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How to work on lists

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1 How do I…?

Given any list
, how do I...?

1.1 Basics

  • Get the size of the list.
length xs
  • Turn a list backwards.
reverse xs

1.2 Finding / searching

  • Get the Nth element out of a list.
xs !! n
head xs
returns the first element of the list.)
last xs
returns the last element of the list.)
  • Get a list of all elements that match some condition.
filter my_test xs
(Returns everything that passes the test.)
  • Find the highest/lowest element of a list.
minimum xs
maximum xs
(Works not just for numbers but anything that is a member of the
class. In particular, that includes characters and strings.)

1.3 Adding

  • Add an element to the start of a list.
new_element : xs
  • Add an element to the end of a list.
xs ++ [new_element]
  • Insert an element into the middle of a list.
Generally, you will have to split the list into two smaller lists, put the new element to in the middle, and then join everything back together. For example:
let (ys,zs) = splitAt n xs   in   ys ++ [new_element] ++ zs
  • Join two lists together.
list1 ++ list2

1.4 Deleting

  • Delete the first N elements from a list.
drop n xs
tail xs
removes just one element.)
init xs
removes just the last element.)
  • Make a new list containing just the first N elements from an existing list.
take n xs
  • Split a list into two smaller lists (at the Nth position).
splitAt n xs
(Returns a tuple of two lists.)
  • Delete the just Nth element of a list.
This is tricky. AFAIK, there is no built-in function that does this. You have to split the list in two, remove the element from one list, and then join them back together, like this:
let (ys,zs) = splitAt n xs   in   ys ++ (tail zs)
tail xs
removes the first element.)
init xs
removes the last element. Slow if the list is big.)
  • Delete elements that meet some condition.
Haskell has a function called
which will do this for you. Beware though: it should really be named 'select' instead. For example,
filter odd xs
returns a list of odd numbers. That is, it deletes everything that is not odd.

1.5 Testing various conditions

  • Check if a list is empty.
null xs
  • Find out whether any list element passes a given test.
any my_test xs
  • Check whether all list elements pass a given test.
all my_test xs

1.6 Modifying the list or its elements

  • Apply a function to all list elements.
map my_function xs
  • Apply a function to just some elements of a list.
Assuming you only want to apply function
to elements for which function
returns true, you can do this:
map (\x -> if p x then f x else x) xs
  • Convert a list of foos into a list of bars.
Find or write a function to convert foo into bar, and then apply it to the whole list using
  • Number the elements of a list (so I can process each one differently according to its position).
zip xs [0..]
(For example,
zip ['a','b','c'] [0..]
  • Apply a list of functions to a single element to get a list of results.
It's not in the book, but it's easy when you know how:
map ($ my_element) xs
  • Total up a list of numbers.
sum xs
product xs
will multiply all the elements together instead of adding them.)
  • Sort a list.
You'll need to import
first, but then you can just do
sort xs
  • Find out if some item is in a list.
my_element `elem` xs

1.7 Lists and IO

  • Execute a list of IO actions.
If you're hard-core:
map (>>=) xs
If you're a normal human being:
sequence xs
(Note: you might need to use
if the actions don't return any data.)
  • Execute an IO action on each element of a list.
You could map the IO function over your list (resulting in a list of actions) and then perform them using the trick above. But it's much simpler to do this:
mapM  my_action xs
mapM_ my_action xs
(Depending on whether you want the action to have access to the previous result or not.)

2 Notes about speed

Haskell lists are ordinary single-linked lists. (Look up the term in any book on data structures.) This gives them certain speed properties which are well worth knowing.

2.1 Fast operations

The following operations are always 'fast':

  • Prepend 1 element (the
  • head
    (get first element)
  • tail
    (remove first element)

2.2 Slower operations

Any function that does something with the Nth element or the first N elements generally gets slower as N increases. The following all slow down as
gets larger:
  • xs !! n
  • take n xs
  • drop n xs
  • splitAt n xs
Any function which needs to process the entire list obviously gets slower as the list gets bigger. The following all slow down as the list
gets larger:
  • length xs
  • list1 ++ list2
    (speed depends only on the size of
  • last xs
  • map my_fn xs
  • filter my_test xs
  • zip my_fn list1 list2
    (speed depends on the smallest of the two lists - as does the size of the result list!)
  • x `elem` xs
  • sum xs
  • minimum xs
  • maximum xs


module has many functions for sorting, modifying and building lists.