Introduction to Haskell

In mathematics, functions have a domain an codomain. In Haskell, functions have types or signatures. They often can be omitted in Haskell, but can also be explicitly written as in:

f :: Integer -> Integer -> Integer
f x y = x + y

or:

f :: Bool -> Bool
f True = False
f False = True

The previous example illustrates that we can define functions by specifying a behaviour for given values.

3. Write a function together with its signature, which implements boolean AND:

myand :: Bool -> Bool -> Bool
...

5. Write an implementation for a function ifp which takes a boolean, expressions $ e_1$ and $ e_2$ and returns $ e_1$ if the boolean is true and $ e_2$ otherwise.

ifp = ...

6. Write a function which takes three integers and returns the largest. Hint - sometimes parentheses are important in function calls.

f :: Integer -> Integer -> Integer -> Integer

In Haskell, we can use the if construct, in a manner almost identical to the above implementation, e.g.

f x = if x == 0 then 1 else 0

The previous function returns 1 if x is equal to 0 and 0 otherwise. A more elegant way is to use guards:

f x
   | x == 0 = 1
   | otherwise = 0

More generally, guards can be used as follows:

<function_name> <parameters>
  | <boolean_condition_1> = <expression_1>
  | <boolean_condition_2> = <expression_2>
  ...
  | otherwise = <expression_n>

x. Solve the previous exercise using guards

«Explain lists, head, tail»

x. Implement reversal

13. Write a function which extracts the third to last number from a list and returns True, if that number is odd (hint: the function mod may be useful)

            V
   f [3,4,5,2,3,9] = False
   f [3,4,2,1,4,4] = True

«Explain pattern matching»

x. Implement the previous exercise using patterns

14. Implement a function which returns the sum of integers from a list.

15. Implement a function which takes a list of booleans and returns false if at least one boolean from the list is false.

16. Implement a function which filters out all odd numbers from a list.

17. Implement a function which takes a list of booleans and returns a list of integers. In the latter, (True becomes 1 and False becomes 0). Example: f [False, True, False] = [0,1,0].

«Explain char and strings»

x. Write a function which removes all empty strings from a list.

x. Write a function which removes all strings of size smaller than 3. Do not use the builtin function length.

x. Write a function which removes all strings having the third letter equal to 'a'.

x. Write a function which:

• removes all strings which are not names. A name always starts with an uppercase.
• removes the last name from the resulting list of names. A name always comprises of the first name followed by the last name.