Cats（2）－ Free语法组合，Coproduct-ADT composition
上篇我们介绍了Free类型可以作为一种嵌入式编程语言DSL在函数式编程中对某种特定功能需求进行描述。一个完整的应用可能会涉及多样的关联功能，但如果我们为每个应用都设计一套DSL的话，那么在我们的函数式编程中将会不断重复的功能相似的DSL。我们应该秉承函数式编程的核心思想：函数组合（compositionality）来实现DSL的组合：把DSL拆解成最基础语句ADT，然后用这些ADT来组合成适合应用功能要求的完整DSL。我们还是使用上篇那个Interact DSL，这次再增加一个Login功能：
1 package demo.app
2 import cats.free.{Free,Inject}
3 object FreeModules {
4 object ADTs {
5 sealed trait Interact[+A]
6 object Interact {
7 case class Ask(prompt: String) extends Interact[String]
8 case class Tell(msg: String) extends Interact[Unit]
9 type FreeInteract[A] = Free[Interact,A]
10 def ask(prompt: String): FreeInteract[String] = Free.liftF(Ask(prompt))
11 def tell(msg: String): FreeInteract[Unit] = Free.liftF(Tell(msg))
12 }
13
14 sealed trait Login[+A]
15 object Login {
16 type FreeLogin[A] = Free[Login,A]
17 case class Authenticate(user: String, pswd: String) extends Login[Boolean]
18 def authenticate(user: String, pswd: String): FreeLogin[Boolean] =
19 Free.liftF(Authenticate(user,pswd))
20 }
21
22 }
23
24 }
上面我们增加了个Login类。我们先来进行DSL编程：
1 object DSLs {
2 import ADTs._
3 import Interact._
4 import Login._
5 val interactDSL: FreeInteract[Unit] = for {
6 first <- ask("What's your first name?")
7 last <- ask("What's your last name?")
8 _ <- tell(s"Hello, $first $last!")
9 } yield()
10
11 val loginDSL: FreeLogin[Boolean] = for {
12 login <- authenticate("Tiger","123")
13 } yield login
14 }
很明显，用一种DSL编程是无法满足Login功能需要的。我们需要像下面这样的DSL：
1 val interactLoginDSL: Free[???,Boolean] = for {
2 uid <- ask("Enter your User ID:")
3 psw <- ask("Enter your Password:")
4 aut <- authenticate(uid,pwd)
5 } yield aut
不过上面的???应该是什么呢？它应该是Interact和Login的集合。cats提供了Coproduct，它是一个树形数据结构：
/** `F` on the left and `G` on the right of [[scala.util.Either]].
*
* @param run The underlying [[scala.util.Either]].
*/
final case class Coproduct[F[_], G[_], A](run: Either[F[A], G[A]]) {...}
Coproduct 的每一个节点（Either[F[A],G[A]]）都是一个ADT，F[A]或者G[A]。我们可以用多层递归Coproduce结构来构建一个多语法的树形结构，如：
1 type H[A] = Coproduct[F,G,A]
2 type I[A] = Coproduct[H,X,A]
3 type J[A] = Coproduct[J,Y,A] //ADT(F,G,X,Y)
用Coproduct的树形结构可以容纳多种DSL的ADT。在上面的例子里我们需要一个组合的语法InteractLogin：
1 type InteractLogin[A] = Coproduct[Interact,Login,A]
cats提供了Inject类来构建Coproduct：
sealed abstract class Inject[F[_], G[_]] {
def inj[A](fa: F[A]): G[A]
def prj[A](ga: G[A]): Option[F[A]]
}
private[free] sealed abstract class InjectInstances {
implicit def catsFreeReflexiveInjectInstance[F[_]]: Inject[F, F] =
new Inject[F, F] {
def inj[A](fa: F[A]): F[A] = fa
def prj[A](ga: F[A]): Option[F[A]] = Some(ga)
}
implicit def catsFreeLeftInjectInstance[F[_], G[_]]: Inject[F, Coproduct[F, G, ?]] =
new Inject[F, Coproduct[F, G, ?]] {
def inj[A](fa: F[A]): Coproduct[F, G, A] = Coproduct.leftc(fa)
def prj[A](ga: Coproduct[F, G, A]): Option[F[A]] = ga.run.fold(Some(_), _ => None)
}
implicit def catsFreeRightInjectInstance[F[_], G[_], H[_]](implicit I: Inject[F, G]): Inject[F, Coproduct[H, G, ?]] =
new Inject[F, Coproduct[H, G, ?]] {
def inj[A](fa: F[A]): Coproduct[H, G, A] = Coproduct.rightc(I.inj(fa))
def prj[A](ga: Coproduct[H, G, A]): Option[F[A]] = ga.run.fold(_ => None, I.prj)
}
}
inj[A](fa: F[A]):G[A]代表将F[A]注入更大的语法集G[A]。cats提供了三种实现了ink函数的Inject隐式实例：
1、catsFreeReflexiveInjectInstance:Inject[F,F]：对单一语法，无须构建Coproduct
2、catsFreeLeftInjectInstance:Inject[F,Coproduct[F,G,?]]：构建Coproduct结构并将F放在左边
3、catsFreeRightInjectInstance:Inject[F,Coproduct[H,G,?]]：把F注入到已经包含H,G的Coproduct[H,G,?]
