08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
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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