Types Lab 2

gistfile1.txt

{- 1. write an ADT which encodes arithmetic expressions containing +, * or parentheses -}
data Expr a =

{-- 2. display an expression nicely --}
instance Show a => Show (Expr a) where

{- 3. write a function which evaluates an expression. Also, write it's type -}

{- 4. Write a function which eliminates parentheses from an expression.
    e * (3) = e * 3
    (3) * e = e * (3)
    e * (e' + e'') = e * e' + e * e''
    (e' + e'') * e = e * (e' + e'')
    e * (e' * e'') = e * e' * e''
    (e' * e'') * e = e * (e' * e'')
    e + (e') = e + e' 
    (e') + e = e + (e')
-}

{- 5. Define a mini-programming language working with Numerics.
   The programming language has the following construct:
   x = e (assignment)
   if e then e' else e'' (conditional. Can only be an expression 0 evaluates to false, everything else evaluates to true)
   e ; e' (sequence)
   return x (x can only be a variable)
 -}

{- 6. display a program nicely -}

{- 7. define a function whose name must also be eval, which can evaluate a program -}