Peano Numbers scala 实现
package objsets
/**
* Peano numbers
* 实现自然数，但是不使用标准库中的 numerical class
*/
abstract class Nat {
def isZero: Boolean
def predecessor: Nat
// 没有用到数字，而是利用了一个更加抽象的概念(在scala实现中是对象的构造)
def successor: Nat = new Succ(this)
def +(that: Nat): Nat
def -(that: Nat): Nat
}
/**
* 需要定义一个边界 Zero , 对于边界的数字需要做好特别处理
*/
object Zero extends Nat {
override def isZero: Boolean = true
override def predecessor: Nat = throw new Error("0.predecessor")
override def +(that: Nat): Nat = that
override def -(that: Nat): Nat = if (that.isZero) that else throw new Error("negative number.")
}
// use case class which "compares by structure, not by reference".
case class Succ(n: Nat) extends Nat {
override def isZero: Boolean = false
override def predecessor: Nat = n
// 一层层的对象构造
override def +(that: Nat): Nat = new Succ(n + that)
override def -(that: Nat): Nat = if (that.isZero) this else n - that.predecessor
}
测试
package objsets
trait Fixture {
val one = new Succ(Zero)
val two = new Succ(one)
}
object Test {
def main(args: Array[String]): Unit = {
new Fixture {
assert(Zero.successor == one)
}
new Fixture {
assert(one.successor == two)
}
new Fixture {
assert((one + Zero) == one)
}
new Fixture {
assert((one + one) == two)
}
}
}
