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.
45 lines
1.2 KiB
Text
45 lines
1.2 KiB
Text
inductive ListSplit {α : Type u} : List α → Type u
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| split l₁ l₂ : ListSplit (l₁ ++ l₂)
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def splitList {α : Type _} : (l : List α) → ListSplit l
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| [] => ListSplit.split [] []
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| h :: t => ListSplit.split [h] t
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def len : List α → Nat
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| [] => 0
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| a :: [] => 1
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| l =>
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match splitList l with
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| ListSplit.split fst snd => len fst + len snd
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termination_by l => l.length
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decreasing_by
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all_goals sorry
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-- The equational theorems are
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#check @len.eq_1
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#check @len.eq_2
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#check @len.eq_3 -- It is conditional, and may be tricky to use.
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#check @len.eq_def
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theorem len_nil : len ([] : List α) = 0 := by
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simp [len]
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theorem len_1 (a : α) : len [a] = 1 := by
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simp [len]
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theorem len_2 (a b : α) (bs : List α) : len (a::b::bs) = 1 + len (b::bs) := by
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conv => lhs; unfold len
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cases bs <;> simp [splitList, len_1]
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theorem len_cons (a : α) (as : List α) : len (a::as) = 1 + len as := by
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cases as with
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| nil => simp [len_1, len_nil]
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| cons b bs => simp [len_2]
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theorem listlen : ∀ l : List α, l.length = len l := by
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intro l
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induction l with
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| nil => simp [len]
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| cons h t ih =>
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simp [List.length, len_cons, ih]
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rw [Nat.add_comm]
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