62f14514da
This PR updates various error messages produced by or associated with built-in tactics and adapts their formatting to current conventions.
121 lines
3.4 KiB
Text
121 lines
3.4 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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because 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 defined using classical reasoning, proving an instance exists rather than giving a concrete construction. The `decide` tactic works by evaluating a decision procedure via reduction, and it cannot make progress with such instances. This can occur due to the `open scoped Classical` 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 where
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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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because 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 defined using tactics such as `rw` or `simp`. To avoid tactics, make use of functions such as `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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because 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 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 defined using tactics such as `rw` or `simp`. To avoid tactics, make use of functions such as `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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Reverting free variables.
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-/
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/--
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error: Expected type must not contain free variables
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x + 1 ≤ 5
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Hint: Use the `+revert` option to automatically clean up and revert free variables
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-/
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#guard_msgs in
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example (x : Nat) (h : x < 5) : x + 1 ≤ 5 := by decide
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example (x : Nat) (h : x < 5) : x + 1 ≤ 5 := by decide +revert
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/--
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Can handle universe levels.
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-/
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instance (p : PUnit.{u} → Prop) [Decidable (p PUnit.unit)] : Decidable (∀ x : PUnit.{u}, p x) :=
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decidable_of_iff (p PUnit.unit) (by constructor; rintro _ ⟨⟩; assumption; intro h; apply h)
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example : ∀ (x : PUnit.{u}), x = PUnit.unit := by decide
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