6d46e31ad8
This PR adds the `Try.Config.merge` flag (`true` by default) to the
`try?` tactic. When set to `true`, `try?` compresses suggestions such
as:
```lean
· induction xs, ys using bla.induct
· grind only [List.length_reverse]
· grind only [bla]
```
into:
```lean
induction xs, ys using bla.induct <;> grind only [List.length_reverse, bla]
```
This PR also ensures `try?` does not generate suggestions that mixes
`grind` and `grind only`, or `simp` and `simp only` tactics.
This PR also adds the `try? +harder` option (previously called `lib`),
but it has not been fully implemented yet.
188 lines
3.8 KiB
Text
188 lines
3.8 KiB
Text
set_option grind.warning false
|
||
%reset_grind_attrs
|
||
|
||
/--
|
||
info: Try these:
|
||
• simp
|
||
• simp only [ne_eq, reduceCtorEq, not_false_eq_true]
|
||
• grind
|
||
• grind only
|
||
• simp_all
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : [1, 2] ≠ [] := by
|
||
try?
|
||
|
||
/--
|
||
info: Try these:
|
||
• simp +arith
|
||
• simp +arith only [ge_iff_le]
|
||
• grind
|
||
• grind only
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : 4 + x + y ≥ 1 + x := by
|
||
try?
|
||
|
||
/--
|
||
info: Try these:
|
||
• simp +arith
|
||
• grind
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : 4 + x + y ≥ 1 + x := by
|
||
try? -only
|
||
|
||
/--
|
||
info: Try these:
|
||
• grind
|
||
• grind only
|
||
-/
|
||
#guard_msgs (info) in
|
||
example (f : Nat → Nat) : f a = b → a = c → f c = b := by
|
||
try?
|
||
|
||
def f : Nat → Nat
|
||
| 0 => 1
|
||
| _ => 2
|
||
|
||
/--
|
||
info: Try these:
|
||
• grind [= f]
|
||
• grind only [f]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : f (f 0) > 0 := by
|
||
try?
|
||
|
||
/--
|
||
info: Try these:
|
||
• grind [= f.eq_def]
|
||
• grind only [= f.eq_def]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : f x > 0 := by
|
||
try?
|
||
|
||
def app : List α → List α → List α
|
||
| [], bs => bs
|
||
| a::as, bs => a :: app as bs
|
||
|
||
/--
|
||
info: Try these:
|
||
• rfl
|
||
• grind [= app]
|
||
• grind only [app]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : app [a, b] [c] = [a, b, c] := by
|
||
try?
|
||
|
||
/--
|
||
info: Try these:
|
||
• (induction as, bs using app.induct) <;> grind [= app]
|
||
• (induction as, bs using app.induct) <;> grind only [app]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : app (app as bs) cs = app as (app bs cs) := by
|
||
try?
|
||
|
||
/--
|
||
info: Try this: (induction as, bs using app.induct) <;> grind [= app]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : app (app as bs) cs = app as (app bs cs) := by
|
||
try? (max := 1)
|
||
|
||
/--
|
||
info: Try these:
|
||
• · expose_names; induction as, bs_1 using app.induct <;> grind [= app]
|
||
• · expose_names; induction as, bs_1 using app.induct <;> grind only [app]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : app (app as bs) cs = app as (app bs cs) := by
|
||
have bs := 20 -- shadow variable in the goal
|
||
try?
|
||
|
||
/--
|
||
info: Try these:
|
||
• · expose_names; induction as, bs using app.induct <;> grind [= app]
|
||
• · expose_names; induction as, bs using app.induct <;> grind only [app]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : app (app as bs) cs = app as (app bs cs) := by
|
||
revert as bs cs
|
||
intro _ _ _
|
||
-- `as`, `bs`, and `cs` now have inaccessible names.
|
||
try?
|
||
|
||
def concat : List α → α → List α
|
||
| .nil, b => .cons b .nil
|
||
| .cons a as, b => .cons a (concat as b)
|
||
|
||
attribute [simp] concat
|
||
|
||
/--
|
||
info: Try these:
|
||
• (induction as, a using concat.induct) <;> simp_all
|
||
• (induction as, a using concat.induct) <;> simp [*]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example (as : List α) (a : α) : concat as a = as ++ [a] := by
|
||
try? -only
|
||
|
||
/--
|
||
info: Try these:
|
||
• (induction as, a using concat.induct) <;> simp_all
|
||
• ·
|
||
induction as, a using concat.induct
|
||
· simp
|
||
· simp [*]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example (as : List α) (a : α) : concat as a = as ++ [a] := by
|
||
try? -only -merge
|
||
|
||
|
||
def foo : Nat → Nat
|
||
| 0 => 1
|
||
| x+1 => foo x - 1
|
||
|
||
|
||
/--
|
||
info: Try this: ·
|
||
induction x using foo.induct
|
||
· grind [= foo]
|
||
· sorry
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : foo x > 0 := by
|
||
try? +missing -only -- `try?` does not solve all subgoals.
|
||
sorry
|
||
|
||
/--
|
||
error: tactic 'try?' failed, consider using `grind` manually, or `try? +missing` for partial proofs containing `sorry`
|
||
x : Nat
|
||
⊢ foo x > 0
|
||
-/
|
||
#guard_msgs (error) in
|
||
example : foo x > 0 := by
|
||
try?
|
||
|
||
@[simp] def bla : List Nat → List Nat → List Nat
|
||
| [], ys => ys.reverse
|
||
| _::xs, ys => bla xs ys
|
||
|
||
attribute [grind] List.length_reverse bla
|
||
|
||
/--
|
||
info: Try these:
|
||
• (induction xs, ys using bla.induct) <;> grind
|
||
• (induction xs, ys using bla.induct) <;> simp_all
|
||
• (induction xs, ys using bla.induct) <;> simp [*]
|
||
• (induction xs, ys using bla.induct) <;> simp only [bla, List.length_reverse, *]
|
||
• (induction xs, ys using bla.induct) <;> grind only [List.length_reverse, bla]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : (bla xs ys).length = ys.length := by
|
||
try?
|