How to implement function composition in scala
We are going to discuss how to define function in Scala, and also practice mathematical function composition. I hope you will know how beautiful the Scala code is.
Posted by Mark Yang on December 21, 2015

# How to implement function composition in scala

## What’s function composition

This is the definition from wiki－“In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.” You can also say that a parameter of such function is another function, for example

this is a summation fucntion, a, b, and g(x) are parameters of the function. We can show like this as a function

a and b are variables, g(x) is a function, so f(a,b,g(x)) is a function composition.

## Functions in Scala

I=>O means a function that I as a type of parameter and O as a type of output in Scala, like

val f1:Double=>Double=
x=>Math.pow(x,2)
//f1(x)=x^2. e.g. f1(2)=4
val f2:(Double,Double)=>Double=
(x,y)=>Math.pow(x,2)+Math.pow(y,2)
//f2(x)=x^2+y^2 e.g. f2(2,3)=13

x and y can be replaced by any identifier you define. Now some people may have known how to implement function composition, but before that, we can practice summation function f(a,b,g(x)) by using recursive method.

def f(a:Int,b:Int,g:Int=>Int):Int={
if (a>b) 0
else f(a+1,b,g)+g(a)
}

Note The types of the parameters and the output of g(x) are all integers (Int=>Int).

Now we can implement the summation fucnction form 1 to 10, $f(1,10,g(x))=\sum_{1}^{10}g(x)$

val constant:Int=>Int=x=>x

val pow:Int=>Int=x=>Math.pow(x,2).toInt //pow is a function that Int to Int

f(1,10,constant)

f(1,10,pow)

Wait! That’s all?? Of course not, we can represent this function in a more concise way in Scala

val fc: ((Int) => Int) => Int= f(1,10,_)
//or
val fc=f(1,10,_:Int => Int)

Here we use “_” to represent g:Int=>Int. Type of fc is ((Int) => Int) => Int, we can think fc’s parameter as a type of (Int)=> Int, the function of output Int. The benefit is decreasing repeat of codes.

fc(constant) //as like f(1,10,constant)

fc(pow) //f(1,10,pow)

Note The line val fc=f(1,10,_) would fail. you need to specify type of _, because compiler can not recognize it.

## Summary

Now we know how to define a function in Scala, and practice summation function. Then we use amazing _ in Scala to implement mathematical function composition. Hope they are useful for you.

### Refrerences

Scala Partially Applied Functions