bf809b5298
This PR changes where errors are displayed when trying to use `coinductive` keyword when targeting things that do not live in `Prop`. Instead of displaying the error above the first element of the mutual block, it is displayed above the erroneous definition. --------- Co-authored-by: Rob23oba <152706811+Rob23oba@users.noreply.github.com>
265 lines
7.9 KiB
Text
265 lines
7.9 KiB
Text
-- set_option trace.Elab.coinductive true
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set_option pp.proofs true
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section
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variable (α : Type)
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/--
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docstring
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-/
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coinductive infSeq (r : α → α → Prop) : α → Prop where
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| step : r a b → infSeq r b → infSeq r a
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/--
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info: infSeq.step (α : Type) (r : α → α → Prop) {a b : α} : r a b → infSeq α r b → infSeq α r a
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-/
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#guard_msgs in
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#check infSeq.step
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theorem casesOnTest (r : α → α → Prop) (a : α) : infSeq α r a → ∃ b, r a b := by
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intro h
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cases h
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case step b _ hr => exists b
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-- `match` support does not work yet
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/--
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error: Invalid pattern: Expected a constructor or constant marked with `[match_pattern]`
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Hint: These are similar:
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'Lean.Order.iterates.below.step',
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'Lean.Order.iterates.step',
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'Nat.le.below.step',
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'Nat.le.step',
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'infSeq._functor.step'
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---
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error: Case tag `rhs` not found.
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Note: There are no cases to select.
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-/
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#guard_msgs in
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theorem casesOnTest' (r : α → α → Prop) (a : α) : infSeq α r a → ∃ b, r a b := by
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intro h
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match h with
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| step b _ hr => exists b
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/--
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info: infSeq.casesOn (α : Type) (r : α → α → Prop) {motive : (a : α) → infSeq α r a → Prop} {a✝ : α} (t : infSeq α r a✝)
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(step : ∀ {a b : α} (a_1 : r a b) (a_2 : infSeq α r b), motive a (infSeq.step α r a_1 a_2)) : motive a✝ t
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-/
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#guard_msgs in
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#check infSeq.casesOn
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/--
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info: infSeq.functor_unfold (α : Type) (r : α → α → Prop) (a✝ : α) : infSeq α r a✝ = infSeq._functor α r (infSeq α r) a✝
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-/
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#guard_msgs in
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#check infSeq.functor_unfold
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/-- info: infSeq (α : Type) (r : α → α → Prop) : α → Prop -/
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#guard_msgs in
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#check infSeq
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/--
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info: inductive infSeq._functor : (α : Type) → (α → α → Prop) → (α → Prop) → α → Prop
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number of parameters: 3
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constructors:
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infSeq._functor.step : ∀ (α : Type) (r : α → α → Prop) (infSeq._functor.call : α → Prop) {a b : α},
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r a b → infSeq._functor.call b → infSeq._functor α r infSeq._functor.call a
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-/
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#guard_msgs in
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#print infSeq._functor
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/--
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info: def infSeq._functor.existential : (α : Type) → (α → α → Prop) → (α → Prop) → α → Prop :=
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fun α r infSeq._functor.call a => ∃ b, r a b ∧ infSeq._functor.call b
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-/
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#guard_msgs in
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#print infSeq._functor.existential
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/--
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info: infSeq._functor.existential_equiv (α : Type) (r : α → α → Prop) (infSeq._functor.call : α → Prop) (a✝ : α) :
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infSeq._functor α r infSeq._functor.call a✝ ↔ ∃ b, r a✝ b ∧ infSeq._functor.call b
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-/
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#guard_msgs in
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#check infSeq._functor.existential_equiv
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/--
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info: infSeq.coinduct (α : Type) (r : α → α → Prop) (pred : α → Prop) (hyp : ∀ (a : α), pred a → ∃ b, r a b ∧ pred b)
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(a✝ : α) : pred a✝ → infSeq α r a✝
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-/
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#guard_msgs in
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#check infSeq.coinduct
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/--
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info: infSeq.step (α : Type) (r : α → α → Prop) {a b : α} : r a b → infSeq α r b → infSeq α r a
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-/
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#guard_msgs in
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#check infSeq.step
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end
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section
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mutual
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coinductive tick : Prop where
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| mk : ¬tock → tick
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inductive tock : Prop where
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| mk : ¬tick → tock
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end
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/--
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info: tick._functor.casesOn {tick._functor.call tock._functor.call : Prop}
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{motive_1 : tick._functor tick._functor.call tock._functor.call → Prop}
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(t : tick._functor tick._functor.call tock._functor.call)
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(mk : ∀ (a : ¬tock._functor.call), motive_1 (tick._functor.mk tick._functor.call tock._functor.call a)) : motive_1 t
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-/
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#guard_msgs in
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#check tick._functor.casesOn
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/-- info: tick.mk : ¬tock → tick -/
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#guard_msgs in
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#check tick.mk
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/-- info: tock.mk : ¬tick → tock -/
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#guard_msgs in
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#check tock.mk
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/-- info: tock._functor (tick._functor.call tock._functor.call : Prop) : Prop -/
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#guard_msgs in
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#check tock._functor
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/-- info: tock._functor.existential (tick._functor.call tock._functor.call : Prop) : Prop -/
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#guard_msgs in
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#check tock._functor.existential
