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symbolic_formula.cc
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symbolic_formula.cc
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// NOLINTNEXTLINE(build/include): Its header file is included in symbolic.h.
#include <cstddef>
#include <iostream>
#include <limits>
#include <memory>
#include <set>
#include <sstream>
#include "drake/common/drake_assert.h"
#include "drake/common/symbolic.h"
#define DRAKE_COMMON_SYMBOLIC_DETAIL_HEADER
#include "drake/common/symbolic_formula_cell.h"
#undef DRAKE_COMMON_SYMBOLIC_DETAIL_HEADER
namespace drake {
namespace symbolic {
using std::make_shared;
using std::numeric_limits;
using std::ostream;
using std::ostringstream;
using std::set;
using std::shared_ptr;
using std::string;
bool operator<(FormulaKind k1, FormulaKind k2) {
return static_cast<int>(k1) < static_cast<int>(k2);
}
Formula::Formula(std::shared_ptr<const FormulaCell> ptr)
: ptr_{std::move(ptr)} {}
Formula::Formula(const Variable& var)
: ptr_{make_shared<const FormulaVar>(var)} {}
FormulaKind Formula::get_kind() const {
DRAKE_ASSERT(ptr_ != nullptr);
return ptr_->get_kind();
}
void Formula::HashAppend(DelegatingHasher* hasher) const {
using drake::hash_append;
hash_append(*hasher, get_kind());
ptr_->HashAppendDetail(hasher);
}
Variables Formula::GetFreeVariables() const {
DRAKE_ASSERT(ptr_ != nullptr);
return ptr_->GetFreeVariables();
}
bool Formula::EqualTo(const Formula& f) const {
DRAKE_ASSERT(ptr_ != nullptr);
DRAKE_ASSERT(f.ptr_ != nullptr);
if (ptr_ == f.ptr_) {
// pointer equality
return true;
}
if (get_kind() != f.get_kind()) {
return false;
}
// Same kind/hash, but it could be the result of hash collision,
// check structural equality.
return ptr_->EqualTo(*(f.ptr_));
}
bool Formula::Less(const Formula& f) const {
const FormulaKind k1{get_kind()};
const FormulaKind k2{f.get_kind()};
if (k1 < k2) {
return true;
}
if (k2 < k1) {
return false;
}
return ptr_->Less(*(f.ptr_));
}
bool Formula::Evaluate(const Environment& env,
RandomGenerator* const random_generator) const {
DRAKE_ASSERT(ptr_ != nullptr);
if (random_generator == nullptr) {
return ptr_->Evaluate(env);
} else {
return ptr_->Evaluate(
PopulateRandomVariables(env, GetFreeVariables(), random_generator));
}
}
bool Formula::Evaluate(RandomGenerator* const random_generator) const {
DRAKE_ASSERT(ptr_ != nullptr);
return Evaluate(Environment{}, random_generator);
}
Formula Formula::Substitute(const Variable& var, const Expression& e) const {
DRAKE_ASSERT(ptr_ != nullptr);
return Formula{ptr_->Substitute({{var, e}})};
}
Formula Formula::Substitute(const Substitution& s) const {
DRAKE_ASSERT(ptr_ != nullptr);
if (!s.empty()) {
return Formula{ptr_->Substitute(s)};
}
return *this;
}
string Formula::to_string() const {
ostringstream oss;
oss << *this;
return oss.str();
}
Formula Formula::True() {
static Formula tt{make_shared<const FormulaTrue>()};
return tt;
}
Formula Formula::False() {
static Formula ff{make_shared<const FormulaFalse>()};
return ff;
}
Formula forall(const Variables& vars, const Formula& f) {
return Formula{make_shared<const FormulaForall>(vars, f)};
}
Formula make_conjunction(const set<Formula>& formulas) {
set<Formula> operands;
for (const Formula& f : formulas) {
if (is_false(f)) {
// Short-circuits to False.
// f₁ ∧ ... ∧ False ∧ ... ∧ fₙ => False
return Formula::False();
}
if (is_true(f)) {
// Drop redundant True.
// f₁ ∧ ... ∧ True ∧ ... ∧ fₙ => f₁ ∧ ... ∧ fₙ
continue;
}
if (is_conjunction(f)) {
// Flattening.
