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590 lines
20 KiB
PHP
590 lines
20 KiB
PHP
<?php
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namespace Psalm\Internal;
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use function array_filter;
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use function array_keys;
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use function array_map;
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use function array_merge;
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use function array_pop;
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use function array_unique;
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use function array_values;
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use function count;
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use function in_array;
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use Psalm\Exception\ComplicatedExpressionException;
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use function substr;
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class Algebra
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{
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/**
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* @param array<string, non-empty-list<non-empty-list<string>>> $all_types
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*
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* @return array<string, non-empty-list<non-empty-list<string>>>
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*
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* @psalm-pure
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*/
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public static function negateTypes(array $all_types): array
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{
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return array_filter(
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array_map(
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/**
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* @param non-empty-list<non-empty-list<string>> $anded_types
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*
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* @return list<non-empty-list<string>>
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*/
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function (array $anded_types): array {
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if (count($anded_types) > 1) {
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$new_anded_types = [];
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foreach ($anded_types as $orred_types) {
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if (count($orred_types) > 1) {
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return [];
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}
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$new_anded_types[] = self::negateType($orred_types[0]);
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}
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return [$new_anded_types];
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}
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$new_orred_types = [];
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foreach ($anded_types[0] as $orred_type) {
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$new_orred_types[] = [self::negateType($orred_type)];
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}
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return $new_orred_types;
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},
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$all_types
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)
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);
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}
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/**
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* @psalm-pure
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*/
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public static function negateType(string $type): string
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{
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if ($type === 'mixed') {
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return $type;
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}
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return $type[0] === '!' ? substr($type, 1) : '!' . $type;
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}
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/**
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* This is a very simple simplification heuristic
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* for CNF formulae.
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*
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* It simplifies formulae:
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* ($a) && ($a || $b) => $a
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* (!$a) && (!$b) && ($a || $b || $c) => $c
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*
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* @param list<Clause> $clauses
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*
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* @return list<Clause>
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*
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* @psalm-pure
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*/
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public static function simplifyCNF(array $clauses): array
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{
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$cloned_clauses = [];
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// avoid strict duplicates
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foreach ($clauses as $clause) {
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$unique_clause = $clause->makeUnique();
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$cloned_clauses[$unique_clause->hash] = $unique_clause;
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}
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// remove impossible types
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foreach ($cloned_clauses as $clause_a_hash => $clause_a) {
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if (!$clause_a->reconcilable || $clause_a->wedge) {
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continue;
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}
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if (count($clause_a->possibilities) !== 1 || count(array_values($clause_a->possibilities)[0]) !== 1) {
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foreach ($cloned_clauses as $clause_b) {
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if ($clause_a === $clause_b || !$clause_b->reconcilable || $clause_b->wedge) {
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continue;
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}
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if (array_keys($clause_a->possibilities) === array_keys($clause_b->possibilities)) {
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$opposing_keys = [];
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foreach ($clause_a->possibilities as $key => $a_possibilities) {
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$b_possibilities = $clause_b->possibilities[$key];
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if ($a_possibilities === $b_possibilities) {
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continue;
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}
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if (count($a_possibilities) === 1 && count($b_possibilities) === 1) {
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if ($a_possibilities[0] === '!' . $b_possibilities[0]
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|| $b_possibilities[0] === '!' . $a_possibilities[0]
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) {
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$opposing_keys[] = $key;
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continue;
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}
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}
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continue 2;
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}
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if (count($opposing_keys) === 1) {
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unset($cloned_clauses[$clause_a_hash]);
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$clause_a = $clause_a->removePossibilities($opposing_keys[0]);
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if (!$clause_a) {
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continue 2;
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}
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$cloned_clauses[$clause_a->hash] = $clause_a;
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}
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}
