使用 Scalaz（或 Shapeless）为每个子类创建 Monoids

Question

是否可以为每个子class创建幺半群？例如，

package currency 

final case class GBP[A: Monoid](amount: A)

object Implicits {
  implicit class CurrencyOps[A: Monoid](a: A) {
    def GBP = currency.GBP(a)
  }

  implicit def gbpMonoid[A: Monoid]: Monoid[GBP[A]] = new Monoid[GBP[A]] {
    override def zero =
      GBP(Monoid[A].zero)

    override def append(f1: GBP[A], f2: => GBP[A]): GBP[A] =
      GBP(Semigroup[A].append(f1.amount, f2.amount))
  }
}

test("GBP support plus") {
  1.GBP |+| 2.GBP shouldBe 3.GBP // passed
}

我想添加更多代表货币的大小写 classes（例如 USD、EUR、..）

sealed trait Currency
final case class GBP[A: Monoid](amount: A) extends Currency
final case class USD[A: Monoid](amount: A) extends Currency
final case class EUR[A: Monoid](amount: A) extends Currency

因此，我必须为新案例 classes 实现幺半群。这有点样板。

implicit class CurrencyOps[A: Monoid](a: A) {
  def GBP = currency.GBP(a)
  def EUR = currency.EUR(a)
  def USD = currency.USD(a)
}

implicit def gbpMonoid[A: Monoid]: Monoid[GBP[A]] = new Monoid[GBP[A]] {
  override def zero =
    GBP(Monoid[A].zero)

  override def append(f1: GBP[A], f2: => GBP[A]): GBP[A] =
    GBP(Semigroup[A].append(f1.amount, f2.amount))
}

implicit def usdMonoid[A: Monoid]: Monoid[USD[A]] = new Monoid[USD[A]] {
  override def zero =
    USD(Monoid[A].zero)

  override def append(f1: USD[A], f2: => USD[A]): USD[A] =
    USD(Semigroup[A].append(f1.amount, f2.amount))
}

implicit def eurMonoid[A: Monoid]: Monoid[EUR[A]] = new Monoid[EUR[A]] {
  override def zero =
    EUR(Monoid[A].zero)

  override def append(f1: EUR[A], f2: => EUR[A]): EUR[A] =
    EUR(Semigroup[A].append(f1.amount, f2.amount))
}

Answer 1

小建议

首先，我想建议从案例 classes 中删除 Monoid 要求，因为它们将在每个 Currency 实例中携带隐式值。如果没有这个要求，您的包装器可能会更有效率，甚至可以实现为 value classes:

  sealed trait Currency extends Any
  final case class GBP[A](amount: A) extends AnyVal with Currency
  final case class USD[A](amount: A) extends AnyVal with Currency
  final case class EUR[A](amount: A) extends AnyVal with Currency

无形实现

从这里您可以根据需要通过 shapeless 构建简单的实现：

import scalaz._
import shapeless._

implicit def monoidCurrency[A, C[_] <: Currency]
(implicit monoid: Monoid[A], gen: Generic.Aux[C[A], A :: HNil]) =
  new Monoid[C[A]] {
    def zero: C[A] = gen.from(monoid.zero :: HNil)
    def append(f1: C[A], f2: => C[A]): C[A] = {
      val x = gen.to(f1).head
      val y = gen.to(f2).head
      gen.from(monoid.append(x, y) :: HNil)
    }
  }

并验证

import scalaz.syntax.monoid._
import scalaz.std.anyVal._

println(2.USD |+| 3.USD) // USD(5)

进一步改进

你完全可以摆脱无形。考虑这样的实现：

trait CurrencyUnit{
  def show(amounts: String) = s"$amounts $this"
}

final case class Currency[A, U <: CurrencyUnit](amount: A) extends AnyVal

CurrencyUnit 现在不是 class 的问题，它只是编译时类型标签

implicit case object GBP extends CurrencyUnit
implicit case object USD extends CurrencyUnit{
  override def show(amounts: String) = s"$$$amounts "
}
implicit case object EUR extends CurrencyUnit

implicit class CurrencyOps[A](a: A) {
  def GBP = Currency[A, GBP.type](a)
  def EUR = Currency[A, EUR.type](a)
  def USD = Currency[A, USD.type](a)
}

您可以根据需要进行配置

import scalaz.syntax.show._

implicit def currencyShow[A: Show, U <: CurrencyUnit](implicit unit: U) =
  new Show[Currency[A, U]] {
    override def shows(f: Currency[A, U]) = unit.show(f.amount.shows)
  }

最重要的是通过 scalaz.Isomorphism.Iso 功能轻松派生类型 classes：

import Isomorphism._

implicit def currencyIso[A, U <: CurrencyUnit] = new (Currency[A, U] <=> A) {
  def to: (Currency[A, U]) => A = _.amount
  def from: (A) => Currency[A, U] = Currency[A, U]
}

implicit def currencyMonoid[A: Monoid, U <: CurrencyUnit] =
  new IsomorphismMonoid[Currency[A, U], A] {
    def G: Monoid[A] = implicitly
    def iso: Currency[A, U] <=> A = implicitly
  }

终于可以验证这个方案了

import scalaz.syntax.monoid._
import scalaz.std.anyVal._

println((2.USD |+| 3.USD).shows) //

使用 Scalaz（或 Shapeless）为每个子类创建 Monoids

Creating Monoids for every subclass using Scalaz (or Shapeless)

scala

scalaz

shapeless

小建议

无形实现

进一步改进