0xMiden / 0xMiden/air-script

Sort boundary constraints

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Rust
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96
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Description

The order in which the boundary constraints are defined is important. For example:

```
boundary_constraints:
enf p.last = 1
enf p.first = 1
```

Is not the same as:

```
boundary_constraints:
enf p.first = 1
enf p.last = 1
```

The first will emit the following code for the winterfell backend:

```
fn get_aux_assertions>(&self, aux_rand_elements: &AuxTraceRandElements) -> Vec> {
let mut result = Vec::new();
result.push(Assertion::single(0, 0, E::ONE));
result.push(Assertion::single(0, self.last_step(), E::ONE));
result
}
```

And the later

```
fn get_aux_assertions>(&self, aux_rand_elements: &AuxTraceRandElements) -> Vec> {
let mut result = Vec::new();
result.push(Assertion::single(0, self.last_step(), E::ONE));
result.push(Assertion::single(0, 0, E::ONE));
result
}
```

The issue is that the order of `Vec>` determines the order of the composition coefficients, so proofs of the two systems above are not interchangeable. Additionally, this may introduce bugs across different backends, since the order of the coefficients is implicitly defined and can easily become out of sync.

To fix the issue above an ordering is required. A proposal is to sort by `(trace, column_name, step)`, similar to https://github.com/0xPolygonMiden/air-script/issues/314

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