def listL (a : List α) := if a = [] then 1 else 2
def listR (a : List α) := if [] = a then 1 else 2

/-- info: 1 -/
#guard_msgs in #eval @listL Nat []
/-- info: 2 -/
#guard_msgs in #eval listL [""]
/-- info: 1 -/
#guard_msgs in #eval @listL Nat []
/-- info: 2 -/
#guard_msgs in #eval listL [()]


-- test instance diamonds
example :
    @List.instDecidableEqNil α [] = @List.instDecidableNilEq α [] := by
  with_reducible_and_instances rfl

section
variable {α : Type u} [DecidableEq α]
example (x : List α) :
    instDecidableEqList x [] = List.instDecidableEqNil x := by
  with_reducible_and_instances rfl

example (x : List α) :
    instDecidableEqList [] x = List.instDecidableNilEq x := by
  with_reducible_and_instances rfl
end


-- List decidable equality using `withPtrEqDecEq`
def listDecEqAux {α} [s : DecidableEq α] : ∀ (as bs : List α), Decidable (as = bs)
| [],    []    => isTrue rfl
| [],    b::bs => isFalse $ fun h => List.noConfusion rfl (heq_of_eq h)
| a::as, []    => isFalse $ fun h => List.noConfusion rfl (heq_of_eq h)
| a::as, b::bs =>
  match s a b with
  | isTrue h₁  =>
    match withPtrEqDecEq as bs (fun _ => listDecEqAux as bs) with
    | isTrue h₂  => isTrue $ h₁ ▸ h₂ ▸ rfl
    | isFalse h₂ => isFalse $ fun h => List.noConfusion rfl (heq_of_eq h) (fun _ h₃ => absurd (eq_of_heq h₃) h₂)
  | isFalse h₁ => isFalse $ fun h => List.noConfusion rfl (heq_of_eq h) (fun h₂ _ => absurd (eq_of_heq h₂) h₁)

instance List.optimizedDecEq {α} [DecidableEq α] : DecidableEq (List α) :=
fun a b => withPtrEqDecEq a b (fun _ => listDecEqAux a b)