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.
161 lines
2.9 KiB
Text
161 lines
2.9 KiB
Text
set_option pp.analyze false
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def p (x y : Nat) := x = y
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/--
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trace: x y : Nat
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⊢ x + y = y.add x
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-/
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#guard_msgs in
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example (x y : Nat) : p (x + y) (y + x + 0) := by
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conv =>
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whnf
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congr
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. rfl
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. whnf; rfl
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trace_state
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rw [Nat.add_comm]
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rfl
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/--
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trace: x y : Nat
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⊢ x + y = y.add x
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-/
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#guard_msgs in
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example (x y : Nat) : p (x + y) (y + x + 0) := by
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conv =>
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whnf
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rhs
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whnf
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trace_state
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rw [Nat.add_comm]
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rfl
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/--
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trace: x y : Nat
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⊢ x.add y = y.add x
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-/
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#guard_msgs in
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example (x y : Nat) : p (x + y) (y + x + 0) := by
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conv =>
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whnf
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lhs
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whnf
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conv =>
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rhs
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whnf
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trace_state
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apply Nat.add_comm x y
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/--
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trace: x y : Nat
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| x + y
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-/
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#guard_msgs in
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example (x y : Nat) : p (x + y) (0 + y + x) := by
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conv =>
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whnf
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rhs
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rw [Nat.zero_add, Nat.add_comm]
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trace_state
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rfl
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done
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axiom div_self (x : Nat) : x ≠ 0 → x / x = 1
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example (h : x ≠ 0) : x / x + x = x.succ := by
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conv =>
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lhs
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arg 1
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rw [div_self]
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rfl
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tactic => assumption
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done
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show 1 + x = x.succ
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rw [Nat.succ_add, Nat.zero_add]
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example (h1 : x ≠ 0) (h2 : y = x / x) : y = 1 := by
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conv at h2 =>
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rhs
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rw [div_self]
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rfl
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tactic => assumption
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assumption
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example : id (fun x => 0 + x) = id := by
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conv =>
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lhs
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arg 1
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ext y
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rw [Nat.zero_add]
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rfl
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def f (x : Nat) :=
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if x > 0 then
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x + 1
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else
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x + 2
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example (g : Nat → Nat) (h₁ : g x = x + 1) (h₂ : x > 0) : g x = f x := by
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conv =>
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rhs
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simp [f, h₂]
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exact h₁
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example (h₁ : f x = x + 1) (h₂ : x > 0) : f x = f x := by
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conv =>
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rhs
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simp [f, h₂]
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exact h₁
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/--
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trace: x y : Nat
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f : Nat → Nat → Nat
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g : Nat → Nat
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h₁ : ∀ (z : Nat), f z z = z
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h₂ : ∀ (x y : Nat), f (g x) (g y) = y
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⊢ f (g (0 + y)) (f (g x) (g x)) = x
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---
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trace: x y : Nat
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f : Nat → Nat → Nat
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g : Nat → Nat
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h₁ : ∀ (z : Nat), f z z = z
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h₂ : ∀ (x y : Nat), f (g x) (g y) = y
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⊢ f (g y) (f (g x) (g x)) = x
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-/
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#guard_msgs in
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example (x y : Nat) (f : Nat → Nat → Nat) (g : Nat → Nat) (h₁ : ∀ z, f z z = z) (h₂ : ∀ x y, f (g x) (g y) = y) : f (g (0 + y)) (f (g x) (g (x + 0))) = x := by
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conv in _ + 0 => apply Nat.add_zero
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trace_state
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conv in 0 + _ => apply Nat.zero_add
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trace_state
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simp [h₁, h₂]
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set_option linter.unusedVariables false
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/--
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trace: x y : Nat
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f : Nat → Nat → Nat
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g : Nat → Nat
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h₁ : ∀ (z : Nat), f z z = z
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h₂ : ∀ (x y : Nat), f (g x) (g y) = y
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h₃ : f (g x) (g x) = 0
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⊢ g x = 0
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---
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trace: x y : Nat
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f : Nat → Nat → Nat
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g : Nat → Nat
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h₁ : ∀ (z : Nat), f z z = z
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h₂ : ∀ (x y : Nat), f (g x) (g y) = y
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h₃ : g x = 0
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⊢ g x = 0
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-/
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#guard_msgs in
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example (x y : Nat) (f : Nat → Nat → Nat) (g : Nat → Nat)
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(h₁ : ∀ z, f z z = z) (h₂ : ∀ x y, f (g x) (g y) = y)
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(h₃ : f (g (0 + x)) (g x) = 0)
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: g x = 0 := by
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conv at h₃ in 0 + x => apply Nat.zero_add
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trace_state
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conv at h₃ => lhs; apply h₁
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trace_state
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assumption
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