有了这三种实例后我们可以根据解析到的隐式实例类型使用inj函数通过Coproduct构建更大的语法集了。我们可以通过implicitly来验证一下Interact和Login语法的Inject隐式实例：
1 val selfInj = implicitly[Inject[Interact,Interact]]
2 type LeftInterLogin[A] = Coproduct[Interact,Login,A]
3 val leftInj = implicitly[Inject[Interact,LeftInterLogin]]
4 type RightInterLogin[A] = Coproduct[Login,LeftInterLogin,A]
5 val rightInj = implicitly[Inject[Interact,RightInterLogin]]
现在我们可以用Inject.inj和Free.liftF把Interact和Login升格成Free[G,A]。G是个类型变量，Interact和Login在Coproduct的最终左右位置由当前Inject隐式实例类型决定：
1 object ADTs {
2 sealed trait Interact[+A]
3 object Interact {
4 case class Ask(prompt: String) extends Interact[String]
5 case class Tell(msg: String) extends Interact[Unit]
6 type FreeInteract[A] = Free[Interact,A]
7 //def ask(prompt: String): FreeInteract[String] = Free.liftF(Ask(prompt))
8 //def tell(msg: String): FreeInteract[Unit] = Free.liftF(Tell(msg))
9 def ask[G[_]](prompt: String)(implicit I: Inject[Interact,G]): Free[G,String] =
10 Free.liftF(I.inj(Ask(prompt)))
11 def tell[G[_]](msg: String)(implicit I: Inject[Interact,G]): Free[G,Unit] =
12 Free.liftF(I.inj(Tell(msg)))
13 }
14
15 sealed trait Login[+A]
16 object Login {
17 type FreeLogin[A] = Free[Login,A]
18 case class Authenticate(user: String, pswd: String) extends Login[Boolean]
19 //def authenticate(user: String, pswd: String): FreeLogin[Boolean] =
20 // Free.liftF(Authenticate(user,pswd))
21 def authenticate[G[_]](user: String, pswd: String)(implicit I: Inject[Login,G]): Free[G,Boolean] =
22 Free.liftF(I.inj(Authenticate(user,pswd)))
23 }
现在我们可以用混合语法的DSL来编程了：
1 object DSLs {
2 import ADTs._
3 import Interact._
4 import Login._
5 val interactDSL: FreeInteract[Unit] = for {
6 first <- ask("What's your first name?")
7 last <- ask("What's your last name?")
8 _ <- tell(s"Hello, $first $last!")
