Grcov report - boolean.rs

1

use conjure_cp::essence_expr;

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3

use conjure_cp::ast::Metadata;

4

use conjure_cp::ast::{Atom, CnfClause, Expression as Expr, Literal, Moo};

5

use conjure_cp::rule_engine::{

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    ApplicationError::RuleNotApplicable, ApplicationResult, Reduction, register_rule,

7

};

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use conjure_cp::ast::AbstractLiteral::Matrix;

10

use conjure_cp::ast::{Domain, SymbolTable};

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use crate::utils::is_literal;

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fn create_bool_aux(symbols: &mut SymbolTable) -> Expr {

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    let name = symbols.gensym(&Domain::bool());

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    symbols.insert(name.clone());

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    Expr::Atomic(

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        Metadata::new(),

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        Atom::Reference(conjure_cp::ast::Reference::new(name)),

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fn create_clause(exprs: Vec<Expr>) -> Option<CnfClause> {

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    let mut new_terms = vec![];

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    for expr in exprs {

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        if let Expr::Atomic(_, Atom::Literal(Literal::Bool(x))) = expr {

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            // true ~~> entire or is true

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            // false ~~> remove false from the or

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            if x {

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                return None;

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34

        } else if let Expr::Not(_, ref inner) = expr {

35

            if let Expr::Atomic(_, Atom::Literal(Literal::Bool(x))) = inner.as_ref() {

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                // check for nested literal

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                if !x {

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                    return None;

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            } else {

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                new_terms.push(expr);

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43

        } else {

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            new_terms.push(expr);

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    Some(CnfClause::new(new_terms))

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// TODO: Optimize all logic operators for constants

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// TODO: If a clause simplifies to false, it should skip the solver and give no solutions

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/// Applies the Tseytin and transformation to series of variables, returns the new expression, symbol table and clauses

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pub fn tseytin_and(

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    exprs: &Vec<Expr>,

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    clauses: &mut Vec<CnfClause>,

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    symbols: &mut SymbolTable,

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) -> Expr {

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    let new_expr = create_bool_aux(symbols);

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    let mut full_conj: Vec<Expr> = vec![new_expr.clone()];

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    for x in exprs {

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        clauses.extend(create_clause(vec![

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            Expr::Not(Metadata::new(), Moo::new(new_expr.clone())),

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            x.clone(),

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        ]));

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        full_conj.push(Expr::Not(Metadata::new(), Moo::new(x.clone())));

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    clauses.extend(create_clause(full_conj));

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    new_expr

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/// Applies the Tseytin not transformation to a variable, returns the new expression, symbol table and clauses

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pub fn tseytin_not(x: Expr, clauses: &mut Vec<CnfClause>, symbols: &mut SymbolTable) -> Expr {

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    let new_expr = create_bool_aux(symbols);

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    clauses.extend(create_clause(vec![

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        Expr::Not(Metadata::new(), Moo::new(x.clone())),

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        Expr::Not(Metadata::new(), Moo::new(new_expr.clone())),

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    ]));

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    clauses.extend(create_clause(vec![x, new_expr.clone()]));

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    new_expr

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/// Applies the Tseytin or transformation to series of variables, returns the new expression, symbol table and clauses

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pub fn tseytin_or(

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    exprs: &Vec<Expr>,

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    clauses: &mut Vec<CnfClause>,

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    symbols: &mut SymbolTable,

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) -> Expr {

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    let new_expr = create_bool_aux(symbols);

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    let mut full_conj: Vec<Expr> = vec![Expr::Not(Metadata::new(), Moo::new(new_expr.clone()))];

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    for x in exprs {

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        clauses.extend(create_clause(vec![

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            Expr::Not(Metadata::new(), Moo::new(x.clone())),

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            new_expr.clone(),

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        ]));

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        full_conj.push(x.clone());

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    clauses.extend(create_clause(full_conj));

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    new_expr

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/// Applies the Tseytin iff transformation to two variables, returns the new expression, symbol table and clauses

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pub fn tseytin_iff(

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    x: Expr,

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    y: Expr,

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    clauses: &mut Vec<CnfClause>,

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    symbols: &mut SymbolTable,

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) -> Expr {

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    let new_expr = create_bool_aux(symbols);

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    clauses.extend(create_clause(vec![

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        Expr::Not(Metadata::new(), Moo::new(x.clone())),

