Filtering a List Haskell

Question

I just started learning Haskell about filtering lists. Suppose I have the following list : [2, 3, 4, 5, 8, 10, 11] I would like to keep only those numbers in the list, which are not divisible by the other members.

The result of our example would be : [2, 3, 5, 11]

Answer 1

[x | x <- src, all (\y -> x `rem` y /= 0) (filter (<x) src)]
where src = [2,3,4,5,8,10,11]

It should be noted that you actually also mean dividable by other numbers that are below it, and not just any number in that list, which is why there's a filter in the 2nd argument for all.

The result, of course, is the one you expect in your question: [2,3,5,11].

---

Here's how it works (and if I'm missing anything, let me know and I'll update).

I'll explain the code side-by-side with normal English. I suggest you just read just the English first, and afterwards see how each statement is expressed in code - I think it should be the most friendly for a newcomer.
Also note that I flipped the arguments for filter and all below (it is invalid!) to make the explanation fluid.

[x|: Construct a list made out of x
x <- src: Where x is an element from src
,: But only the elements that satisfy the following predicate/rule:
all of the numbers from
(filter src (<x)): src that are lesser-than the current x
(\y -> x 'rem' y /= 0): must not yield a remainder equal to 0.
]

For the code part to make sense, make sure you've familiarized yourself with all, filter, rem, and the syntax for: list comprehensions, lambda expressions, sections, and backticks.

Answer 2

On GHC,

Prelude> :m + Data.List
Prelude Data.List> nubBy (\a b -> rem a b == 0) [2,3,4,5,8,10,11]
[2,3,5,11]

does the trick. On Haskell98-compatible systems (e.g. Hugs), use nubBy (\b a -> rem a b == 0).

This answer was posted as a comment by Will Ness.