Can't seem to get my head around the 'list difference' (\\) operator

Question

I have heard the term 'list difference' (\\) operator in Haskell but still don't quite know how to get my head around it. Any examples or ideas?

Answer 1

The (\\) operator (and the difference function ) implements set difference , so, if you have two lists, a and b , it returns only those elements of a that are not in b , as illustrated:

Answer 2

Simply put, it takes two lists, goes through the second and for each item, removes the first instance of the same item from the first list.

> [1..10] \\ [2, 3, 5, 8]
[1,4,6,7,9,10]
> [1, 2, 1, 2, 1, 2] \\ [2]
[1,1,2,1,2]
> [1, 2, 1, 2, 1, 2] \\ [2, 2]
[1,1,1,2]
> [1, 2, 1, 2, 1, 2] \\ [2, 2, 1]
[1,1,2]

Answer 3

xs \\ ys is all the elements in xs that are not in ys . Maybe a list comprehension will clarify this:

xs \\ ys = [ x | x <- xs, x `notElem` ys ]

or, if you could do this in Haskell,

xs \\ ys = [ x | x `elem` xs, x `notElem` ys ]

This comes from set theory 'sset difference . The basic idea is that you are "subtracting" one collection of elements from another, hence the term "difference".

Answer 4

Suppose, you have a list of things, for example cities. Let's take for instance this list:

a = ["London","Brussels","Tokio","Los Angeles","Berlin","Beijing"]

Now you want to remove all cities that are in Europe. You know, that those cities are in Europe:

b = ["Glasgow","Paris","Bern","London","Madrid","Amsterdam","Berlin","Brussels"]

To get a list of cities in a , that are not in Europe, so that are not in b , you can use (\\) :

a \\ b = ["Tokio","Los Angeles","Beijing"]