Sets are not Functors

set.scala

scala> :paste
// Entering paste mode (ctrl-D to finish)

case class A(x: Int)(y: Int) { def toB = B(x, y) }
case class B(x: Int, y: Int) { def toA = A(x)(y) }

// Exiting paste mode, now interpreting.

defined class A
defined class B

scala> val set = Set(B(1,1), B(1,2))
set: scala.collection.immutable.Set[B] = Set(B(1,1), B(1,2))

scala> val s1 = set.map(_.toA).map(_.toB)
s1: scala.collection.immutable.Set[B] = Set(B(1,1))

scala> val s2 = set.map(_.toA.toB)
s2: scala.collection.immutable.Set[B] = Set(B(1,1), B(1,2))

The problem here is that toB doesn't respect the equivalence relation defined by the auto-generated A#equals method.