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.
89 lines
2.2 KiB
Text
89 lines
2.2 KiB
Text
namespace Ex1
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def f (n : Nat) : Option { r : Nat // r ≤ n } :=
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match n with
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| 0 => some ⟨0, Nat.le_refl _⟩
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| n+1 => match f n with
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| some ⟨m, h₁⟩ =>
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have : m < n+1 := Nat.lt_of_le_of_lt h₁ (Nat.lt_succ_self _)
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match f m with
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| some ⟨r, h₂⟩ => some ⟨r, Nat.le_trans h₂ (Nat.le_trans h₁ (Nat.le_succ _))⟩
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| none => none
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| none => none
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end Ex1
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namespace Ex2
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def f (n : Nat) : Option { r : Nat // r ≤ n } :=
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if h : n = 0 then
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some ⟨0, h ▸ Nat.le_refl _⟩
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else
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match f (n-1) with
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| some ⟨m, h₁⟩ =>
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have : m < n := Nat.lt_of_le_of_lt h₁ (Nat.pred_lt h)
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match f m with
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| some ⟨r, h₂⟩ => some ⟨r, Nat.le_trans h₂ (Nat.le_trans h₁ (Nat.pred_le _))⟩
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| none => none
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| none => none
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end Ex2
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namespace Ex3
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def f' (n : Nat) : Option { r : Nat // r ≤ n } :=
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match n with
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| 0 => some ⟨0, Nat.le_refl _⟩
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| n+1 => match f' n with
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| some ⟨m, h₁⟩ =>
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have : m < n+1 := Nat.lt_of_le_of_lt h₁ (Nat.lt_succ_self _)
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match f' m with
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| some ⟨r, h₂⟩ => some ⟨r, Nat.le_trans h₂ (Nat.le_trans h₁ (Nat.le_succ _))⟩
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| none => none
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| none => none
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theorem f'_ne_none (n : Nat) : f' n ≠ none := by
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match n with
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| 0 => simp [f']
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| n+1 =>
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simp [f']
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have ih₁ := f'_ne_none n
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split
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next m h₁ he =>
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have : m < n+1 := Nat.lt_of_le_of_lt h₁ (Nat.lt_succ_self _)
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have ih₂ := f'_ne_none m
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split
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next => simp
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next h => contradiction
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next => contradiction
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def f (n : Nat) : Option Nat :=
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match f' n with
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| some r => some r.1
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| none => none
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theorem f_eq (n : Nat) :
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f n = match n with
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| 0 => some 0
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| n => match f (n - 1) with
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| some m => f m
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| none => none := by
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unfold f
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split
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next r h =>
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revert h
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split <;> try simp [f']
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next => intro h; subst h; simp
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next hne =>
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cases n <;> simp [f']
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next => contradiction
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next n _ =>
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split <;> try simp
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next r hrn h₁ =>
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split <;> simp
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next => intro he; subst he; simp [*]
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next h_eq_none =>
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have hne := f'_ne_none n
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contradiction
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end Ex3
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