Following up #5928, updates the syntax for `omega` and `solve_by_elim`
and restores the syntax quotations in their implementations.
Following up #5898, uses the new tactic syntax in the library, replacing
all uses of `(config := ...)`.
Previously, the tactic state shown at `decreasing_by` would leak lots of
details about the translation, and mention `invImage`, `PSigma` etc.
This is not nice.
So this introduces `clean_wf`, which is like `simp_wf` but using
`simp`'s `only` mode, and runs this unconditionally. This should clean
up the goal to a reasonable extent.
Previously `simp_wf` was an unrestricted `simp […]` call, but we
probably don’t want arbitrary simplification to happen at this point, so
this now became `simp only` call. For backwards compatibility,
`decreasing_with` begins with `try simp`. The `simp_wf` tactic
is still available to not break too much existing code; it’s docstring
suggests to no longer use it.
With `set_option cleanDecreasingByGoal false` one can disable the use of
`clean_wf`. I hope this is only needed for debugging and understanding.
Migration advise: If your `decreasing_by` proof begins with `simp_wf`,
either remove that (if the proof still goes through), or replace with
`simp`.
I am a bit anxious about running even `simp only` unconditionally here,
as it may do more than some user might want, e.g. because of options
like `zetaDelta := true`. We'll see if we need to reign in this tactic
some more.
I wonder if in corner cases the `simp_wf` tactic might be able to close
the goal, and if that is a problem. If so, we may have to promote simp’s
internal `mayCloseGoal` parameter to a simp configuration option and use
that here.
fixes#4928
`Nat.succ_eq_add_one` and `Nat.pred_eq_sub_one` are now simp lemmas. For
theorems about `Nat.succ` or `Nat.pred` without corresponding theorem
for `+ 1` or `- 1`, this adds the corresponding theorem.
Because of the last-added-tried-first rule for macros, all the special
purpose `decreasing_trivial` rules are tried for most recursive
definitions out there, and because they use `apply` and `assumption`
with default transparency may cause some definitoins to be unfolded over
and over again.
A quick test with one of the functions in the leansat project shows that
elaboration time goes down from 600ms to 375ms when using
```
decreasing_by all_goals decreasing_with with_reducible decreasing_trivial
```
instead of
```
decreasing_by all_goals decreasing_with decreasing_trivial
```
This change uses `with_reducible` in most of these macros.
This means that these tactics will no longer work when the
relations/definitions they look for is hidden behind a definition.
This affected in particular `Array.sizeOf_get`, which now has a
companion `sizeOf_getElem`.
In addition, there were three tactics using `apply` to apply Nat-related
lemmas
that we now expect `omega` to solve. We still need them when building
`Init` modules
that don’t have access to `omega`, but they now live in
`decreasing_trivial_pre_omega`,
meant to be only used internally.
with this, more functions will be proven terminating automatically,
namely those where after `simp_wf`, lexicographic order handling,
possibly `subst_vars` the remaining goal can be solved by `omega`.
Note that `simp_wf` already does simplification of the goal, so
this adds `omega`, not `(try simp) <;> omega` here.
There are certainly cases where `(try simp) <;> omega` will solve more
goals (e.g. due to the `subst_vars` in `decreasing_with`), and
`(try simp at *) <;> omega` even more. This PR errs on the side of
taking
smaller steps.
Just appending `<;> omega` to the existing
`simp (config := { arith := true, failIfUnchanged := false })` call
doesn’t work nicely, as that leaves forms like `Nat.sub` in the goal
that
`omega` does not seem to recognize.
This does *not* remove any of the existing ad-hoc `decreasing_trivial`
rules based on `apply` and `assumption`, to not regress over the status
quo (these rules may apply in cases where `omega` wouldn't “see”
everything, but `apply` due to defeq works).
Additionally, just extending makes bootstrapping easier; early in `Init`
where
`omega` does not work yet these other tactics can still be used.
(Using a single `omega`-based tactic was tried in #3478 but isn’t quite
possible yet, and will be postponed until we have better automation
including forward reasoning.)
Previously `decreasing_with` failed if `simp_wf` closes the goal on its
own. This can cause undesired regressions when new `simp` lemmas are
introduced.
Closes#2018.
