FP Laboratory 4

Functions working with lists

Implement following functions:

• Create a function that takes first n elements of the list.

take :: a -> [a] -> [a]

• Create a function that takes the remaining list after the first n elements.

drop :: a -> [a] -> a

• Create a function that find the smallest element in the list. Consider input restrictions.

minimum :: [a] -> a -- Is this right?

• Find all prime divisors of a given number.

divisors :: a -> [a]

Functions working with lists and tuples

Implement following functions:

• Create a function that merge two lists into one list of tuples.

zipThem:: [a] -> [b] -> [(a,b)]

• Create a function that compute Cartesian product of two vectors.

dotProduct :: [a] -> [b] -> [(a,b)]

• Create a function that computes n-th number in the Fibonacci sequence. The function should be use n bigger then 50 and get the result in less then a second).

fibonacci :: Int -> Int

List comprehension

Using the list comprehension implement following functions:

• Create a function that generates a list of all odd numbers in given interval.

oddList :: Int -> Int -> [Int]

• Create a function that takes a string and converts all characters to upper case letters.

allToUpper :: String -> String

• Create a function that removes all upper case letters from a string.

removeAllUpper :: String -> String

• Create functions that computes union and intersection of two sets.

union :: [a] -> [a] -> [a]
intersection :: [a] -> [a] -> [a]