chore: restore splitAt pointer equality behaviour (#922)

Batteries/Data/List/Basic.lean

@@ -117,8 +117,14 @@ splitAt 2 [a, b, c] = ([a, b], [c])
 ```
 -/
 def splitAt (n : Nat) (l : List α) : List α × List α := go l n [] where
-  /-- Auxiliary for `splitAt`: `splitAt.go xs n acc = (acc.reverse ++ take n xs, drop n xs)`. -/
+  /--
+  Auxiliary for `splitAt`:
+  `splitAt.go l xs n acc = (acc.reverse ++ take n xs, drop n xs)` if `n < xs.length`,
+  and `(l, [])` otherwise.
+  -/
   go : List α → Nat → List α → List α × List α
+  | [], _, _ => (l, []) -- This branch ensures the pointer equality of the result with the input
+                        -- without any runtime branching cost.
   | x :: xs, n+1, acc => go xs n (x :: acc)
   | xs, _, acc => (acc.reverse, xs)
 

Batteries/Data/List/Lemmas.lean

@@ -192,18 +192,21 @@ theorem get?_set_of_lt' (a : α) {m n} (l : List α) (h : m < length l) :
 /-! ### splitAt -/
 
 theorem splitAt_go (n : Nat) (l acc : List α) :
-    splitAt.go l n acc = (acc.reverse ++ l.take n, l.drop n) := by
-  induction l generalizing n acc with
+    splitAt.go l xs n acc =
+      if n < xs.length then (acc.reverse ++ xs.take n, xs.drop n) else (l, []) := by
+  induction xs generalizing n acc with
   | nil => simp [splitAt.go]
   | cons x xs ih =>
     cases n with
     | zero => simp [splitAt.go]
     | succ n =>
       rw [splitAt.go, take_succ_cons, drop_succ_cons, ih n (x :: acc),
-        reverse_cons, append_assoc, singleton_append]
+        reverse_cons, append_assoc, singleton_append, length_cons]
+      simp only [Nat.succ_lt_succ_iff]
 
 theorem splitAt_eq (n : Nat) (l : List α) : splitAt n l = (l.take n, l.drop n) := by
   rw [splitAt, splitAt_go, reverse_nil, nil_append]
+  split <;> simp_all [take_of_length_le, drop_of_length_le]
 
 /-! ### eraseP -/