One of the more powerful features Scala has is the ability to generically abstract across things that take type parameters. This feature is known as Higher Kinded Types (HKT).

This feature allows us to write a library that works with a much wider array of classes, whereas without the feature you are condemned to bespoke and error ridden code duplication for each class that may want the functionality.

Type constructors

Essentially what HKT gives us is the ability to generalize across type constructors – where a type constructor is anything that has a type parameter. For instance List[_]* is not a type, the underscore is a hole into which another type may be plugged, constructing a complete type. List[String] and List[Int] being examples of complete (or distinct) types.

Kinds

Now that we have a type constructor we can think of several different kinds of them, classified by how many type parameters they take. The simplest – like List[_] – that take a single param have the kind:

(* -> *)

This says: given one type, produce another. For instance, given String produce the type List[String].

Something that takes two parameters, say Map[_, _], or Function1[_, _] has the kind:

(* -> * -> *)

This says: given one type, then another, produce the final type. For instance given the key type Int and the value type String produce the type Map[Int, String].

Furthermore, you can have kinds that are themselves parameterized by higher kinded types. So, something could not only take a type, but take something that itself takes type parameters. An example would be the covariant functor: Functor[F[_]], it has the kind:

((* -> *) -> *)

This says: given a simple higher kinded type, produce the final type. For instance given a type constructor like List produce the final type Functor[List].

Utility

Say we have some standard pattern for our data-structures where we want to be able to consistently apply an operation of the same shape. Functors are a nice example, the covariant functor allows us to take a box holding things of type A, and a function of A => B and get back a box holding things of type B.

In Java, there is no way to specify that these things share a common interface, or that we simply want transformable boxes. We need to either make this static eg. Guava’s Listsand Iterables, or bespoke on the interface, eg: fugue’s Option or atlassian-util-concurrent’s Promise. There is simply no way to unify these methods on either some super interface or to specify that you have – or require – a “mappable/transformable” box.

With HKT I can represent the covariant functor described above as:
[cc lang=’scala’ ]
trait Functor[F[_]] {
def map[A, B](fa: F[A])(f: A => B): F[B]
}

// implement for java’s List
// note that the presence of mutation in the Java collections
// breaks the Functor laws
import java.util.{ List => JList }
implicit object JavaListFunctor extends Functor[JList] {
import collection.JavaConverters._

def map[A, B](fa: JList[A])(f: A => B): JList[B] =
(for (a B): Box2[B] =
Box2(f(b.a1), f(b.a2))
}

// and use it**
def describe[A, F[_]: Functor](fa: F[A]) =
implicitly[Functor[F]].map(fa)(a => a.toString)

case class Holder(i: Int)
val jlist: JList[Holder] = {
val l = new java.util.ArrayList[Holder]()
l add Holder(1); l add Holder(2); l add Holder(3)
l
}

val list = describe(jlist) // list: java.util.List[String] = [Holder(1), Holder(2), Holder(3)]

val box2 = describe(Box2(Holder(4), Holder(5)) // box: Box2[String] = Box2(Holder(4),Holder(5))
[/cc]

So, we have a describe function that works for any type that we can map over!

We could also use this with a traditional subtyping approach to have our boxes implement the map method directly with the appropriate signature. This is a little more convoluted, but still possible:

[cc lang=’scala’]
/**
* note we need a recursive definition of F as a subtype of Functor
* because we need to refer to it in the return type of map(…)
*/
trait Functor[A, F[_] B): F[B]
}

case class Box[A](a: A) extends Functor[A, Box] {
def map[B](f: A => B) =
Box(f(a))
}

def describe[A, F[A] a.toString)

val box = describe(Box(Holder(6))) // box: Box[String] = Box(Holder(6))
[/cc]

As a bonus, this last example quite nicely shows how subtype polymorphism is strictly less powerful and also more complicated (both syntactically and semantically) than ad-hoc polymorphism via type-classes.

Postscript

These techniques can lead to some very general and powerful libraries, such as scalazspire and shapeless. These libraries may take some getting used to, and as many of these generalizations are inspired by the mother of all generalizations – mathematics – they have names that need learning (like Monad).

However, the techniques are useful without needing to use scalaz. HKT is important for creating type-classes, and creating your own type-classes to encapsulate things like JSON encoding may be of value to your project. There are many ways this can be used within Scala.

If you’re interested in reading more, here’s the original paper for Scala. Among other things, it contains the following very useful graphic:

Also note that the Scala 2.11 REPL is getting a :kind command although its output is a little more convoluted due to the presence of variance annotations on type parameters.

* Strictly speaking, in Scala List[_] is actually an existential type. For the purposes of this post I am using the [_] notation to show the existence of type parameters. Thanks to Stephen Compall for pointing this out.