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        Expr::Not(Metadata::new(), Moo::new(y.clone())),

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        new_expr.clone(),

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    ]));

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    clauses.extend(create_clause(vec![x.clone(), y.clone(), new_expr.clone()]));

127

    clauses.extend(create_clause(vec![

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        x.clone(),

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        Expr::Not(Metadata::new(), Moo::new(y.clone())),

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        Expr::Not(Metadata::new(), Moo::new(new_expr.clone())),

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    ]));

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    clauses.extend(create_clause(vec![

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        Expr::Not(Metadata::new(), Moo::new(x)),

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y,

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        Expr::Not(Metadata::new(), Moo::new(new_expr.clone())),

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    ]));

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    new_expr

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/// Applies the Tseytin imply transformation to two variables, returns the new expression, symbol table and clauses

142

pub fn tseytin_imply(

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    x: Expr,

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    y: Expr,

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    clauses: &mut Vec<CnfClause>,

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    symbols: &mut SymbolTable,

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) -> Expr {

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    let new_expr = create_bool_aux(symbols);

149

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    clauses.extend(create_clause(vec![

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        Expr::Not(Metadata::new(), Moo::new(new_expr.clone())),

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        Expr::Not(Metadata::new(), Moo::new(x.clone())),

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        y.clone(),

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    ]));

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    clauses.extend(create_clause(vec![new_expr.clone(), x]));

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    clauses.extend(create_clause(vec![

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        new_expr.clone(),

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        Expr::Not(Metadata::new(), Moo::new(y)),

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    ]));

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    new_expr

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/// Applies the Tseytin multiplex transformation

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/// cond ? b : a

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///

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/// cond = 1 => b

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/// cond = 0 => a

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#[allow(dead_code)]

170

pub fn tseytin_mux(

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    cond: Expr,

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    a: Expr,

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    b: Expr,

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    clauses: &mut Vec<CnfClause>,

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    symbols: &mut SymbolTable,

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) -> Expr {

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    let new_expr = create_bool_aux(symbols);

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    clauses.extend(create_clause(vec![

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        Expr::Not(Metadata::new(), Moo::new(new_expr.clone())),

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        cond.clone(),

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        a.clone(),

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    ]));

184

    clauses.extend(create_clause(vec![

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        Expr::Not(Metadata::new(), Moo::new(new_expr.clone())),

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        Expr::Not(Metadata::new(), Moo::new(cond.clone())),

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        b.clone(),

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    ]));

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    clauses.extend(create_clause(vec![

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        Expr::Not(Metadata::new(), Moo::new(new_expr.clone())),

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        a.clone(),

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        b.clone(),

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    ]));

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    clauses.extend(create_clause(vec![

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        new_expr.clone(),

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        cond.clone(),

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        Expr::Not(Metadata::new(), Moo::new(a.clone())),

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    ]));

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    clauses.extend(create_clause(vec![

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        new_expr.clone(),

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        Expr::Not(Metadata::new(), Moo::new(cond)),

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        Expr::Not(Metadata::new(), Moo::new(b.clone())),

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    ]));

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    clauses.extend(create_clause(vec![

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        new_expr.clone(),

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        Expr::Not(Metadata::new(), Moo::new(a)),

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        Expr::Not(Metadata::new(), Moo::new(b)),

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    ]));

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    new_expr

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/// Applies the Tseytin xor transformation to two variables, returns the new expression, symbol table and clauses

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#[allow(dead_code)]

216

pub fn tseytin_xor(

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    x: Expr,

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    y: Expr,

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    clauses: &mut Vec<CnfClause>,

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    symbols: &mut SymbolTable,

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) -> Expr {

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    let new_expr = create_bool_aux(symbols);

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    clauses.extend(create_clause(vec![

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        Expr::Not(Metadata::new(), Moo::new(x.clone())),

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        Expr::Not(Metadata::new(), Moo::new(y.clone())),

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        Expr::Not(Metadata::new(), Moo::new(new_expr.clone())),

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    ]));

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    clauses.extend(create_clause(vec![

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        x.clone(),

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        y.clone(),

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        Expr::Not(Metadata::new(), Moo::new(new_expr.clone())),

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    ]));

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    clauses.extend(create_clause(vec![

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        x.clone(),

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        Expr::Not(Metadata::new(), Moo::new(y.clone())),

