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**Being able to manipulate lists is really important in any language**.

Haskell isn’t as difficult as it may seem at first.

I think the majority of negativity towards this language comes from adjusting to it being a declarative language, not an object-oriented one.

## Squaring All Integers in a Given Range (Single Generator)

You don’t need a function to do this. You can run this directly from your GHCi command screen.

The command `[ x^2 | x <- [1..10] ]`

more or less translates to “x to the power of 2, for all x in the range 1 to 10.

The `x <- [1..10]`

part is the **generator**. It generates values for x.

## List Of Ordered Pairs (2 Generators)

The command `[ (x,y) | x <- [1,2,3,4,5], y <- ["a","b","c"] ]`

uses two generators.

One for x, one for y; **each has their own list**.

It will return all combinations.

## Joining a List of Lists (Dependant Generators)

1 2 3 4 5 | -- this program will join a list of lists demoList = [[1,2,3],[4,5],[6,7]] -- just a preset list of lists joinLists :: [[a]] -> [a] -- takes in some list of lists containing some polymorphic type joinLists xss = [ x | xs <- xss, x <- xs ] -- for x in each xs from xss, x |

You’ll notice in this function, the command `[ x | xs <- xss, x <- xs ]`

is used.

**This can be understood simply as**:

- a list containing “x”s
- where the “xs”s are pulled from the input “xss”
- and the “x”s are pulled from the “xs”s

This uses a **dependant generator** in that, we cannot get to `x <- xs`

without getting `xs <- xss`

first.

## Get All Even Numbers in a Given Range (Uses a Guard)

If we want to find all even numbers in a given range we can do that. We’ll be using a *generator* of `x , [1..n]`

which gives us a list of all numbers from 1 to `n`

the input. However, we want to *guard* against the odd numbers, so we need to use `x mod 2 == 0`

so we’re only given numbers that *divide* by `2`

and leave a remainder of `.`

1 2 | allEvenUpto :: Integer -> [Integer] allEvenUpto n = [ x | x <- [1..n], x `mod` 2 == ] |

The generator is guarded in this case by `x mod 2 == 0`

.

Only when the guard is true, is the `x`

generated and put into the list for returning.

## Get List of Factors for a Given Number

This program is very similar to the “all even in range” example. We’re generating all x between 1 and (input) n, where `n mod x`

is equal to 0.

The `mod`

part is useful for determining whether something divides into something. If `n mod x == 0`

then it must be a factor. For example, `2 mod 4`

would equal 0. However, `2 mod 5`

would be equal to `1`

because there is `1`

remaining after the division.

1 2 | getFactors :: Integer -> [Integer] getFactors n = [ x | x <- [1..n], n `mod` x == ] |

This program works really well for this purpose. It returns the list of all factors for the given input `n`

.

You can see in the above example that for each of the numbers `[1,2,5,10]`

they are a factor of `10`

.