わたしのScalazプログラミングその２

型クラスについて。

例によって有理数で。

case class Rational(n: Int, d: Int)

view raw rational1.scala hosted with ❤ by GitHub

Groupのインスタンスを定義します。
Groupとは、結合演算子、単位元、逆元を持つもののことです。

	trait RationalInstances {
	implicit object rationalInstance extends Group[Rational] {
	def zero = Rational(0, 1)
	def inverse(r: Rational) = Rational(-r.n, r.d)
	def append(r1: Rational, r2: => Rational) =
	Rational(r1.n * r2.d + r2.n * r1.d, r1.d * r2.d)
	}
	}
	object Rational extends RationalInstances

view raw rational2.scala hosted with ❤ by GitHub

動かしてみる。

	scala> import scalaz._, Scalaz._
	import scalaz._
	import Scalaz._
	scala> Rational(1, 2) |+| Rational(2, 3)
	res0: Rational = Rational(7,6)
	scala> Rational(1, 2) |-| Rational(2, 3)
	res1: Rational = Rational(-1,6)
	scala> Rational(1, 2) multiply 2
	res2: Rational = Rational(4,4)
	scala> -Rational(1, 2)
	res3: Rational = Rational(-1,2)

view raw repl1.scala hosted with ❤ by GitHub

Groupのインスタンスを定義するだけでこれだけのことができます。

自分でデータ型を定義するときは、インスタンス自体に関数を定義より、データ型にメソッドとして定義したほうがいいかもしれません。
また、Groupのインスタンスからメソッドが定義できます。

	case class Rational(n: Int, d: Int) {
	def +(r: Rational) =
	Rational(n * r.d + r.n * d, d * r.d)
	def -(r: Rational) =
	Rational.rationalInstance.minus(this, r)
	def unary_- = Rational(-n, d)
	}
	trait RationalInstances { self: Rational.type =>
	implicit object rationalInstance extends Group[Rational] {
	def zero = Rational(0, 1)
	def inverse(r: Rational) = -r
	def append(r1: Rational, r2: => Rational) = r1 + r2
	}
	}
	object Rational extends RationalInstances

view raw rational4.scala hosted with ❤ by GitHub

	scala> Rational(1, 2) + Rational(2, 3)
	res0: Rational = Rational(7,6)
	scala> Rational(1, 2) - Rational(2, 3)
	res1: Rational = Rational(-1,6)

view raw repl2.scala hosted with ❤ by GitHub

乗算、除算も定義してみます。

	import scalaz._, Scalaz._, Tags._
	case class Rational(n: Int, d: Int) {
	def +(r: Rational) =
	Rational(n * r.d + r.n * d, d * r.d)
	def -(r: Rational) =
	Rational.rationalInstance.minus(this, r)
	def *(r: Rational) =
	Rational(n * r.n, r.d * d)
	def /(r: Rational): Rational =
	Rational.rationalMultiplicationInstance.minus(Tag(this), Tag(r))
	def unary_- = Rational(-n, d)
	def unary_~ = Rational(d, n)
	}
	trait RationalInstances { self: Rational.type =>
	implicit object rationalInstance extends Group[Rational] {
	def zero = Rational(0, 1)
	def inverse(r: Rational) = -r
	def append(r1: Rational, r2: => Rational) = r1 + r2
	}
	implicit object rationalMultiplicationInstance extends Group[Rational @@ Multiplication] {
	def zero = Tag(Rational(1, 1))
	def inverse(r: Rational @@ Multiplication) = Tag(~r)
	def append(r1: Rational @@ Multiplication, r2: => Rational @@ Multiplication) =
	Tag(r1 * r2)
	}
	}
	object Rational extends RationalInstances

view raw rational5.scala hosted with ❤ by GitHub

	scala> import scalaz._, Scalaz._, Tags._
	import scalaz._
	import Scalaz._
	scala> Rational(1, 2) * Rational(2, 3)
	res0: Rational = Rational(2,6)
	scala> Rational(1, 2) / Rational(2, 3)
	res1: Rational = Rational(3,4)
	scala> Foldable[List].fold(List(Rational(1, 2), Rational(2, 3)))
	res2: Rational = Rational(7,6)
	scala> Foldable[List].fold(List(Tag[Rational, Multiplication](Rational(1, 2)), Tag[Rational, Multiplication](Rational(2, 3))))
	res3: scalaz.package.@@[Rational,scalaz.Tags.Multiplication] = Rational(2, 6)

view raw repl3.scala hosted with ❤ by GitHub

べんり！