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symbolic_formula_test.cc
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symbolic_formula_test.cc
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#include <algorithm>
#include <cmath>
#include <exception>
#include <limits>
#include <map>
#include <random>
#include <set>
#include <stdexcept>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#include <gtest/gtest.h>
#include "drake/common/drake_assert.h"
#include "drake/common/drake_copyable.h"
#include "drake/common/drake_throw.h"
#include "drake/common/symbolic.h"
#include "drake/common/test_utilities/expect_no_throw.h"
#include "drake/common/test_utilities/is_memcpy_movable.h"
#include "drake/common/test_utilities/symbolic_test_util.h"
namespace drake {
using std::numeric_limits;
using test::IsMemcpyMovable;
namespace symbolic {
namespace {
using std::map;
using std::runtime_error;
using std::set;
using std::transform;
using std::unordered_map;
using std::unordered_set;
using std::vector;
using test::all_of;
using test::any_of;
using test::ExprEqual;
using test::FormulaEqual;
using test::FormulaLess;
using test::FormulaNotEqual;
using test::FormulaNotLess;
using test::VarEqual;
// Checks if a given 'formulas' is ordered by Formula::Less.
void CheckOrdering(const vector<Formula>& formulas) {
for (size_t i{0}; i < formulas.size(); ++i) {
for (size_t j{0}; j < formulas.size(); ++j) {
if (i < j) {
EXPECT_PRED2(FormulaLess, formulas[i], formulas[j])
<< "(Formulas[" << i << "] = " << formulas[i] << ")"
<< " is not less than "
<< "(Formulas[" << j << "] = " << formulas[j] << ")";
EXPECT_PRED2(FormulaNotLess, formulas[j], formulas[i])
<< "(Formulas[" << j << "] = " << formulas[j] << ")"
<< " is less than "
<< "(Formulas[" << i << "] = " << formulas[i] << ")";
} else if (i > j) {
EXPECT_PRED2(FormulaLess, formulas[j], formulas[i])
<< "(Formulas[" << j << "] = " << formulas[j] << ")"
<< " is not less than "
<< "(Formulas[" << i << "] = " << formulas[i] << ")";
EXPECT_PRED2(FormulaNotLess, formulas[i], formulas[j])
<< "(Formulas[" << i << "] = " << formulas[i] << ")"
<< " is less than "
<< "(Formulas[" << j << "] = " << formulas[j] << ")";
} else {
// i == j
EXPECT_PRED2(FormulaNotLess, formulas[i], formulas[j])
<< "(Formulas[" << i << "] = " << formulas[i] << ")"
<< " is less than "
<< "(Formulas[" << j << "] = " << formulas[j] << ")";
EXPECT_PRED2(FormulaNotLess, formulas[j], formulas[i])
<< "(Formulas[" << j << "] = " << formulas[j] << ")"
<< " is less than "
<< "(Formulas[" << i << "] = " << formulas[i] << ")";
}
}
}
}
// Provides common variables that are used by the following tests.
class SymbolicFormulaTest : public ::testing::Test {
protected:
const Variable var_x_{"x", Variable::Type::CONTINUOUS};
const Variable var_y_{"y", Variable::Type::CONTINUOUS};
const Variable var_z_{"z", Variable::Type::CONTINUOUS};
const Variable var_b1_{"x", Variable::Type::BOOLEAN};
const Variable var_b2_{"y", Variable::Type::BOOLEAN};
const Expression x_{var_x_};
const Expression y_{var_y_};
const Expression z_{var_z_};
const Expression e1_{x_ + y_};
const Expression e1_prime_{x_ + y_};
const Expression e2_{x_ - y_};
const Expression e3_{x_ + z_};
const Formula b1_{var_b1_};
const Formula b2_{var_b2_};
const Formula tt_{Formula::True()};
const Formula ff_{Formula::False()};
const Formula f1_{x_ + y_ > 0};
const Formula f2_{x_ * y_ < 5};
const Formula f3_{x_ / y_ < 5};
const Formula f4_{x_ - y_ < 5};
const Formula f_eq_{e1_ == 0.0};
const Formula f_neq_{e1_ != 0.0};
const Formula f_lt_{e1_ < 0.0};
const Formula f_lte_{e1_ <= 0.0};
const Formula f_gt_{e1_ > 0.0};
const Formula f_gte_{e1_ >= 0.0};
const Formula f_and_{f1_ && f2_};
const Formula f_or_{f1_ || f2_};
const Formula not_f_or_{!f_or_};
const Formula f_forall_{forall({var_x_, var_y_}, f_or_)};
const Formula f_isnan_{isnan(Expression::NaN())};
const Environment env1_{{var_x_, 1}, {var_y_, 1}};
const Environment env2_{{var_x_, 3}, {var_y_, 4}};
const Environment env3_{{var_x_, -2}, {var_y_, -5}};
const Environment env4_{{var_x_, -1}, {var_y_, -1}};
// The following matrices will be initialized in SetUp().
