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.
141 lines
5.6 KiB
Text
141 lines
5.6 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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namespace Map2
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mutual
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def map2a (f : Nat → Nat → Bool) : List Nat → List Nat → List Bool
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| x::xs, y::ys => f x y::map2b f xs ys
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| _, _ => []
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termination_by structural x => x
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def map2b (f : Nat → Nat → Bool) : List Nat → List Nat → List Bool
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| x::xs, y::ys => f x y::map2a f xs ys
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| _, _ => []
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termination_by structural x => x
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end
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/--
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info: Map2.map2a.mutual_induct (motive_1 motive_2 : List Nat → List Nat → Prop)
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(case1 : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), motive_2 xs ys → motive_1 (x :: xs) (y :: ys))
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(case2 :
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∀ (t x : List Nat),
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(∀ (x_1 : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t = x_1 :: xs → x = y :: ys → False) → motive_1 t x)
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(case3 : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), motive_1 xs ys → motive_2 (x :: xs) (y :: ys))
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(case4 :
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∀ (t x : List Nat),
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(∀ (x_1 : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t = x_1 :: xs → x = y :: ys → False) → motive_2 t x) :
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(∀ (a a_1 : List Nat), motive_1 a a_1) ∧ ∀ (a a_1 : List Nat), motive_2 a a_1
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-/
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#guard_msgs in
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#check map2a.mutual_induct
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/--
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info: Map2.map2a.induct (motive_1 motive_2 : List Nat → List Nat → Prop)
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(case1 : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), motive_2 xs ys → motive_1 (x :: xs) (y :: ys))
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(case2 :
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∀ (t x : List Nat),
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(∀ (x_1 : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t = x_1 :: xs → x = y :: ys → False) → motive_1 t x)
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(case3 : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), motive_1 xs ys → motive_2 (x :: xs) (y :: ys))
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(case4 :
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∀ (t x : List Nat),
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(∀ (x_1 : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t = x_1 :: xs → x = y :: ys → False) → motive_2 t x)
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(a✝ a✝¹ : List Nat) : motive_1 a✝ a✝¹
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-/
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#guard_msgs in
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#check map2a.induct
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end Map2
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