Functional Programming Exercises

Exercises for Chapters 1 to 3

• Provide a function to check if a character is alphanumeric (i.e. lower case, upper case or numeric).
• Define a function intmax which takes a number pair and returns the greater of its two components.
• Write the function plus using a stack recursive style.
• Write a function called int_divide which divides one whole number (positive or negative) by another; the function should not use any arithmetic operators except for subtraction, addition and unary minus.
• Which of the following are legal list constructions? and why are the others illegal?

         list1 = 1 : []
         list2 = 1 : [] : []
         list3 = 1 : [1]
         list4 = [] : [1]
         list5 = [1] : [1] : []
  

• Use structural induction to design the function mytake, which takes a number n and a list and returns a list containing the first n items in the input list (the rest of the input list is discarded).
• Modify the program skip (see handouts from lecture 8) so that it will permit nested brackets.

Exercises for Chapter 4

• Give the types of the following compositions (see the book or the online manual for definitions of the biult-in functions code and show):

        tl . (++ [])
        abs . fst
        code . code
        show . tl
  

• Explain why the function myiterate (see the handouts for lecture 9) is not robust and provide a robust version.
• Write a function applylist which takes a list of functions (each of type (*->**) ) and an item (of type *) and returns a list of the results of applying each function to the item. For example:

  applylist [(+ 10),(* 3)] 2  
  

  will evaluate to [12,6].
• Explain why the following definitions are equivalent:

        f1 x alist = map (plus x) alist
        f2 x = map (plus x)
        f3 = (map . plus)
  

• Rewrite the function map in terms of foldr.
• Define the function mydropwhile which takes a list and a predicate (a function that returns a Boolean) as arguments and returns the list without the initial sublist of members which satisfy the predicate. For example the application:

  mydropwhile (~=0) [1,2,1,1,2,1,0,1,2,1,1]
  

  returns the result [0,1,2,1,1].