Eigen::Matrix<Expression, 2, 2> m_static_2x2_;
MatrixX<Expression> m_dynamic_2x2_;
Eigen::Matrix<Expression, 3, 3> m_static_3x3_;
// The following formulas will be initialized in SetUp().
Formula f_psd_static_2x2_;
Formula f_psd_dynamic_2x2_;
Formula f_psd_static_3x3_;
void SetUp() override {
// clang-format off
m_static_2x2_ << (x_ + y_), -1.0,
-1.0, y_;
m_dynamic_2x2_.resize(2, 2);
m_dynamic_2x2_ << (x_ + y_), 1.0,
1.0, y_;
m_static_3x3_ << (x_ + y_), 3.14, z_,
3.14, y_, z_ * z_,
z_, z_ * z_, 1.0;
// clang-format on
f_psd_static_2x2_ = positive_semidefinite(m_static_2x2_);
f_psd_dynamic_2x2_ = positive_semidefinite(m_dynamic_2x2_);
f_psd_static_3x3_ = positive_semidefinite(m_static_3x3_);
}
};
TEST_F(SymbolicFormulaTest, LessKind) {
// clang-format off
CheckOrdering({
Formula::False(),
Formula::True(),
b1_,
b2_,
x_ == y_,
x_ != y_,
x_> y_,
x_ >= y_,
x_ < y_,
x_ <= y_,
f1_ && f2_,
f1_ || f2_,
!f1_,
f_forall_,
f_isnan_,
f_psd_static_2x2_,
f_psd_dynamic_2x2_,
f_psd_static_3x3_});
// clang-format on
}
TEST_F(SymbolicFormulaTest, LessTrueFalse) {
CheckOrdering({Formula::False(), Formula::True()});
}
TEST_F(SymbolicFormulaTest, LessEq) {
const Formula f1{x_ == y_};
const Formula f2{x_ == z_};
const Formula f3{y_ == z_};
CheckOrdering({f1, f2, f3});
}
TEST_F(SymbolicFormulaTest, LessNeq) {
const Formula f1{x_ != y_};
const Formula f2{x_ != z_};
const Formula f3{y_ != z_};
CheckOrdering({f1, f2, f3});
}
TEST_F(SymbolicFormulaTest, LessGt) {
const Formula f1{x_ > y_};
const Formula f2{x_ > z_};
const Formula f3{y_ > z_};
CheckOrdering({f1, f2, f3});
}
TEST_F(SymbolicFormulaTest, LessGeq) {
const Formula f1{x_ >= y_};
const Formula f2{x_ >= z_};
const Formula f3{y_ >= z_};
CheckOrdering({f1, f2, f3});
}
TEST_F(SymbolicFormulaTest, LessLt) {
const Formula f1{x_ < y_};
const Formula f2{x_ < z_};
const Formula f3{y_ < z_};
CheckOrdering({f1, f2, f3});
}
TEST_F(SymbolicFormulaTest, LessLeq) {
const Formula f1{x_ <= y_};
const Formula f2{x_ <= z_};
const Formula f3{y_ <= z_};
CheckOrdering({f1, f2, f3});
}
TEST_F(SymbolicFormulaTest, LessAnd) {
const Formula and1{f1_ && f2_ && f3_};
const Formula and2{f1_ && f3_};
const Formula and3{f2_ && f3_};
CheckOrdering({and1, and2, and3});
}
TEST_F(SymbolicFormulaTest, LessOr) {
const Formula or1{f1_ || f2_ || f3_};
const Formula or2{f1_ || f3_};
const Formula or3{f2_ || f3_};
CheckOrdering({or1, or2, or3});
