如何制作自己的理解兼容的scala monad？

Question

我想在 Scala 中实现我自己的易于理解的 monad 和 functor。

让我们以两个愚蠢的 monad 为例。一个 monad 是一个状态 monad，它包含一个“Int”，您可以对其进行映射或平面映射。

val maybe = IntMonad(5)
maybe flatMap( a => 3 * ( a map ( () => 2 * a ) ) )
// returns IntMonad(30)

另一个 monad 采用这样的函数组合...

val func = FunctionMonad( () => println("foo") )
val fooBar = func map ( () => println("bar") )
fooBar()
// foo
// bar
// returns Unit

这个例子可能有一些错误，但你明白了。

我希望能够在 Scala 的 for-comprehension 中使用这两种不同类型的组合 Monad。像这样：

val myMonad = IntMonad(5)
for {
    a <- myMonad
    b <- a*2
    c <- IntMonad(b*2)
} yield c    
// returns IntMonad(20)

我不是 Scala 大师，但你懂的

Answer 1

对于要在 for-comprehension 中使用的类型，您实际上只需要为其定义返回相同类型实例的 map 和 flatMap 方法。在语法上，编译器将 for-comprehension 转换为一系列 flatMaps，然后是 yield 的最终 map。只要这些方法具有适当的签名，它就可以工作。

我不太确定你的例子是什么，但这是一个相当于 Option 的简单例子：

sealed trait MaybeInt {
    def map(f: Int => Int): MaybeInt
    def flatMap(f: Int => MaybeInt): MaybeInt
}

case class SomeInt(i: Int) extends MaybeInt {
    def map(f: Int => Int): MaybeInt = SomeInt(f(i))
    def flatMap(f: Int => MaybeInt): MaybeInt = f(i)
}

case object NoInt extends MaybeInt {
    def map(f: Int => Int): MaybeInt = NoInt
    def flatMap(f: Int => MaybeInt): MaybeInt = NoInt
}

我有两个子类型的共同特征（不过，我可以拥有尽可能多的子类型）。公共特征MaybeInt 强制每个子类型符合map/flatMap 接口。

scala> val maybe = SomeInt(1)
maybe: SomeInt = SomeInt(1)

scala> val no = NoInt
no: NoInt.type = NoInt

for {
  a <- maybe
  b <- no
} yield a + b

res10: MaybeInt = NoInt

for {
  a <- maybe
  b <- maybe
} yield a + b

res12: MaybeInt = SomeInt(2)

此外，您还可以添加foreach 和filter。如果你也想处理这个（没有收益）：

for(a <- maybe) println(a)

您可以添加foreach。如果你想使用if 守卫：

for(a <- maybe if a > 2) yield a

您需要filter 或withFilter。

一个完整的例子：

sealed trait MaybeInt { self =>
    def map(f: Int => Int): MaybeInt
    def flatMap(f: Int => MaybeInt): MaybeInt
    def filter(f: Int => Boolean): MaybeInt
    def foreach[U](f: Int => U): Unit
    def withFilter(p: Int => Boolean): WithFilter = new WithFilter(p)

    // Based on Option#withFilter
    class WithFilter(p: Int => Boolean) {
        def map(f: Int => Int): MaybeInt = self filter p map f
        def flatMap(f: Int => MaybeInt): MaybeInt = self filter p flatMap f
        def foreach[U](f: Int => U): Unit = self filter p foreach f
        def withFilter(q: Int => Boolean): WithFilter = new WithFilter(x => p(x) && q(x))
    }
}

case class SomeInt(i: Int) extends MaybeInt {
    def map(f: Int => Int): MaybeInt = SomeInt(f(i))
    def flatMap(f: Int => MaybeInt): MaybeInt = f(i)
    def filter(f: Int => Boolean): MaybeInt = if(f(i)) this else NoInt
    def foreach[U](f: Int => U): Unit = f(i)
}

case object NoInt extends MaybeInt {
    def map(f: Int => Int): MaybeInt = NoInt
    def flatMap(f: Int => MaybeInt): MaybeInt = NoInt
    def filter(f: Int => Boolean): MaybeInt = NoInt
    def foreach[U](f: Int => U): Unit = ()
}