ce73bbe277
When the `decide` tactic fails, it can try to give hints about the failure: - It tells you which `Decidable` instances it unfolded, by making use of the diagnostics feature. - If it encounters `Eq.rec`, it gives you a hint that one of these instances was likely defined using tactics. - If it encounters `Classical.choice`, it hints that you might have classical instances in scope. - During this, it tries to process `Decidable.rec`s and matchers to pin blame on a particular instance that failed to reduce. This idea comes from discussion with Heather Macbeth [on Zulip](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Decidable.20with.20structures/near/449409870).
40 lines
1.4 KiB
Text
40 lines
1.4 KiB
Text
-- NB: well-founded recursion, so irreducible
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def sorted_from_var [x: LE α] [DecidableRel x.le] (a: Array α) (i: Nat): Bool :=
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if h: i + 1 < a.size then
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have : i < a.size := Nat.lt_of_succ_lt h
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a[i] ≤ a[i+1] && sorted_from_var a (i + 1)
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else
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true
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termination_by a.size - i
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def check_sorted [x: LE α] [DecidableRel x.le] (a: Array α): Bool :=
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sorted_from_var a 0
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-- works (because `rfl` of closed terms resorts to kernel defeq, see #3772)
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example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] := by
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rfl
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/--
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error: tactic 'decide' failed for proposition
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check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] = true
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since its 'Decidable' instance
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instDecidableEqBool (check_sorted #[0, 3, 3, 5, 8, 10, 10, 10]) true
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did not reduce to 'isTrue' or 'isFalse'.
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After unfolding the instances 'instDecidableEqBool' and 'Bool.decEq', reduction got stuck at the 'Decidable' instance
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match check_sorted #[0, 3, 3, 5, 8, 10, 10, 10], true with
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| false, false => isTrue ⋯
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| false, true => isFalse ⋯
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| true, false => isFalse ⋯
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| true, true => isTrue ⋯
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-/
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#guard_msgs in
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example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] := by
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decide -- fails because `decide` uses `.default` transparency, and `sorted_from_var` is marked as irreducible
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unseal sorted_from_var in
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example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] := by
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decide -- works
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example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] := by
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with_unfolding_all decide -- should work
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