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}
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continue;
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}
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$clause_var = array_keys($clause_a->possibilities)[0];
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$only_type = array_pop(array_values($clause_a->possibilities)[0]);
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$negated_clause_type = self::negateType($only_type);
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foreach ($cloned_clauses as $clause_b_hash => $clause_b) {
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if ($clause_a === $clause_b || !$clause_b->reconcilable || $clause_b->wedge) {
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continue;
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}
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if (isset($clause_b->possibilities[$clause_var]) &&
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in_array($negated_clause_type, $clause_b->possibilities[$clause_var], true)
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) {
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$clause_var_possibilities = array_values(
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array_filter(
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$clause_b->possibilities[$clause_var],
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function (string $possible_type) use ($negated_clause_type): bool {
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return $possible_type !== $negated_clause_type;
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}
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)
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);
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unset($cloned_clauses[$clause_b_hash]);
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if (!$clause_var_possibilities) {
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$updated_clause = $clause_b->removePossibilities($clause_var);
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if ($updated_clause) {
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$cloned_clauses[$updated_clause->hash] = $updated_clause;
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}
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} else {
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$updated_clause = $clause_b->addPossibilities(
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$clause_var,
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$clause_var_possibilities
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);
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$cloned_clauses[$updated_clause->hash] = $updated_clause;
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}
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}
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}
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}
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$simplified_clauses = [];
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foreach ($cloned_clauses as $clause_a) {
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$is_redundant = false;
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foreach ($cloned_clauses as $clause_b) {
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if ($clause_a === $clause_b
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|| !$clause_b->reconcilable
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|| $clause_b->wedge
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|| $clause_a->wedge
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) {
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continue;
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}
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if ($clause_a->contains($clause_b)) {
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$is_redundant = true;
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break;
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}
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}
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if (!$is_redundant) {
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$simplified_clauses[] = $clause_a;
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}
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}
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return $simplified_clauses;
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}
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/**
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* Look for clauses with only one possible value
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*
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* @param list<Clause> $clauses
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* @param array<string, bool> $cond_referenced_var_ids
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* @param array<string, array<int, array<int, string>>> $active_truths
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*
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* @return array<string, list<array<int, string>>>
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*/
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public static function getTruthsFromFormula(
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array $clauses,
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?int $creating_conditional_id = null,
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array &$cond_referenced_var_ids = [],
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array &$active_truths = []
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): array {
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$truths = [];
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$active_truths = [];
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if ($clauses === []) {
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return [];
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}
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foreach ($clauses as $clause) {
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if (!$clause->reconcilable || count($clause->possibilities) !== 1) {
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continue;
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}
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foreach ($clause->possibilities as $var => $possible_types) {
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if ($var[0] === '*') {
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continue;
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}
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// if there's only one possible type, return it
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if (count($possible_types) === 1) {
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$possible_type = array_pop($possible_types);
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if (isset($truths[$var]) && !isset($clause->redefined_vars[$var])) {
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$truths[$var][] = [$possible_type];
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} else {
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$truths[$var] = [[$possible_type]];
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}
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if ($creating_conditional_id && $creating_conditional_id === $clause->creating_conditional_id) {
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if (!isset($active_truths[$var])) {
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$active_truths[$var] = [];
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}
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$active_truths[$var][count($truths[$var]) - 1] = [$possible_type];
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}
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} else {
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// if there's only one active clause, return all the non-negation clause members ORed together
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$things_that_can_be_said = array_filter(
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$possible_types,
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function (string $possible_type): bool {
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return $possible_type[0] !== '!';
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}
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);
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if ($things_that_can_be_said && count($things_that_can_be_said) === count($possible_types)) {
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$things_that_can_be_said = array_unique($things_that_can_be_said);
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if ($clause->generated && count($possible_types) > 1) {
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unset($cond_referenced_var_ids[$var]);
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}
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/** @var array<int, string> $things_that_can_be_said */