}
TEST_F(SymbolicFormulaTest, LessNot) {
const Formula not1{!f1_};
const Formula not2{!f2_};
const Formula not3{!f3_};
CheckOrdering({not1, not2, not3});
}
TEST_F(SymbolicFormulaTest, LessForall) {
const Formula forall1{forall({var_x_, var_y_}, f1_)};
const Formula forall2{forall({var_x_, var_y_, var_z_}, f1_)};
const Formula forall3{forall({var_x_, var_y_, var_z_}, f2_)};
CheckOrdering({forall1, forall2, forall3});
}
TEST_F(SymbolicFormulaTest, True) {
EXPECT_PRED2(FormulaEqual, Formula::True(), Formula{tt_});
EXPECT_TRUE(Formula::True().Evaluate());
EXPECT_EQ(Formula::True().GetFreeVariables().size(), 0u);
EXPECT_EQ(Formula::True().to_string(), "True");
EXPECT_TRUE(is_true(Formula::True()));
}
TEST_F(SymbolicFormulaTest, False) {
EXPECT_PRED2(FormulaEqual, Formula::False(), Formula{ff_});
EXPECT_FALSE(Formula::False().Evaluate());
EXPECT_EQ(Formula::False().GetFreeVariables().size(), 0u);
EXPECT_EQ(Formula::False().to_string(), "False");
EXPECT_TRUE(is_false(Formula::False()));
}
TEST_F(SymbolicFormulaTest, Variable) {
// Tests is_variable and get_variable functions.
EXPECT_TRUE(is_variable(b1_));
EXPECT_TRUE(is_variable(b2_));
EXPECT_PRED2(VarEqual, get_variable(b1_), var_b1_);
EXPECT_PRED2(VarEqual, get_variable(b2_), var_b2_);
}
TEST_F(SymbolicFormulaTest, IsNaN) {
// Things that aren't NaN are !isnan.
const Expression zero{0};
const Formula zero_is_nan{isnan(zero)};
EXPECT_FALSE(zero_is_nan.Evaluate());
// Things that _are_ NaN are exceptions, which is consistent with Expression
// disallowing NaNs to be evaluated at runtime.
const Expression nan{NAN};
const Formula nan_is_nan{isnan(nan)};
EXPECT_THROW(nan_is_nan.Evaluate(), runtime_error);
// Buried NaNs are safe.
const Formula ite_nan1{isnan(if_then_else(tt_, zero, nan))};
EXPECT_FALSE(ite_nan1.Evaluate());
// This case will be evaluated to NaN and we will have runtime_error.
const Formula ite_nan2{isnan(if_then_else(ff_, zero, nan))};
EXPECT_THROW(ite_nan2.Evaluate(), runtime_error);
// Formula isnan(x / y) should throw a runtime_error when evaluated with
// an environment mapping both of x and y to zero, because 0.0 / 0.0 = NaN.
const Expression x_div_y{x_ / y_};
const Environment env1{{var_x_, 0.0}, {var_y_, 0.0}};
EXPECT_THROW(isnan(x_div_y).Evaluate(env1), runtime_error);
// If the included expression `e` is not evaluated to NaN, `isnan(e)` should
// return false.
