Symbolic simplification in Haskell (using recursion?)

Question

How can I give a general rule that includes all the expressions below? E.g one expression, another one for sub and one for mult. I need to use recursion but i got confused..

Answer 1

The recursion comes in when you need to deal with nested expressions. For instance, how do you simply (Plus (Plus 2 3) (Plus 4 5))?

One approach is to break it into two functions. Move the one level logic (which you show above) into its own function. The main simplify function might have a rule similar to the following for Plus:

simplify (Plus x y) = simplify_one_level (Plus (simplify x) (simplify y))