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$truths[$var] = [$things_that_can_be_said];
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if ($creating_conditional_id && $creating_conditional_id === $clause->creating_conditional_id) {
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$active_truths[$var] = [$things_that_can_be_said];
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}
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}
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}
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}
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}
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return $truths;
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}
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/**
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* @param non-empty-list<Clause> $clauses
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*
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* @return list<Clause>
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*
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* @psalm-pure
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*/
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public static function groupImpossibilities(array $clauses): array
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{
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$complexity = 1;
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$seed_clauses = [];
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$clause = array_pop($clauses);
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if (!$clause->wedge) {
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if ($clause->impossibilities === null) {
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throw new \UnexpectedValueException('$clause->impossibilities should not be null');
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}
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foreach ($clause->impossibilities as $var => $impossible_types) {
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foreach ($impossible_types as $impossible_type) {
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$seed_clause = new Clause(
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[$var => [$impossible_type]],
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$clause->creating_conditional_id,
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$clause->creating_object_id
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);
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$seed_clauses[] = $seed_clause;
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++$complexity;
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}
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}
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}
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if (!$clauses || !$seed_clauses) {
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return $seed_clauses;
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}
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while ($clauses) {
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$clause = array_pop($clauses);
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$new_clauses = [];
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foreach ($seed_clauses as $grouped_clause) {
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if ($clause->impossibilities === null) {
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throw new \UnexpectedValueException('$clause->impossibilities should not be null');
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}
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foreach ($clause->impossibilities as $var => $impossible_types) {
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foreach ($impossible_types as $impossible_type) {
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$new_clause_possibilities = $grouped_clause->possibilities;
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if (isset($grouped_clause->possibilities[$var])) {
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$new_clause_possibilities[$var] = array_values(
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array_unique(
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array_merge([$impossible_type], $new_clause_possibilities[$var])
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)
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);
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$removed_indexes = [];
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for ($i = 0, $l = count($new_clause_possibilities[$var]); $i < $l; $i++) {
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for ($j = $i + 1; $j < $l; $j++) {
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$ith = $new_clause_possibilities[$var][$i];
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$jth = $new_clause_possibilities[$var][$j];
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if ($ith === '!' . $jth || $jth === '!' . $ith) {
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$removed_indexes[$i] = true;
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$removed_indexes[$j] = true;
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}
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}
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}
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if ($removed_indexes) {
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$new_possibilities = array_values(
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\array_diff_key(
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$new_clause_possibilities[$var],
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$removed_indexes
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)
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);
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if (!$new_possibilities) {
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unset($new_clause_possibilities[$var]);
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} else {
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$new_clause_possibilities[$var] = $new_possibilities;
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}
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}
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} else {
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$new_clause_possibilities[$var] = [$impossible_type];
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}
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if (!$new_clause_possibilities) {
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continue;
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}
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$new_clause = new Clause(
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$new_clause_possibilities,
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$grouped_clause->creating_conditional_id,
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$clause->creating_object_id,
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false,
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true,
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true,
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[]
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);
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$new_clauses[] = $new_clause;
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++$complexity;
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if ($complexity > 20000) {
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throw new ComplicatedExpressionException();
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}
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}
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}
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}
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$seed_clauses = $new_clauses;
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}
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return $seed_clauses;
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}
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/**
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* @param list<Clause> $left_clauses
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* @param list<Clause> $right_clauses
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*
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* @return list<Clause>
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*
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* @psalm-pure
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*/
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public static function combineOredClauses(
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array $left_clauses,
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array $right_clauses,
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int $conditional_object_id
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): array {
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$clauses = [];
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$all_wedges = true;
