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.
85 lines
2.5 KiB
Text
85 lines
2.5 KiB
Text
universe u
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def concat {α} : List α → α → List α
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| [], a => [a]
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| x::xs, a => x :: concat xs a
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def last {α} : (xs : List α) → xs ≠ [] → α
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| [], h => by contradiction
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| [a], h => a
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| _::a::as, h => last (a::as) (fun h => by injection h)
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def dropLast {α} : List α → List α
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| [] => []
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| [a] => []
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| a::as => a :: dropLast as
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variable {α}
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theorem concatEq (xs : List α) (h : xs ≠ []) : concat (dropLast xs) (last xs h) = xs := by
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match xs, h with
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| [], h => contradiction
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| [x], h => rfl
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| x₁::x₂::xs, h => simp [concat, dropLast, last, concatEq (x₂::xs)]
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theorem lengthCons {α} (x : α) (xs : List α) : (x::xs).length = xs.length + 1 :=
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rfl
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theorem eqNilOfLengthZero {α} : (xs : List α) → xs.length = 0 → xs = []
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| [], h => rfl
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| x::xs, h => by rw [lengthCons] at h; contradiction
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theorem dropLastLen {α} (xs : List α) : (n : Nat) → xs.length = n+1 → (dropLast xs).length = n := by
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match xs with
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| [] => intros; contradiction
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| [a] =>
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intro n h
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have : 1 = n + 1 := h
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have : 0 = n := by injection this
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subst this
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rfl
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| x₁::x₂::xs =>
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intro n h
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cases n with
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| zero =>
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simp at h
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| succ n =>
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have : (x₁ :: x₂ :: xs).length = xs.length + 2 := by simp
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have : xs.length = n := by rw [this] at h; injection h with h; injection h
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simp [dropLast, dropLastLen (x₂::xs) xs.length (lengthCons ..), this]
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@[inline]
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def concatElim {α}
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(motive : List α → Sort u)
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(base : Unit → motive [])
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(ind : (xs : List α) → (a : α) → motive xs → motive (concat xs a))
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(xs : List α)
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: motive xs :=
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let rec @[specialize] aux : (n : Nat) → (xs : List α) → xs.length = n → motive xs
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| 0, xs, h => by
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have aux := eqNilOfLengthZero _ h
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subst aux
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apply base ()
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| n+1, xs, h => by
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have notNil : xs ≠ [] := by intro h1; subst h1; injection h
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let ih := aux n (dropLast xs) (dropLastLen _ _ h)
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let aux := ind (dropLast xs) (last xs notNil) ih
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rw [concatEq] at aux
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exact aux
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aux xs.length xs rfl
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-- The generated code is tail recursive
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def test (xs : List Nat) : IO Unit :=
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concatElim (motive := fun _ => IO Unit)
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(fun _ => pure ())
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(fun xs x r => do IO.println s!"step xs: {xs} x: {x}"; r)
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xs
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/--
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info: step xs: [1, 2, 3] x: 4
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step xs: [1, 2] x: 3
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step xs: [1] x: 2
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step xs: [] x: 1
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-/
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#guard_msgs in
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#eval test [1, 2, 3, 4]
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