9 } yield()
10
11 val loginDSL: FreeLogin[Boolean] = for {
12 login <- authenticate("Tiger","123")
13 } yield login
14
15 type InteractLogin[A] = Coproduct[Interact,Login,A]
16 val interactLoginDSL: Free[InteractLogin,Boolean] = for {
17 uid <- ask[InteractLogin]("Enter your User ID:")
18 pwd <- ask[InteractLogin]("Enter your Password:")
19 aut <- authenticate[InteractLogin](uid,pwd)
20 } yield aut
21 }
在interactLoginDSL里所有ADT通过Inject隐式实例都被自动升格成统一的Free[Coproduct[Interact,Login,A]]。
interactLogin的功能实现方式之一示范如下：
1 object IMPLs {
2 import cats.{Id,~>}
3 import ADTs._,Interact._,Login._
4 import DSLs._
5 object InteractConsole extends (Interact ~> Id) {
6 def apply[A](ia: Interact[A]): Id[A] = ia match {
7 case Ask(p) => {println(p); readLine}
8 case Tell(m) => println(m)
9 }
10 }
11 object LoginMock extends (Login ~> Id) {
12 def apply[A](la: Login[A]): Id[A] = la match {
13 case Authenticate(u,p) => if (u == "Tiger" && p == "123") true else false
14 }
15 }
16 val interactLoginMock: (InteractLogin ~> Id) = InteractConsole.or(LoginMock)
17 }
这个interactLoginMock就是一个Interact,Login混合语法程序的功能实现。不过我们还是应该赋予Login一个比较实在点的实现：我们可以用一种依赖注入方式通过Reader数据类型把外部系统的用户密码验证的方法传入：
1 import Dependencies._
2 import cats.data.Reader
3 type ReaderPass[A] = Reader[PasswordControl,A]
4 object LoginToReader extends (Login ~> ReaderPass) {
5 def apply[A](la: Login[A]): ReaderPass[A] = la match {
6 case Authenticate(u,p) => Reader{pc => pc.matchUserPassword(u,p)}
7 }
8 }
9 object InteractToReader extends (Interact ~> ReaderPass) {
10 def apply[A](ia: Interact[A]): ReaderPass[A] = ia match {
11 case Ask(p) => {println(p); Reader(pc => readLine)}
12 case Tell(m) => {println(m); Reader(pc => ())}
13 }
14 }
15 val userLogin: (InteractLogin ~> ReaderPass) = InteractToReader or LoginToReader
假设用户密码验证由外部另一个系统负责，PasswordControl是与这个外部系统的界面（interface）：
1 object Dependencies {
2 trait PasswordControl {
3 val mapPasswords: Map[String,String]
4 def matchUserPassword(uid: String, pwd: String): Boolean
5 }
6 }
我们用Reader来注入PasswordControl这个外部依赖（dependency injection IOC）。因为Interact和Login结合形成的是一个统一的语句集，所以我们必须进行Interact与ReaderPass对应。下面我们先构建一个PasswordControl对象作为模拟数据，然后试运行：
1 object catsComposeFree extends App {
2 import Dependencies._
3 import FreeModules._
4 import DSLs._
5 import IMPLs._
6 object UserPasswords extends PasswordControl {
7 override val mapPasswords: Map[String, String] = Map(
8 "Tiger" -> "123",
9 "John" -> "456"
10 )
11 override def matchUserPassword(uid: String, pwd: String): Boolean =
12 mapPasswords.getOrElse(uid,pwd+"!") == pwd
13 }
14
15 val r = interactLoginDSL.foldMap(userLogin).run(UserPasswords)
16 println(r)
17
18 }
运算结果：
1 Enter your User ID:
2 Tiger
3 Enter your Password:
4 123
5 true
6 ...
7 Enter your User ID:
8 Chan
9 Enter your Password:
10 123
11 false
我们再用这个混合的DSL编个稍微完整点的程序：
1 val userLoginDSL: Free[InteractLogin,Unit] = for {
2 uid <- ask[InteractLogin]("Enter your User ID:")
3 pwd <- ask[InteractLogin]("Enter your Password:")
4 aut <- authenticate[InteractLogin](uid,pwd)
5 _ <- if (aut) tell[InteractLogin](s"Hello $uid")
6 else tell[InteractLogin]("Sorry, who are you?")
7 } yield()
运算这个程序不需要任何修改：
1 //val r = interactLoginDSL.foldMap(userLogin).run(UserPasswords)
2 //println(r)
3 userLoginDSL.foldMap(userLogin).run(UserPasswords)
现在结果变成了：
1 Enter your User ID:
2 Tiger
3 Enter your Password:
4 123
5 Hello Tiger
6 ...
