CIS 554 Haskell 1: Exercises
Fall 2012, David Matuszek

Purposes of this assignment

Details

How to read type declarations

In the Haskell REPL, :t thing will tell you the type of thing. Here are some examples:

Type Interpretation
not :: Bool -> Bool not is a function that, given a boolean value, returns a boolean value.
head :: [a] -> a head takes a list of some arbitrary type a, and returns a value of type a.
mod :: Integral a => a -> a -> a mod takes two values of type a, which must be an Integral type, and returns a value of type a.
map :: (a -> b) -> [a] -> [b] map takes a function from a to b, and a list of a, and returns a list of b.

Simple Haskell exercises

Write the following functions. Where built-in equivalents exist, do not define a function in terms of the equivalent built-in function. For example, don't say let member = elem. (You can use elem in other definitions, though.)

The following functions can all be defined in a single line, so try to do so. They do not need to work for infinite lists.

member :: Eq a => a -> [a] -> Bool
Returns true if the element occurs in the list.
count :: (Num a, Eq a1) => a1 -> [a1] -> a
Counts the number of times a value occurs in a list.
forall :: (a -> Bool) -> [a] -> Bool
Tests whether all elements of a list satisfy a given condition.
exists :: (a -> Bool) -> [a] -> Bool
Tests whether any element of a list satisfies a given condition.
single :: (a -> Bool) -> [a] -> Bool
Tests whether exactly one element of a list satisfies a given condition.
mostly :: (a -> Bool) -> [a] -> Bool
True if there are more elements in the list that satisfy the predicate than elements that fail to satisfy the predicate.
The following functions implement common set operations. At least some of them can be written as a single line. Except for isSet and makeSet, you may assume that the lists are "sets," that is, contain no duplicate elements.
isSet :: Eq a => [a] -> Bool
True if the list contains no duplicate elements
makeSet :: Eq a => [a] -> [a]
Remove duplicate elements from a list.
subset :: Eq a => [a] -> [a] -> Bool
True if every element in the first set also occurs in the second set.
equalSet :: Eq a => [a] -> [a] -> Bool
True if the two sets contain the same elements (not necessarily in the same order).
setDiff :: Eq a => [a] -> [a] -> [a]
The set of values that are in the first set but not in the second set.
setUnion :: Eq a => [a] -> [a] -> [a]
The set of values that are in either or both sets.
setIntersection :: Eq a => [a] -> [a] -> [a]
The set of values that are in both sets.

Testing

Provide tests for the above functions. Haskell does not come with a testing framework, and I would rather not ask you to download and install one, so here's a very small framework for you to use.

assertTrue :: Bool -> String -> IO ()
assertTrue x claim = if x
                       then putStrLn claim
                       else putStrLn $ "*** Untrue: " ++ claim   

assertFalse :: Bool -> String -> IO ()
assertFalse x claim = assertTrue (not x) claim  

assertEqual :: (Eq a, Show a) => a -> a -> IO ()
assertEqual x y = if x == y
                    then putStrLn $ (show x) ++ " equals " ++ (show y)
                    else putStrLn $ "*** " ++ (show x) ++ " does not equal " ++ (show y)
And here is a brief example of its use:
main = do
  assertTrue (member 3 [1, 2, 3, 4]) "3 is in the list [1, 2, 3, 4]"
  assertFalse (member 7 [1, 2, 3, 4]) "7 is not in the list [1, 2, 3, 4]"
  assertEqual 3 (count 'a' "abracadabra")

A small program

There are various measures of "readability"--how good a reader need to be in order to understand a passage of English text. These measures are based on the average length of words (usually measured in syllables) and the average length of sentences (measured in words). The result is usually given as the number of years a child has to have attended school (her grade level) in order to understand the text. These measures are crude, but better than nothing. Your assignment is to let the user read in a passage of text (from a file), apply the formulae, and print out the results.

Your program should read in a sample of text from a file, and use a variation of the Lix index to determine the readability of the text. It basically counts long sentences and big words. (I picked this one because it doesn't require counting syllables!) The formula to apply is:

words/sentences + 100 * (words >= 6 characters)/words

where:

The Haskell function words may be helpful. (There is also an unwords, which you should know about but probably won't need.) However, you will still have to remove punctuation marks from the ends of words in order to count how long they are.

Finally, don't get hung up on the details. The Lix measure isn't rocket science, and I won't care if your results are off by a few percent.

Due date

Your program is due before 6am Wednesday, October 17. Submit via Blackboard.