====== 7. Haskell type-classes ======

1. Enroll the type ''Extended'' shown below, in class ''Eq'':
<code haskell>
data Extended = Infinity | Value Integer 
</code>

2. Enroll the type ''Formula a'' in class ''Eq'':
<code haskell>
data Formula a = Atom a |
                 Or (Formula a) (Formula a) |
                 And (Formula a) (Formula a) |
                 Not (Formula a)
</code>

3. Enroll the type ''Set a'', defined below, in class ''Num''. Implement operation ''(+)'' as set reunion and ''(*)'' as set intersection.
Implement also ''fromInteger'' which takes an integer x and returns the set ''{x}''.
<code haskell>
data Set a = F (a->Bool)
</code>

4. In the last lab, we have worked with the following datatypes and functions:
<code haskell>
data PExpr = Val Integer |
             Var String  |
             PExpr :+: PExpr 
             
eval_pexpr :: Dict -> PExpr -> Integer

data BExpr = PExpr :==: PExpr | 
            PExpr :<: PExpr |
            Not BExpr |
            BExpr :&&: BExpr 
            
eval_bexpr :: Dict -> BExpr -> Bool

data Prog = PlusPlus Var |       
            Var :=: PExpr |     
            DeclareInt Var |     
            Begin Prog Prog |     
            While BExpr Prog |     
            If BExpr Prog Prog      
      
eval :: Dict -> Prog -> Dict                         
</code>
We have three different datatypes and three evaluation methods, one for each type. 
  * The first type models arithmetic expressions and it's evaluation produces an integer
  * The second type models boolean expressions (comparisons) and evaluates to a boolean
  * The third type models programs and evaluates to a dictionary, holding the final values for each variable

Design a class called ''Eval'' which contains a unique ''eval'' method. How should the class parameters be?

Enrol types ''PExpr'', ''BExpr'' and ''Prog'' in this class, thus eliminating the need for multiple evaluation function names.