Introduction to Functional Programming
|DAY: October 17, 2011||TIME: 8:30 -- 12:30||PLACE: M-salar|
Koen Lindström Claessen, Datavetenskap|
An English (or English-Swedish, or English-X) dictionary
Completing Part I gives a 3 or a G;
(5 small assignments)
(2 larger assignments)
|Please read the following guidelines carefully:|
You have to complete 4 out of the following 5 assignments to get a pass on the exam.
1. Implement a function
removeIndex :: Int -> [a] -> [a]
that given an index i and a list xs, removes the element that is at index i. We start counting positions at 0.
Main> removeIndex 3 "bepacepa" "bepcepa" Main> removeIndex 0 [2,3,17,4] [3,17,4]
The function may assume that the list contains enough elements for the index i to be removed. (So, you may do whatever you want if the index i is too small or too large.)
2. Implement a function
emails :: String -> [String]
that given a text (as a string), returns a list with all e-mail addresses in that text. An e-mail address is a word with exactly one occurrence of the @-sign.
Main> emails "firstname.lastname@example.org and email@example.com are my friends" ["firstname.lastname@example.org", "email@example.com"] Main> emails "koen@chalmers@se is not right, mister firstname.lastname@example.org" ["email@example.com"]
3. Consider the following recursive datatype, used to represent arithmetic expressions with variables (denoted as X).
data Expr = Num Int | Add Expr Expr | X
Now, implement a function
numVars :: Expr -> Int
that counts the number of variable occurrences in the tree.
Main> numVars (Num 3) 0 Main> numVars X 1 Main> numVars (Add X (Add (Num 13) X)) 2
4. Anna is writing a QuickCheck property involving the functions reverse and ++. She has written:
prop_Reverse_Append :: [Int] -> [Int] -> Bool prop_Reverse_Append xs ys = reverse (xs ++ ys) == ...
But then she got stuck.
Can you help Anna by giving a Haskell expression you can write instead of the ... which makes the property correct? (It should be something different than the left-hand side of course.)
5. Write a function
palindrome :: IO ()
which asks the user to type in a word, and then says if that word is a palindrome or not. (A palindrome is a word that is spelled the same, regardless of reading it forwards or backwards. Examples of palindromes are "rotator" and "level"; reading them backwards yield the same word again.)
Main> palindrome Type in a word> racecar racecar is a palindrome! Main> palindrome Type in a word> haskell haskell is not a palindrome! Main> palindrome Type in a word> apa apa is a palindrome!
Do not work on this part if you only want to get a 3 or a G!
If you want to get a 4, you have to do Part I, plus one of the following assignments.
If you want to get a 5 or a VG, you have to do Part I, plus both of the following assignments.
6. In this assignment, you will implement a text processing function called fill that fills paragraphs of text. Your function will take two arguments: (1) an integer indicating the line width of the text, and (2) a list of words. It should then produce a list of lines (the text) containing all the words in the right order, but not exceeding the specified line width.
The type of the function is thus:
fill :: Int -> [String] -> [String] -- width words lines
Here are two examples of its use, demonstrating the effect of line widths 35 and 50 on the same text (taken from the Wikipedia entry on cats):
Main> do s <- readFile "wp_cats.txt"; putStr (unlines (fill 35 (words s))) The cat (Felis catus), also known as the domestic cat or housecat to distinguish it from other felids and felines, is a small, usually furry, domesticated, carnivorous mammal that is valued by humans for its companionship and for its ability to hunt vermin and household pests. Main> do s <- readFile "wp_cats.txt"; putStr (unlines (fill 50 (words s))) The cat (Felis catus), also known as the domestic cat or housecat to distinguish it from other felids and felines, is a small, usually furry, domesticated, carnivorous mammal that is valued by humans for its companionship and for its ability to hunt vermin and household pests.Hint:
7. The HyperText Markup Language, better known as HTML, is a language for describing documents. All webpages are written using HTML.
Documents written in HTML have a structure that is determined by the use of tags. We can enclose a certain part of our document within certain tags, in order to indicate this structure. To enclose a part of a document in tags, we use matching open tags and close tags. For example:(In reality, tags contain more information than just the tag name (such as B, EM, P, etc.), but for simplicity we do not deal with that here.)
Here is an example of HTML code:
Welcome to my website!<P><B>My hobbies are <EM>Haskell</EM> programming and playing <EM>Myst</EM>.</B></P><P>Thanks for visiting! <EM>firstname.lastname@example.org</EM></P>And here is what it would look like in a browser:
Welcome to my website!We can represent HTML documents in Haskell in the following way. First, we realize that a document consists of a bunch of document parts.
My hobbies are Haskell programming and playing Myst.
Thanks for visiting! email@example.com
type Doc = [DocPart]
There are two kinds of document parts: (1) A piece of text, (2) A whole document enclosed in a certain kind of tag.
data DocPart = Text String | Tag String Doc
The example piece of HTML above can be represented by the following Haskell expression:
annasSida :: Doc annasSida = [ Text "Welcome to my website!" , Tag "P" [ Tag "B" [ Text "My hobbies are " , Tag "EM" [ Text "Haskell" ] , Text " programming and playing " , Tag "EM" [ Text "Myst" ] , Text "." ] ] , Tag "P" [ Text "Thanks for visiting! " , Tag "EM" [ Text "firstname.lastname@example.org" ] ] ]Sometimes, a web site looks strange in a certain browser, but fine in another browser. This is because not all browsers understand all tags in the same way. Sometimes a browser gets so confused by a certain tag, that it is better just to remove that tag from a document completely. When doing this, one should not also remove the part of the document that is enclosed within these tags.
Define a function:
removeTag :: String -> Doc -> Docthat removes the given tag from a given document, but keeps the information enclosed in those tags.
Main> showDoc (removeTag "B" (removeTag "EM" annasSida)) "Welcome to my website!<P>My hobbies are Haskell programming and playing Myst.</P><P>Thanks for visiting! email@example.com</P>"
(In the above example, we use the function:
showDoc :: Doc -> Stringthat produces a String containing the actual HTML code of the given document. For example, if the argument to showDoc is annasSida, then the result should be the HTML code as a String shown earlier. So, you do not have to implement showDoc.)