// f₁ ∧ ... ∧ (fᵢ₁ ∧ ... ∧ fᵢₘ) ∧ ... ∧ fₙ
// => f₁ ∧ ... ∧ fᵢ₁ ∧ ... ∧ fᵢₘ ∧ ... ∧ fₙ
const auto& operands_in_f = get_operands(f);
operands.insert(operands_in_f.cbegin(), operands_in_f.cend());
} else {
operands.insert(f);
}
}
if (operands.empty()) {
// ⋀{} = True
return Formula::True();
}
if (operands.size() == 1) {
return *(operands.begin());
}
// TODO(soonho-tri): Returns False if both f and ¬f appear in operands.
return Formula{make_shared<const FormulaAnd>(operands)};
}
Formula operator&&(const Formula& f1, const Formula& f2) {
return make_conjunction({f1, f2});
}
Formula operator&&(const Variable& v, const Formula& f) {
return Formula(v) && f;
}
Formula operator&&(const Formula& f, const Variable& v) {
return f && Formula(v);
}
Formula operator&&(const Variable& v1, const Variable& v2) {
return Formula(v1) && Formula(v2);
}
Formula make_disjunction(const set<Formula>& formulas) {
set<Formula> operands;
for (const Formula& f : formulas) {
if (is_true(f)) {
// Short-circuits to True.
// f₁ ∨ ... ∨ True ∨ ... ∨ fₙ => True
return Formula::True();
}
if (is_false(f)) {
// Drop redundant False.
// f₁ ∨ ... ∨ False ∨ ... ∨ fₙ => f₁ ∨ ... ∨ fₙ
continue;
}
if (is_disjunction(f)) {
// Flattening.
// f₁ ∨ ... ∨ (fᵢ₁ ∨ ... ∨ fᵢₘ) ∨ ... ∨ fₙ
// => f₁ ∨ ... ∨ fᵢ₁ ∨ ... ∨ fᵢₘ ∨ ... ∨ fₙ
const auto& operands_in_f = get_operands(f);
operands.insert(operands_in_f.cbegin(), operands_in_f.cend());
} else {
operands.insert(f);
}
}
if (operands.empty()) {
// ⋁{} = False
return Formula::False();
}
if (operands.size() == 1) {
return *(operands.begin());
}
// TODO(soonho-tri): Returns True if both f and ¬f appear in operands.
return Formula{make_shared<const FormulaOr>(operands)};
}
Formula operator||(const Formula& f1, const Formula& f2) {
return make_disjunction({f1, f2});
}
Formula operator||(const Variable& v, const Formula& f) {
return Formula(v) || f;
}
Formula operator||(const Formula& f, const Variable& v) {
return f || Formula(v);
}
Formula operator||(const Variable& v1, const Variable& v2) {
return Formula(v1) || Formula(v2);
}
Formula operator!(const Formula& f) {
if (f.EqualTo(Formula::True())) {
return Formula::False();
}
if (f.EqualTo(Formula::False())) {
return Formula::True();
}
// Simplification: ¬(¬f₁) => f₁
if (is_negation(f)) {
return get_operand(f);
}
return Formula{make_shared<const FormulaNot>(f)};
}
Formula operator!(const Variable& v) { return !Formula(v); }
ostream& operator<<(ostream& os, const Formula& f) {
DRAKE_ASSERT(f.ptr_ != nullptr);
return f.ptr_->Display(os);
}
Formula operator==(const Expression& e1, const Expression& e2) {
// Simplification: E1 - E2 == 0 => True
const Expression diff{e1 - e2};
if (diff.get_kind() == ExpressionKind::Constant) {
return diff.Evaluate() == 0.0 ? Formula::True() : Formula::False();
}
return Formula{make_shared<const FormulaEq>(e1, e2)};
}
Formula operator!=(const Expression& e1, const Expression& e2) {
// Simplification: E1 - E2 != 0 => True
const Expression diff{e1 - e2};
if (diff.get_kind() == ExpressionKind::Constant) {
return diff.Evaluate() != 0.0 ? Formula::True() : Formula::False();
}
return Formula{make_shared<const FormulaNeq>(e1, e2)};
}
Formula operator<(const Expression& e1, const Expression& e2) {
// Simplification: E1 - E2 < 0 => True
const Expression diff{e1 - e2};
if (diff.get_kind() == ExpressionKind::Constant) {
return diff.Evaluate() < 0 ? Formula::True() : Formula::False();
}
return Formula{make_shared<const FormulaLt>(e1, e2)};
}
Formula operator<=(const Expression& e1, const Expression& e2) {
// Simplification: E1 - E2 <= 0 => True
const Expression diff{e1 - e2};
if (diff.get_kind() == ExpressionKind::Constant) {
return diff.Evaluate() <= 0 ? Formula::True() : Formula::False();
}
return Formula{make_shared<const FormulaLeq>(e1, e2)};
}
Formula operator>(const Expression& e1, const Expression& e2) {
// Simplification: E1 - E2 > 0 => True
