226a90f1eb
This PR adds `+grind` and `+try?` options to `exact?` and `apply?`
tactics.
## `+grind` option
When `+grind` is enabled, `grind` is used as a fallback discharger for
subgoals that `solve_by_elim` cannot close. The proof is wrapped in
`Grind.Marker` so suggestions display `(by grind)` instead of the
complex grind proof term.
Example:
```lean
axiom foo (x : Nat) : x < 37 → 5 < x → x.log2 < 6
/--
info: Try this:
[apply] exact foo x (by grind) (by grind)
-/
#guard_msgs in
example (x : Nat) (h₁ : x < 30) (h₂ : 8 < x) : x.log2 < 6 := by
exact? +grind
```
## `+try?` option
When `+try?` is enabled, `try?` is used as a fallback discharger for
subgoals. This is useful when subgoals require induction or other
strategies that `try?` can find but `solve_by_elim` and `grind` cannot.
Example:
```lean
inductive MyList (α : Type _) where
| nil : MyList α
| cons : α → MyList α → MyList α
axiom MyListProp : MyList α → Prop
@[grind .] axiom mylist_nil : MyListProp (MyList.nil : MyList α)
@[grind .] axiom mylist_cons : ∀ (x : α) (xs : MyList α), MyListProp xs → MyListProp (MyList.cons x xs)
axiom qux (xs : MyList α) (p : MyListProp xs) : MyListProp2 xs
/--
info: Try this:
[apply] exact qux xs (by try?)
-/
example (xs : MyList α) : MyListProp2 xs := by
exact? +try?
```
🤖 Prepared with Claude Code
---------
Co-authored-by: Claude <noreply@anthropic.com>
94 lines
2.3 KiB
Text
94 lines
2.3 KiB
Text
/-!
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# Tests for `exact? +grind` and `apply? +grind`
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These tests verify that the `+grind` option is accepted syntactically and
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enables `grind` as a fallback discharger for subgoals.
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-/
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/--
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info: Try this:
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[apply] exact List.ne_nil_of_length_pos h
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-/
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#guard_msgs in
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example (l : List Nat) (h : 0 < l.length) : l ≠ [] := by exact?
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/--
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info: Try this:
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[apply] exact List.ne_nil_of_length_pos (h trivial)
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-/
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#guard_msgs in
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example (l : List Nat) (h : True → 0 < l.length) : l ≠ [] := by exact?
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example (l : List Nat) (h : 1 < l.length) : l ≠ [] := by exact List.ne_nil_of_length_pos (by grind)
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/--
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info: Try this:
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[apply] exact List.ne_nil_of_length_pos (by grind)
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-/
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#guard_msgs in
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example (l : List Nat) (h : 1 < l.length) : l ≠ [] := by
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exact? +grind
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/--
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info: Try this:
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[apply] exact List.ne_nil_of_length_pos (by grind)
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-/
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#guard_msgs in
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example {P : Prop} (l : List Nat) (p : P) (h : P → 1 < l.length) : l ≠ [] := by
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exact? +grind
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axiom foo (x : Nat) : x < 37 → 5 < x → x.log2 < 6
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/--
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info: Try this:
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[apply] exact foo x (by grind) (by grind)
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-/
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#guard_msgs in
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example (x : Nat) (h₁ : x < 30) (h₂ : 8 < x) : x.log2 < 6 := by
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exact? +grind
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inductive MyList (α : Type _) where
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| nil : MyList α
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| cons : α → MyList α → MyList α
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axiom MyListProp : MyList α → Prop
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axiom MyListProp2 : MyList α → Prop
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@[grind .] axiom mylist_nil : MyListProp (MyList.nil : MyList α)
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@[grind .] axiom mylist_cons : ∀ (x : α) (xs : MyList α), MyListProp xs → MyListProp (MyList.cons x xs)
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/--
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info: Try these:
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[apply] (induction xs) <;> grind
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[apply] (induction xs) <;> grind only [mylist_nil, mylist_cons]
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[apply] ·
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induction xs
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· grind => instantiate only [mylist_nil]
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· grind => instantiate only [mylist_cons]
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-/
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#guard_msgs in
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example (xs : MyList α) : MyListProp xs := by
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try?
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axiom qux (xs : MyList α) (p : MyListProp xs) : MyListProp2 xs
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/--
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info: Try these:
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[apply] (induction xs) <;> grind
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[apply] (induction xs) <;> grind only [mylist_nil, mylist_cons]
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[apply] ·
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induction xs
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· grind => instantiate only [mylist_nil]
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· grind => instantiate only [mylist_cons]
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-/
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#guard_msgs in
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example (xs : MyList α) : MyListProp2 xs := by
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exact qux xs (by try?)
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/--
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info: Try this:
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[apply] exact qux xs (by try?)
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-/
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example (xs : MyList α) : MyListProp2 xs := by
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exact? +try?
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