This PR changes all `lean-toolchain` to use relative toolchain paths
instead of `lean4` and `lean4-stage0` identifiers, which removes the
need for manually linking toolchains via Elan.
After this PR, at least Elan 4.2.0 and 0.0.224 of the Lean VS Code
extension will be needed to edit core.
Co-authored-by: Claude Sonnet 4.6 <noreply@anthropic.com>
This PR adds a clone of the `mvcgen` tactic based on `SymM` and
evaluates it based on a ported `add_sub_cancel` benchmark. Notably, it
can reuse all the existing `@[spec]`-annotated theorems to generate VCs.
(It doesn't do control-flow splitting, simp rules on the program
expression or handling of lets; we'll get there.)
It is quite fast already, with the kernel being the bottle-neck:
```
goal_50: 69.524305 ms, kernel: 155.327778 ms
goal_100: 93.834221 ms, kernel: 407.370786 ms
goal_150: 131.364098 ms, kernel: 762.936720 ms
goal_200: 169.577172 ms, kernel: 1181.199093 ms
goal_250: 206.421738 ms, kernel: 1707.539380 ms
```
```
goal_200: 169.458637 ms, kernel: 1186.221085 ms
goal_400: 322.819718 ms, kernel: 3791.613854 ms
goal_600: 474.929013 ms, kernel: 7763.373757 ms
goal_800: 634.379422 ms, kernel: 13107.810430 ms
```
It is best compared to the `solveUsingSym <n> false true` measurements
of the SymM `add_sub_cancel` benchmark (`false`: without intermediate
eager simplification). For `n=200`, it reports
```
goal_200: 779.482300 ms, kernel: 742.097404 ms
```
suggesting that the generated proof term could be improved for kernel
reduction. (TODO.)
I'm unsure whether `solveUsingSym` is run in interpreted mode, so take
the >400% speedup with a grain of salt.
We can definitely conclude that VC generation time is currently not a
bottleneck compared to kernel checking time.
Plot for discharging goals of sizes 100..800:
<img width="1000" height="600" alt="Code_Generated_Image(1)"
src="https://github.com/user-attachments/assets/90e76a45-fa46-4d02-912a-c3355e2aa094"
/>
Plot comparing Kernel and Goal time:
<img width="1000" height="600" alt="Code_Generated_Image(2)"
src="https://github.com/user-attachments/assets/5849ba0f-1d83-4f2d-98dd-fa65b840bb4e"
/>
