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Functions
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use conjure_cp::ast::{Atom, Expression as Expr, Literal};
use conjure_cp::ast::{SATIntEncoding, SymbolTable};
use conjure_cp::rule_engine::ApplicationError;
use conjure_cp::rule_engine::{
ApplicationError::RuleNotApplicable, ApplicationResult, Reduction, register_rule,
};
use crate::sat::boolean::{tseytin_and, tseytin_iff, tseytin_not, tseytin_or};
use conjure_cp::ast::Metadata;
use conjure_cp::ast::Moo;
use conjure_cp::into_matrix_expr;
/// This function confirms that all of the input expressions are order SATInts, and returns vectors for each input of their bits
/// This function also normalizes order SATInt operands to a common value range.
pub fn validate_order_int_operands(
exprs: Vec<Expr>,
) -> Result<(Vec<Vec<Expr>>, i32, i32), ApplicationError> {
// Iterate over all inputs
// Check they are order and calulate a lower and upper bound
let mut global_min: i32 = i32::MAX;
let mut global_max: i32 = i32::MIN;
for operand in &exprs {
let Expr::SATInt(_, SATIntEncoding::Order, _, (local_min, local_max)) = operand else {
return Err(RuleNotApplicable);
global_min = global_min.min(*local_min);
global_max = global_max.max(*local_max);
}
// build out by iterating over each operand and expanding it to match the new bounds
let out: Vec<Vec<Expr>> = exprs
.into_iter()
.map(|expr| {
let Expr::SATInt(_, SATIntEncoding::Order, inner, (local_min, local_max)) = expr else {
let Some(v) = inner.as_ref().clone().unwrap_list() else {
// calulcate how many trues/falses to prepend/append
let prefix_len = (local_min - global_min) as usize;
let postfix_len = (global_max - local_max) as usize;
let mut bits = Vec::with_capacity(v.len() + prefix_len + postfix_len);
// add `true`s to start
bits.extend(std::iter::repeat_n(
Expr::Atomic(Metadata::new(), Atom::Literal(Literal::Bool(true))),
prefix_len,
));
bits.extend(v);
// add `false`s to end
Expr::Atomic(Metadata::new(), Atom::Literal(Literal::Bool(false))),
postfix_len,
Ok(bits)
})
.collect::<Result<_, _>>()?;
Ok((out, global_min, global_max))
/// Encodes a < b for order integers.
///
/// `x < y` iff `exists i . (NOT x_i AND y_i)`
fn sat_order_lt(
a_bits: Vec<Expr>,
b_bits: Vec<Expr>,
clauses: &mut Vec<conjure_cp::ast::CnfClause>,
symbols: &mut SymbolTable,
) -> Expr {
let mut result = Expr::Atomic(Metadata::new(), Atom::Literal(Literal::Bool(false)));
for (a_i, b_i) in a_bits.iter().zip(b_bits.iter()) {
// (NOT a_i AND b_i)
let not_a_i = tseytin_not(a_i.clone(), clauses, symbols);
let current_term = tseytin_and(&vec![not_a_i, b_i.clone()], clauses, symbols);
// accumulate (NOT a_i AND b_i) into OR term
result = tseytin_or(&vec![result, current_term], clauses, symbols);
result
/// Converts an integer literal to SATInt form
/// ```text
/// 3
/// ~~>
/// SATInt([true;int(1..), (3, 3)])
/// ```
#[register_rule(("SAT_Order", 9500))]
fn literal_sat_order_int(expr: &Expr, _: &SymbolTable) -> ApplicationResult {
let value = {
if let Expr::Atomic(_, Atom::Literal(Literal::Int(value))) = expr {
*value
} else {
Ok(Reduction::pure(Expr::SATInt(
Metadata::new(),
SATIntEncoding::Order,
Moo::new(into_matrix_expr!(vec![Expr::Atomic(
Atom::Literal(Literal::Bool(true)),
)])),
(value, value),
)))
/// Builds CNF for equality between two order SATInt bit-vectors.
