cdbe29b46d
An important part of the interface of a function is the parameter names, for making used of named arguments. This PR makes the parameter names print in a reliable way. The parameters of the type now appear as hygienic names if they cannot be used as named arguments. Modifies the heuristic for how parameters are chosen to appear before or after the colon. The rule is now that parameters start appearing after the colon at the first non-dependent non-instance-implicit parameter that has a name unusable as a named argument. This is a refinement of #2846. Fixes the issue where consecutive hygienic names pretty print without a space separating them, so we now have `(x✝ y✝ : Nat)` rather than `(x✝y✝ : Nat)`. Breaking change: `Lean.PrettyPrinter.Formatter.pushToken` now takes an additional boolean `ident` argument, which should be `true` for identifiers. Used to insert discretionary space between consecutive identifiers. Closes #5810
94 lines
3.7 KiB
Text
94 lines
3.7 KiB
Text
/-!
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A few tests for functional induction theorems generated from mutual recursive inductives.
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Some more tests are in `structuralMutual.lean` and `funind_structural`.
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-/
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set_option guard_msgs.diff true
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inductive Tree (α : Type u) : Type u where
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| node : α → (Bool → List (Tree α)) → Tree α
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-- Recursion over nested inductive
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mutual
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def Tree.size : Tree α → Nat
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| .node _ tsf => 1 + size_aux (tsf true) + size_aux (tsf false)
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termination_by structural t => t
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def Tree.size_aux : List (Tree α) → Nat
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| [] => 0
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| t :: ts => size t + size_aux ts
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end
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/--
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info: Tree.size.induct.{u_1} {α : Type u_1} (motive_1 : Tree α → Prop) (motive_2 : List (Tree α) → Prop)
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(case1 :
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∀ (a : α) (tsf : Bool → List (Tree α)), motive_2 (tsf true) → motive_2 (tsf false) → motive_1 (Tree.node a tsf))
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(case2 : motive_2 []) (case3 : ∀ (t : Tree α) (ts : List (Tree α)), motive_1 t → motive_2 ts → motive_2 (t :: ts))
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(a✝ : Tree α) : motive_1 a✝
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-/
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#guard_msgs in
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#check Tree.size.induct
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-- Recursion over nested inductive, functions in the “wrong” order (auxiliary first)
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mutual
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def Tree.size_aux' : List (Tree α) → Nat
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| [] => 0
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| t :: ts => size' t + size_aux' ts
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def Tree.size' : Tree α → Nat
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| .node _ tsf => 1 + size_aux' (tsf true) + size_aux' (tsf false)
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termination_by structural t => t
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end
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/--
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info: Tree.size_aux'.mutual_induct.{u_1} {α : Type u_1} (motive_1 : List (Tree α) → Prop) (motive_2 : Tree α → Prop)
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(case1 :
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∀ (a : α) (tsf : Bool → List (Tree α)), motive_1 (tsf true) → motive_1 (tsf false) → motive_2 (Tree.node a tsf))
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(case2 : motive_1 []) (case3 : ∀ (t : Tree α) (ts : List (Tree α)), motive_2 t → motive_1 ts → motive_1 (t :: ts)) :
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(∀ (a : List (Tree α)), motive_1 a) ∧ ∀ (a : Tree α), motive_2 a
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-/
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#guard_msgs in
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#check Tree.size_aux'.mutual_induct
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-- Similar, but with many packed functions
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mutual
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def Tree.size_aux1 : List (Tree α) → Nat
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| [] => 0
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| t :: ts => size2 t + size_aux2 ts
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def Tree.size1 : Tree α → Nat
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| .node _ tsf => 1 + size_aux2 (tsf true) + size_aux3 (tsf false)
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termination_by structural t => t
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def Tree.size_aux2 : List (Tree α) → Nat
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| [] => 0
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| t :: ts => size3 t + size_aux3 ts
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def Tree.size2 : Tree α → Nat
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| .node _ tsf => 1 + size_aux3 (tsf true) + size_aux1 (tsf false)
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def Tree.size_aux3 : List (Tree α) → Nat
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| [] => 0
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| t :: ts => size1 t + size_aux1 ts
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def Tree.size3 : Tree α → Nat
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| .node _ tsf => 1 + size_aux1 (tsf true) + size_aux2 (tsf false)
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end
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/--
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info: Tree.size_aux1.mutual_induct.{u_1} {α : Type u_1} (motive_1 motive_2 motive_3 : List (Tree α) → Prop)
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(motive_4 motive_5 motive_6 : Tree α → Prop)
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(case1 :
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∀ (a : α) (tsf : Bool → List (Tree α)), motive_2 (tsf true) → motive_3 (tsf false) → motive_4 (Tree.node a tsf))
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(case2 :
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∀ (a : α) (tsf : Bool → List (Tree α)), motive_1 (tsf true) → motive_2 (tsf false) → motive_5 (Tree.node a tsf))
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(case3 :
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∀ (a : α) (tsf : Bool → List (Tree α)), motive_3 (tsf true) → motive_1 (tsf false) → motive_6 (Tree.node a tsf))
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(case4 : motive_1 []) (case5 : ∀ (t : Tree α) (ts : List (Tree α)), motive_6 t → motive_2 ts → motive_1 (t :: ts))
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(case6 : motive_2 []) (case7 : ∀ (t : Tree α) (ts : List (Tree α)), motive_5 t → motive_3 ts → motive_2 (t :: ts))
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(case8 : motive_3 []) (case9 : ∀ (t : Tree α) (ts : List (Tree α)), motive_4 t → motive_1 ts → motive_3 (t :: ts)) :
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(∀ (a : List (Tree α)), motive_1 a) ∧
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(∀ (a : List (Tree α)), motive_2 a) ∧
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(∀ (a : List (Tree α)), motive_3 a) ∧
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(∀ (a : Tree α), motive_4 a) ∧ (∀ (a : Tree α), motive_5 a) ∧ ∀ (a : Tree α), motive_6 a
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-/
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#guard_msgs in
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#check Tree.size_aux1.mutual_induct
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