On Wed, 12 Oct 2011 17:38:51 +0200, Alexander Raasch
Hi,
I wrote this program to work with formulas in propositional logic:
data Formula = | Variable Char | Not Formula | And Formula Formula | Or Formula Formula | Imply Formula Formula | Equivalent Formula Formula deriving (Eq)
It would be better to have Formula only include a few basic primitives (And, Or and Not is a popular choice), and define the rest in terms of those. More on that in the answer to your second question.
instance Show Formula where show (Variable v) = [v] show (Not f) = "~" ++ show f show (And f g) = "(" ++ show f ++ " & " ++ show g ++ ")" show (Or f g) = "(" ++ show f ++ " v " ++ show g ++ ")" show (Imply f g ) = "(" ++ show f ++ " -> " ++ show g ++ ")" show (Equivalent f g ) = "(" ++ show f ++ " <-> " ++ show g ++ ")"
To make a formula you can do something like:
ghci> let f = Or (Variable 'C') (And (Variable 'A') (Not (Variable 'C'))) ghci> f (C v (A & ~C))
So, my questions are:
1. Do you think this is an elegant solution or would you define custom operators (or, and, ->, <->) instead? Or something completely different?
You can still define such operators afterwards, and I think it would make formulas easier to read and write, for example: (<&&>) :: Formula -> Formula a <&&> b = And a b
2. If I pack this code into a module how would add a new logic connective like xor or nand to Formula? Meaning, can I add another type constructor to it?
If you chose a set of "primitives" capable of expressing every other formula, you can define xor, nand, etc. later as normal functions: nand :: Formula -> Formula -> Formula nand a b = Not (And a b)
3. Is there a way to "nest" data definitions, e.g. I would like to replace the 'Variable Char' type constructor by 'Literal Char', whereas a Literal is either a Variable or a negated Variable. Literals can be negated, too.
The parameters to constructors are not limited to built-in types and the type you are defining. So for your example, something like this would work: data Literal = Variable Char | NegVar Char data Formula = Literal | And ....... That would of course introduce some redundancy, since `Not (Variable c)' and `NegVar c' would represent the same formula. Cheers, Daniel