/// This function is used by both eq and neq rules, with the output negated for neq.
/// Returns (expr, clauses, symbols).
fn sat_order_eq_expr(
lhs_bits: &[Expr],
rhs_bits: &[Expr],
symbols: &SymbolTable,
) -> (Expr, Vec<conjure_cp::ast::CnfClause>, SymbolTable) {
let bit_count = lhs_bits.len();
let mut output = true.into();
let mut new_symbols = symbols.clone();
let mut new_clauses = vec![];
for i in 0..bit_count {
let comparison = tseytin_iff(
lhs_bits[i].clone(),
rhs_bits[i].clone(),
&mut new_clauses,
&mut new_symbols,
);
output = tseytin_and(
&vec![comparison, output],
(output, new_clauses, new_symbols)
/// Converts a = expression between two order SATInts to a boolean expression in cnf
/// SATInt(a) = SATInt(b) ~> Bool
#[register_rule(("SAT_Order", 9100))]
fn eq_sat_order(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {
let Expr::Eq(_, lhs, rhs) = expr else {
let (binding, _, _) =
validate_order_int_operands(vec![lhs.as_ref().clone(), rhs.as_ref().clone()])?;
let [lhs_bits, rhs_bits] = binding.as_slice() else {
let (output, new_clauses, new_symbols) = sat_order_eq_expr(lhs_bits, rhs_bits, symbols);
Ok(Reduction::cnf(output, new_clauses, new_symbols))
/// Converts a != expression between two order SATInts to a boolean expression in cnf
fn neq_sat_order(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {
let Expr::Neq(_, lhs, rhs) = expr else {
}; // considered covered
return Err(RuleNotApplicable); // consider covered
let (mut output, mut new_clauses, mut new_symbols) =
sat_order_eq_expr(lhs_bits, rhs_bits, symbols);
output = tseytin_not(output, &mut new_clauses, &mut new_symbols);
/// Converts a </>/<=/>= expression between two order SATInts to a boolean expression in cnf
/// SATInt(a) </>/<=/>= SATInt(b) ~> Bool
/// Note: < and <= are rewritten by swapping operands to reuse lt logic.
fn ineq_sat_order(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {
let (lhs, rhs, negate) = match expr {
// A < B -> sat_order_lt(A, B)
Expr::Lt(_, x, y) => (x, y, false),
// A > B -> sat_order_lt(B, A)
Expr::Gt(_, x, y) => (y, x, false),
// A <= B -> NOT (B < A)
Expr::Leq(_, x, y) => (y, x, true),
// A >= B -> NOT (A < B)
Expr::Geq(_, x, y) => (x, y, true),
_ => return Err(RuleNotApplicable),
let mut output = sat_order_lt(
lhs_bits.clone(),
rhs_bits.clone(),
if negate {
/// Converts a - expression for a SATInt to a new SATInt
/// -SATInt(a) ~> SATInt(b)
fn neg_sat_order(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {
let Expr::Neg(_, value) = expr else {
let (binding, old_min, old_max) = validate_order_int_operands(vec![value.as_ref().clone()])?;
let [val_bits] = binding.as_slice() else {
let new_min = -old_max;
let new_max = -old_min;
let n = val_bits.len();
let mut out: Vec<Expr> = Vec::with_capacity(n);
let ff = Expr::Atomic(Metadata::new(), Atom::Literal(Literal::Bool(false)));
for i in 0..n {
let idx = n - i;
let src = if idx == n {
ff.clone()
val_bits[idx].clone()
let neg_bit = tseytin_not(src, &mut new_clauses, &mut new_symbols);
out.push(neg_bit);
Ok(Reduction::cnf(
Expr::SATInt(
Moo::new(into_matrix_expr!(out)),
(new_min, new_max),
),
new_clauses,
new_symbols,
))