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use log::trace;
use crate::{lang::Formula, And, Neg, Or};
pub fn to_cnf(formula: Formula) -> Formula {
trace!("Converting {formula} to CNF");
let nnf = super::prenex_norm::to_nnf(formula);
let cnf = dist_or_over_and(nnf);
return cnf;
}
fn dist_or_over_and(formula: Formula) -> Formula {
match formula {
Formula::Pred(pred) => Formula::Pred(pred),
Formula::True => Formula::True,
Formula::False => Formula::False,
Formula::And(left, right) => And!(dist_or_over_and(*left), dist_or_over_and(*right)),
Formula::Or(left, right) => match (dist_or_over_and(*left), dist_or_over_and(*right)) {
(Formula::And(subleft, subright), right) => And!(
dist_or_over_and(Or!(*subleft, right.clone())),
dist_or_over_and(Or!(*subright, right))
),
(left, Formula::And(subleft, subright)) => And!(
dist_or_over_and(Or!(left.clone(), *subleft)),
dist_or_over_and(Or!(left, *subright))
),
(left, right) => Or!(left, right),
},
Formula::Neg(subformula) => Neg!(dist_or_over_and(*subformula)),
Formula::Imply(_, _) => unreachable!("After conversion to NNF, there shouldn't be ->"),
Formula::Iff(_, _) => unreachable!("After conversion to NNF, there shouldn't be <->"),
Formula::Forall(var, subformula) => {
Formula::Forall(var, Box::new(dist_or_over_and(*subformula)))
}
Formula::Exists(var, subformula) => {
Formula::Exists(var, Box::new(dist_or_over_and(*subformula)))
}
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::{
lang::{Fun, Obj, Pred, Term, Var},
And, Forall, Fun, Neg, Obj, Or, Pred, Var,
};
#[test]
fn test_to_cnf_1() {
let formula = Forall!(
"x",
Forall!(
"w",
Forall!(
"y",
Forall!(
"z",
Or!(
Pred!("p", [Var!("x")]),
And!(
And!(Pred!("p", [Var!("w")]), Pred!("p", [Var!("y")])),
Pred!("p", [Var!("z")])
)
)
)
)
)
); // forall x. forall w. forall y. forall z. (p(x) \/ ((p(w) /\ p(y)) /\ p(z)))
let result_formula = Forall!(
"x",
Forall!(
"w",
Forall!(
"y",
Forall!(
"z",
And!(
And!(
Or!(Pred!("p", [Var!("x")]), Pred!("p", [Var!("w")])),
Or!(Pred!("p", [Var!("x")]), Pred!("p", [Var!("y")]))
),
Or!(Pred!("p", [Var!("x")]), Pred!("p", [Var!("z")]))
)
)
)
)
); // forall x. forall w. forall y. forall z. (((p(x) \/ p(w)) /\ (p(x) \/ p(y))) /\ (p(x) \/ p(z)))
assert_eq!(to_cnf(formula), result_formula);
}
#[test]
fn test_to_cnf_2() {
let formula = Forall!(
"x",
Or!(
And!(Neg!(Pred!("p", [Var!("x")])), Pred!("q", [Var!("x")])),
And!(Neg!(Pred!("r", [Var!("x")])), Pred!("r", [Var!("x")]))
)
); // forall x. ((~p(x) /\ q(x)) \/ (~r(x) /\ r(x)))
let result_formula = Forall!(
"x",
And!(
And!(
Or!(Neg!(Pred!("p", [Var!("x")])), Neg!(Pred!("r", [Var!("x")]))),
Or!(Neg!(Pred!("p", [Var!("x")])), Pred!("r", [Var!("x")]))
),
And!(
Or!(Pred!("q", [Var!("x")]), Neg!(Pred!("r", [Var!("x")]))),
Or!(Pred!("q", [Var!("x")]), Pred!("r", [Var!("x")]))
)
)
); // forall x. (((~p(x) \/ ~r(x)) /\ (~p(x) \/ r(x))) /\ ((q(x) \/ ~r(x)) /\ (q(x) \/ r(x))))
assert_eq!(to_cnf(formula), result_formula);
}
#[test]
fn test_to_cnf_3() {
let formula = Forall!(
"z",
Forall!(
"x",
And!(
Or!(
Neg!(Pred!("p", [Var!("z"), Obj!("a")])),
Or!(
Neg!(Pred!("p", [Var!("z"), Var!("x")])),
Neg!(Pred!("p", [Var!("x"), Var!("z")]))
)
),
Or!(
Pred!("p", [Var!("z"), Obj!("a")]),
And!(
Pred!("p", [Var!("z"), Fun!("f", [Var!("z")])]),
Pred!("p", [Fun!("f", [Var!("z")]), Var!("z")])
)
)
)
)
);
// forall z. forall x.((
// (~p(z, a) \/ (~p(z, x) \/ ~p(x, z)))
// /\ (p(z, a) \/ (p(z, f(z)) /\ p(f(z), z)))
// ))
let result_formula = Forall!(
"z",
Forall!(
"x",
And!(
Or!(
Neg!(Pred!("p", [Var!("z"), Obj!("a")])),
Or!(
Neg!(Pred!("p", [Var!("z"), Var!("x")])),
Neg!(Pred!("p", [Var!("x"), Var!("z")]))
)
),
And!(
Or!(
Pred!("p", [Var!("z"), Obj!("a")]),
Pred!("p", [Var!("z"), Fun!("f", [Var!("z")])])
),
Or!(
Pred!("p", [Var!("z"), Obj!("a")]),
Pred!("p", [Fun!("f", [Var!("z")]), Var!("z")])
)
)
)
)
);
// forall z.(forall x.(
// (~p(z, a) \/ ~p(z, x) \/ ~p(x, z))
// /\ (p(z, a) \/ p(z, f(z)))
// /\ (p(z, a) \/ p(f(z), z))
// ))
assert_eq!(to_cnf(formula), result_formula);
}
}