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...
Luke
On 11/1/07, Jim Burton
I am trying to rewrite sentences in a logical language into DNF, and wonder if someone would point out where I'm going wrong. My dim understanding of it is that I need to move And and Not inwards and Or out, but the function below fails, for example:
dnf (Or (And A B) (Or (And C D) E)) And (Or A (And (Or C E) (Or D E))) (Or B (And (Or C E) (Or D E)))
data LS = Var | Not LS | And LS LS | Or LS LS --convert sentences to DNF dnf :: LS -> LS dnf (And (Or s1 s2) s3) = Or (And (dnf s1) (dnf s3)) (And (dnf s2) (dnf s3)) dnf (And s1 (Or s2 s3)) = Or (And (dnf s1) (dnf s2)) (And (dnf s1) (dnf s3)) dnf (And s1 s2) = And (dnf s1) (dnf s2) dnf (Or s1 s2) = Or (dnf s1) (dnf s2) dnf (Not (Not d)) = dnf d dnf (Not (And s1 s2)) = Or (Not (dnf s1)) (Not (dnf s2)) dnf (Not (Or s1 s2)) = And (Not (dnf s1)) (Not (dnf s2)) dnf s = s
Thanks,
Jim
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