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Common Functions

head, last

  • Signature:
head :: [a] -> a
last :: [a] -> a

  • Description:

    • head xs is the first element of the list xs.
    • last xs is the last element of the list xs. Error if xs is empty.

  • Examples:

ghci> head [1..6]
1
ghci> last [1..6]
6

tail, init

  • Signature:
tail :: [a] -> [a]
init :: [a] -> [a]

  • Description:

    • tail xs is the list xs without its first element.
    • init xs is the list without its last element. Error if xs is empty.

  • Examples:

ghci> tail [1..4]
[2,3,4]
ghci> init [1..4]
[1,2,3]

reverse

  • Signature:
reverse :: [a] -> [a]
  • Description:

reverse xs is the list xs backwards.

  • Examples:
ghci> reverse [1..4]
[4, 3, 2, 1]
ghci> reverse [True, False, False]
[False, False, True]

length

  • Signature:
length :: [a] -> Int
  • Description:

length xs is the number of elements in the list xs.

  • Examples:
ghci> length []
0
ghci> length [1..5]
5
ghci> length "Angela"
6

null

  • Signature:
null :: [a] -> Bool
  • Description:

null xs indicates if the list xs is empty.

  • Examples:
ghci> null []
True
ghci> null [1..8]
False

elem

  • Signature:
elem :: Eq a => a -> [a] -> Bool
  • Description:

elem x xs indicates if x is in the list xs.

  • Examples:
ghci> elem 6 [1..10]
True
ghci> 6 `elem` [1..10]
True
ghci> 'k' `elem` "Ethan"
False

Indexing (!!)

  • Signature:
(!!) :: [a] -> Int -> a
  • Description:

xs !! i is the ith element of the list xs (starting from zero).

  • Examples:
ghci> [1..10] !! 3
4
ghci> [1..10] !! 11
Exception: index too large

Concatenation of two lists

  • Signature:
(++) :: [a] -> [a] -> [a]
  • Description:

xs ++ ys is the resulting list of putting ys after xs.

  • Examples:
ghci> "JIM" ++ "MY"
"JIMMY"
ghci> [1..5] ++ [1..3]
[1,2,3,4,5,1,2,3]

maximum, minimum

  • Signature:
maximum :: Ord a => [a] -> a
minimum :: Ord a => [a] -> a

  • Description:

  • maximum xs is the biggest element of the list (non empty!) xs.

  • minimum xs is the smallest element of the list (non empty!) xs.

  • Examples:

ghci> maximum [1..10]
10
ghci> minimum [1..10]
1
ghci> minimum []
Exception: empty list

sum, product

  • Signature:
sum     :: Num a => [a] -> a
product :: Num a => [a] -> a

  • Description:

  • sum xs is the sum of the list xs.

  • prod xs is the product of the list xs.

  • Examples:

ghci> sum [1..5]
15

factorial n = product [1..n]
ghci> factorial 5
120

take, drop

  • Signature:
take :: Int -> [a] -> [a]
drop :: Int -> [a] -> [a]

  • Description:

  • take n xs is the prefix of length n of the list xs.

  • drop n xs is the suffix of the list xs when the first n elements are removed.

  • Examples:

ghci> take 3 [1..7]
[1, 2, 3]
ghci> drop 3 [1..7]
[4, 5, 6, 7]

zip

  • Signature:
zip :: [a] -> [b] -> [(a, b)]

  • Description:

  • zip xs ys is the list that combines, in order, each pair of elements of xs and ys. If they are missing, they are lost.

  • Examples:

ghci> zip [1, 2, 3] ['a', 'b', 'c']
[(1, 'a'), (2, 'b'), (3, 'c')]
ghci> zip [1..10] [1..3]
[(1, 1), (2, 2), (3, 3)]

repeat

  • Signature:
repeat :: a -> [a]

  • Description:

  • repeat x is the infinite list where all elements are x.

  • Examples:

ghci> repeat 3
[3, 3, 3, 3, 3, 3, 3, 3, ...]
ghci> take 4 (repeat 3)
[3, 3, 3, 3]

concat

  • Signature:
concat :: [[a]] -> [a]
  • Description:

concat xs is the list that concatenates all the lists of xs.

  • Examples:
ghci> concat [[1, 2, 3], [], [3], [1, 2]]
[1, 2, 3, 3, 1, 2]