This PR sets up the new integrated test/bench suite. It then migrates
all benchmarks and some related tests to the new suite. There's also
some documentation and some linting.
For now, a lot of the old tests are left alone so this PR doesn't become
even larger than it already is. Eventually, all tests should be migrated
to the new suite though so there isn't a confusing mix of two systems.
This PR changes the signature of `Array.swap`, so it takes `Nat`
arguments with tactic provided bounds checking. It also renames
`Array.swap!` to `Array.swapIfInBounds`.
This PR modifies the signature of the functions `Nat.fold`,
`Nat.foldRev`, `Nat.any`, `Nat.all`, so that the function is passed the
upper bound. This allows us to change runtime array bounds checks to
compile time checks in many places.
@Kha I had some unexpected surprises, but it is a good change.
Here is the summary.
1- We could get rid of `a %ₙ b` and `ModN` class. We can use `HMod`
instead. It was a positive surprise since I didn't remember we had
this `ModN` class.
2- Coercions are never used in heterogeneous operators. This is
expected since `a * b` is now notation for `HMul.hMul a b`, and
`a` and `b` may have different types. I manually added instances such
as `HMul Nat Int Int`. However, I did not try to add generic instances
such as
```
instance [Coe a b] [Mul b] : HMul a b b where
hMul x y := mul (coe x) y
```
I will try later.
3- Give `h : cs.size > 0`, I got a type error at
```
let idx : Fin cs.size := ⟨cs.size - 1, Nat.predLt h⟩
```
`Nat.predLt h` has type `Nat.pred cs.size < cs.size`
However, `Nat.pred cs.size` doesn't unify with `cs.size - 1`.
The problem is that we can't synthesize the `HSub` instance until
we apply the default instances.
It worked before because `isDefEq` would force the pending TC
problem `Sub Nat` to be resolved, and after that we would be able
to reduce `cs.size - 1` and establish that it is definitionally
equal to `Nat.pred cs.size`.
I considered two possible workarounds
a) `let idx : Fin cs.size := ⟨cs.size - (1:Nat), Nat.predLt h⟩`
b) `let idx : Fin cs.size := ⟨cs.size - 1, by exact Nat.predLt h⟩`
The first one works because we are not providing enough information
for synthesizing the `HSub` instance. The second works because it
postpones the elaboration of `Nat.predLt h`. The default instances
will be applied before we start applying tactics.
4- The `.` notation is affected too. For example, `(x + 1).toUInt8`
doesn't work since we don't know the type of `x+1` until we apply
default instances. I fixed it by using `(x + (1:Nat)).toUInt8`.
Another possible fix is `Nat.toUInt8 (x + 1)`.
Similarly, `(x+1).fold ...` doesn't work.
5- The following code failed to be elaborated
```
indent (push s!"{ss'}\n") (some (0 - Format.getIndent (← getOptions)))
```
It was working before, but it relied on how the expected type is
propagated. The elaborator process
```
some (0 - Format.getIndent (← getOptions))
```
with expected type `(Option Int)`. So, the `-` is interpreted as
`Int.sub` although `Format.getIndent (← getOptions)` has type `Nat`.
In the new `HSub`, the expected type doesn't really influence TC
resolution since it is an `outparam`. So, we failed with the error
failed to synthesize `HSub Nat Nat Int`.
One possible fix was to add the instance `HSub Nat Nat Int` with
`Int.sub`, but I used the following fix
```
some ((0 : Int) - Format.getIndent (← getOptions))
```
which makes it clear that we want the `Int.sub` operator instead of
`Nat.sub`.
