This PR fixes a performance issue that occurs when generating equation
lemmas for functions that use match-expressions containing several
literals. This issue was exposed by #9322 and arises from a combination
of factors:
1. Literal values are compiled into a chain of dependent if-then-else
expressions.
2. Dependent if-then-else expressions are significantly more expensive
to simplify than regular ones.
3. The `split` tactic selects a target, splits it, and then invokes
`simp` on the resulting subgoals. Moreover, `simp` traverses the entire
goal bottom-up and does not stop after reaching the target.
This PR addresses the issue by introducing a custom simproc that avoids
recursively simplifying nested if-then-else expressions. It does **not**
alter the user-facing behavior of the `split` tactic because such a
change would be highly disruptive. Instead, the PR adds a new flag,
`backward.split` to control the behavior of the user-facing `split`
tactic. It is currently set to `true`, i.e., the old behavior is still
the default one. In a future PR, we should set this flag to `false` by
default and begin repairing all affected proofs.
closes#9322
This PR implements `Simp.Config.implicitDefEqsProofs`. When `true`
(default: `true`), `simp` will **not** create a proof term for a
rewriting rule associated with an `rfl`-theorem. Rewriting rules are
provided by users by annotating theorems with the attribute `@[simp]`.
If the proof of the theorem is just `rfl` (reflexivity), and
`implicitDefEqProofs := true`, `simp` will **not** create a proof term
which is an application of the annotated theorem.
The default setting does change the existing behavior. Users can use
`simp -implicitDefEqProofs` to force `simp` to create a proof term for
`rfl`-theorems. This can positively impact proof checking time in the
kernel.
This PR also fixes an issue in the `split` tactic that has been exposed
by this feature. It was looking for `split` candidates in proofs and
implicit arguments. See new test for issue exposed by the previous
feature.
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Co-authored-by: Kim Morrison <kim@tqft.net>
