Hello. I am new to typefull programming, so I've got a question. I have a simple mathematical expression (addition, product and exponentiation only):
data Expr = I Int -- integer constant | V -- symbolic variable | Sum [Expr] | Prod [Expr] | Pow Expr Expr
What I want is normalize\simplify this expression. Eg `Prod [Pow V (I 0), Pow V (I 1)] ` must be simplified to just `V`. What techniques should I use to write `normalize` function? Simplification rules are quite simple:
normalize (Sum [a]) = normalize a normalize (Sum xs) | (I 0) `elem` xs = map nomalize . Sum $ filter (/= I 0) xs | otherwise = map normalize xs normalize (Prod xs) | (I 0) `elem` xs = I 0 normalize (Prod xs) | (I 1) `elem` xs = map nomalize . Prod $ filter (/= I 1) xs | otherwise = map normalize xs normalize (Pow a (I 0)) = I 1 normalize (Pow a (I 1)) = normalize a
and so on. But rules like theese cannot simplify some expressions, for example, `Prod [Pow V (I 0), Pow V (I 1)] `.