f9dc77673b
This PR lets recursive functions defined by well-founded recursion use a different `fix` function when the termination measure is of type `Nat`. This fix-point operator use structural recursion on “fuel”, initialized by the given measure, and is thus reasonable to reduce, e.g. in `by decide` proofs. Extra provisions are in place that the fixpoint operator only starts reducing when the fuel is fully known, to prevent “accidential” defeqs when the remaining fuel for the recursive calls match the initial fuel for that recursive argument. To opt-out, the idiom `termination_by (n,0)` can be used. We still use `@[irreducible]` as the default for such recursive definitions, to avoid unexpected `defeq` lemmas. Making these functions `@[semireducible]` by default showed performance regressions in lean. When the measure is of type `Nat`, the system will accept an explicit `@[semireducible]` without the usual warning. Fixes #5234. Fixes: #11181.
162 lines
4.4 KiB
Text
162 lines
4.4 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.CoreM
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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: @[defeq] 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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