** An alternate syntax for a context-bound is an explicit implicit block:
[cc lang=’scala’]
def describe2[A, F[_]](fa: F[A])(implicit functor: Functor[F]) =
functor.map(fa) { _.toString }
[/cc]

https://www.atlassian.com/blog/archives/scala-types-of-a-higher-kind

Scala: Types of a higher kind的更多相关文章

  1. Scala Types 2

    存在类型 形式: forSome { type ... } 或 forSome { val ... } 主要为了兼容 Java 的通配符 示例 Array[_] // 等价于 Array[T] for ...

  2. Scala Types 1

    在 Scala 中所有值都有一种对应的类型 单例类型 形式:value.type,返回类型 value / null 场景1:链式API调用时的类型指定 class Super { def m1(t: ...

  3. Beginning Scala study note(8) Scala Type System

    1. Unified Type System Scala has a unified type system, enclosed by the type Any at the top of the h ...

  4. scala速成记录1

    选择  Learning Scala这本书,两百多页,足够薄. 安装 http://www.scala-lang.org/  下载Binary的版本.bin里边有所有操作系统下运行的可以运行的交互式s ...

  5. Scala 中的函数式编程基础(二)

    主要来自 Scala 语言发明人 Martin Odersky 教授的 Coursera 课程 <Functional Programming Principles in Scala>. ...

  6. geotrellis使用(十九)spray-json框架介绍

    Geotrellis系列文章链接地址http://www.cnblogs.com/shoufengwei/p/5619419.html 目录 前言 spray-json简介 spray-json使用 ...

  7. 论文笔记之:Visual Tracking with Fully Convolutional Networks

    论文笔记之:Visual Tracking with Fully Convolutional Networks ICCV 2015  CUHK 本文利用 FCN 来做跟踪问题,但开篇就提到并非将其看做 ...

  8. Akka(33): Http:Marshalling,to Json

    Akka-http是一项系统集成工具.这主要依赖系统之间的数据交换功能.因为程序内数据表达形式与网上传输的数据格式是不相同的,所以需要对程序高级结构化的数据进行转换(marshalling or se ...

  9. 【原创】大叔问题定位分享(11)Spark中对大表子查询加limit为什么会报Broadcast超时错误

    当两个表需要join时,如果一个是大表,一个是小表,正常的map-reduce流程需要shuffle,这会导致大表数据在节点间网络传输,常见的优化方式是将小表读到内存中并广播到大表处理,避免shuff ...

随机推荐

  1. Markdown 基本使用

    My First Markdown 标签(空格分隔): 未分类 # Markdown 11种基本语法## 设置标题在此输入正文标题设置(让字体变大,和word的标题意思一样)在Markdown当中设置 ...

  2. Groovy简单再入门

    以前试过,忘得差不多了,趁这次从JAVA一直撸到SERVLET,SPRING,GROOVY,GRAILS的机会,再弄一次吧... def authors = [ "Peter Ledbroo ...

  3. java.lang.ClassFormatError: Unknown constant tag 0 in class file

    在通过文件上传之后,运行java程序,突然发现这么一个错误:java.lang.ClassFormatError: Unknown constant tag 0 in class file,通过网上查 ...

  4. Android 聊天表情输入、表情翻页带效果、下拉刷新聊天记录

    经过一个星期的折腾,最终做完了这个Android 聊天表情输入.表情翻页带效果.下拉刷新聊天记录.这仅仅是一个单独聊天表情的输入,以及聊天的效果实现.由于我没有写server,所以没有两方聊天的效果. ...

  5. Homebrew 命令

    安装(需要 Ruby):ruby -e "$(curl -fsSL https://raw.github.com/Homebrew/homebrew/go/install)" 搜索 ...

  6. 一条SQL语句求每月连续低温时间

    近期为某个项目写存储过程做统计.其中有个是这样的: 求每个月至少连续3个小时低于某个温度值的时间(小时). 假设有个全年温度表: CREATE TABLE #t(m INT, h INT ,t DEC ...

  7. Color a Tree HDU - 6241

    /* 十分巧妙的二分 题意选最少的点涂色 使得满足输入信息: 1 x的子树涂色数不少于y 2 x的子树外面涂色数不少于y 我们若是把2转化到子树内最多涂色多少 就可以维护这个最小和最大 如果我们二分出 ...

  8. mysql-5.5 for linux源码安装

    mysql-5.5 for linux源码安装 1.使用Yum安装依赖软件包 # yum install -y gcc gcc-c++ gcc-g77 autoconf automake bison  ...

  9. luogu1026 统计单词个数

    题目大意 给出一个长度不超过200的由小写英文字母组成的字母串(约定;该字串以每行20个字母的方式输入,且保证每行一定为20个).要求将此字母串分成k份(1< k< =40),且每份中包含 ...

  10. PCB MS SQL SERVER版本管控工具source_safe_for_sql_server

    PCB由于业务关系复杂,业务触发一个事件时,可能需与数据库多个表进行关连处理才能拿到数据结果, 而表关连并不是简单的关连,实际是要进行大量数据筛选,逻辑判断,转换等过程...这个过程是复杂的 想一想, ...