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405 lines
11 KiB
C++
405 lines
11 KiB
C++
#include <Interpreters/TreeCNFConverter.h>
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#include <Parsers/IAST.h>
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#include <Parsers/ASTFunction.h>
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#include <Parsers/ASTIdentifier.h>
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#include <Common/checkStackSize.h>
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#include <IO/Operators.h>
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namespace DB
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{
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namespace ErrorCodes
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{
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extern const int LOGICAL_ERROR;
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extern const int INCORRECT_QUERY;
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extern const int TOO_MANY_TEMPORARY_COLUMNS;
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}
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namespace
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{
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bool isLogicalFunction(const ASTFunction & func)
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{
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return func.name == "and" || func.name == "or" || func.name == "not";
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}
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size_t countAtoms(const ASTPtr & node)
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{
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checkStackSize();
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if (node->as<ASTIdentifier>() || node->as<ASTLiteral>())
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return 1;
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const auto * func = node->as<ASTFunction>();
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if (func && !isLogicalFunction(*func))
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return 1;
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size_t num_atoms = 0;
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for (const auto & child : node->children)
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num_atoms += countAtoms(child);
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return num_atoms;
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}
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/// Splits AND(a, b, c) to AND(a, AND(b, c)) for AND/OR
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void splitMultiLogic(ASTPtr & node)
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{
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checkStackSize();
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auto * func = node->as<ASTFunction>();
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if (func && (func->name == "and" || func->name == "or"))
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{
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if (func->arguments->children.size() < 2)
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throw Exception(ErrorCodes::INCORRECT_QUERY, "Bad AND or OR function. Expected at least 2 arguments");
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if (func->arguments->children.size() > 2)
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{
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ASTPtr res = func->arguments->children[0]->clone();
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for (size_t i = 1; i < func->arguments->children.size(); ++i)
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res = makeASTFunction(func->name, res, func->arguments->children[i]->clone());
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node = res;
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}
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auto * new_func = node->as<ASTFunction>();
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for (auto & child : new_func->arguments->children)
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splitMultiLogic(child);
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}
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else if (func && func->name == "not")
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{
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for (auto & child : func->arguments->children)
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splitMultiLogic(child);
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}
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}
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/// Push NOT to leafs, remove NOT NOT ...
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void traversePushNot(ASTPtr & node, bool add_negation)
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{
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checkStackSize();
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auto * func = node->as<ASTFunction>();
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if (func && (func->name == "and" || func->name == "or"))
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{
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if (add_negation)
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{
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if (func->arguments->children.size() != 2)
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throw Exception(ErrorCodes::LOGICAL_ERROR, "Bad AND or OR function. Expected at least 2 arguments");
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/// apply De Morgan's Law
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node = makeASTFunction(
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(func->name == "and" ? "or" : "and"),
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func->arguments->children[0]->clone(),
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func->arguments->children[1]->clone());
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}
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auto * new_func = node->as<ASTFunction>();
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for (auto & child : new_func->arguments->children)
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traversePushNot(child, add_negation);
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}
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else if (func && func->name == "not")
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{
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if (func->arguments->children.size() != 1)
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throw Exception(ErrorCodes::INCORRECT_QUERY, "Bad NOT function. Expected 1 argument");
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/// delete NOT
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node = func->arguments->children[0]->clone();
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traversePushNot(node, !add_negation);
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}
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else
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{
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if (add_negation)
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node = makeASTFunction("not", node->clone());
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}
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}
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/// Push Or inside And (actually pull AND to top)
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bool traversePushOr(ASTPtr & node, size_t num_atoms, size_t max_atoms)
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{
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if (max_atoms && num_atoms > max_atoms)
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return false;
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checkStackSize();
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auto * func = node->as<ASTFunction>();
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if (func && (func->name == "or" || func->name == "and"))
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{
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for (auto & child : func->arguments->children)
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if (!traversePushOr(child, num_atoms, max_atoms))
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return false;
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}
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if (func && func->name == "or")
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{
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assert(func->arguments->children.size() == 2);
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size_t and_node_id = func->arguments->children.size();
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for (size_t i = 0; i < func->arguments->children.size(); ++i)
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{
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auto & child = func->arguments->children[i];
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auto * and_func = child->as<ASTFunction>();
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if (and_func && and_func->name == "and")
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and_node_id = i;
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}
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if (and_node_id == func->arguments->children.size())
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return true;
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const size_t other_node_id = 1 - and_node_id;
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const auto * and_func = func->arguments->children[and_node_id]->as<ASTFunction>();
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auto a = func->arguments->children[other_node_id];
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auto b = and_func->arguments->children[0];
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auto c = and_func->arguments->children[1];
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/// apply the distributive law ( a or (b and c) -> (a or b) and (a or c) )
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node = makeASTFunction(
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"and",
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makeASTFunction("or", a->clone(), b),
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makeASTFunction("or", a, c));
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/// Count all atoms from 'a', because it was cloned.
