Take a proposition and find all the variables it contains.

tautologies.hs

-- given a proposition, return a list with all the variables that show up
collectVars :: Prop -> [String]
collectVars (Const  _   ) = []
collectVars (Var    s   ) = [s]
collectVars (Neg    prop) = nub $ collectVars prop
-- these four patterns are rather annoying
collectVars (And    p1 p2) = nub $ (collectVars p1) ++ (collectVars p2)
collectVars (Or     p1 p2) = nub $ (collectVars p1) ++ (collectVars p2)
collectVars (Equiv  p1 p2) = nub $ (collectVars p1) ++ (collectVars p2)
collectVars (Impl   p1 p2) = nub $ (collectVars p1) ++ (collectVars p2)