numcat.scala

// We can write this type class parameterized by the morphism and a type A 
trait CCCNumExt[->[_, _], A] {
  def negateC: A -> A
  def addC: (A, A) -> A
  def mulC: (A, A) -> A
}

// and implement it for Function1 and any Numeric A
implicit def Function1CCCNumExt[A](implicit N: Numeric[A]): CCCNumExt[Function1, A] = new CCCNumExt[Function1, A] {
  def negateC: A => A = N.negate _
  def addC: ((A, A)) => A = { case (a, b) => N.plus(a, b) }
  def mulC: ((A, A)) => A = { case (a, b) => N.times(a, b) }
}

// just note the trick: we put A in the trait type parameters
// to be able to constrain it later with Numeric