feat: use omega in default decreasing_trivial #3503
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with this, more functions will be proven terminating automatically, namely those where after `simp_wf`, lexicographic order handling, possibly subst_vars and `simp` all remaining goals can be handled by `omega`. 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, this 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.)
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with this, hopefully more obvious array accesses will be handled automatically. Just like #3503, this PR does not investiate which of the exitsting tactics in `get_elem_tactic_trivial` are subsumed now and could be dropped without (too much) breakage.
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with this, hopefully more obvious array accesses will be handled automatically. Just like #3503, this PR does not investiate which of the exitsting tactics in `get_elem_tactic_trivial` are subsumed now and could be dropped without (too much) breakage.
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with this, more functions will be proven terminating automatically,
namely those where after
simp_wf, lexicographic order handling,possibly
subst_varsthe remaining goal can be solved byomega.Note that
simp_wfalready does simplification of the goal, sothis adds
omega, not(try simp) <;> omegahere.There are certainly cases where
(try simp) <;> omegawill solve moregoals (e.g. due to the
subst_varsindecreasing_with), and(try simp at *) <;> omegaeven more. This PR errs on the side of takingsmaller steps.
Just appending
<;> omegato the existingsimp (config := { arith := true, failIfUnchanged := false })calldoesn’t work nicely, as that leaves forms like
Nat.subin the goal thatomegadoes not seem to recognize.This does not remove any of the existing ad-hoc
decreasing_trivialrules based on
applyandassumption, to not regress over the statusquo (these rules may apply in cases where
omegawouldn't “see”everything, but
applydue to defeq works).Additionally, just extending makes bootstrapping easier; early in
Initwhereomegadoes not work yet these other tactics can still be used.(Using a single
omega-based tactic was tried in #3478 but isn’t quitepossible yet, and will be postponed until we have better automation
including forward reasoning.)