const Expression diff{e1 - e2};
if (diff.get_kind() == ExpressionKind::Constant) {
return diff.Evaluate() > 0 ? Formula::True() : Formula::False();
}
return Formula{make_shared<const FormulaGt>(e1, e2)};
}
Formula operator>=(const Expression& e1, const Expression& e2) {
// Simplification: E1 - E2 >= 0 => True
const Expression diff{e1 - e2};
if (diff.get_kind() == ExpressionKind::Constant) {
return diff.Evaluate() >= 0 ? Formula::True() : Formula::False();
}
return Formula{make_shared<const FormulaGeq>(e1, e2)};
}
Formula isnan(const Expression& e) {
return Formula{make_shared<const FormulaIsnan>(e)};
}
Formula isinf(const Expression& e) {
const double inf{numeric_limits<double>::infinity()};
return (-inf == e) || (e == inf);
}
Formula isfinite(const Expression& e) {
const double inf{numeric_limits<double>::infinity()};
return (-inf < e) && (e < inf);
}
Formula positive_semidefinite(const Eigen::Ref<const MatrixX<Expression>>& m) {
return Formula{make_shared<const FormulaPositiveSemidefinite>(m)};
}
Formula positive_semidefinite(const MatrixX<Expression>& m,
const Eigen::UpLoType mode) {
switch (mode) {
case Eigen::Lower:
return Formula{make_shared<const FormulaPositiveSemidefinite>(
m.triangularView<Eigen::Lower>())};
case Eigen::Upper:
return Formula{make_shared<const FormulaPositiveSemidefinite>(
m.triangularView<Eigen::Upper>())};
default:
throw std::runtime_error(
"positive_semidefinite is called with a mode which is neither "
"Eigen::Lower nor Eigen::Upper.");
}
}
bool is_false(const Formula& f) { return is_false(*f.ptr_); }
bool is_true(const Formula& f) { return is_true(*f.ptr_); }
bool is_variable(const Formula& f) { return is_variable(*f.ptr_); }
bool is_equal_to(const Formula& f) { return is_equal_to(*f.ptr_); }
bool is_not_equal_to(const Formula& f) { return is_not_equal_to(*f.ptr_); }
bool is_greater_than(const Formula& f) { return is_greater_than(*f.ptr_); }
bool is_greater_than_or_equal_to(const Formula& f) {
return is_greater_than_or_equal_to(*f.ptr_);
}
bool is_less_than(const Formula& f) { return is_less_than(*f.ptr_); }
bool is_less_than_or_equal_to(const Formula& f) {
return is_less_than_or_equal_to(*f.ptr_);
}
bool is_relational(const Formula& f) {
return is_equal_to(f) || is_not_equal_to(f) || is_greater_than(f) ||
is_greater_than_or_equal_to(f) || is_less_than(f) ||
is_less_than_or_equal_to(f);
}
bool is_conjunction(const Formula& f) { return is_conjunction(*f.ptr_); }
bool is_disjunction(const Formula& f) { return is_disjunction(*f.ptr_); }
bool is_nary(const Formula& f) {
return is_conjunction(f) || is_disjunction(f);
}
bool is_negation(const Formula& f) { return is_negation(*f.ptr_); }
bool is_forall(const Formula& f) { return is_forall(*f.ptr_); }
bool is_isnan(const Formula& f) { return is_isnan(*f.ptr_); }
bool is_positive_semidefinite(const Formula& f) {
return is_positive_semidefinite(*f.ptr_);
}
const Variable& get_variable(const Formula& f) {
DRAKE_ASSERT(is_variable(f));
return to_variable(f)->get_variable();
}
const Expression& get_lhs_expression(const Formula& f) {
DRAKE_ASSERT(is_relational(f));
return to_relational(f)->get_lhs_expression();
}
const Expression& get_rhs_expression(const Formula& f) {
DRAKE_ASSERT(is_relational(f));
return to_relational(f)->get_rhs_expression();
}
const set<Formula>& get_operands(const Formula& f) {
return to_nary(f)->get_operands();
}
const Formula& get_operand(const Formula& f) {
return to_negation(f)->get_operand();
}
const Variables& get_quantified_variables(const Formula& f) {
return to_forall(f)->get_quantified_variables();
}
const Formula& get_quantified_formula(const Formula& f) {
return to_forall(f)->get_quantified_formula();
}
const MatrixX<Expression>& get_matrix_in_positive_semidefinite(
const Formula& f) {
return to_positive_semidefinite(f)->get_matrix();
}
} // namespace symbolic
} // namespace drake