7 Enter your User ID:
8 CHAN
9 Enter your Password:
10 123
11 Sorry, who are you?
如果我们在这两个语法的基础上再增加一个模拟权限管理的语法，ADT设计如下：
1 sealed trait Auth[+A]
2 object Auth {
3 case class Authorize(uid: String) extends Auth[Boolean]
4 def authorize[G[_]](uid:String)(implicit I: Inject[Auth,G]): Free[G,Boolean] =
5 Free.liftF(I.inj(Authorize(uid)))
6 }
假设实际的权限管理依赖外部系统，我们先定义它的界面：
1 object Dependencies {
2 trait PasswordControl {
3 val mapPasswords: Map[String,String]
4 def matchUserPassword(uid: String, pwd: String): Boolean
5 }
6 trait PermControl {
7 val mapAuthorized: Map[String,Boolean]
8 def authorized(uid: String): Boolean
9 }
10 }
再用三种语法合成的DSL来编一段程序：
1 import Auth._
2 type Permit[A] = Coproduct[Auth,InteractLogin,A]
3 val userPermitDSL: Free[Permit,Unit] = for {
4 uid <- ask[Permit]("Enter your User ID:")
5 pwd <- ask[Permit]("Enter your Password:")
6 auth <- authenticate[Permit](uid,pwd)
7 perm <- if(auth) authorize[Permit](uid)
8 else Free.pure[Permit,Boolean](false)
9 _ <- if (perm) tell[Permit](s"Hello $uid, welcome to the program!")
10 else tell[Permit]("Sorry, no no no!")
11 } yield()
很遗憾，这段代码无法通过编译，cats还无法处理多层递归Coproduct。对Coproduct的处理scalaz还是比较成熟的，我在之前写过一篇scalaz Coproduct Free的博客，里面用的例子就是三种语法的DSL。实际上不单只是Coproduct的问题，现在看来cats.Free对即使很简单的应用功能也有着很复杂无聊的代码需求，这是我们无法接受的。由于Free编程在函数式编程里占据着如此重要的位置，我们暂时还没有其它选择，所以必须寻找一个更好的编程工具才行，freeK就是个这样的函数组件库。我们将在下篇讨论里用freeK来实现多种语法DSL编程。
无论如何，我还是把这篇讨论的示范代码附在下面：
1 import cats.data.Coproduct
2 import cats.free.{Free, Inject}
3 object FreeModules {
4 object ADTs {
5 sealed trait Interact[+A]
6 object Interact {
7 case class Ask(prompt: String) extends Interact[String]
8 case class Tell(msg: String) extends Interact[Unit]
9 type FreeInteract[A] = Free[Interact,A]
10 //def ask(prompt: String): FreeInteract[String] = Free.liftF(Ask(prompt))
11 //def tell(msg: String): FreeInteract[Unit] = Free.liftF(Tell(msg))
12 def ask[G[_]](prompt: String)(implicit I: Inject[Interact,G]): Free[G,String] =
13 Free.liftF(I.inj(Ask(prompt)))
14 def tell[G[_]](msg: String)(implicit I: Inject[Interact,G]): Free[G,Unit] =
15 Free.liftF(I.inj(Tell(msg)))
16 }
17
18 sealed trait Login[+A]
19 object Login {
20 type FreeLogin[A] = Free[Login,A]
21 case class Authenticate(user: String, pswd: String) extends Login[Boolean]
22 //def authenticate(user: String, pswd: String): FreeLogin[Boolean] =
23 // Free.liftF(Authenticate(user,pswd))
24 def authenticate[G[_]](user: String, pswd: String)(implicit I: Inject[Login,G]): Free[G,Boolean] =
25 Free.liftF(I.inj(Authenticate(user,pswd)))
26 }
27
28 sealed trait Auth[+A]
29 object Auth {
30 case class Authorize(uid: String) extends Auth[Boolean]
31 def authorize[G[_]](uid:String)(implicit I: Inject[Auth,G]): Free[G,Boolean] =
32 Free.liftF(I.inj(Authorize(uid)))
33 }
34 val selfInj = implicitly[Inject[Interact,Interact]]
35 type LeftInterLogin[A] = Coproduct[Interact,Login,A]
36 val leftInj = implicitly[Inject[Interact,LeftInterLogin]]
37 type RightInterLogin[A] = Coproduct[Login,LeftInterLogin,A]
38 val rightInj = implicitly[Inject[Interact,RightInterLogin]]
39 }
40
41 object DSLs {
42 import ADTs._
43 import Interact._
44 import Login._
45 val interactDSL: FreeInteract[Unit] = for {
46 first <- ask("What's your first name?")