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/--
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info: tick.coinduct (pred_1 pred_2 : Prop) (hyp_1 : pred_1 → pred_2 → False) (hyp_2 : (pred_1 → False) → pred_2) :
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pred_1 → tick
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-/
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#guard_msgs in
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#check tick.coinduct
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/--
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info: tock._functor.existential_equiv (tick._functor.call tock._functor.call : Prop) :
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tock._functor tick._functor.call tock._functor.call ↔ ¬tick._functor.call
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-/
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#guard_msgs in
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#check tock._functor.existential_equiv
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/--
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info: tock.induct (pred_1 pred_2 : Prop) (hyp_1 : pred_1 → pred_2 → False) (hyp_2 : (pred_1 → False) → pred_2) : tock → pred_2
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-/
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#guard_msgs in
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#check tock.induct
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/--
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info: tick.mutual_induct (pred_1 pred_2 : Prop) (hyp_1 : pred_1 → pred_2 → False) (hyp_2 : (pred_1 → False) → pred_2) :
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(pred_1 → tick) ∧ (tock → pred_2)
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-/
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#guard_msgs in
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#check tick.mutual_induct
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end
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/-- error: `coinductive` keyword can only be used to define predicates -/
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#guard_msgs in
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coinductive my_nat where
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| zero : my_nat
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| succ : my_nat → my_nat
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def Set := Nat → Prop
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coinductive Foo : Set where
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/--
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info: Foo.coinduct (pred : Set) (hyp : ∀ (a : Nat), pred a → False) (a✝ : Nat) : pred a✝ → Foo a✝
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-/
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#guard_msgs in
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#check Foo.coinduct
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coinductive Bar : Set where
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| make : Bar 42
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/--
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info: Bar.coinduct (pred : Set) (hyp : ∀ (a : Nat), pred a → a = 42) (a✝ : Nat) : pred a✝ → Bar a✝
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-/
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#guard_msgs in
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#check Bar.coinduct
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coinductive dependentTest : (n : Nat) → (Vector α n) → Prop where
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| mk (x : α) : dependentTest m v → dependentTest (m+1) (v.push x)
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/--
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info: dependentTest.coinduct.{u_1} {α : Type u_1} (pred : (n : Nat) → Vector α n → Prop)
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(hyp : ∀ (n : Nat) (a : Vector α n), pred n a → ∃ m v x, pred m v ∧ n = m + 1 ∧ a ≍ v.push x) (n : Nat)
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(a✝ : Vector α n) : pred n a✝ → dependentTest n a✝
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-/
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#guard_msgs in
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#check dependentTest.coinduct
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/-
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Duplicated parameters and dependent types
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-/
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coinductive dependentTest2 : (n : Nat) → (m : Nat) → (Vector α (m + n)) → (Vector α (m + n)) → Prop where
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| mk (x : α) : dependentTest2 0 n v v → dependentTest2 0 (n + 1) (v.push x) (v.push x)
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coinductive dependentTest3 : (α : Type) → (ls : List α) → (vec : Vector α ls.length) → (Vector α vec.size) → Prop where
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| mk : dependentTest3 Nat [a] (Vector.singleton a) (Vector.singleton a)
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| mk2 : dependentTest3 String ["hi"] (Vector.singleton b) (Vector.singleton c)
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/--
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info: dependentTest3.casesOn
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{motive :
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(α : Type) →
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(ls : List α) → (vec : Vector α ls.length) → (a : Vector α vec.size) → dependentTest3 α ls vec a → Prop}
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{α : Type} {ls : List α} {vec : Vector α ls.length} {a✝ : Vector α vec.size} (t : dependentTest3 α ls vec a✝)
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(mk : ∀ {a : Nat}, motive Nat [a] (Vector.singleton a) (Vector.singleton a) dependentTest3.mk)
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(mk2 : ∀ {b c : String}, motive String ["hi"] (Vector.singleton b) (Vector.singleton c) dependentTest3.mk2) :
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motive α ls vec a✝ t
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-/
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#guard_msgs in
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#check dependentTest3.casesOn
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coinductive test1 (r: α → α → Prop) : α → α → Prop where
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| mk : r a b → test1 r a b → test1 r a a
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| mk2 : test1 r a a
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coinductive test2 (r: α → α → Prop) : α → α → Prop where
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| mk : r a b → test2 r b b → test2 r a a
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/--
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error: Cannot define an coinductive predicate and a constructor with the same name `A.mk`
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---
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error: Cannot define an coinductive predicate and a constructor with the same name `A.mk`
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-/
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#guard_msgs in
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mutual
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coinductive A : Prop where
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| mk : A.mk → A
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coinductive A.mk : Prop where
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| mk : A → A.mk
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end
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macro "test%" : command => `(command|
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coinductive MacroTest : Prop where | mk : MacroTest
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)
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/-- error: Coinductive predicates are not allowed inside of macro scopes -/
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#guard_msgs in
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test%
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namespace unsafe_test
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unsafe coinductive infSeq2 (r : α → α → Prop) : α → Prop where
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| step : r a b → infSeq2 r b → infSeq2 r a
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end unsafe_test
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/--
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@ +4:14...20
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error: `coinductive` keyword can only be used to define predicates
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-/
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#guard_msgs (positions := true) in
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mutual
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coinductive wrong1 : Prop where
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coinductive wrong2 where
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| zero : wrong2
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| succ : wrong1 → wrong2
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end
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