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jonaprieto avatar jonaprieto commented on June 2, 2024

From the same source:

(* ------------------------------------------------------------------------- *)
(* Negation normal form.                                                     *)
(* ------------------------------------------------------------------------- *)

fun nnf fm = toFormula (fromFormula fm);

    case fm of
      Formula.True => True
    | Formula.False => False
    | Formula.Atom atm => Literal (Atom.freeVars atm, (true,atm))
    | Formula.Not p => negateFromFormula p
    | Formula.And (p,q) => And2 (fromFormula p, fromFormula q)
    | Formula.Or (p,q) => Or2 (fromFormula p, fromFormula q)
    | Formula.Imp (p,q) => Or2 (negateFromFormula p, fromFormula q)
    | Formula.Iff (p,q) => Xor2 (negateFromFormula p, fromFormula q)
    | Formula.Forall (v,p) => Forall1 (v, fromFormula p)
    | Formula.Exists (v,p) => Exists1 (v, fromFormula p)

and negateFromFormula fm =
    case fm of
      Formula.True => False
    | Formula.False => True
    | Formula.Atom atm => Literal (Atom.freeVars atm, (false,atm))
    | Formula.Not p => fromFormula p
    | Formula.And (p,q) => Or2 (negateFromFormula p, negateFromFormula q)
    | Formula.Or (p,q) => And2 (negateFromFormula p, negateFromFormula q)
    | Formula.Imp (p,q) => And2 (fromFormula p, negateFromFormula q)
    | Formula.Iff (p,q) => Xor2 (fromFormula p, fromFormula q)
    | Formula.Forall (v,p) => Exists1 (v, negateFromFormula p)
    | Formula.Exists (v,p) => Forall1 (v, negateFromFormula p);

from agda-metis.

jonaprieto avatar jonaprieto commented on June 2, 2024 
local
  fun normalize fm =
      let
        val p = polarity fm
        val fm = applyPolarity p fm
      in
        (freeVars fm, count fm, p, singleton fm)
      end;
in
  fun Xor2 (False,f2) = f2
    | Xor2 (f1,False) = f1
    | Xor2 (True,f2) = negate f2
    | Xor2 (f1,True) = negate f1
    | Xor2 (f1,f2) =
      let
        val (fv1,c1,p1,s1) = case f1 of Xor x => x | _ => normalize f1
        and (fv2,c2,p2,s2) = case f2 of Xor x => x | _ => normalize f2

        val s = Set.symmetricDifference s1 s2

        val fm =
            case Set.size s of
              0 => False
            | 1 => Set.pick s
            | n =>
              if n = Set.size s1 + Set.size s2 then
                Xor (NameSet.union fv1 fv2, countXor2 (c1,c2), true, s)
              else
                Xor (freeVarsSet s, countXorSet s, true, s)

        val p = p1 = p2
      in
        applyPolarity p fm
      end;
end;

where

fun polarity True = true
  | polarity False = false
  | polarity (Literal (_,(pol,_))) = not pol
  | polarity (And _) = true
  | polarity (Or _) = false
  | polarity (Xor (_,_,pol,_)) = pol
  | polarity (Exists _) = true
  | polarity (Forall _) = false;

and

fun applyPolarity true fm = fm
  | applyPolarity false fm = negate fm;

from agda-metis.

jonaprieto avatar jonaprieto commented on June 2, 2024 
 fun nameNormalize inf =
      case inf of
        Normalize.Axiom _ => "canonicalize"
      | Normalize.Definition _ => "canonicalize"
      | Normalize.Simplify _ => "simplify"
      | Normalize.Conjunct _ => "conjunct"
      | Normalize.Specialize _ => "specialize"
      | Normalize.Skolemize _ => "skolemize"
      | Normalize.Clausify _ => "clausify";

  fun ppNormalize mapping inf = Print.skip;

  fun nameProof inf =
      case inf of
        Proof.Axiom _ => "canonicalize"
      | Proof.Assume _ => "assume"
      | Proof.Subst _ => "subst"
      | Proof.Resolve _ => "resolve"
      | Proof.Refl _ => "refl"
      | Proof.Equality _ => "equality";

from agda-metis.

jonaprieto avatar jonaprieto commented on June 2, 2024

Closed by 43108f4

from agda-metis.

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