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        new_expr.clone(),

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    ]));

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    clauses.extend(create_clause(vec![

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        Expr::Not(Metadata::new(), Moo::new(x)),

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y,

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        new_expr.clone(),

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    ]));

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    new_expr

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/// Converts a single boolean atom to a clause

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///

250

/// ```text

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///  a

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///  ~~>

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///

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///  new clauses:

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///  clause(a)

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/// ```

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#[register_rule(("SAT", 8400))]

258

9

fn remove_single_atom(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {

259

    // The single atom must not be within another expression

260

9

    let Expr::Root(_, children) = expr else {

261

9

        return Err(RuleNotApplicable);

262

};

263

264

    // Find the position of the first reference atom with boolean domain

265

    let Some(pos) = children.iter().position(

266

        |e| matches!(e, Expr::Atomic(_, Atom::Reference(x)) if x.domain().is_some_and(|d| d.is_bool())),

267

    ) else {

268

        return Err(RuleNotApplicable);

269

};

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    // Clone the children since expr is borrowed immutably

272

    let mut new_children = children.clone();

273

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    let removed = new_children.remove(pos);

275

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    let new_clauses = vec![CnfClause::new(vec![removed])];

277

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    // If now empty, replace with `true`

279

    if new_children.is_empty() {

280

        new_children.push(essence_expr!(true));

281

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    let new_expr = Expr::Root(Metadata::new(), new_children);

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    Ok(Reduction::cnf(new_expr, new_clauses, symbols.clone()))

286

9

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/// Converts an and/or expression to an aux variable, using the tseytin transformation

289

///

290

/// ```text

291

///  and(a, b, c, ...)

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///  ~~>

293

///  __0

294

///

295

///  new variables:

296

///  find __0: bool

297

///

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///  new clauses:

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///  clause(__0, not(a), not(b), not(c), ...)

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///  clause(not(__0), a)

301

///  clause(not(__0), b)

302

///  clause(not(__0), c)

303

///  ...

304

///

305

///  ---------------------------------------

306

///

307

///  clause(a, b, c, ...)

308

///  ~~>

309

///  __0

310

///

311

///  new variables:

312

///  find __0: bool

313

///

314

///  new clauses:

315

///  clause(not(__0), a, b, c, ...)

316

///  clause(__0, not(a))

317

///  clause(__0, not(b))

318

///  clause(__0, not(c))

319

///  ...

320

/// ```

321

#[register_rule(("SAT", 8500))]

322

9

fn apply_tseytin_and_or(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {

323

9

    let exprs = match expr {

324

        Expr::And(_, exprs) | Expr::Or(_, exprs) => exprs,

325

9

        _ => return Err(RuleNotApplicable),

326

};

327

328

    let Expr::AbstractLiteral(_, Matrix(exprs_list, _)) = exprs.as_ref() else {

329

        return Err(RuleNotApplicable);

330

};

331

332

    for x in exprs_list {

333

        if !is_literal(x) {

334

            return Err(RuleNotApplicable);

335

};

336

337

338

    let new_expr;

339

    let mut new_clauses = vec![];

340

    let mut new_symbols = symbols.clone();

341

342

    match expr {

343

        Expr::And(_, _) => {

344

            new_expr = tseytin_and(exprs_list, &mut new_clauses, &mut new_symbols);

345

346

        Expr::Or(_, _) => {

347

            new_expr = tseytin_or(exprs_list, &mut new_clauses, &mut new_symbols);

348

349

        _ => return Err(RuleNotApplicable),

350

};

351

352

    Ok(Reduction::cnf(new_expr, new_clauses, new_symbols))

353

9

354

355

/// Converts a not expression to an aux variable, using the tseytin transformation

356

///

357

/// ```text

358

///  not(a)

359

///  ~~>

360

///  __0

361

///

362

///  new variables:

363

///  find __0: bool

364

///

365

///  new clauses:

366

///  clause(__0, a)

367

///  clause(not(__0), not(a))

368

/// ```

369

#[register_rule(("SAT", 9005))]

370

9

fn apply_tseytin_not(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {

371

9

    let Expr::Not(_, x) = expr else {

372

9

        return Err(RuleNotApplicable);

373

};

374

375

    let Expr::Atomic(_, _) = x.as_ref() else {

376

        return Err(RuleNotApplicable);

377

};

