 - 3; (<) {}
  5; {} // Notice that no intermediate relation is specified here, so `calc!` will consider the top-level relation `R`; here `<=`.
  y;
}