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.
49 lines
1.8 KiB
Text
49 lines
1.8 KiB
Text
@[simp] def List.count' [DecidableEq α] : List α → α → Nat
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| [], _ => 0
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| a::as, b => if a = b then as.count' b + 1 else as.count' b
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inductive StarsAndBars : Nat → Nat → Type where
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| nil : StarsAndBars 0 0
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| star : StarsAndBars s b → StarsAndBars (s+1) b
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| bar : StarsAndBars s b → StarsAndBars s (b+1)
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namespace StarsAndBars
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namespace Ex1
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def toList : StarsAndBars s b → { bs : List Bool // bs.count' false = s ∧ bs.count' true = b }
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| nil => ⟨[], by simp⟩
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| star h => ⟨false :: toList h, by simp [(toList h).2]⟩
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| bar h => ⟨true :: toList h, by simp [(toList h).2]⟩
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theorem toList_star (h : StarsAndBars s b) (h') : toList (star h) = ⟨false :: toList h, h'⟩ := by
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rfl
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theorem toList_bar (h : StarsAndBars s b) (h') : toList (bar h) = ⟨true :: toList h, h'⟩ := by
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rfl
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end Ex1
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/- Same example with explicit proofs -/
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namespace Ex2
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theorem toList_star_proof (h : bs.count' false = s ∧ bs.count' true = b) : (false :: bs).count' false = s.succ ∧ (false :: bs).count' true = b := by
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simp [*]
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theorem toList_bar_proof (h : bs.count' false = s ∧ bs.count' true = b) : (true :: bs).count' false = s ∧ (true :: bs).count' true = b.succ := by
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simp [*]
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def toList : StarsAndBars s b → { bs : List Bool // bs.count' false = s ∧ bs.count' true = b }
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| nil => ⟨[], by simp⟩
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| star h => ⟨false :: toList h, toList_star_proof (toList h).property⟩
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| bar h => ⟨true :: toList h, toList_bar_proof (toList h).property⟩
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theorem toList_star (h : StarsAndBars s b) : toList (star h) = ⟨false :: toList h, toList_star_proof (toList h).property⟩ := by
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rfl
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theorem toList_bar (h : StarsAndBars s b) : toList (bar h) = ⟨true :: toList h, toList_bar_proof (toList h).property⟩ := by
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rfl
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end Ex2
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end StarsAndBars
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