af4c693030
This PR improves the E-matching pattern inference procedure in `grind`.
Consider the following theorem:
```lean
@[grind →]
theorem eq_empty_of_append_eq_empty {xs ys : Array α} (h : xs ++ ys = #[]) : xs = #[] ∧ ys = #[] :=
append_eq_empty_iff.mp h
```
Before this PR, `grind` inferred the following pattern:
```lean
@HAppend.hAppend _ _ _ _ #2 #1
```
Note that this pattern would match any `++` application, even if it had
nothing to do with arrays. With this PR, the inferred pattern becomes:
```lean
@HAppend.hAppend (Array #3) (Array _) (Array _) _ #2 #1
```
With the new pattern, the theorem will not be considered by `grind` for
goals that do not involve `Array`s.
68 lines
2 KiB
Text
68 lines
2 KiB
Text
def Set (α : Type) := α → Bool
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def insertElem [DecidableEq α] (s : Set α) (a : α) : Set α :=
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fun x => a = x || s x
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def contains (s : Set α) (a : α) : Bool :=
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s a
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theorem contains_insert [DecidableEq α] (s : Set α) (a : α) : contains (insertElem s a) a := by
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simp [contains, insertElem]
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grind_pattern contains_insert => contains (insertElem s a) a
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-- TheoremPattern activation test
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set_option trace.grind.ematch true
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set_option trace.grind.ematch.pattern true
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/-- info: [grind.ematch] activated `contains_insert`, [@contains #3 (@insertElem _ #2 #1 #0) #0] -/
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#guard_msgs (info) in
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example [DecidableEq α] (s₁ s₂ : Set α) (a₁ a₂ : α) :
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s₂ = insertElem s₁ a₁ → a₁ = a₂ → contains s₂ a₂ := by
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grind
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/-- info: [grind.ematch] activated `contains_insert`, [@contains #3 (@insertElem _ #2 #1 #0) #0] -/
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#guard_msgs (info) in
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example [DecidableEq α] (s₁ s₂ : Set α) (a₁ a₂ : α) :
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¬ contains s₂ a₂ → s₂ = insertElem s₁ a₁ → a₁ = a₂ → False := by
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grind
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def a := 10
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def b := 20
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def foo (x : List Nat) (y : List Nat) := x ++ y ++ x
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theorem fooThm : foo x [a, b] = x ++ [a, b] ++ x := rfl
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/-- info: [grind.ematch.pattern] fooThm: [foo #0 `[[a, b]]] -/
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#guard_msgs in
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grind_pattern fooThm => foo x [a, b]
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/--
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info: [grind.internalize] foo x y
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[grind.internalize] [a, b]
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[grind.internalize] Nat
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[grind.internalize] a
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[grind.internalize] [b]
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[grind.internalize] b
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[grind.internalize] []
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[grind.ematch] activated `fooThm`, [foo #0 `[[a, b]]]
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[grind.internalize] x
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[grind.internalize] y
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[grind.internalize] z
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-/
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#guard_msgs (info) in
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set_option trace.grind.internalize true in
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example : foo x y = z → False := by
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fail_if_success grind
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sorry
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theorem arrEx [Add α] (as : Array α) (h₁ : i < as.size) (h₂ : i = j) : as[i]+as[j] = as[i] + as[i] := by sorry
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/--
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info: [grind.ematch.pattern] arrEx: [@HAdd.hAdd #6 _ _ _ (@getElem (Array _) `[Nat] _ _ _ #2 #5 _) (@getElem (Array _) `[Nat] _ _ _ #2 #4 _)]
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-/
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#guard_msgs in
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grind_pattern arrEx => as[i]+as[j]'(h₂▸h₁)
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