Now that you’ve seen how to write your own higher-order functions, let’s take a quick look at a more real-world example.

Imagine for a moment that the `List`

class doesn’t have its own `map`

method, and you want to write your own.
A good first step when creating functions is to accurately state the problem.
Focusing only on a `List[Int]`

, you state:

I want to write a

`map`

method that can be used to apply a function to each element in a`List[Int]`

that it’s given, returning the transformed elements as a new list.

Given that statement, you start to write the method signature.
First, you know that you want to accept a function as a parameter, and that function should transform an `Int`

into some generic type `A`

, so you write:

```
def map(f: (Int) => A
```

The syntax for using a generic type requires declaring that type symbol before the parameter list, so you add that:

```
def map[A](f: (Int) => A
```

Next, you know that `map`

should also accept a `List[Int]`

:

```
def map[A](f: (Int) => A, xs: List[Int])
```

Finally, you also know that `map`

returns a transformed `List`

that contains elements of the generic type `A`

:

```
def map[A](f: (Int) => A, xs: List[Int]): List[A] = ???
```

That takes care of the method signature.
Now all you have to do is write the method body.
A `map`

method applies the function it’s given to every element in the list it’s given to produce a new, transformed list.
One way to do this is with a `for`

expression:

```
for x <- xs yield f(x)
```

`for`

expressions often make code surprisingly simple, and for our purposes, that ends up being the entire method body.

Putting it together with the method signature, you now have a standalone `map`

method that works with a `List[Int]`

:

```
def map[A](f: (Int) => A, xs: List[Int]): List[A] =
for x <- xs yield f(x)
```

### Make it generic

As a bonus, notice that the `for`

expression doesn’t do anything that depends on the type inside the `List`

being `Int`

.
Therefore, you can replace `Int`

in the type signature with the generic type parameter `B`

:

```
def map[A,B](f: (B) => A, xs: List[B]): List[A] =
for x <- xs yield f(x)
```

Now you have a `map`

method that works with any `List`

.

These examples demonstrate that `map`

works as desired:

```
def double(i : Int) = i * 2
map(double, List(1, 2, 3)) // List(2,4,6)
def strlen(s: String) = s.length
map(strlen, List("a", "bb", "ccc")) // List(1, 2, 3)
```

Now that you’ve seen how to write methods that accept functions as input parameters, let’s look at methods that return functions.