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num_atoms += countAtoms(a);
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return traversePushOr(node, num_atoms, max_atoms);
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}
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return true;
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}
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/// transform ast into cnf groups
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void traverseCNF(const ASTPtr & node, CNFQuery::AndGroup & and_group, CNFQuery::OrGroup & or_group)
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{
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checkStackSize();
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auto * func = node->as<ASTFunction>();
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if (func && func->name == "and")
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{
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for (auto & child : func->arguments->children)
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{
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CNFQuery::OrGroup group;
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traverseCNF(child, and_group, group);
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if (!group.empty())
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and_group.insert(std::move(group));
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}
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}
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else if (func && func->name == "or")
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{
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for (auto & child : func->arguments->children)
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{
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traverseCNF(child, and_group, or_group);
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}
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}
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else if (func && func->name == "not")
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{
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if (func->arguments->children.size() != 1)
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throw Exception(ErrorCodes::INCORRECT_QUERY, "Bad NOT function. Expected 1 argument");
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or_group.insert(CNFQuery::AtomicFormula{true, func->arguments->children.front()});
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}
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else
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{
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or_group.insert(CNFQuery::AtomicFormula{false, node});
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}
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}
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void traverseCNF(const ASTPtr & node, CNFQuery::AndGroup & result)
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{
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CNFQuery::OrGroup or_group;
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traverseCNF(node, result, or_group);
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if (!or_group.empty())
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result.insert(or_group);
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}
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}
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std::optional<CNFQuery> TreeCNFConverter::tryConvertToCNF(
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const ASTPtr & query, size_t max_growth_multiplier)
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{
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auto cnf = query->clone();
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size_t num_atoms = countAtoms(cnf);
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splitMultiLogic(cnf);
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traversePushNot(cnf, false);
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size_t max_atoms = max_growth_multiplier
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? std::max(MAX_ATOMS_WITHOUT_CHECK, num_atoms * max_growth_multiplier)
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: 0;
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if (!traversePushOr(cnf, num_atoms, max_atoms))
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return {};
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CNFQuery::AndGroup and_group;
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traverseCNF(cnf, and_group);
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CNFQuery result{std::move(and_group)};
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return result;
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}
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CNFQuery TreeCNFConverter::toCNF(
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const ASTPtr & query, size_t max_growth_multiplier)
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{
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auto cnf = tryConvertToCNF(query, max_growth_multiplier);
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if (!cnf)
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throw Exception(ErrorCodes::TOO_MANY_TEMPORARY_COLUMNS,
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"Cannot convert expression '{}' to CNF, because it produces to many clauses."
