order-monoid.scala

import scalaz._
import Scalaz._

case class Cosa(str: String, f: Float, n: Int)

import scalaz.Order.orderBy

val orderByStr = orderBy { c: Cosa => c.str }
val orderByF = orderBy { c: Cosa => c.f }
val orderByN = orderBy { c: Cosa => c.n }

val combinedOrder = orderByStr |+| orderByF |+| orderByN

combinedOrder(Cosa("a",1.0f,2),Cosa("a",1.0f,2)) // EQ
combinedOrder(Cosa("a",1.0f,3),Cosa("a",1.0f,2)) // GT
combinedOrder(Cosa("a",1.0f,2),Cosa("a",1.0f,1)) // GT
combinedOrder(Cosa("a",1.0f,1),Cosa("a",1.0f,2)) // LT
combinedOrder(Cosa("ab",0.0f,1),Cosa("abc",0.0f,1)) // LT

implicit val cosaOrdering = combinedOrder.toScalaOrdering
val l = List(Cosa("ab",0.0f,1),Cosa("abc",0.0f,1),Cosa("defg",1.0f,2),Cosa("ab",1.0f,1),Cosa("abc",1.0f,2),Cosa("defg",1.0f,1))
l.sorted == List(Cosa("ab",0.0f,1), Cosa("ab",1.0f,1), Cosa("abc",0.0f,1), Cosa("abc",1.0f,2), Cosa("defg",1.0f,1), Cosa("defg",1.0f,2))