theorem-prover 0.1.1

Implementation of a theorem prover for first-order logic.
Documentation 
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use std::collections::HashSet;

use log::trace;

use crate::lang::{Formula, Term, Var};

use super::Environment;

pub fn remove_free_vars(formula: Formula) -> Formula {
    trace!("Removing free variables from {formula}");
    let mut free_vars = vec![];
    let mut env = Environment::new();
    find_free_vars(&formula, &mut env, &mut free_vars);
    remove_duplicate(free_vars)
        .iter()
        .rfold(formula, |acc, free_var| {
            Formula::Exists(free_var.clone(), Box::new(acc))
        })
}

fn find_free_vars(formula: &Formula, env: &mut Environment, free_vars: &mut Vec<Var>) {
    match formula {
        Formula::Pred(pred) => pred
            .get_args()
            .iter()
            .for_each(|arg| find_free_vars_in_terms(arg, env, free_vars)),
        Formula::True => {}
        Formula::False => {}
        Formula::And(left, right) => {
            find_free_vars(left, env, free_vars);
            find_free_vars(right, env, free_vars);
        }
        Formula::Or(left, right) => {
            find_free_vars(left, env, free_vars);
            find_free_vars(right, env, free_vars);
        }
        Formula::Neg(subformula) => {
            find_free_vars(subformula, env, free_vars);
        }
        Formula::Imply(left, right) => {
            find_free_vars(left, env, free_vars);
            find_free_vars(right, env, free_vars);
        }
        Formula::Iff(left, right) => {
            find_free_vars(left, env, free_vars);
            find_free_vars(right, env, free_vars);
        }
        Formula::Forall(var, subformula) => {
            env.push_scope();
            env.add(var.clone(), Term::Var(var.clone()));
            find_free_vars(subformula, env, free_vars);
            env.pop_scope();
        }
        Formula::Exists(var, subformula) => {
            env.push_scope();
            env.add(var.clone(), Term::Var(var.clone()));
            find_free_vars(subformula, env, free_vars);
            env.pop_scope();
        }
    }
}

fn find_free_vars_in_terms(term: &Term, env: &mut Environment, free_vars: &mut Vec<Var>) {
    match term {
        Term::Obj(_) => {}
        Term::Var(var) => {
            if let None = env.find(var) {
                free_vars.push(var.clone());
            }
        }
        Term::Fun(f) => f
            .get_args()
            .iter()
            .for_each(|arg| find_free_vars_in_terms(arg, env, free_vars)),
    }
}

fn remove_duplicate(vec: Vec<Var>) -> Vec<Var> {
    let mut new_vec = vec![];
    let mut set = HashSet::new();
    for x in vec {
        if !set.contains(&x) {
            new_vec.push(x.clone());
        }
        set.insert(x);
    }
    new_vec
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::{
        lang::{Pred, Term, Var},
        And, Exists, Forall, Imply, Neg, Pred, Var,
    };

    #[test]
    fn test_remove_free_vars_simple() {
        let formula = Forall!(
            "x",
            And!(
                Pred!("p", [Var!("x"), Var!("z")]),
                Exists!("y", Pred!("q", [Var!("y"), Var!("w")]))
            )
        ); // forall x. (p(x,z) /\ exists y. q(y,w))
        let expected_result = Exists!("z", Exists!("w", formula.clone()));
        assert_eq!(remove_free_vars(formula), expected_result);
    }

    #[test]
    fn test_remove_free_vars_1() {
        let formula = Imply!(
            Pred!("p", [Var!("x")]),
            Imply!(
                Exists!(
                    "x",
                    Imply!(Pred!("q", [Var!("x")]), Pred!("r", [Var!("x"), Var!("y")]))
                ),
                Pred!("q", [Var!("x")])
            )
        ); // p(x) -> (forall x. (q(x) -> r(x, y)) -> q(x))
        let result_formula = Exists!("x", Exists!("y", formula.clone()));
        assert_eq!(remove_free_vars(formula), result_formula);
    }

    #[test]
    fn test_remove_free_vars_2() {
        let formula = Forall!(
            "y",
            And!(
                Pred!("p", [Var!["y"]]),
                Neg!(Forall!(
                    "z",
                    Imply!(
                        Pred!("r", [Var!("z")]),
                        Pred!("q", [Var!("y"), Var!("z"), Var!("w")])
                    )
                ))
            )
        ); // forall y. (p(y) /\ ~(forall z. (r(z) -> q(y, z, w))))
        let result_formula = Exists!("w", formula.clone());
        assert_eq!(remove_free_vars(formula), result_formula);
    }
}