Haskell Worksheet 1, due Monday, February 24

Table Comparing Scheme and Haskell Basics

          {- this is a
             multi-line
             comment -}
        

   [1 .. 7]  ===> [1, 2,3, 4, 5, 6, 7]
   [1, 3 .. 7] ===>[1, 3, 5, 6]
   [-3 .. 3] ===> [-3, -1, 1, 3]
   [x | x <- [1 .. ], (mod x 2) == 0]
         ===> list of all positive even integers
   take 7 [x | x <- [1 .. ], (mod x 2) == 0]
         ===> [2,4,6,8,10,12,14]
          

   (if
       then-action
       else-action)
          

   if (condition)
      then then-action
      else else-action
        

Two examples for determining the length of a list.

(This is provides an implementation for the length functions in both Scheme and Haskell.)

    (define mycount
       (lambda (lst)
           (mycount-kernel 0 lst)
    )  )
    (define mycount-kernel
       (lambda (count-so-far ls)
          (if (null? ls)
                count-so-far
                (mycount-kernel (+ 1 count-so-far) (cdr ls))
    )  )  )

  myCount lst = myCountKernel 0 lst

  myCountKernel countSoFar ls =
     if (ls == [ ])
        then countSoFar
        else myCountKernel (1 + countSoFar) (tail ls)

Problems for this Worksheet 1 with Haskell

This worksheet marks a transition in the course from working with functional problem solving with Scheme to functional problem solving with Haskell. Thus, this lab considers problem done previously in Scheme. For this lab,

• all code should be written in Haskell
• only if-then-else conditionals should be used as needed (never patterns or guards).
• except when otherwise stated, when using recursion, tail recursion is preferred, but do NOT consider defining local functions (one function defined within another).

1. Write a function to implement f(x) = x2 - 3x + 2, and evaluate the function for x = 0, 1, 2, 3, 4.

2. Define a procedure that computes the volume of a sphere, given its radius.

3. Define a procedure that, given the radius of a circle, returns its circumference and area on a list.

4. Write a function classify that has a number as a parameter and returns the appropriate string: "negative", "zero", or "positive".

5. Write a function byTwos that with two parameters (a starting and ending value) and returns a list of numbers beginning at the starting number and progressing in increments of 2 until the ending value is exceeded.

      byTwos  1 11 ===> [1, 3, 5, 7, 9, 11]
      byTwos  1 10 ===> [1, 3, 5, 7, 9]
      byTwos  2 9 ===> [2, 4, 6, 8]
      byTwos (-7) 7 ===> [-7, -5, -3, -1, 1, 3, 5, 7]
           

   Note: this can be done directly in Haskell, no need for recursion!

      classify -7 ===> "negative"
      classify 0  ===> "zero"
      classify 3.141592 ===> "positive"
       

6. Define Texas ranges for the following:

         [(-2) .. 5]
         [-1 .. 5]
         [(-1.3) .. 3.3]
         [2.5 .. 7.7]
         [2.5, 3 .. 6]
         [2.5, 3, 3.5 .. 6]
         [6 .. 2]
       

   In each case, indicate what result is obtained, and briefly explain why.

7. Explain what the following function does and explain why.

         niceList value = (take value (cycle [3, 1, 4, 1, 5]))
       

8. Consider the following function.

         niceList value = (take (5*value) (repeat value))
       

   1. Describe what this function does when given a numeric parameter, and explain why this result is returned.
   2. What happens if this function is given a string or a letter as its parameter, and explain briefly.

9. Write a function myRepeat with parameter value that returns a list with value copies of 1, 2, 3, ..., value

      myRepeat 1  ===> [1]
      myRepeat 3  ===> [1, 2, 3, 1, 2, 3, 1, 2, 3]
      myRepeat 0  ===> [ ]
         

10. Consider multiples of either 11 or 13.

    1. Using the idea of a list comprehension, write an expression that defines an infinite list of numbers that are multiples or 11 or 13.
    2. Using your your answer to part a, define a function multiples11Or13 which has an integer parameter num and returns a list of the first num multiples of 11 or 13.

         multiples11Or13  1 ===> [11]
         multiples11Or13  2 ===> [11, 13]
         multiples11Or13  5 ===> [11, 13, 22, 26, 33]
               

11. Write a function identifyConsonants that takes a string as parameter and returns a string of all uppercase and lowercase consonants.

            identifyConsonants "This is A TEsT" ===> "ThssTsT"
          

    Hint: Look at the examples in the reading on list comprehensions.

Extra Credit Problem

12. Computing a Polynomial

    A polynomial function has the form

    p(x) = a_nxⁿ + a_n-1x^n-1 + ... + a₂x² + a₁x + a₀

    Write a Haskell function computePoly that takes two parameters:

    • an x value, and
    • an list n+1 coefficients [a_n, a_n-1, ..., a₁, a₀].

    and returns the value of the polynomial p(x).

    Notes:

    • computePoly should make only one pass through the list of coefficients.
    • Both the number x and the elements of the list a should be real numbers.
    • The number x may be used in a multiplication operation no more than n times in the entire computation. (Thus, recomputing xⁱ from scratch for each of the n terms is not acceptable for this problem.)
    • Power functions often require many multiplication operations, so use of any power functions in this problem would violate the condition that no more than n multiplications are allowed in the entire solution to this problem. (To be specific, use of a power function in this program will yield an automatic score of 0 for this problem.)
    • As a hint, you may want to search for discussion of Horner's Rule either in a book on numerical analysis or on the Web.
    • Be sure that the list element a[n] is used as the coefficient of xⁿ (not the coefficient of x⁰).
    • Your write up will need to include testing for computePoly.
    • Be sure your testing covers an appropriate range of cases.

    ---

    created 8 February 2020 revised 10 February 2020
    For more information, please contact Henry M. Walker at walker@cs.grinnell.edu.