This document contains the first hand-in assignment ("lab") for the course. It's a small one just to get the ball rolling. See the course home page for the deadline (it is soon!).
We suggest that you find a lab partner and work together in pairs. (When you are done, please submit your solution using the Fire system.)
Please note that lab assignment 2 and onwards must be submitted by groups of exactly two people.
Lab assignment 1: the power function
In this lab assignment, you will implement the well-known "power" function in two different new ways. The power function takes two arguments n and k and computes nk. Your implementation only has to work for non-negative k.
You have possibly seen one implementation of this function in the lecture. If not here it is:
You will implement two more ways in this lab assignment.power :: Integer -> Integer -> Integer power n k | k < 0 = error "power: negative argument" power n 0 = 1 power n k = n * power n (k-1)
Part 1In order to calculate
powern k, for a given n and k, how many computing "steps" are being used?
0takes 1 step.
1takes 1 step, and then uses
2takes 1 step, and then uses
3takes 1 step, and then uses
- And so forth.
Part 2A different way of computing the power function is to use the standard Haskell function
product, which calculates the product (multiplication) of all elements in a list.
power n k, first construct
a list with k elements, all being n,
and then use
Implement this idea as a Haskell function
You have to come up with a way of producing a list with k
elements, all being equal to n.
Use a list comprehension, or use the standard
If you use
replicate, you might want to
use the function
Use Hoogle to find out more about
standard functions (and also to search for standard functions by their type).
Part 3A different approach to calculating the power function uses fewer computing steps.
We use the fact that, if k is even, we can calculate nk as follows:
nk = (n2)k/2 (k is even)In other words:
nk = (n * n)k/2 (k is even)So, instead of recursively using the case for k-1, we use the (much smaller) case for k/2.
If k is not even, we simply go one step down in order to arrive at an even k, just as in the original definition of power:
nk = n * (nk-1) (k is not even)
To sum up, to calculate
power n k:
- If k is even, we use (n * n)k/2
- If k is odd, we use n*(nk-1)
- Do not forget to add a base case (what do you do when k=0?)
- You need to find out when numbers are even or odd. Use the standard Haskell
- To divide integer numbers, use the function
div(and not the function
/, which is used to divide floating point and rational numbers)
Part 4We would like the three functions
power2to calculate the same thing. It is probably a good idea to test this!
A. Come up with a number of test cases (inputs you will test your functions on). Argue why you have chosen these test cases. (Think about for what inputs the functions are defined, and for what inputs the functions are not defined.)
B. Implement a function
prop_powers which given n
and k checks that
power n k,
power1 n k, and
power2 n k
all give the same answer.
C. Write all the test cases you suggested in part A as a Haskell function that performs all test cases. It is probably a good idea to use the function that you defined in part B.
Hint: You can use a list comprehension to combine all possible cases
you would like to test for n and k. Use the standard Haskell function
combine the results. If you are not familiar with list
comprehensions, you do not have to use these.
Try running quickcheck on the function
It will probably fail. If so, define a new version,
for which quickcheck succeeds.
The new version should of course still test the intended property!
Submission GuidelinesSee the course home page for lab deadlines.
Write your answers in one file, called Lab1.hs. For each part, use Haskell comments to indicate what part of the file contains the answer to that part. For answers in natural language, use English; write your answers also in Haskell comments.
Before you submit your code, Clean It Up! Remember, submitting clean code is Really Important, and simply the polite thing to do. After you feel you are done, spend some time on cleaning your code; make it simpler, remove unneccessary things, etc. We will reject your solution if it is not clean. Clean code:
- Does not have long lines (< 78 characters)
- Has a consistent layout
- Has type signatures for all top-level functions
- Has good comments
- Has no junk (junk is unused code, commented code, unneccessary comments)
- Has no overly complicated function definitions
- Does not contain any repetitive code (copy-and-paste programming)
To the Fire System