66471ba6e2
This PR adds the new attributes `[grind =>]` and `[grind <=]` for controlling pattern selection and minimizing the number of places where we have to use verbose `grind_pattern` command. It also fixes a bug in the new pattern selection procedure, and improves the automatic pattern selection for local lemmas. The tests `grind_constProp.lean` and `no_grind_constProp.lean` are the same use case with and without `grind`.
73 lines
2.1 KiB
Text
73 lines
2.1 KiB
Text
def Set (α : Type) := α → Bool
|
||
|
||
def insertElem [DecidableEq α] (s : Set α) (a : α) : Set α :=
|
||
fun x => a = x || s x
|
||
|
||
def contains (s : Set α) (a : α) : Bool :=
|
||
s a
|
||
|
||
theorem contains_insert [DecidableEq α] (s : Set α) (a : α) : contains (insertElem s a) a := by
|
||
simp [contains, insertElem]
|
||
|
||
grind_pattern contains_insert => contains (insertElem s a) a
|
||
|
||
-- TheoremPattern activation test
|
||
|
||
set_option trace.grind.ematch true
|
||
set_option trace.grind.ematch.pattern true
|
||
|
||
/--
|
||
info: [grind.ematch] activated `contains_insert`, [@contains #3 (@insertElem ? #2 #1 #0) #0]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example [DecidableEq α] (s₁ s₂ : Set α) (a₁ a₂ : α) :
|
||
s₂ = insertElem s₁ a₁ → a₁ = a₂ → contains s₂ a₂ := by
|
||
grind
|
||
|
||
/--
|
||
info: [grind.ematch] reinsert `contains_insert`
|
||
[grind.ematch] activated `contains_insert`, [@contains #3 (@insertElem ? #2 #1 #0) #0]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example [DecidableEq α] (s₁ s₂ : Set α) (a₁ a₂ : α) :
|
||
¬ contains s₂ a₂ → s₂ = insertElem s₁ a₁ → a₁ = a₂ → False := by
|
||
grind
|
||
|
||
def a := 10
|
||
def b := 20
|
||
def foo (x : List Nat) (y : List Nat) := x ++ y ++ x
|
||
|
||
theorem fooThm : foo x [a, b] = x ++ [a, b] ++ x := rfl
|
||
|
||
/-- info: [grind.ematch.pattern] fooThm: [foo #0 `[[a, b]]] -/
|
||
#guard_msgs in
|
||
grind_pattern fooThm => foo x [a, b]
|
||
|
||
|
||
/--
|
||
info: [grind.internalize] foo x y
|
||
[grind.internalize] [a, b]
|
||
[grind.internalize] Nat
|
||
[grind.internalize] a
|
||
[grind.internalize] [b]
|
||
[grind.internalize] b
|
||
[grind.internalize] []
|
||
[grind.ematch] activated `fooThm`, [foo #0 `[[a, b]]]
|
||
[grind.internalize] x
|
||
[grind.internalize] y
|
||
[grind.internalize] z
|
||
-/
|
||
#guard_msgs (info) in
|
||
set_option trace.grind.internalize true in
|
||
example : foo x y = z → False := by
|
||
fail_if_success grind
|
||
sorry
|
||
|
||
theorem arrEx [Add α] (as : Array α) (h₁ : i < as.size) (h₂ : i = j) : as[i]+as[j] = as[i] + as[i] := by sorry
|
||
|
||
|
||
/--
|
||
info: [grind.ematch.pattern] arrEx: [@HAdd.hAdd #6 ? ? ? (@getElem ? `[Nat] ? ? ? #2 #5 ?) (@getElem ? `[Nat] ? ? ? #2 #4 ?)]
|
||
-/
|
||
#guard_msgs in
|
||
grind_pattern arrEx => as[i]+as[j]'(h₂▸h₁)
|