Gain insights into Haskell's functional programming by learning to write pure functions, use pattern matching, recursion, and Lists, define data types, and execute IO operations.

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Functional programming is a problem-solving paradigm that differs drastically from the imperative programming style of languages like C++ or Java. While functional programming principles have invaded most modern programming languages to some degree, there is no language that embraces this paradigm quite as Haskell does. As a result, Haskell code can reach a level of expressiveness, safety, and elegance that is difficult to achieve in other programming languages.

This course will introduce you to the core concepts of functional programming in Haskell. You will learn how to write pure functions using techniques such as pattern matching and recursion, and how to work with Haskell's powerful List data type. You will understand the basics of Haskell's powerful type system and define your own data types. Finally, you’ll learn how to perform IO operations the Haskell way. By the end of this course, you’ll have a new paradigm to add under your belt and you can start using functional programming in your own projects.

Learn Functional Programming in Haskell

In the previous lessons, we learned how to write recursive functions on lists. There are a few recursion patterns that occur again and again. They can be abstracted in higher-order functions on lists. This allows us to write expressive list functions without worrying too much about implementing explicit recursion. 

# Map

The first recursion pattern we will look at is **transforming** list elements. For example, we might want to round each double in a list to its nearest integer.

roundList :: [Double] -> [Int]
roundList [] = []
roundList (x:xs) = round x : roundList xs

main = print (roundList [1.3, 3.7, 4.0484])

Or we might want to lowercase each character in a string.


import Data.Char

lowerString :: [Char] -> [Char]
lowerString [] = []
lowerString (x:xs) = toLower x : lowerString xs

main = print (lowerString "HELLO, HOW ARE YOU?")

Both specific functions follow the same general pattern:

1. They act on a list with some element type `a` and return another list with some element type `b`.
2. They apply a function of type `a -> b` (e.g. `round`, `toLower`) element wise to the list.

This pattern is captured by the general function `map`, available in the Haskell Prelude. Its implementation is
```
map :: (a -> b) -> [a] -> [b]
map _ [] = []
map f (x:xs) = f x : map f xs
```
Using the higher-order function `map` we can  write more concise versions of `roundList` and `lowerString`:

```
roundList = map round
lowerString = map toLower
```
As these examples show, it is common to use higher-order list functions with partial application to obtain specific list functions. In other words, we are reading the type declaration of `map` as 
```
map :: (a -> b) -> ([a] -> [b])
```
Thus, we can see `map` as a transformation of functions. It lifts a function `f` on values of type `a` to a function `map f` on lists of type `[a]`.

Check out map and filter - two higher-order functions commonly used on lists.

Introduction

First Steps with Haskell

Techniques for Writing Functions

Working with Lists

Creating Data Types

Input and Output

Conclusion

Appendix

Higher-Order Functions on Lists I: Map and Filter