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.
37 lines
1.3 KiB
Text
37 lines
1.3 KiB
Text
def f : Nat → Nat → Nat
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| 0, y => y
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| x+1, y+1 => f (x-2) y
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| x+1, 0 => 0
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example : f 0 y = y :=
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rfl -- Error, it does not hold by reflexivity since the recursion is on `y`
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example : f 0 0 = 0 := rfl
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example : f 0 (y+1) = y+1 := rfl
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inductive Vector' (α : Type u) : Nat → Type u where
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| nil : Vector' α 0
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| cons : α → Vector' α n → Vector' α (n+1)
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namespace Vector'
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def insert (a: α): Fin (n+1) → Vector' α n → Vector' α (n+1)
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| ⟨0 , _⟩, xs => cons a xs
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| ⟨i+1, h⟩, cons x xs => cons x $ xs.insert a ⟨i, Nat.lt_of_succ_lt_succ h⟩
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theorem insert_at_0_eq_cons1 (a: α) (v: Vector' α n): v.insert a ⟨0, Nat.zero_lt_succ n⟩ = cons a v :=
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(rfl) -- Error, it does not hold by reflexivity because the recursion is on v
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example (a : α) : nil.insert a ⟨0, by simp +arith⟩ = cons a nil :=
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rfl
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example (a : α) (b : α) (bs : Vector' α n) : (cons b bs).insert a ⟨0, by simp +arith⟩ = cons a (cons b bs) :=
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rfl
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theorem insert_at_0_eq_cons2 (a: α) (v: Vector' α n): v.insert a ⟨0, Nat.zero_lt_succ n⟩ = cons a v := by
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rw [insert]
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theorem insert_at_0_eq_cons3 (a: α) (v: Vector' α n): v.insert a ⟨0, Nat.zero_lt_succ n⟩ = cons a v := by
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simp only [insert]
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end Vector'
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