61186629d6
This PR implements the option `revert`, which is set to `false` by default. To recover the old `grind` behavior, you should use `grind +revert`. Previously, `grind` used the `RevSimpIntro` idiom, i.e., it would revert all hypotheses and then re-introduce them while simplifying and applying eager `cases`. This idiom created several problems: * Users reported that `grind` would include unnecessary parameters. See [here](https://leanprover.zulipchat.com/#narrow/channel/270676-lean4/topic/Grind.20aggressively.20includes.20local.20hypotheses.2E/near/554887715). * Unnecessary section variables were also being introduced. See the new test contributed by Sebastian Graf. * Finally, it prevented us from supporting arbitrary parameters as we do in `simp`. In `simp`, I implemented a mechanism that simulates local universe-polymorphic theorems, but this approach could not be used in `grind` because there is no mechanism for reverting (and re-introducing) local universe-polymorphic theorems. Adding such a mechanism would require substantial work: I would need to modify the local context object. I considered maintaining a substitution from the original variables to the new ones, but this is also tricky, because the mapping would have to be stored in the `grind` goal objects, and it is not just a simple mapping. After reverting everything, I would need to keep a sequence of original variables that must be added to the mapping as we re-introduce them, but eager case splits complicate this quite a bit. The whole approach felt overly messy. The new behavior `grind -revert` addresses all these issues. None of the `grind` proofs in our test suite broke after we fixed the bugs exposed by the new feature. That said, the traces and counterexamples produced by `grind` are different. The new proof terms are also different.
79 lines
2.4 KiB
Text
79 lines
2.4 KiB
Text
namespace List
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protected def diff {α} [BEq α] : List α → List α → List α
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| l, [] => l
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| l₁, a :: l₂ => if l₁.elem a then List.diff (l₁.erase a) l₂ else List.diff l₁ l₂
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def Subperm (l₁ l₂ : List α) : Prop := ∃ l, l ~ l₁ ∧ l <+ l₂
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open Perm (swap)
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theorem Perm.subperm_left {l l₁ l₂ : List α} (p : l₁ ~ l₂) : Subperm l l₁ ↔ Subperm l l₂ :=
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sorry
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theorem Sublist.subperm {l₁ l₂ : List α} (s : l₁ <+ l₂) : Subperm l₁ l₂ := sorry
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theorem Subperm.perm_of_length_le {l₁ l₂ : List α} :
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Subperm l₁ l₂ → length l₂ ≤ length l₁ → l₁ ~ l₂ :=
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sorry
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end List
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variable {α : Type} [DecidableEq α] {l₁ l₂ : List α}
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open List
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/--
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error: `grind` failed
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case grind.1.1.1.1.1.1.1.1.1
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α : Type
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inst : DecidableEq α
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l₁ l₂ : List α
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hl : l₂.Subperm l₁
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p : α → Bool
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h : ¬countP p l₁ = countP p (l₁.diff l₂ ++ l₂)
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w : α
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h_2 : ¬count w (l₁.diff l₂ ++ l₂) = count w l₁
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w_1 : α
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h_4 : ¬count w_1 l₁ = count w_1 (l₁.diff l₂ ++ l₂)
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left : l₂ ⊆ l₁
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right : ∀ {a : α}, a ∈ l₂ → a ∈ l₁
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left_1 : filter p l₂ <+ filter p l₁
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w_2 : List α
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left_2 : w_2 <+ l₁
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right_2 : filter p l₂ = filter p w_2
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w_3 : List α
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left_3 : w_3 <+ l₁
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right_3 : filter p l₂ = filter p w_3
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h_9 : (filter p l₂).length = (filter p l₁).length
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w_4 : α
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h_11 : ¬count w_4 (l₁.diff l₂ ++ l₂) = count w_4 l₂
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w_5 : α
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h_13 : ¬count w_5 l₂ = count w_5 (l₁.diff l₂ ++ l₂)
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left_4 : l₁.diff l₂ ~ l₁
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right_4 : ∀ (a : α), count a (l₁.diff l₂) = count a l₁
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w_6 : α
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h_16 : ¬count w_6 (l₁.diff l₂ ++ l₂) = count w_6 (l₁.diff l₂)
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w_7 : α
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h_18 : ¬count w_7 (l₁.diff l₂) = count w_7 (l₁.diff l₂ ++ l₂)
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left_5 : l₁.diff l₂ ~ l₂
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right_5 : ∀ (a : α), count a (l₁.diff l₂) = count a l₂
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left_6 : l₂ ~ l₁
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right_6 : ∀ (a : α), count a l₂ = count a l₁
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left_7 : l₂ ~ l₁.diff l₂
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right_7 : ∀ (a : α), count a l₂ = count a (l₁.diff l₂)
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left_8 : l₁ ~ l₁.diff l₂
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right_8 : ∀ (a : α), count a l₁ = count a (l₁.diff l₂)
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left_9 : l₁ ~ l₂
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right_9 : ∀ (a : α), count a l₁ = count a l₂
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⊢ False
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-/
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#guard_msgs in
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theorem countP_diff (hl : Subperm l₂ l₁) (p : α → Bool) :
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countP p l₁ = countP p (l₁.diff l₂ ++ l₂) := by
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grind -verbose [
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List.Perm.subperm_left,
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List.Sublist.subperm,
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List.Subperm.perm_of_length_le,
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List.Perm.countP_congr
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]
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