"Scala" high-order functions and currying

Higher order functions

In mathematics and computer science, higher-order functions are functions that meet at least one of the following conditions:

- 接受一个或多个函数作为输入- 输出一个函数

In mathematics they are also called operators (operators) or functional. The derivative in calculus is a common example, because it maps a function to another function.

Examples of higher order functions

Suppose there is a function that sums all the integers in a given two-digit interval:

def sumInts(a: Int, b: Int): Int =   if0else1, b)

If the sum of squares of consecutive integers is now required:

def square(x: Int): Int = x * xdef sumSquares(a: Int, b: Int): Int =   if0else1, b)

If you want to calculate the sum of the power of 2:

defif01else2 * powerOfTwo(x-1)def sumPowersOfTwo(a: Int, b: Int): Int =   if0else powerOfTwo(a) + sumPowersOfTwo(a+1, b)

The above function is an additive form of f (n) from A to B, and we can extract the common part of these functions to rewrite the function sum, where the defined F is passed in as a parameter to the higher-order function sum:

def  sum (f:int = = int, a:int, b:int): Int = if (a > B) 0  else  F (a) + sum (F, A+1 , b) def  ID (x:int): Int = x< Span class= "Hljs-keyword" >def Square (x:int): Int = x * Xdef  poweroftwo (x:int) : Int = if  (x = = 0 ) 1  else  2  * poweroftwo (X-1 ) def  sumints (A:int, b:int): Int = SUM (ID, a, b) def  sumsquared (A:int, b:int): Int = SUM (square, A, b) def  Sumpowersoftwo (A:int, b:int): Int = SUM (Poweroftwo, A, b) 

Useful higher-order functions

The map method applies a function to all elements of a collection and returns the result; foreach applies the function to each element.

//打印三角形scala> (19).map("^" * _).foreach(println _)^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The filter method outputs all elements that match a particular condition:

scala> (1920)res14: scala.collection.immutable.IndexedSeq[Int] = Vector(2468)

You can familiarize yourself with higher-order functions by practicing some common methods of accepting function parameters in the Scala collection library.

Currying

Curry (currying) refers to the process of turning a function that accepts two parameters into a new function that takes a parameter. The new function returns a function that takes the original second argument as a parameter.

Functions that return functions

In the above example of a higher order function, def sumInts(a: Int, b: Int): Int = sum(x => x, a, b) we def sumSquared(a: Int, b: Int): Int = sum(x => x*x, a, b) define a new function, the above two functions each pass a and b two parameters into the SUM function, can we simplify these parameters to make the function definition simpler?
We can simplify the parameter by returning the function's function:

def sum(f: Int => Int): (Int, Int) => Int = {    def sumF(a: Int, b: Int): Int =         if0        else f(a) + sumF(a+1, b)    sumF}//于是得到如下定义，这样就简化了参数def sumInts = sum(x => x)def sumSquared = sum(x => x * x)def sumPowersOfTwo = sum(powerOfTwo)

Multiple parameter lists

According to the above example, can we simplify, omit sumInts , sumSquared sumPowersOfTwo The form of these intermediate functions?
Replace the function with a sum(square)(1, 10) function sumSquared .
In general, this type of function is left-associative: sum(square)(1, 10) == (sum(square))(1, 10) .

We can define the sum function like this:

def sum(f: Int => Int)(a: Int, b: Int): Int =   if0else1, b)

This makes the function writing more concise.

In general, a multi-parameter function is defined as def f(args1)...(argsn) = E ,
When n > 1 o'clock, equal to def f(args1)...(args n-1) = {def g(argsn) = E; g} or def f(args1)...(args n-1) = (argsn => E) .
If you repeat this process n times, get it def f = (args1 => (args2 => ... (argsn => E) ) ) .
This function definition is called curry (currying).

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"Scala" high-order functions and currying