====== 2. Pattern matching and basic types in Haskell ======

===== 2.1. Pattern matching =====

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:

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

2.1.2. 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]'').

2.1.3 (!) Write the **same** function, this time using only the **cons** ('':'') operator as well as **patterns**. 

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

===== 2.2. Types in Haskell =====

2.2.1. What are the types of ''x,y,z,w'' and that of ''l'' in the implementation below?
<code haskell>
f (x:y:z:w:l) = w
f _ = 0
</code>

How about:
<code haskell>
f (x:y:z:w:l) = w
</code>
What is the difference?
    
2.2.2. What is the type of the function:
<code haskell>
f x y = (x,y)
</code>

In the body of a function definition, '','' is a **base constructor** for pairs. The following are pairs: ''(1,2), ("Matei",20), ([1,2],3)''. Note that there is no restriction on the type of the first and second values of a pair. 

2.2.3. What is the type of the function:
<code haskell>
f 'a' _ = []
f x y = x:y
</code>

In Haskell, the type ''String'' is equivalent to ''[Char]'' (hence strings are lists of chars). Strings can be introspected using patterns just like any other list.

2.2.4. Let f be the function below:
<code haskell>
    f "321CB" [("321CB", ["Matei", "Andrei", "Mihai"]), ("322CB",["George", "Matei"])] = ["Matei", "Mihai"]
</code>

What is the signature of ''f''?


===== 2.3. Strings in Haskell =====

2.3.1. Write a function which takes a list of words and makes the first letter of each word uppercase.

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

2.3.3. (!) 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>

2.3.4. (!) 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''.

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

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

2.3.7. 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>