Scalaz(7)- typeclass:Applicative-idomatic function application

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    Applicative,正如它的名称所示,就是FP模式的函数施用(function application)。我们在前面的讨论中不断提到FP模式的操作一般都在管道里进行的,因为FP的变量表达形式是这样的:F[A],即变量A是包嵌在F结构里的。Scalaz的Applicative typeclass提供了各种类型的函数施用(function application)和升格(lifting)方法。与其它scalaz typeclass使用方式一样,我们只需要实现了针对自定义类型的Applicative实例就可以使用这些方法了。以下是Applicative trait的部分定义:scalaz/Applicative.scala

1 trait Applicative[F[_]] extends Apply[F] { self =>

2 ////

3 def point[A](a: => A): F[A]

4

5 // alias for point

6 final def pure[A](a: => A): F[A] = point(a)

7 。。。

我们首先需要实现抽象函数point,然后由于Applicative继承了Apply,我们看看Apply trait有什么抽象函数需要实现的;scalaz/Apply.scala

1 trait Apply[F[_]] extends Functor[F] { self =>

2 ////

3 def ap[A,B](fa: => F[A])(f: => F[A => B]): F[B]

4 。。。

我们还需要实现抽象函数ap。注意Apply又继承了Functor,所以我们还需要实现map,一旦实现了Applicative实例就能同时获取了Functor实例。

现在我们先设计一个自定义类型作为下面的范例:

1 trait Configure[+A] {

2 def get: A

3 }

4 object Configure {

5 def apply[A](data: => A) = new Configure[A] { def get = data }

6 }

7 Configure("env string") //> res0: Exercises.ex4.Configure[String] = [email protected]

8 //| d08e

Configure[+A]是个典型的FP类型。通过实现特殊命名apply的函数作为类型构建器,我们可以这样构建实例:Configure("some string")。现在我们按照scalaz隐式解析(implicit resolution)惯例在伴生对象(companion object)里定义隐式Applicative实例:

 1 import scalaz._

2 import Scalaz._

3 object ex4 {

4 trait Configure[+A] {

5 def get: A

6 }

7 object Configure {

8 def apply[A](data: => A) = new Configure[A] { def get = data }

9 implicit val configFunctor = new Functor[Configure] {

10 def map[A,B](ca: Configure[A])(f: A => B): Configure[B] = Configure(f(ca.get))

11 }

12 implicit val configApplicative = new Applicative[Configure] {

13 def point[A](a: => A) = Configure(a)

14 def ap[A,B](ca: => Configure[A])(cfab: => Configure[A => B]): Configure[B] = cfab map {fab => fab(ca.get)}

15 }

16 }

由于Apply继承了Functor,我们必须先获取Configure的Functor实例。现在我们可以针对Configure类型使用Applicative typeclass的功能函数了。Applicative typeclass的组件函数可以分为几种主要类型:

1、Applicative实例构建函数,point:

1 "abc".point[Configure] //> res1: Exercises.ex4.Configure[String] = [email protected]

2 //| 9631

3 12.point[Configure] //> res2: Exercises.ex4.Configure[Int] = [email protected]

4 //| 9

5 5.point[Option] //> res3: Option[Int] = Some(5)

看款式应该是通过隐式转换实现的:scalaz/syntax/ApplicativeSyntax.scala

 1 trait ToApplicativeOps extends ToApplicativeOps0 with ToApplyOps {

2 implicit def ToApplicativeOps[F[_],A](v: F[A])(implicit F0: Applicative[F]) =

3 new ApplicativeOps[F,A](v)

4

5 ////

6 implicit def ApplicativeIdV[A](v: => A) = new ApplicativeIdV[A] {

7 lazy val self = v

8 }

9

10 trait ApplicativeIdV[A] extends Ops[A] {

11 def point[F[_] : Applicative]: F[A] = Applicative[F].point(self)

12 def pure[F[_] : Applicative]: F[A] = Applicative[F].point(self)

13 def η[F[_] : Applicative]: F[A] = Applicative[F].point(self)

14 } ////

15 }

是通过implicit def ApplicativeIDV[A](v: => A)实现的。

 

2、对F[T}类型进行F[A =>B]式的函数施用(从管道里提供作用函数)。施用函数款式是这样的:

1 def ap[A,B](fa: => F[A])(f: => F[A => B]): F[B]

对比Functor函数map:map[A,B](fa: F[A])(f: A => B]): F[B], 分别只在提供操作函数A=>B的方式:ap在F结构内部提供,又或者换句话说ap提供的是高阶函数F[A=>B]。从函数款式看来,ap要比map功能更加强大。因为我们可以用ap实现map, 反之不可:

1 def map[A,B](fa: Configure[A])(f: A => B) = ap(fa)(point(f))

通过ap2,ap3,ap4 ...款式的函数我们可以把 F[A],F[B],F[C],F[D]...多个值连接起来:scalaz/Apply.scala

1 def ap2[A,B,C](fa: => F[A], fb: => F[B])(f: F[(A,B) => C]): F[C] =

2 ap(fb)(ap(fa)(map(f)(_.curried)))

3 def ap3[A,B,C,D](fa: => F[A], fb: => F[B], fc: => F[C])(f: F[(A,B,C) => D]): F[D] =

4 ap(fc)(ap2(fa,fb)(map(f)(f => ((a:A,b:B) => (c:C) => f(a,b,c)))))

5 def ap4[A,B,C,D,E](fa: => F[A], fb: => F[B], fc: => F[C], fd: => F[D])(f: F[(A,B,C,D) => E]): F[E] =

6 ap2(fc, fd)(ap2(fa,fb)(map(f)(f => ((a:A,b:B) => (c:C, d:D) => f(a,b,c,d)))))

7 def ap5[A,B,C,D,E,R](fa: => F[A], fb: => F[B], fc: => F[C], fd: => F[D], fe: => F[E])(f: F[(A,B,C,D,E) => R]): F[R] =

8 ap2(fd, fe)(ap3(fa,fb,fc)(map(f)(f => ((a:A,b:B,c:C) => (d:D, e:E) => f(a,b,c,d,e)))))

9 ...

试着在Configure类型上使用ap:

1 Apply[Configure].ap2(Configure(1),Configure(2))(((_: Int) + (_: Int)).point[Configure])

2 //> res4: Exercises.ex4.Configure[Int] = [email protected]

3 //| f或者用注入方法(injected method)<*>:scalaz/Syntax/ApplySyntax.scala

或者用注入方法(injected method)<*>:scalaz/Syntax/ApplySyntax.scala

1 (Configure(1) <*> {Configure(2) <*> {Configure(3) <*> {(((_:Int)+(_:Int)+(_:Int)).curried).point[Configure]}}}).get

2 //> res5: Int = 6

以上的Apply[Configure]是通过Apply typeclass的构建函数apply实现的:scalaz/Apply.scala

1 object Apply {

2 @inline def apply[F[_]](implicit F: Apply[F]): Apply[F] = F

 

3、简化一下ap的写法,只用提供f:(A,B) => C这样的基本操作函数:scalaz/Apply.scala

1 def apply2[A, B, C](fa: => F[A], fb: => F[B])(f: (A, B) => C): F[C] =

2 ap(fb)(map(fa)(f.curried))

3 def apply3[A, B, C, D](fa: => F[A], fb: => F[B], fc: => F[C])(f: (A, B, C) => D): F[D] =

4 apply2(apply2(fa, fb)((_, _)), fc)((ab, c) => f(ab._1, ab._2, c))

5 def apply4[A, B, C, D, E](fa: => F[A], fb: => F[B], fc: => F[C], fd: => F[D])(f: (A, B, C, D) => E): F[E] =

6 apply2(apply2(fa, fb)((_, _)), apply2(fc, fd)((_, _)))((t, d) => f(t._1, t._2, d._1, d._2))

7 def apply5[A, B, C, D, E, R](fa: => F[A], fb: => F[B], fc: => F[C], fd: => F[D], fe: => F[E])(f: (A, B, C, D, E) => R): F[R] =

8 apply2(apply3(fa, fb, fc)((_, _, _)), apply2(fd, fe)((_, _)))((t, t2) => f(t._1, t._2, t._3, t2._1, t2._2))

9 ...

用在Configure类型上:

1 (Apply[Configure].apply2(Configure(1),Configure(2))(((_: Int) + (_: Int)))).get

2 //> res6: Int = 3

3 (^(Configure(1),Configure(2))((_:Int)+(_:Int))).get

4 //> res7: Int = 3

5 (^^(Configure(1),Configure(2),Configure(3))((_:Int)+(_:Int)+(_:Int))).get

6 //> res8: Int = 6

这个^,^^是apply2,apply3的注入方法:scalaz/syntax/ApplySyntax.scala

 1 def ^[A,B,C](fa: => F[A], fb: => F[B])(

2 f: (A, B) => C): F[C] =

3 F.apply2(fa, fb)(f)

4

5 def ^^[A,B,C,D](fa: => F[A], fb: => F[B], fc: => F[C])(

6 f: (A, B, C) => D): F[D] =

7 F.apply3(fa, fb, fc)(f)

8

9 def ^^^[A,B,C,D,E](fa: => F[A], fb: => F[B], fc: => F[C], fd: => F[D])(

10 f: (A,B,C,D) => E): F[E] =

11 F.apply4(fa, fb, fc, fd)(f)

12

13 def ^^^^[A,B,C,D,E,I](fa: => F[A], fb: => F[B], fc: => F[C], fd: => F[D], fe: => F[E])(