const Environment env2{{var_x_, 3.0}, {var_y_, 2.0}};
EXPECT_FALSE(isnan(x_div_y).Evaluate(env2));
}
TEST_F(SymbolicFormulaTest, EqualTo1) {
const Formula f_eq{x_ == y_};
const Formula f_ne{x_ != y_};
const Formula f_lt{x_ < y_};
const Formula f_le{x_ <= y_};
const Formula f_gt{x_ > y_};
const Formula f_ge{x_ >= y_};
EXPECT_PRED2(FormulaEqual, f_eq, f_eq);
EXPECT_PRED2(FormulaEqual, f_eq, x_ == y_);
EXPECT_PRED2(FormulaNotEqual, f_eq, x_ == z_);
EXPECT_PRED2(FormulaNotEqual, f_eq, f_ne);
EXPECT_PRED2(FormulaNotEqual, f_eq, f_lt);
EXPECT_PRED2(FormulaNotEqual, f_eq, f_le);
EXPECT_PRED2(FormulaNotEqual, f_eq, f_gt);
EXPECT_PRED2(FormulaNotEqual, f_eq, f_ge);
EXPECT_PRED2(FormulaNotEqual, f_ne, f_eq);
EXPECT_PRED2(FormulaEqual, f_ne, f_ne);
EXPECT_PRED2(FormulaEqual, f_ne, x_ != y_);
EXPECT_PRED2(FormulaNotEqual, f_ne, x_ != z_);
EXPECT_PRED2(FormulaNotEqual, f_ne, f_lt);
EXPECT_PRED2(FormulaNotEqual, f_ne, f_le);
EXPECT_PRED2(FormulaNotEqual, f_ne, f_gt);
EXPECT_PRED2(FormulaNotEqual, f_ne, f_ge);
EXPECT_PRED2(FormulaNotEqual, f_lt, f_eq);
EXPECT_PRED2(FormulaNotEqual, f_lt, f_ne);
EXPECT_PRED2(FormulaEqual, f_lt, f_lt);
EXPECT_PRED2(FormulaEqual, f_lt, x_ < y_);
EXPECT_PRED2(FormulaNotEqual, f_lt, x_ < z_);
EXPECT_PRED2(FormulaNotEqual, f_lt, f_le);
EXPECT_PRED2(FormulaNotEqual, f_lt, f_gt);
EXPECT_PRED2(FormulaNotEqual, f_lt, f_ge);
EXPECT_PRED2(FormulaNotEqual, f_le, f_eq);
EXPECT_PRED2(FormulaNotEqual, f_le, f_ne);
EXPECT_PRED2(FormulaNotEqual, f_le, f_lt);
EXPECT_PRED2(FormulaEqual, f_le, f_le);
EXPECT_PRED2(FormulaEqual, f_le, x_ <= y_);
EXPECT_PRED2(FormulaNotEqual, f_le, x_ <= z_);
EXPECT_PRED2(FormulaNotEqual, f_le, f_gt);
EXPECT_PRED2(FormulaNotEqual, f_le, f_ge);
EXPECT_PRED2(FormulaNotEqual, f_gt, f_eq);
EXPECT_PRED2(FormulaNotEqual, f_gt, f_ne);
EXPECT_PRED2(FormulaNotEqual, f_gt, f_lt);
EXPECT_PRED2(FormulaNotEqual, f_gt, f_le);
EXPECT_PRED2(FormulaEqual, f_gt, f_gt);
EXPECT_PRED2(FormulaEqual, f_gt, x_ > y_);
EXPECT_PRED2(FormulaNotEqual, f_gt, x_ > z_);
EXPECT_PRED2(FormulaNotEqual, f_gt, f_ge);
EXPECT_PRED2(FormulaNotEqual, f_ge, f_eq);
EXPECT_PRED2(FormulaNotEqual, f_ge, f_ne);
EXPECT_PRED2(FormulaNotEqual, f_ge, f_lt);
EXPECT_PRED2(FormulaNotEqual, f_ge, f_le);
EXPECT_PRED2(FormulaNotEqual, f_ge, f_gt);
EXPECT_PRED2(FormulaEqual, f_ge, f_ge);
EXPECT_PRED2(FormulaEqual, f_ge, x_ >= y_);
EXPECT_PRED2(FormulaNotEqual, f_ge, x_ >= z_);
}
TEST_F(SymbolicFormulaTest, EqualTo2) {
const Formula f1{x_ == y_};
const Formula f2{y_ > z_};
const Formula f_and{f1 && f2};
const Formula f_or{f1 || f2};
const Formula f_not{!f1};
EXPECT_PRED2(FormulaEqual, f_and, f_and);
EXPECT_PRED2(FormulaNotEqual, f_and, f_or);
EXPECT_PRED2(FormulaNotEqual, f_and, f_not);
EXPECT_PRED2(FormulaNotEqual, f_or, f_and);
EXPECT_PRED2(FormulaEqual, f_or, f_or);
EXPECT_PRED2(FormulaNotEqual, f_or, f_not);
EXPECT_PRED2(FormulaNotEqual, f_not, f_and);
EXPECT_PRED2(FormulaNotEqual, f_not, f_or);
EXPECT_PRED2(FormulaEqual, f_not, f_not);
}
TEST_F(SymbolicFormulaTest, EqualTo3) {
