feat: close goals using match-expression conditions in grind
#6783
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
leodemoura
added
the
changelog-language
github-actions
bot
added
the
toolchain-available
|
Mathlib CI status (docs):
|
luisacicolini
pushed a commit
to opencompl/lean4
that referenced
this pull request
Feb 24, 2025
…nprover#6783) This PR adds support for closing goals using `match`-expression conditions that are known to be true in the `grind` tactic state. `grind` can now solve goals such as: ```lean def f : List Nat → List Nat → Nat | _, 1 :: _ :: _ => 1 | _, _ :: _ => 2 | _, _ => 0 example : z = a :: as → y = z → f x y > 0 ``` Without `grind`, we would use the `split` tactic. The first two goals, corresponding to the first two alternatives, are closed using `simp`, and the the third using the `match`-expression condition produced by `split`. The proof would proceed as follows. ```lean example : z = a :: as → y = z → f x y > 0 := by intros unfold f split next => simp next => simp next h => /- ... _ : z = a :: as _ : y = z ... h : ∀ (head : Nat) (tail : List Nat), y = head :: tail → False |- 0 > 0 -/ subst_vars /- ... h : ∀ (head : Nat) (tail : List Nat), a :: as = head :: tail → False |- 0 > 0 -/ have : False := h a as rfl contradiction ``` Here is the same proof using `grind`. ```lean example : z = a :: as → y = z → f x y > 0 := by grind [f.eq_def] ```
luisacicolini
pushed a commit
to opencompl/lean4
that referenced
this pull request
Feb 25, 2025
…nprover#6783) This PR adds support for closing goals using `match`-expression conditions that are known to be true in the `grind` tactic state. `grind` can now solve goals such as: ```lean def f : List Nat → List Nat → Nat | _, 1 :: _ :: _ => 1 | _, _ :: _ => 2 | _, _ => 0 example : z = a :: as → y = z → f x y > 0 ``` Without `grind`, we would use the `split` tactic. The first two goals, corresponding to the first two alternatives, are closed using `simp`, and the the third using the `match`-expression condition produced by `split`. The proof would proceed as follows. ```lean example : z = a :: as → y = z → f x y > 0 := by intros unfold f split next => simp next => simp next h => /- ... _ : z = a :: as _ : y = z ... h : ∀ (head : Nat) (tail : List Nat), y = head :: tail → False |- 0 > 0 -/ subst_vars /- ... h : ∀ (head : Nat) (tail : List Nat), a :: as = head :: tail → False |- 0 > 0 -/ have : False := h a as rfl contradiction ``` Here is the same proof using `grind`. ```lean example : z = a :: as → y = z → f x y > 0 := by grind [f.eq_def] ```
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
This PR adds support for closing goals using
match-expression conditions that are known to be true in thegrindtactic state.grindcan now solve goals such as:Without
grind, we would use thesplittactic. The first two goals, corresponding to the first two alternatives, are closed usingsimp, and the the third using thematch-expression condition produced bysplit. The proof would proceed as follows.Here is the same proof using
grind.