14 f: (A,B,C,D,E) => I): F[I] =

15 F.apply5(fa, fb, fc, fd, fe)(f)

16 ...

另一种表达方式是通过ApplicativeBuilder typeclass实现的注入方法|@|:

1 ((Configure(1) |@| Configure(2) |@| Configure(3))((_:Int)+(_:Int)+(_:Int))).get

2 //> res9: Int = 6

效果是一样的。我们用一个实际的简单例子来示范一下Applicative的具体函数施用:

 1 def configName(name: String): Configure[String] = Configure(name)

2 //> configName: (name: String)Exercises.ex4.Configure[String]

3 def configID(userid: String): Configure[String] = Configure(userid)

4 //> configID: (userid: String)Exercises.ex4.Configure[String]

5 def configPwd(pwd: String): Configure[String] = Configure(pwd)

6 //> configPwd: (pwd: String)Exercises.ex4.Configure[String]

7 case class WebLogForm(name:String, id: String, pwd: String)

8

9 def logOnWeb(name: String, userid: String, pwd: String) =

10 ^^(configName(name),configID(userid), configPwd(pwd))(WebLogForm(_,_,_))

11 //> logOnWeb: (name: String, userid: String, pwd: String)Exercises.ex4.Configur

12 //| e[Exercises.ex4.WebLogForm]

13 def logOnWeb1(name: String, userid: String, pwd: String) =

14 (configName(name) |@| configID(userid) |@| configPwd(pwd))(WebLogForm(_,_,_))

15 //> logOnWeb1: (name: String, userid: String, pwd: String)Exercises.ex4.Configu

16 //| re[Exercises.ex4.WebLogForm]

值得注意的是:用Applicative施用configName,configID,configPwd时,这三个函数之间没有依赖关系。特别适合并行运算或fail-fast,因为无论如何这三个函数都一定会运行。这种Applicative的函数施用体现了它在并行运算中的优势。

 

4、Applicative style 函数施用。上面提到的|@|操作并不是一种操作函数而是一种层级式持续函数施用模式。具体实现在ApplicativeBuilder typeclass里:scalaz/ApplicativeBuilder.scala

 1 private[scalaz] trait ApplicativeBuilder[M[_], A, B] {

2 val a: M[A]

3 val b: M[B]

4

5 def apply[C](f: (A, B) => C)(implicit ap: Apply[M]): M[C] = ap.apply2(a, b)(f)

6

7 def tupled(implicit ap: Apply[M]): M[(A, B)] = apply(Tuple2.apply)

8

9 def ⊛[C](cc: M[C]) = new ApplicativeBuilder3[C] {

10 val c = cc

11 }

12

13 def |@|[C](cc: M[C]) = ⊛(cc)

14

15 sealed trait ApplicativeBuilder3[C] {

16 val c: M[C]

17

18 def apply[D](f: (A, B, C) => D)(implicit ap: Apply[M]): M[D] = ap.apply3(a, b, c)(f)

19

20 def tupled(implicit ap: Apply[M]): M[(A, B, C)] = apply(Tuple3.apply)

21

22 def ⊛[D](dd: M[D]) = new ApplicativeBuilder4[D] {

23 val d = dd

24 }

25

26 def |@|[D](dd: M[D]) = ⊛(dd)

27

28 sealed trait ApplicativeBuilder4[D] {

29 val d: M[D]

30

31 def apply[E](f: (A, B, C, D) => E)(implicit ap: Apply[M]): M[E] = ap.apply4(a, b, c, d)(f)

32

33 def tupled(implicit ap: Apply[M]): M[(A, B, C, D)] = apply(Tuple4.apply)

34

35 def ⊛[E](ee: M[E]) = new ApplicativeBuilder5[E] {

36 val e = ee

37 }

38

39 def |@|[E](ee: M[E]) = ⊛(ee)

40 ...

