Hey folks,
On Nov 1, 2007 6:41 PM, Luke Palmer
A good way to approach this is data-structure-driven programming. You want a data structure which represents, and can _only_ represent, propositions in DNF. So:
data Term = Pos Var | Neg Var type Conj = [Term] type DNF = [Conj]
Then write:
dnf :: LS -> DNF
The inductive definition of dnf is straightforward given this output type...
Jim, if you don't want to see an attempt at a solution, don't read further. I'm learning too and found this an interesting problem. Luke, is this similar to what you meant? data LS = Var String | Not LS | And LS LS | Or LS LS deriving Show data Term = Pos String | Neg String deriving Show type Conj = [Term] type DNF = [Conj] dnf :: LS -> DNF dnf (Var s) = [[Pos s]] dnf (Or l1 l2) = (dnf l1) ++ (dnf l2) dnf (And l1 l2) = [t1 ++ t2 | t1 <- dnf l1, t2 <- dnf l2] dnf (Not (Not d)) = dnf d dnf (Not (And l1 l2)) = (dnf $ Not l1) ++ (dnf $ Not l2) dnf (Not (Or l1 l2)) = [t1 ++ t2 | t1 <- dnf $ Not l1, t2 <- dnf $ Not l2] dnf (Not (Var s)) = [[Neg s]] -- test cases x = (Or (And (Var "A") (Var "B")) (Or (And (Not $ Var "C") (Var "D")) (Var "E"))) y = (Not (And (Var "A") (Var "B"))) z = (Not (And (Not y) y)) Also, is it correct? cheers, Arnar