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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).
104 lines
2.8 KiB
Text
104 lines
2.8 KiB
Text
/-!
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# Tests of the `decide` tactic
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-/
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/-!
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Success
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-/
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#guard_msgs in
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example : 2 + 2 ≠ 5 := by decide
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/-!
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False proposition
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-/
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/--
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error: tactic 'decide' proved that the proposition
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1 ≠ 1
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is false
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-/
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#guard_msgs in
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example : 1 ≠ 1 := by decide
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/-!
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Irreducible decidable instance
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-/
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opaque unknownProp : Prop
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/--
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error: tactic 'decide' failed for proposition
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unknownProp
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since its 'Decidable' instance
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Classical.propDecidable unknownProp
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did not reduce to 'isTrue' or 'isFalse'.
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After unfolding the instance 'Classical.propDecidable', reduction got stuck at the 'Decidable' instance
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Classical.choice ⋯
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Hint: Reduction got stuck on 'Classical.choice', which indicates that a 'Decidable' instance is
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defined using classical reasoning, proving an instance exists rather than giving a concrete
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construction. The 'decide' tactic works by evaluating a decision procedure via reduction, and it
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cannot make progress with such instances. This can occur due to the 'opened scoped Classical'
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command, which enables the instance 'Classical.propDecidable'.
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-/
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#guard_msgs in
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open scoped Classical in
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example : unknownProp := by decide
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/-!
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Reporting unfolded instances and give hint about Eq.rec.
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From discussion with Heather Macbeth on Zulip
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-/
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structure Nice (n : Nat) : Prop :=
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(large : 100 ≤ n)
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theorem nice_iff (n : Nat) : Nice n ↔ 100 ≤ n := ⟨Nice.rec id, Nice.mk⟩
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def baz (n : Nat) : Decidable (Nice n) := by
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rw [nice_iff]
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infer_instance
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instance : Decidable (Nice n) := baz n
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/--
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error: tactic 'decide' failed for proposition
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Nice 102
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since its 'Decidable' instance
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instDecidableNice
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did not reduce to 'isTrue' or 'isFalse'.
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After unfolding the instances 'baz' and 'instDecidableNice', reduction got stuck at the 'Decidable' instance
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⋯ ▸ inferInstance
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Hint: Reduction got stuck on '▸' (Eq.rec), which suggests that one of the 'Decidable' instances is
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defined using tactics such as 'rw' or 'simp'. To avoid tactics, make use of functions such as
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'inferInstanceAs' or 'decidable_of_decidable_of_iff' to alter a proposition.
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-/
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#guard_msgs in
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example : Nice 102 := by decide
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/-!
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Following `Decidable.rec` to give better messages
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-/
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/--
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error: tactic 'decide' failed for proposition
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¬Nice 102
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since its 'Decidable' instance
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instDecidableNot
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did not reduce to 'isTrue' or 'isFalse'.
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After unfolding the instances 'baz', 'instDecidableNice' and 'instDecidableNot', reduction got stuck
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at the 'Decidable' instance
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⋯ ▸ inferInstance
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Hint: Reduction got stuck on '▸' (Eq.rec), which suggests that one of the 'Decidable' instances is
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defined using tactics such as 'rw' or 'simp'. To avoid tactics, make use of functions such as
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'inferInstanceAs' or 'decidable_of_decidable_of_iff' to alter a proposition.
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-/
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#guard_msgs in
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example : ¬ Nice 102 := by decide
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