378

379

    if !is_literal(x.as_ref()) {

380

        return Err(RuleNotApplicable);

381

};

382

383

    let mut new_clauses = vec![];

384

    let mut new_symbols = symbols.clone();

385

386

    let new_expr = tseytin_not(x.as_ref().clone(), &mut new_clauses, &mut new_symbols);

387

388

    Ok(Reduction::cnf(new_expr, new_clauses, new_symbols))

389

9

390

391

/// Converts an iff/boolean equality expression to an aux variable, using the tseytin transformation

392

///

393

/// ```text

394

/// find a, b : bool

395

///  a <-> b OR a = b

396

///  ~~>

397

///  __0

398

///

399

///  new clauses:

400

///  find __0: bool

401

///

402

///  new clauses:

403

///  clause(not(a), not(b), __0)

404

///  clause(a, b, __0)

405

///  clause(a, not(b), not(__0))

406

///  clause(not(a), b, not(__0))

407

/// ```

408

#[register_rule(("SAT", 8500))]

409

9

fn apply_tseytin_iff_eq(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {

410

    // Check for iff or eq

411

9

    let (x, y) = match expr {

412

        Expr::Iff(_, x, y) | Expr::Eq(_, x, y) => (x, y),

413

9

        _ => return Err(RuleNotApplicable),

414

};

415

416

    if !is_literal(x.as_ref()) || !is_literal(y.as_ref()) {

417

        return Err(RuleNotApplicable);

418

};

419

420

    let mut new_clauses = vec![];

421

    let mut new_symbols = symbols.clone();

422

423

    let new_expr = tseytin_iff(

424

        x.as_ref().clone(),

425

        y.as_ref().clone(),

426

        &mut new_clauses,

427

        &mut new_symbols,

428

);

429

430

    Ok(Reduction::cnf(new_expr, new_clauses, new_symbols))

431

9

432

433

/// Converts an implication expression to an aux variable, using the tseytin transformation

434

///

435

/// ```text

436

///  a -> b

437

///  ~~>

438

///  __0

439

///

440

///  new variables:

441

///  find __0: bool

442

///

443

///  new clauses:

444

///  clause(not(__0), not(a), b)

445

///  clause(__0, a)

446

///  clause(__0, not(b))

447

/// ```

448

#[register_rule(("SAT", 8500))]

449

9

fn apply_tseytin_imply(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {

450

9

    let Expr::Imply(_, x, y) = expr else {

451

9

        return Err(RuleNotApplicable);

452

};

453

454

    if !is_literal(x.as_ref()) || !is_literal(y.as_ref()) {

455

        return Err(RuleNotApplicable);

456

};

457

458

    let new_expr;

459

    let mut new_clauses = vec![];

460

    let mut new_symbols = symbols.clone();

461

462

    new_expr = tseytin_imply(

463

        x.as_ref().clone(),

464

        y.as_ref().clone(),

465

        &mut new_clauses,

466

        &mut new_symbols,

467

);

468

469

    Ok(Reduction::cnf(new_expr, new_clauses, new_symbols))

470

9

471

472

/// Converts a boolean != expression to an aux variable, using the tseytin transformation

473

///

474

/// ```text

475

///  find a, b : bool

476

///  a != b

477

///  ~~>

478

///  __0

479

///

480

///  new clauses:

481

///  find __0: bool

482

///

483

///  new clauses:

484

///  clause(not(a), not(b), not(__0))

485

///  clause(a, b, not(__0))

486

///  clause(a, not(b), __0)

487

///  clause(not(a), b, __0)

488

/// ```

489

#[register_rule(("SAT", 8500))]

490

9

fn apply_tseytin_xor_neq(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {

491

9

    let Expr::Neq(_, x, y) = expr else {

492

9

        return Err(RuleNotApplicable);

493

};

494

495

    if !is_literal(x.as_ref()) || !is_literal(y.as_ref()) {

496

        return Err(RuleNotApplicable);

497

};

498

499

    let mut new_clauses = vec![];

500

    let mut new_symbols = symbols.clone();

501

502

    let new_expr = tseytin_xor(

503

        x.as_ref().clone(),

504

        y.as_ref().clone(),

505

        &mut new_clauses,

506

        &mut new_symbols,

507

);

508

509

    Ok(Reduction::cnf(new_expr, new_clauses, new_symbols))

510

9