Add mergeSort example

Author: mbovel

tests/run-custom-args/qualified-types/mergeSort.check

@@ -0,0 +1,4 @@
+Unsorted: ArraySeq(5, 3, 8, 1, 2, 7, 4, 6)
+Sorted:   ArraySeq(1, 2, 3, 4, 5, 6, 7, 8)
+Unsorted: ArraySeq(7, 4, 5, 3, 2, 6, 1)
+Sorted:   ArraySeq(1, 2, 3, 4, 5, 6, 7)

tests/run-custom-args/qualified-types/mergeSort.scala

@@ -0,0 +1,49 @@
+type Pos = {x: Int with x >= 0}
+
+def safeDiv(x: Pos, y: Pos with y > 1): {res: Pos with res < x} =
+  (x / y).runtimeChecked
+
+object SafeSeqs:
+  opaque type SafeSeq[T] = Seq[T]
+  object SafeSeq:
+    def fromSeq[T](seq: Seq[T]): SafeSeq[T] = seq
+    def apply[T](elems: T*): SafeSeq[T] = fromSeq(elems)
+  extension [T](a: SafeSeq[T])
+    def len: Pos = a.length.runtimeChecked
+    def apply(i: Pos with i < a.len): T =  a(i)
+    def splitAt(i: Pos with i < a.len): (SafeSeq[T], SafeSeq[T]) = a.splitAt(i)
+    def ++(that: SafeSeq[T]): SafeSeq[T] = a ++ that
+  extension [T](a: SafeSeq[T] with a.len > 0)
+    def head: T = a.head
+    def tail: SafeSeq[T] = a.tail
+
+import SafeSeqs.*
+
+def merge[T: Ordering as ord](left: SafeSeq[T], right: SafeSeq[T]): SafeSeq[T] =
+  (left, right) match
+    case (left: SafeSeq[T], right: SafeSeq[T] with right.len > 0) =>
+      if ord.lt(left.head, right.head) then SafeSeq(left.head) ++ merge(left.tail, right)
+      else SafeSeq(right.head) ++ merge(left, right.tail)
+    case _ =>
+      if left.len == 0 then right
+      else left
+
+def mergeSort[T: Ordering](list: SafeSeq[T]): SafeSeq[T] =
+  val len = list.len
+  val middle = safeDiv(len, 2)
+  if middle == 0 then
+    list
+  else
+    val (left, right) = list.splitAt(middle)
+    merge(mergeSort(left), mergeSort(right))
+
+@main def Test =
+  val nums = SafeSeq(5, 3, 8, 1, 2, 7, 4, 6)
+  val sortedNums = mergeSort(nums)
+  println(s"Unsorted: $nums")
+  println(s"Sorted:   $sortedNums")
+
+  val nums2 = SafeSeq(7, 4, 5, 3, 2, 6, 1)
+  val sortedNums2 = mergeSort(nums2)
+  println(s"Unsorted: $nums2")
+  println(s"Sorted:   $sortedNums2")