可以看得出(F[A] |@| F[B] |@| F[C])((A,B,C) => D)这个表达式中的两个|@|符号分别代表ApplicativeBuilder2(F[B])及ApplicativeBuilder3(F[C])。

这是另一种通过函数施用实现连接Applicative类型值的方式。

 

 

5、产生tuple:(F[A],F[B])合并成F[(A,B)]:scalaz/Apply.scala

 

1 def tuple2[A,B](fa: => F[A], fb: => F[B]): F[(A,B)] =

2 apply2(fa, fb)((_,_))

3 def tuple3[A,B,C](fa: => F[A], fb: => F[B], fc: => F[C]): F[(A,B,C)] =

4 apply3(fa, fb, fc)((_,_,_))

5 def tuple4[A,B,C,D](fa: => F[A], fb: => F[B], fc: => F[C], fd: => F[D]): F[(A,B,C,D)] =

6 apply4(fa, fb, fc, fd)((_,_,_,_))

7 def tuple5[A,B,C,D,E](fa: => F[A], fb: => F[B], fc: => F[C], fd: => F[D], fe: => F[E]): F[(A,B,C,D,E)] =

8 apply5(fa, fb, fc, fd, fe)((_,_,_,_,_))

9 ...

比如:

1 Apply[Configure].tuple2(Configure("abc"),Configure(123))

2 //> res10: Exercises.ex4.Configure[(String, Int)] = Exercises.ex4$Configure$$an

3 //| [email protected]

4 Apply[Configure].tuple3(Configure("abc"),Configure(123),Configure(true))

5 //> res11: Exercises.ex4.Configure[(String, Int, Boolean)] = Ex

具体用来干什么,我现在还说不上来。

 

 

6、把一个普通函数升格(lift)成高阶函数,如:(A,B) => C 升格成 (F[A],F[B]) => F[C]: scalaz/Apply.scala

 

1 def lift2[A, B, C](f: (A, B) => C): (F[A], F[B]) => F[C] =

2 apply2(_, _)(f)

3 def lift3[A, B, C, D](f: (A, B, C) => D): (F[A], F[B], F[C]) => F[D] =

4 apply3(_, _, _)(f)

5 def lift4[A, B, C, D, E](f: (A, B, C, D) => E): (F[A], F[B], F[C], F[D]) => F[E] =

6 apply4(_, _, _, _)(f)

7 def lift5[A, B, C, D, E, R](f: (A, B, C, D, E) => R): (F[A], F[B], F[C], F[D], F[E]) => F[R] =

8 apply5(_, _, _, _, _)(f)

9 ...

这种函数升格方式在用FP方式使用OOP库函数时更加方便。最典型的例子是Option类型在FP中结合OOP函数库的使用。如果我们希望在使用OOP库函数时使用Option类型的输入参数和返回值,那我们就可以通过函数升格(function lifting)来实现这样的功能。

1 val of2 = Apply[Option].lift2((_: Int) + (_: Int))//> of2 : (Option[Int], Option[Int]) => Option[Int] = <function2>

2 of2(Some(1),Some(2)) //> res12: Option[Int] = Some(3)

3 val of3 = Apply[List].lift3((s1: String, s2: String, s3: String) => s1 + " "+s2+" "+s3)

4 //> of3 : (List[String], List[String], List[String]) => List[String] = <functi

5 //| on3>

6 of3(List("How"),List("are"),List("you?")) //> res13: List[String] = List(How are you?)

我们分别用lift2,lift3把普通函数升格成Option和List高阶函数。

再来个更实际一点的例子:在java.sql.DriverManager库里有个getConnection函数。它的函数款式是:getConnection(p1:String,p2:String,p3:String): java.sql.Connection

虽然我没有它的源代码,但我还是想使用我自定义的类型Configure作为参数,我可以这样:

1 import java.sql.DriverManager

2

3 val sqlConnect = Apply[Configure] lift3 java.sql.DriverManager.getConnection

4 //> sqlConnect : (Exercises.ex4.Configure[String], Exercises.ex4.Configure[Str

5 //| ing], Exercises.ex4.Configure[String]) => Exercises.ex4.Configure[java.sql.

6 //| Connection] = <function3>

7 sqlConnect(Configure("Source"),Configure("User"),Configure("Password"))

8 //> res12: Exercises.ex4.Configure[java.sql.Connection] = Exercises.ex4$Configu

9 //| [email protected]

的确这样可以使我继续在FP模式中工作。

 

总结来说:Applicative typeclass提供了一套函数施用方式。它是通过一个包嵌在容器结构的高阶函数实现管道内的施用。Applicative typeclass还提供了方法将普通函数升格到高阶函数使FP和OOP混合模式的函数施用更安全方便。

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


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