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.
95 lines
2.9 KiB
Text
95 lines
2.9 KiB
Text
theorem all_eq_not_any_not (l : List α) (p : α → Bool) :
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l.all p = !l.any fun x => binderNameHint x p (!p x)
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:= List.all_eq_not_any_not
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/--
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error: Failed: `fail` tactic was invoked
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names : List String
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⊢ (!names.any fun name => !"Waldo".isPrefixOf name) = true
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-/
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#guard_msgs in
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example (names : List String) : names.all (fun name => "Waldo".isPrefixOf name) = true := by
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rw [all_eq_not_any_not]
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fail
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/--
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error: Failed: `fail` tactic was invoked
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names : List String
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⊢ (names.any fun name => !"Waldo".isPrefixOf name) = false
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-/
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#guard_msgs in
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example (names : List String) : names.all (fun name => "Waldo".isPrefixOf name) = true := by
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simp [all_eq_not_any_not, -List.any_eq_false]
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fail
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def List.myAll (p : α → Bool) (xs : List α) : Bool := !(xs.any fun x => !p x)
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theorem myAll_eq_not_any_not (l : List α) (p : α → Bool) :
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l.myAll p = !l.any fun x => binderNameHint x p (!p x)
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:= rfl
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/--
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error: Failed: `fail` tactic was invoked
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names : List String
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⊢ (!names.any fun name => !"Waldo".isPrefixOf name) = true
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-/
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#guard_msgs in
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example (names : List String) : names.myAll (fun name => "Waldo".isPrefixOf name) = true := by
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dsimp [myAll_eq_not_any_not]
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fail
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-- Check if we can pick the second binder by providing arguments to `f` in `binderNameHint`
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-- (It will beta-reduce it)
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-- Why this not in standard lib (maybe with the more complex form of recognizing lambdas that
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-- ignore arguments?)
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@[simp]
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theorem List.mapIdx_eq_map (l : List α) (f : α → β) : (l.mapIdx fun _ x => f x) = l.map f := by
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induction l <;> simp_all
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set_option linter.unusedVariables false in
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theorem zipWith_eq_map_idx_zipWith (l1 : List α) (l2 : List β) (f : α → β → γ) :
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List.zipWith f l1 l2 = (List.zip l1 l2).mapIdx
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(fun i ⟨a, b⟩ => binderNameHint a f <| binderNameHint b (f a) <| f a b)
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:= by simp [List.zip_eq_zipWith, List.map_zipWith]
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/--
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error: Failed: `fail` tactic was invoked
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l1 l2 : List Nat
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⊢ (List.mapIdx
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(fun i x =>
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match x with
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| (x, y) => x + y)
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(l1.zip l2)).isEmpty =
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true
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-/
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#guard_msgs in
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example (l1 l2 : List Nat) :
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(List.zipWith (fun x y => x + y) l1 l2).isEmpty := by
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rw [zipWith_eq_map_idx_zipWith]
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fail
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-- For now, binder name hints do not work in other tactics, like `apply`
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-- (but at least `simp` or `dsimp` removes them)
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theorem myAll_eq_not_any_not_iff {l : List α} {p : α → Bool} :
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l.myAll p ↔ !l.any fun x => binderNameHint x p (!p x)
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:= by simp [myAll_eq_not_any_not]
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/--
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error: unsolved goals
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names : List String
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⊢ (!names.any fun x => !"Waldo".isPrefixOf x) = true
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---
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trace: names : List String
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⊢ (!names.any fun x => binderNameHint x (fun name => "Waldo".isPrefixOf name) !"Waldo".isPrefixOf x) = true
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-/
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#guard_msgs in
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example (names : List String) : names.myAll (fun name => "Waldo".isPrefixOf name) = true := by
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apply myAll_eq_not_any_not_iff.mpr
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trace_state
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dsimp
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done
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