9c00a59339
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.)
19 lines
604 B
Text
19 lines
604 B
Text
wf1.lean:3:12-3:19: error: fail to show termination for
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g
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with errors
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argument #1 was not used for structural recursion
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failed to eliminate recursive application
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g (x - 1)
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argument #2 was not used for structural recursion
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insufficient number of parameters at recursive application
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g (x - 1)
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structural recursion cannot be used
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Could not find a decreasing measure.
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The arguments relate at each recursive call as follows:
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(<, ≤, =: relation proved, ? all proofs failed, _: no proof attempted)
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x y
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1) 3:12-19 ≤ ?
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Please use `termination_by` to specify a decreasing measure.
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