mirror of
https://github.com/leanprover/lean4.git
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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.
214 lines
5.1 KiB
Lean4
214 lines
5.1 KiB
Lean4
/-!
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Checks the generalization behavior of `fun_induction`.
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In particular that it behaves the same as `induction … using ….induct`.
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-/
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variable (xs ys : List Nat)
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variable (P : ∀ {α}, List α → Prop)
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-- We re-define this here to avoid stage0 complications
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def zipWith (f : α → β → γ) : (xs : List α) → (ys : List β) → List γ
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| x::xs, y::ys => f x y :: zipWith f xs ys
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| _, _ => []
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/--
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error: unsolved goals
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case case1
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : P (xs✝.zip ys✝)
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⊢ P ((x✝ :: xs✝).zip (y✝ :: ys✝))
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case case2
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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t✝ ys✝ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → ys✝ = y :: ys → False
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⊢ P (t✝.zip ys✝)
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-/
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#guard_msgs in
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example : P (List.zip xs ys) := by
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fun_induction zipWith _ xs ys
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/--
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error: unsolved goals
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case case1
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : xs✝.isEmpty = true → P (xs✝.zip ys✝)
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h : (x✝ :: xs✝).isEmpty = true
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⊢ P ((x✝ :: xs✝).zip (y✝ :: ys✝))
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case case2
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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t✝ ys✝ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → ys✝ = y :: ys → False
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h : t✝.isEmpty = true
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⊢ P (t✝.zip ys✝)
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-/
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#guard_msgs in
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example (h : xs.isEmpty) : P (List.zip xs ys) := by
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fun_induction zipWith _ xs ys
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/--
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error: unsolved goals
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case case1
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : xs✝.isEmpty = true → P (xs✝.zip ys)
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h : (x✝ :: xs✝).isEmpty = true
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⊢ P ((x✝ :: xs✝).zip ys)
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case case2
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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t✝ ys✝ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → ys✝ = y :: ys → False
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h : t✝.isEmpty = true
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⊢ P (t✝.zip ys)
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-/
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#guard_msgs in
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example (h : xs.isEmpty) : P (List.zip xs ys) := by
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fun_induction zipWith _ xs (ys.take 2)
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/--
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error: unsolved goals
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case case1
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : xs✝.isEmpty = true → P (xs✝.zip ys)
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h : (x✝ :: xs✝).isEmpty = true
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⊢ P ((x✝ :: xs✝).zip ys)
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case case2
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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t✝ ys✝ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → ys✝ = y :: ys → False
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h : t✝.isEmpty = true
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⊢ P (t✝.zip ys)
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-/
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#guard_msgs in
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example (h : xs.isEmpty) : P (List.zip xs ys) := by
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induction xs, ys.take 2 using zipWith.induct
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/--
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error: unsolved goals
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case case1
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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h : xs.isEmpty = true
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : P (xs.zip ys✝)
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⊢ P (xs.zip (y✝ :: ys✝))
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case case2
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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h : xs.isEmpty = true
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t✝ ys✝ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → ys✝ = y :: ys → False
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⊢ P (xs.zip ys✝)
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-/
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#guard_msgs in
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example (h : xs.isEmpty) : P (List.zip xs ys) := by
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fun_induction zipWith _ (xs.take 2) ys
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/--
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error: unsolved goals
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case case1
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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h : xs.isEmpty = true
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : P (xs.zip ys✝)
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⊢ P (xs.zip (y✝ :: ys✝))
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case case2
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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h : xs.isEmpty = true
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t✝ ys✝ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → ys✝ = y :: ys → False
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⊢ P (xs.zip ys✝)
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-/
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#guard_msgs in
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example (h : xs.isEmpty) : P (List.zip xs ys) := by
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induction xs.take 2, ys using zipWith.induct
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/--
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error: unsolved goals
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case case1
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P : {α : Type} → List α → Prop
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : ∀ (xs : List Nat), xs.isEmpty = true → P (xs.zip ys✝)
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xs : List Nat
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h : xs.isEmpty = true
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⊢ P (xs.zip (y✝ :: ys✝))
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case case2
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P : {α : Type} → List α → Prop
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t✝ ys✝ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → ys✝ = y :: ys → False
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xs : List Nat
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h : xs.isEmpty = true
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⊢ P (xs.zip ys✝)
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-/
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#guard_msgs in
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example (h : xs.isEmpty) : P (List.zip xs ys) := by
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fun_induction zipWith _ (xs.take 2) ys generalizing xs
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/--
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error: unsolved goals
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case case1
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P : {α : Type} → List α → Prop
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : ∀ (xs : List Nat), xs.isEmpty = true → P (xs.zip ys✝)
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xs : List Nat
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h : xs.isEmpty = true
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⊢ P (xs.zip (y✝ :: ys✝))
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case case2
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P : {α : Type} → List α → Prop
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t✝ ys✝ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → ys✝ = y :: ys → False
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xs : List Nat
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h : xs.isEmpty = true
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⊢ P (xs.zip ys✝)
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-/
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#guard_msgs in
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example (h : xs.isEmpty) : P (List.zip xs ys) := by
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induction xs.take 2, ys using zipWith.induct generalizing xs
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