dc001a01e5
This PR adds the `binderNameHint` gadget. It can be used in rewrite and
simp rules to preserve a user-provided name where possible.
The expression `binderNameHint v binder e` defined to be `e`.
If it is used on the right-hand side of an equation that is applied by a
tactic like `rw` or `simp`,
and `v` is a local variable, and `binder` is an expression that (after
beta-reduction) is a binder
(so `fun w => …` or `∀ w, …`), then it will rename `v` to the name used
in the binder, and remove
the `binderNameHint`.
A typical use of this gadget would be as follows; the gadget ensures
that after rewriting, the local
variable is still `name`, and not `x`:
```
theorem all_eq_not_any_not (l : List α) (p : α → Bool) :
l.all p = !l.any fun x => binderNameHint x p (!p x) := sorry
example (names : List String) : names.all (fun name => "Waldo".isPrefixOf name) = true := by
rw [all_eq_not_any_not]
-- ⊢ (!names.any fun name => !"Waldo".isPrefixOf name) = true
```
This gadget is supported by `simp`, `dsimp` and `rw` in the
right-hand-side of an equation, but not
in hypotheses or by other tactics.
95 lines
2.8 KiB
Text
95 lines
2.8 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 l p
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/--
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error: tactic 'fail' failed
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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: tactic 'fail' failed
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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: tactic 'fail' failed
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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: tactic 'fail' failed
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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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info: 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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