[derives clause] what's the difference between derives and given in object

Question
1

Hello, i have some question about derives clause.
derives generate typeclass in target type companion object, what’s the different from given in companion object?
There is an example in official document.

  • if i give a recursive type, the Eq trait works when use derives explicitly
  • but it fails after i remove the derives clause.

After removing the derives cluase, it still works for types that not recursive.
So, anyone knows why?

import scala.deriving.*
import scala.compiletime.{erasedValue, summonInline}

inline def summonAll[T <: Tuple]: List[Eq[_]] =
  inline erasedValue[T] match
    case _: EmptyTuple => Nil
    case _: (t *: ts) => summonInline[Eq[t]] :: summonAll[ts]

trait Eq[T]:
  def eqv(x: T, y: T): Boolean

object Eq:
  given Eq[Int] with
    def eqv(x: Int, y: Int) = x == y

  given Eq[String] with
    def eqv(x: String, y: String) = x == y

  def check(elem: Eq[_])(x: Any, y: Any): Boolean =
    elem.asInstanceOf[Eq[Any]].eqv(x, y)

  def iterator[T](p: T) = p.asInstanceOf[Product].productIterator

  def eqSum[T](s: Mirror.SumOf[T], elems: => List[Eq[_]]): Eq[T] =
    new Eq[T]:
      def eqv(x: T, y: T): Boolean =
        val ordx = s.ordinal(x)
        (s.ordinal(y) == ordx) && check(elems(ordx))(x, y)

  def eqProduct[T](p: Mirror.ProductOf[T], elems: => List[Eq[_]]): Eq[T] =
    new Eq[T]:
      def eqv(x: T, y: T): Boolean =
        iterator(x).zip(iterator(y)).zip(elems.iterator).forall {
          case ((x, y), elem) => check(elem)(x, y)
        }

  inline given derived[T](using m: Mirror.Of[T]): Eq[T] =
    lazy val elemInstances = summonAll[m.MirroredElemTypes]
    inline m match
      case s: Mirror.SumOf[T]     => eqSum(s, elemInstances)
      case p: Mirror.ProductOf[T] => eqProduct(p, elemInstances)
end Eq


enum Tree[T] derives Eq { // works with derives but fails when remove the derives clause
  case Branch(left: Tree[T], right: Tree[T]) // a recursive type
  case Leaf(elem: T)
}

@main def hello: Unit = 
  summon[Eq[Tree[Int]]].eqv(Tree.Leaf(1),Tree.Leaf(1))