f20cae3729
This PR sets the `irreducible` attribute before generating the equations for recursive definitions. This prevents these equations to be marked as `defeq`, which could lead to `simp` generation proofs that do not type check at default transparency. This issue is surfacing more easily since well-founded recursion on `Nat` is implemented with a dedicated fix point operator (#7965). Before that, `WellFounded.fix` was used, which is inherently not reducing, so we did get the desired result even without the explicit reducibility setting. Fixes #12398.
168 lines
4.5 KiB
Text
168 lines
4.5 KiB
Text
module
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public import Module.Basic
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import all Module.Basic
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import Lean
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/-! `import all` should import private information, privately. -/
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/--
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info: theorem t : f = 1 :=
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testSorry
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-/
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#guard_msgs in
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#print t
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/-- info: true -/
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#guard_msgs in
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#eval (return (← Lean.findDeclarationRanges? ``t).isSome : Lean.CoreM _)
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/--
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error: Type mismatch
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y
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has type
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Vector Unit 1
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but is expected to have type
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Vector Unit f
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Note: The following definitions were not unfolded because their definition is not exposed:
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f ↦ 1
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-/
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#guard_msgs in
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public theorem v (x : Vector Unit f) (y : Vector Unit 1) : x = y := sorry
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/-- error: `dsimp` made no progress -/
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#guard_msgs in
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example : P f := by dsimp only [t]; exact hP1
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example : P f := by simp only [t]; exact hP1
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/-- error: `dsimp` made no progress -/
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#guard_msgs in
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example : P f := by dsimp only [trfl]; exact hP1
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/-- error: `dsimp` made no progress -/
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#guard_msgs in
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example : P f := by dsimp only [trfl']; exact hP1
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example : P f := by dsimp only [trflprivate]; exact hP1
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example : P f := by dsimp only [trflprivate']; exact hP1
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example : P fexp := by dsimp only [fexp_trfl]; exact hP1
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example : P fexp := by dsimp only [fexp_trfl']; exact hP1
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/-- info: @[defeq] private theorem f.eq_def : f = 1 -/
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#guard_msgs in #print sig f.eq_def
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/-- info: @[defeq] private theorem f.eq_unfold : f = 1 -/
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#guard_msgs in #print sig f.eq_unfold
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/-- info: @[defeq] private theorem f_struct.eq_1 : f_struct 0 = 0 -/
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#guard_msgs in #print sig f_struct.eq_1
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/--
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info: private theorem f_struct.eq_def : ∀ (x : Nat),
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f_struct x =
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match x with
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| 0 => 0
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| n.succ => f_struct n
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-/
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#guard_msgs in #print sig f_struct.eq_def
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/--
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info: private theorem f_struct.eq_unfold : f_struct = fun x =>
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match x with
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| 0 => 0
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| n.succ => f_struct n
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-/
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#guard_msgs in #print sig f_struct.eq_unfold
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/-- info: private theorem f_wfrec.eq_1 : ∀ (x : Nat), f_wfrec 0 x = x -/
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#guard_msgs(pass trace, all) in #print sig f_wfrec.eq_1
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/--
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info: private theorem f_wfrec.eq_def : ∀ (x x_1 : Nat),
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f_wfrec x x_1 =
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match x, x_1 with
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| 0, acc => acc
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| n.succ, acc => f_wfrec n (acc + 1)
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-/
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#guard_msgs(pass trace, all) in #print sig f_wfrec.eq_def
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/--
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info: private theorem f_wfrec.eq_unfold : f_wfrec = fun x x_1 =>
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match x, x_1 with
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| 0, acc => acc
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| n.succ, acc => f_wfrec n (acc + 1)
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-/
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#guard_msgs(pass trace, all) in #print sig f_wfrec.eq_unfold
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/--
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info: theorem f_wfrec.induct_unfolding : ∀ (motive : Nat → Nat → Nat → Prop),
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(∀ (acc : Nat), motive 0 acc acc) →
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(∀ (n acc : Nat), motive n (acc + 1) (f_wfrec n (acc + 1)) → motive n.succ acc (f_wfrec n (acc + 1))) →
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∀ (a a_1 : Nat), motive a a_1 (f_wfrec a a_1)
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-/
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#guard_msgs(pass trace, all) in #print sig f_wfrec.induct_unfolding
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/-- info: theorem f_exp_wfrec.eq_1 : ∀ (x : Nat), f_exp_wfrec 0 x = x -/
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#guard_msgs in #print sig f_exp_wfrec.eq_1
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/--
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info: theorem f_exp_wfrec.eq_def : ∀ (x x_1 : Nat),
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f_exp_wfrec x x_1 =
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match x, x_1 with
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| 0, acc => acc
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| n.succ, acc => f_exp_wfrec n (acc + 1)
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-/
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#guard_msgs in #print sig f_exp_wfrec.eq_def
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/--
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info: theorem f_exp_wfrec.eq_unfold : f_exp_wfrec = fun x x_1 =>
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match x, x_1 with
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| 0, acc => acc
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| n.succ, acc => f_exp_wfrec n (acc + 1)
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-/
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#guard_msgs in #print sig f_exp_wfrec.eq_unfold
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/--
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info: theorem f_exp_wfrec.induct_unfolding : ∀ (motive : Nat → Nat → Nat → Prop),
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(∀ (acc : Nat), motive 0 acc acc) →
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(∀ (n acc : Nat), motive n (acc + 1) (f_exp_wfrec n (acc + 1)) → motive n.succ acc (f_exp_wfrec n (acc + 1))) →
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∀ (a a_1 : Nat), motive a a_1 (f_exp_wfrec a a_1)
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-/
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#guard_msgs(pass trace, all) in #print sig f_exp_wfrec.induct_unfolding
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/-! `import all` should allow access to private defs, privately. -/
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public def pub := priv
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/--
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error: Unknown identifier `priv`
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Note: A private declaration `priv✝` (from `Module.Basic`) exists but would need to be public to access here.
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-/
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#guard_msgs in
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@[expose] public def pub' := priv
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#check { x := 1 : StructWithPrivateField }
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/-- error: invalid {...} notation, constructor for `StructWithPrivateField` is marked as private -/
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#guard_msgs in
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#with_exporting
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#check { x := 1 : StructWithPrivateField }
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#check (⟨1⟩ : StructWithPrivateField)
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/--
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error: Invalid `⟨...⟩` notation: Constructor for `StructWithPrivateField` is marked as private
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-/
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#guard_msgs in
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#with_exporting
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#check (⟨1⟩ : StructWithPrivateField)
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/-! #11715: `grind` should not fail to apply private matcher from imported module. -/
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attribute [local grind] func in
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theorem stmt1 : func ctx op = ctx := by
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grind
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