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$has_wedge = false;
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foreach ($left_clauses as $left_clause) {
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foreach ($right_clauses as $right_clause) {
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$all_wedges = $all_wedges && ($left_clause->wedge && $right_clause->wedge);
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$has_wedge = $has_wedge || ($left_clause->wedge && $right_clause->wedge);
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}
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}
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if ($all_wedges) {
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return [new Clause([], $conditional_object_id, $conditional_object_id, true)];
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}
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foreach ($left_clauses as $left_clause) {
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foreach ($right_clauses as $right_clause) {
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if ($left_clause->wedge && $right_clause->wedge) {
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// handled below
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continue;
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}
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/** @var array<string, non-empty-list<string>> */
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$possibilities = [];
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$can_reconcile = true;
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if ($left_clause->wedge ||
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$right_clause->wedge ||
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!$left_clause->reconcilable ||
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!$right_clause->reconcilable
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) {
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$can_reconcile = false;
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}
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foreach ($left_clause->possibilities as $var => $possible_types) {
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if (isset($right_clause->redefined_vars[$var])) {
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continue;
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}
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if (isset($possibilities[$var])) {
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$possibilities[$var] = array_merge($possibilities[$var], $possible_types);
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} else {
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$possibilities[$var] = $possible_types;
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}
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}
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foreach ($right_clause->possibilities as $var => $possible_types) {
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if (isset($possibilities[$var])) {
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$possibilities[$var] = array_merge($possibilities[$var], $possible_types);
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} else {
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$possibilities[$var] = $possible_types;
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}
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}
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if (count($left_clauses) > 1 || count($right_clauses) > 1) {
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foreach ($possibilities as $var => $p) {
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$possibilities[$var] = array_values(array_unique($p));
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}
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}
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foreach ($possibilities as $var_possibilities) {
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if (count($var_possibilities) === 2) {
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if ($var_possibilities[0] === '!' . $var_possibilities[1]
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|| $var_possibilities[1] === '!' . $var_possibilities[0]
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) {
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continue 2;
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}
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}
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}
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$creating_conditional_id =
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$right_clause->creating_conditional_id === $left_clause->creating_conditional_id
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? $right_clause->creating_conditional_id
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: $conditional_object_id;
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$clauses[] = new Clause(
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$possibilities,
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$creating_conditional_id,
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$creating_conditional_id,
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false,
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$can_reconcile,
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$right_clause->generated
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|| $left_clause->generated
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|| count($left_clauses) > 1
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|| count($right_clauses) > 1,
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[]
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);
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}
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}
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if ($has_wedge) {
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$clauses[] = new Clause([], $conditional_object_id, $conditional_object_id, true);
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}
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return $clauses;
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}
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/**
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* Negates a set of clauses
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* negateClauses([$a || $b]) => !$a && !$b
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* negateClauses([$a, $b]) => !$a || !$b
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* negateClauses([$a, $b || $c]) =>
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* (!$a || !$b) &&
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* (!$a || !$c)
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* negateClauses([$a, $b || $c, $d || $e || $f]) =>
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* (!$a || !$b || !$d) &&
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* (!$a || !$b || !$e) &&
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* (!$a || !$b || !$f) &&
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* (!$a || !$c || !$d) &&
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* (!$a || !$c || !$e) &&
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* (!$a || !$c || !$f)
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*
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* @param list<Clause> $clauses
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*
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|
* @return non-empty-list<Clause>
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|
*/
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|
public static function negateFormula(array $clauses): array
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|
{
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|
$clauses = array_filter(
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|
$clauses,
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|
function ($clause) {
|
|
return $clause->reconcilable;
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|
}
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|
);
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|
|
|
if (!$clauses) {
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|
$cond_id = \mt_rand(0, 100000000);
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|
return [new Clause([], $cond_id, $cond_id, true)];
|
|
}
|
|
|
|
$clauses_with_impossibilities = [];
|
|
|
|
foreach ($clauses as $clause) {
|
|
$clauses_with_impossibilities[] = $clause->calculateNegation();
|
|
}
|
|
|
|
unset($clauses);
|
|
|
|
$impossible_clauses = self::groupImpossibilities($clauses_with_impossibilities);
|
|
|
|
if (!$impossible_clauses) {
|
|
$cond_id = \mt_rand(0, 100000000);
|
|
return [new Clause([], $cond_id, $cond_id, true)];
|
|
}
|
|
|
|
$negated = self::simplifyCNF($impossible_clauses);
|
|
|
|
if (!$negated) {
|
|
$cond_id = \mt_rand(0, 100000000);
|
|
return [new Clause([], $cond_id, $cond_id, true)];
|
|
}
|
|
|
|
return $negated;
|
|
}
|
|
}
|