Thank you for joining us for the seventh part of our Haskell series, you will find the previous article here where I explain higher order functions.

In this article we are going to cover three essentials functions in the functional programming world: `map`

, `filter`

and `foldl`

. Then we are going to learn how to compose functions.

## Map

`map`

is a very standard function in functional programming, it basically applies a function to every element of a list and returns a new list. We wrote our own version of `map`

in the previous article using a list comprehension, but Haskell has its own version, and we do not even need to import it !

Let's check the definition:

```
ghci> :t map
map :: (a -> b) -> [a] -> [b]
```

Let's analyze it:

`(a -> b)`

: This is the first parameter, it is a function which take a single parameter of type`a`

and returns a single parameter of type`b`

. It makes sense because most of the time we use`map`

to "transform" data in a list.`[a]`

: This is the second parameter, it is a list of`a`

. It's logical, our function requires`a`

as an "input".`[b]`

: This is the return value, it is a list of`b`

, our "output".

Let's try it out:

```
ghci> map (subtract 3) [1, 2, 3, 4, 5]
[-2,-1,0,1,2]
ghci> map (+10) [1, 2, 3, 4, 5]
[11,12,13,14,15]
```

Looks good.

## Filter

`filter`

is also a very common function in functional programming, it essentially takes a predicate (a function which returns `True`

or `False`

based on the value being tested) to filter out elements from a list.

Let's check the definition:

```
ghci> :t filter
filter :: (a -> Bool) -> [a] -> [a]
```

Let's analyze it:

`(a -> Bool)`

: This is the first parameter, our predicate. It takes an`a`

as a parameter and returns a Boolean. If`True`

it will be added to the new list, else it will be ignored.`[a]`

: This is the second parameter, our list of`[a]`

.`[a]`

: This is the return value, you will note it is still a list of`a`

this time, we do not "transform" the value, hence its type not changing.

Let's try it out:

```
ghci> filter (>3) [1,2,3,4,5]
[4,5]
ghci> filter odd [1,2,3,4,5]
[1,3,5]
```

Looks good, you will note that we do not need any parenthesis for `odd`

because it does not have a parameter.

## Foldl

`foldl`

is also pretty famous in the functional programming world but usually known under a different pseudonym: `reduce`

. This function acts like a `map`

function but "reduces" the result to a summary value, or, to use Haskell terms: it "folds" the result to a summary value. In this very specific situation, it folds the list from the left side (hence `foldl`

, `foldr`

exists for the same purpose but from the right side).

Let's check the definition:

```
ghci> :t foldl
foldl :: Foldable t => (b -> a -> b) -> b -> t a -> b
```

Let's analyze it:

- We discover a new typeclass called
`Foldable`

(documentation) which defines data structure that can be folded to a summary value. `(b -> a -> b)`

: This is our first parameter, it is a function that takes 2 parameters and returns a single value.`b`

is the accumulator (or summary value),`a`

is an element from our Foldable data structure (typically a List, but others exists).`b`

: This is our second parameter, the accumulator.`t a`

: This is our third parameter, the Foldable data structure.`b`

: This is our return value, the accumulator.

Let's try it out:

```
ghci> foldl (\acc x -> acc + x) 0 [1,2,3,4,5]
15
```

So what happened here:

- We are calling
`foldl`

. - Our first parameter is a lambda function with 2 parameters:
`acc`

is the accumulator and`x`

is the current element of the list. - Our second parameter is the accumulator which we initialized to
`0`

. - Our third parameter is the list of values.
- Our result is 15, because it is the result of 0 + 1 + 2 + 3 + 4 + 5

## Function composition

Now, it is pretty common to "chain" functions in programming, functional or not. Because we did not visited yet concepts like `record`

or `data`

, we are going to apply it again on a list of numbers. But soon enough we will be able to demonstrate Haskell features using better test data.

Let's say that we need to negate a number and then add `2`

to it. Because we are familiar with `map`

and lambdas we would write something like this:

```
ghci> map (\x -> negate x + 2) [1,2,3,4,5]
[1,0,-1,-2,-3]
```

Which is perfectly fine, but it can be finer by using the dot operator: `.`

!

Let's try it out:

```
ghci> map ((+2) . negate) [1,2,3,4,5]
[1,0,-1,-2,-3]
```

Looks better, there is less "noise" without any backslash or arrows. But note that `.`

is right associative. I chose `negate`

on purpose to show that the order matter:

```
ghci> map (negate . (+2)) [1,2,3,4,5]
[-3,-4,-5,-6,-7]
```

Your results would be completely different if you would switch the order, so keep it in mind the next time you need to compose functions.

### Additional notes:

If you were looking into "chaining" map and filter, let's say to filter numbers that can be divided by 3 and multiply them by 42 .I recommend doing either of the following things:

**Option 1**: Use the output of `filter`

as the input to `map`

:

```
ghci> map (*42) (filter (\x -> mod x 3 == 0) [1,2,3,4,5,6,7,8,9])
[126,252,378]
```

**Option 2:** Use list comprehensions, which is much more legible in my opinion:

```
ghci> [x * 42 | x <- [1,2,3,4,5,6,7,8,9], (mod x 3 == 0)]
[126,252,378]
```

## Conclusion

Seven down, around three more articles to go ! That's it for the `map`

, `filter`

, `foldl`

and function composition in Haskell. In our next article we are going to discuss about I/O (Input and Output) which we saw very briefly in our first article where we wrote and compiled our first program.

PS: Part 8 can be found here.

*If you have a problem and no one else can help. Maybe you can hire the Kalvad-Team.*