✎ fp:lab03 [books]

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====== 3. Recursive functions and tail-end recursion ======

===== 3.1. Pattern matching revisited =====

It is likely that in the above implementations you used ''head'' and ''tail'', or branch definitions combined with '_' to solve the exercises. Haskell supports a more elegant means of //value introspection//, called **pattern matching**. For instance, in:

<code haskell>
f [] = ...
f (h:t) = ...
</code> 

''(h:t)'' is a **pattern** which denotes a non-empty list where ''h'' is the first element and ''t'' is the rest of the list. In fact, ''[]'' is also a pattern denoting the empty lists. Patterns are **allways** surrounded by round parentheses. They can also be composite, as in the exercise below:

3.1.1. Write a function which returns the number of elements from a list. Use patterns.

3.1.2. Write a function which takes a list of integer lists, and concatenates them. (E.g. ''f [ [1,2,3],[4,5] ] = [1,2,3,4,5]'').

3.1.3 (!) Write the **same** function, this time using only the **cons** ('':'') operator as well as **patterns**. Hint:
<code haskell>
[[1,2,3],[4,5]] =
1:[[2,3],[4,5]] =
1:2:[[3],[4,5]] =
1:2:3:[[],[4,5]] =
1:2:3:[[4,5]] =
1:2:3:4:[[5]] = 
1:2:3:4:5:[[]] =
1:2:3:4:5:[]
</code>

3.1.4. Write a function which removes duplicates from a list of integers.

===== 3.2. Tail-end recursive functions =====

3.2.1 Solve exercise 3.1.3. using a tail-recursive function.

3.2.2. Solve exercise 3.1.4. using a tail-recursive function.

3.2.3. Return all duplicates from a list, using a tail-recursive function. E.g., the duplicates from list ''[1,2,3,4,2,4,2,1]'' are ''[2,4,2,1]''.

===== 3.3. Strings in Haskell =====

In Haskell, strings are implemented as **lists of type** ''Char''. For instance '''a' '' is a char 

3.3.1. Write a function which takes a list of words and makes the first letter of each word uppercase. (Hint: google a respective function of chars).

3.3.2. Write a function which takes a list of words and makes **all** letters uppercase.

3.3.3. (!) Write a function which takes a text and a pattern and returns the number of occurrences of the pattern in the text. 
Example:
<code haskell> 
search "I eat green apples" "eat" = 1
search "ababaab" "aba" = 2
</code>

3.3.4. (!) What does ''f'', defined in exercise 2.2.4., do (note that ''Matei'' and ''Mihai'' both start with letter 'M')? Write an implementation for ''f''.

3.3.5. Write the signature and implement the following function:
<code haskell>
   f ["Matei", "Mihai"] ["Popovici","Dumitru"] = [("Matei","Popovici"), ("Mihai","Dumitru")]
</code>

3.3.6. Implement the following function:
<code haskell>
   f ["Matei", "Mihai"] ["Popovici","Dumitru"] = ["MPopovici", "MDumitru"]
</code>

3.3.7. Write a function which takes a list of pairs - student-name and grade, removes those with grades less than 5, splits the name in substrings, and adds one bonus point to people with three names. Example:
<code haskell>
    f [("Dan Matei Popovici",9),("Mihai",4),("Andrei Alex",6)] =
    	[(["Dan", "Matei", "Popovici"],10),(["Andrei", "Alex"],6)]
</code>