47 last <- ask("What's your last name?")
48 _ <- tell(s"Hello, $first $last!")
49 } yield()
50
51 val loginDSL: FreeLogin[Boolean] = for {
52 login <- authenticate("Tiger","123")
53 } yield login
54
55 type InteractLogin[A] = Coproduct[Interact,Login,A]
56 val interactLoginDSL: Free[InteractLogin,Boolean] = for {
57 uid <- ask[InteractLogin]("Enter your User ID:")
58 pwd <- ask[InteractLogin]("Enter your Password:")
59 aut <- authenticate[InteractLogin](uid,pwd)
60 } yield aut
61 val userLoginDSL: Free[InteractLogin,Unit] = for {
62 uid <- ask[InteractLogin]("Enter your User ID:")
63 pwd <- ask[InteractLogin]("Enter your Password:")
64 aut <- authenticate[InteractLogin](uid,pwd)
65 _ <- if (aut) tell[InteractLogin](s"Hello $uid")
66 else tell[InteractLogin]("Sorry, who are you?")
67 } yield()
68 /* import Auth._
69 type Permit[A] = Coproduct[Auth,InteractLogin,A]
70 val userPermitDSL: Free[Permit,Unit] = for {
71 uid <- ask[Permit]("Enter your User ID:")
72 pwd <- ask[Permit]("Enter your Password:")
73 auth <- authenticate[Permit](uid,pwd)
74 perm <- if(auth) authorize[Permit](uid)
75 else Free.pure[Permit,Boolean](false)
76 _ <- if (perm) tell[Permit](s"Hello $uid, welcome to the program!")
77 else tell[Permit]("Sorry, no no no!")
78 } yield() */
79 }
80 object IMPLs {
81 import cats.{Id,~>}
82 import ADTs._,Interact._,Login._
83 import DSLs._
84 object InteractConsole extends (Interact ~> Id) {
85 def apply[A](ia: Interact[A]): Id[A] = ia match {
86 case Ask(p) => {println(p); readLine}
87 case Tell(m) => println(m)
88 }
89 }
90 object LoginMock extends (Login ~> Id) {
91 def apply[A](la: Login[A]): Id[A] = la match {
92 case Authenticate(u,p) => if (u == "Tiger" && p == "123") true else false
93 }
94 }
95 val interactLoginMock: (InteractLogin ~> Id) = InteractConsole.or(LoginMock)
96 import Dependencies._
97 import cats.data.Reader
98 type ReaderPass[A] = Reader[PasswordControl,A]
99 object LoginToReader extends (Login ~> ReaderPass) {
100 def apply[A](la: Login[A]): ReaderPass[A] = la match {
101 case Authenticate(u,p) => Reader{pc => pc.matchUserPassword(u,p)}
102 }
103 }
104 object InteractToReader extends (Interact ~> ReaderPass) {
105 def apply[A](ia: Interact[A]): ReaderPass[A] = ia match {
106 case Ask(p) => {println(p); Reader(pc => readLine)}
107 case Tell(m) => {println(m); Reader(pc => ())}
108 }
109 }
110 val userLogin: (InteractLogin ~> ReaderPass) = InteractToReader or LoginToReader
111
112 }
113 }
114 object Dependencies {
115 trait PasswordControl {
116 val mapPasswords: Map[String,String]
117 def matchUserPassword(uid: String, pwd: String): Boolean
118 }
119 trait PermControl {
120 val mapAuthorized: Map[String,Boolean]
121 def authorized(uid: String): Boolean
122 }
123 }
124
125 object catsComposeFree extends App {
126 import Dependencies._
127 import FreeModules._
128 import DSLs._
129 import IMPLs._
130 object UserPasswords extends PasswordControl {
131 override val mapPasswords: Map[String, String] = Map(
132 "Tiger" -> "123",
133 "John" -> "456"
134 )
135 override def matchUserPassword(uid: String, pwd: String): Boolean =
136 mapPasswords.getOrElse(uid,pwd+"!") == pwd
137 }
138
139 //val r = interactLoginDSL.foldMap(userLogin).run(UserPasswords)
140 //println(r)
141 userLoginDSL.foldMap(userLogin).run(UserPasswords)
142
143 }