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"Size of boolean formula in CNF can be exponential of size of source formula.");
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return *cnf;
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}
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ASTPtr TreeCNFConverter::fromCNF(const CNFQuery & cnf)
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{
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const auto & groups = cnf.getStatements();
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if (groups.empty())
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return nullptr;
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ASTs or_groups;
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for (const auto & group : groups)
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{
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if (group.size() == 1)
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{
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if ((*group.begin()).negative)
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or_groups.push_back(makeASTFunction("not", (*group.begin()).ast->clone()));
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else
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or_groups.push_back((*group.begin()).ast->clone());
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}
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else if (group.size() > 1)
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{
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or_groups.push_back(makeASTFunction("or"));
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auto * func = or_groups.back()->as<ASTFunction>();
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for (const auto & atom : group)
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{
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if (atom.negative)
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func->arguments->children.push_back(makeASTFunction("not", atom.ast->clone()));
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else
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func->arguments->children.push_back(atom.ast->clone());
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}
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}
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}
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if (or_groups.size() == 1)
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return or_groups.front();
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ASTPtr res = makeASTFunction("and");
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auto * func = res->as<ASTFunction>();
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for (const auto & group : or_groups)
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func->arguments->children.push_back(group);
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return res;
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}
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static void pushPullNotInAtom(CNFQuery::AtomicFormula & atom, const std::unordered_map<std::string, std::string> & inverse_relations)
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{
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auto * func = atom.ast->as<ASTFunction>();
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if (!func)
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return;
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if (auto it = inverse_relations.find(func->name); it != std::end(inverse_relations))
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{
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/// inverse func
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atom.ast = atom.ast->clone();
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auto * new_func = atom.ast->as<ASTFunction>();
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new_func->name = it->second;
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/// add not
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atom.negative = !atom.negative;
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}
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}
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static void pullNotOut(CNFQuery::AtomicFormula & atom)
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{
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static const std::unordered_map<std::string, std::string> inverse_relations = {
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{"notEquals", "equals"},
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{"greaterOrEquals", "less"},
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{"greater", "lessOrEquals"},
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{"notIn", "in"},
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{"notLike", "like"},
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{"notEmpty", "empty"},
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};
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pushPullNotInAtom(atom, inverse_relations);
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}
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void pushNotIn(CNFQuery::AtomicFormula & atom)
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{
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if (!atom.negative)
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return;
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static const std::unordered_map<std::string, std::string> inverse_relations = {
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{"equals", "notEquals"},
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{"less", "greaterOrEquals"},
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{"lessOrEquals", "greater"},
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{"in", "notIn"},
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{"like", "notLike"},
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{"empty", "notEmpty"},
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{"notEquals", "equals"},
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{"greaterOrEquals", "less"},
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{"greater", "lessOrEquals"},
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{"notIn", "in"},
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{"notLike", "like"},
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{"notEmpty", "empty"},
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};
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pushPullNotInAtom(atom, inverse_relations);
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}
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CNFQuery & CNFQuery::pullNotOutFunctions()
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{
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transformAtoms([](const AtomicFormula & atom) -> AtomicFormula
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{
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AtomicFormula result{atom.negative, atom.ast->clone()};
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pullNotOut(result);
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return result;
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});
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return *this;
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}
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CNFQuery & CNFQuery::pushNotInFunctions()
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{
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transformAtoms([](const AtomicFormula & atom) -> AtomicFormula
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{
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AtomicFormula result{atom.negative, atom.ast->clone()};
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pushNotIn(result);
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return result;
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});
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return *this;
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}
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CNFQuery & CNFQuery::reduce()
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{
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while (true)
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{
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AndGroup new_statements = reduceOnceCNFStatements(statements);
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if (statements == new_statements)
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{
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statements = filterCNFSubsets(statements);
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return *this;
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}
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else
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statements = new_statements;
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}
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}
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std::string CNFQuery::dump() const
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{
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WriteBufferFromOwnString res;
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bool first = true;
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for (const auto & group : statements)
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{
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if (!first)
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res << " AND ";
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first = false;
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res << "(";
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bool first_in_group = true;
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for (const auto & atom : group)
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{
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if (!first_in_group)
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res << " OR ";
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first_in_group = false;
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if (atom.negative)
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res << " NOT ";
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res << atom.ast->getColumnName();
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}
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res << ")";
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}
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return res.str();
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}
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}
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