anthem 2.0.0

A command-line application for assisting in the verification of answer set programs
Documentation 
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use crate::{
    syntax_tree::{asp::mini_gringo as asp, fol::sigma_0 as fol},
    translating::formula_representation::{natural, tau_star},
};

pub trait Mu {
    type Output;

    fn mu(self) -> Self::Output;
}

impl Mu for asp::Program {
    type Output = fol::Theory;

    fn mu(self) -> Self::Output {
        let mut formulas: Vec<fol::Formula> = vec![];
        let globals = tau_star::choose_fresh_global_variables(&self);

        for r in self.rules {
            match natural::natural_rule(&r) {
                Some(f) => formulas.push(f),
                None => formulas.push(tau_star::tau_star_rule(&r, &globals)),
            }
        }

        fol::Theory { formulas }
    }
}

#[cfg(test)]
mod tests {
    use {
        super::Mu as _,
        crate::syntax_tree::{asp::mini_gringo as asp, fol::sigma_0 as fol},
    };

    #[test]
    fn test_mu() {
        for (source, target) in [
            (
                "p(X) :- q(X). q(4/2).",
                "forall X (q(X) -> p(X)). forall V1 (exists I$i J$i Q$i R$i (I$i = J$i * Q$i + R$i and (I$i = 4 and J$i = 2) and (J$i != 0 and R$i >= 0 and R$i < J$i) and V1 = Q$i) and #true -> q(V1)).",
            ),
            (
                "p(X) :- q(1..5), a(X). q(1..3) :- p(X).",
                "forall V1 X (V1 = X and (exists Z (exists I$i J$i K$i (I$i = 1 and J$i = 5 and Z = K$i and I$i <= K$i <= J$i) and q(Z)) and exists Z (Z = X and a(Z))) -> p(V1)).\nforall X (p(X) -> forall N0$i (1 <= N0$i <= 3 -> q(N0$i))).",
            ),
        ] {
            let program = source.parse::<asp::Program>().unwrap();
            let mu: fol::Theory = program.mu();
            let mu_string = mu.to_string();
            let target_theory: fol::Theory = target.parse().unwrap();
            let target = target_theory.to_string();
            assert_eq!(
                mu, target_theory,
                "assertion `mu(source) == target` failed:\n mu:\n{mu_string:?}\n target:\n{target:?}",
            );
        }
    }
}