接受函数的函数中的参数类型答案

【问题标题】：Types of parameters in functions that accept functions接受函数的函数中的参数类型
【发布时间】：2016-11-10 14:49:30
【问题描述】：

我正在尝试使用 SICP 学习 Scala，但我在函数的类型定义方面遇到了困难，并且卡在了 SICP。这里构建了一个通用表达式来找到一个数字的平方根（通过定点搜索或牛顿法），而不是：

def sqrt_damp(x: Double) =
  fixed_point(average_damp(y => x / y))(1)

def sqrt_newton(x: Double) =
  fixed_point(newton_method(y => square(y) - x))(1)

基于功能：

def square(x: Double) = x * x           
def average(x: Double, y: Double) = (x + y) / 2                                             
def abs(x: Double) = if (x < 0) -x else x 

val tolerance = 0.00001                   
def fixed_point(f: Double => Double)(first_guess: Double) = {
  def close_enough(v1: Double, v2: Double): Boolean = abs(v1 - v2) < tolerance
  def attempt(guess: Double): Double = {
    val next = f(guess)
    if (close_enough(guess, next)) next else attempt(next)
  }
  attempt(first_guess)
}

def average_damp(f: Double => Double): Double => Double =
  x => average(x, f(x))

val dx = 0.00001                                
def deriv(g: Double => Double): Double => Double =
  x => (g(x + dx) - g(x)) / dx

def newton_transform(g: Double => Double): Double => Double =
  x => x - g(x) / deriv(g)(x)               

def newton_method(g: Double => Double)(guess: Double): Double =
    fixed_point(newton_transform(g))(guess)

平方函数可以概括为：

(define (fixed-point-of-transform g transform guess)
  (fixed-point (transform g) guess))

我试图在 Scala 中表达如下：

 def fixed_point_of_transform(g: Double => Double, transform: Double => Double)(guess: Double): Double =
   fixed_point(transform(g))(guess)

但是上面没有编译并产生错误

type mismatch; found : Double => Double required: Double

编辑，以下工作：

def fixed_point_of_transform(g: Double => Double, transform: (Double => Double) => (Double => Double))(guess: Double): Double =
  fixed_point(transform(g))(guess)

所以现在前面的函数可以定义为：

def sqrt_damp(x: Double) =
    fixed_point_of_transform(y => x / y, average_damp)(1)

def sqrt_newton(x: Double) =
    fixed_point_of_transform(y => square(y) - x, newton_method)(1)

【问题讨论】：

标签： scala types

【解决方案1】：

transform 接受 Double 并返回 Double。您不能将其应用于g，因为g 是一个函数Double => Double。您可以将其应用于g(x)，其中x: Double。我想这就是你想要的：fixed_point((x: Double) => transform(g(x)))(guess)

【讨论】：

我想我现在明白了，谢谢，所以我应该改用transform: (Double => Double) => (Double => Double)