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.)
149 lines
5.3 KiB
Text
149 lines
5.3 KiB
Text
guessLexFailures.lean:11:12-11:46: error: fail to show termination for
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nonTerminating
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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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nonTerminating (Nat.succ n) (Nat.succ m)
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argument #2 was not used for structural recursion
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failed to eliminate recursive application
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nonTerminating (Nat.succ n) (Nat.succ m)
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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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x1 x2
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1) 11:12-46 ? ?
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Please use `termination_by` to specify a decreasing measure.
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guessLexFailures.lean:15:0-18:31: error: 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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x1 x2
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1) 17:12-47 ? ?
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Please use `termination_by` to specify a decreasing measure.
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guessLexFailures.lean:20:4-20:15: error: fail to show termination for
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noArguments
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with errors
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structural recursion cannot be used
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well-founded recursion cannot be used, 'noArguments' does not take any (non-fixed) arguments
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guessLexFailures.lean:22:4-22:23: error: fail to show termination for
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noNonFixedArguments
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with errors
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structural recursion cannot be used
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well-founded recursion cannot be used, 'noNonFixedArguments' does not take any (non-fixed) arguments
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guessLexFailures.lean:27:0-33:31: error: 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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x1 x2 x3
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1) 29:6-25 = = =
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2) 30:6-23 = < _
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3) 31:6-23 < _ _
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Please use `termination_by` to specify a decreasing measure.
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guessLexFailures.lean:37:0-43:31: error: 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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x1 x2 x3 x4
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1) 39:6-27 = = _ =
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2) 40:6-25 = < _ _
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3) 41:6-25 < _ _ _
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Please use `termination_by` to specify a decreasing measure.
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guessLexFailures.lean:48:0-54:31: error: 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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n m l
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1) 50:6-25 = = =
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2) 51:6-23 = < _
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3) 52:6-23 < _ _
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Please use `termination_by` to specify a decreasing measure.
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guessLexFailures.lean:59:6-59:7: error: fail to show termination for
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Mutual.f
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Mutual.g
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Mutual.h
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with errors
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structural recursion does not handle mutually recursive functions
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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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Call from Mutual.f to Mutual.f at 61:8-33:
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n m l
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= = =
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Call from Mutual.f to Mutual.f at 62:8-31:
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n m l
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= < <
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Call from Mutual.f to Mutual.g at 63:8-39:
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n m l
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n < ? ?
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m ? = ?
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H _ _ _
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l ? ? <
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Call from Mutual.g to Mutual.g at 68:8-35:
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n m H l
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? ? _ =
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Call from Mutual.g to Mutual.g at 69:8-33:
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n m H l
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_ _ _ <
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Call from Mutual.g to Mutual.h at 70:8-27:
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n m H l
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x1 _ _ _ ?
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x2 _ _ _ ?
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Call from Mutual.h to Mutual.f at 75:8-33:
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x1 x2
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n _ _
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m _ _
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l _ _
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Call from Mutual.h to Mutual.h at 76:8-27:
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x1 x2
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_ _
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Call from Mutual.h to Mutual.h at 77:8-27:
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x1 x2
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_ _
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Please use `termination_by` to specify a decreasing measure.
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guessLexFailures.lean:89:19-89:32: error: fail to show termination for
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DuplicatedCall.f
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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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DuplicatedCall.f (n + 2) (m + 1)
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argument #2 was not used for structural recursion
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failed to eliminate recursive application
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DuplicatedCall.f (n + 2) (m + 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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x1 x2
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1) 89:19-32 ? ?
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Please use `termination_by` to specify a decreasing measure.
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guessLexFailures.lean:100:0-103:31: error: 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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n m
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1) 101:83-105 ? ?
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Please use `termination_by` to specify a decreasing measure.
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guessLexFailures.lean:113:14-113:31: error: failed to prove termination, possible solutions:
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- Use `have`-expressions to prove the remaining goals
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- Use `termination_by` to specify a different well-founded relation
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- Use `decreasing_by` to specify your own tactic for discharging this kind of goal
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n✝ m n : Nat
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⊢ n < n✝
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guessLexFailures.lean:119:0-123:31: error: 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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n m
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1) 121:31-54 ? ?
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Please use `termination_by` to specify a decreasing measure.
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guessLexFailures.lean:131:14-131:31: error: failed to prove termination, possible solutions:
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- Use `have`-expressions to prove the remaining goals
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- Use `termination_by` to specify a different well-founded relation
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- Use `decreasing_by` to specify your own tactic for discharging this kind of goal
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m n✝ n : Nat
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⊢ n < Nat.succ n✝
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