The `decide!` tactic is like `decide`, but when it tries reducing the
`Decidable` instance it uses kernel reduction rather than the
elaborator's reduction.
The kernel ignores transparency, so it can unfold all definitions (for
better or for worse). Furthermore, by using kernel reduction we can
cache the result as an auxiliary lemma — this is more efficient than
`decide`, which needs to reduce the instance twice: once in the
elaborator to check whether the tactic succeeds, and once again in the
kernel during final typechecking.
While RFC #5629 proposes a `decide!` that skips checking altogether
during elaboration, with this PR's `decide!` we can use `decide!` as
more-or-less a drop-in replacement for `decide`, since the tactic will
fail if kernel reduction fails.
This PR also includes two small fixes:
- `blameDecideReductionFailure` now uses `withIncRecDepth`.
- `Lean.Meta.zetaReduce` now instantiates metavariables while zeta
reducing.
Some profiling:
```lean
set_option maxRecDepth 2000
set_option trace.profiler true
set_option trace.profiler.threshold 0
theorem thm1 : 0 < 1 := by decide!
theorem thm1' : 0 < 1 := by decide
theorem thm2 : ∀ x < 400, x * x ≤ 160000 := by decide!
theorem thm2' : ∀ x < 400, x * x ≤ 160000 := by decide
/-
[Elab.command] [0.003655] theorem thm1 : 0 < 1 := by decide!
[Elab.command] [0.003164] theorem thm1' : 0 < 1 := by decide
[Elab.command] [0.133223] theorem thm2 : ∀ x < 400, x * x ≤ 160000 := by decide!
[Elab.command] [0.252310] theorem thm2' : ∀ x < 400, x * x ≤ 160000 := by decide
-/
```
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
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