const Formula f_forall1{forall({var_x_, var_y_}, f_or_)};
const Formula f_forall2{forall({var_x_, var_y_, var_z_}, f_or_)};
const Formula f_forall3{forall({var_x_, var_y_}, f_and_)};
const Formula f_forall4{forall({var_x_, var_y_, var_z_}, f_and_)};
EXPECT_PRED2(FormulaEqual, f_forall1, f_forall1);
EXPECT_PRED2(FormulaNotEqual, f_forall1, f_forall2);
EXPECT_PRED2(FormulaNotEqual, f_forall1, f_forall3);
EXPECT_PRED2(FormulaNotEqual, f_forall1, f_forall4);
EXPECT_PRED2(FormulaNotEqual, f_forall2, f_forall1);
EXPECT_PRED2(FormulaEqual, f_forall2, f_forall2);
EXPECT_PRED2(FormulaNotEqual, f_forall2, f_forall3);
EXPECT_PRED2(FormulaNotEqual, f_forall2, f_forall4);
EXPECT_PRED2(FormulaNotEqual, f_forall3, f_forall1);
EXPECT_PRED2(FormulaNotEqual, f_forall3, f_forall2);
EXPECT_PRED2(FormulaEqual, f_forall3, f_forall3);
EXPECT_PRED2(FormulaNotEqual, f_forall3, f_forall4);
EXPECT_PRED2(FormulaNotEqual, f_forall4, f_forall1);
EXPECT_PRED2(FormulaNotEqual, f_forall4, f_forall2);
EXPECT_PRED2(FormulaNotEqual, f_forall4, f_forall3);
EXPECT_PRED2(FormulaEqual, f_forall4, f_forall4);
}
TEST_F(SymbolicFormulaTest, Eq) {
const Formula f1{e1_ == e1_}; // true
EXPECT_PRED2(FormulaEqual, f1, Formula::True());
EXPECT_PRED2(FormulaNotEqual, f1, Formula::False());
const Formula f2{e1_ == e1_prime_}; // true
EXPECT_PRED2(FormulaEqual, f2, Formula::True());
EXPECT_PRED2(FormulaNotEqual, f2, Formula::False());
const Formula f3{e1_ == e3_};
EXPECT_PRED2(FormulaNotEqual, f3, Formula::True());
const Formula f4{e2_ == e3_};
EXPECT_PRED2(FormulaNotEqual, f4, Formula::True());
const Formula f5{x_ == x_ + 5}; // false
EXPECT_PRED2(FormulaEqual, f5, Formula::False());
EXPECT_TRUE(all_of({f3, f4}, is_equal_to));
EXPECT_FALSE(any_of({f1, f2, f5}, is_equal_to));
const Environment env{{var_x_, 2}, {var_y_, 3}, {var_z_, 3}};
EXPECT_EQ(f3.Evaluate(env), (2 + 3) == (2 + 3));
EXPECT_EQ(f4.Evaluate(env), (2 - 3) == (2 + 3));
EXPECT_EQ((5 + x_ == 3 + y_).to_string(), "((5 + x) == (3 + y))");
}
TEST_F(SymbolicFormulaTest, Neq) {
const Formula f1{e1_ != e1_}; // false
EXPECT_PRED2(FormulaEqual, f1, Formula::False());
EXPECT_PRED2(FormulaNotEqual, f1, Formula::True());
const Formula f2{e1_ != e1_prime_}; // false
EXPECT_PRED2(FormulaEqual, f2, Formula::False());
EXPECT_PRED2(FormulaNotEqual, f2, Formula::True());
const Formula f3{e1_ != e3_};
EXPECT_PRED2(FormulaNotEqual, f3, Formula::False());
const Formula f4{e2_ != e3_};
EXPECT_PRED2(FormulaNotEqual, f4, Formula::False());
const Formula f5{x_ != x_ + 5}; // true
EXPECT_PRED2(FormulaEqual, f5, Formula::True());
EXPECT_TRUE(all_of({f3, f4}, is_not_equal_to));
EXPECT_FALSE(any_of({f1, f2, f5}, is_not_equal_to));
const Environment env{{var_x_, 2}, {var_y_, 3}, {var_z_, 3}};
EXPECT_EQ(f3.Evaluate(env), (2 + 3) != (2 + 3));
EXPECT_EQ(f4.Evaluate(env), (2 - 3) != (2 + 3));
EXPECT_EQ((5 + x_ != 3 + y_).to_string(), "((5 + x) != (3 + y))");
}
TEST_F(SymbolicFormulaTest, Lt) {
const Formula f1{e1_ < e1_}; // false
EXPECT_PRED2(FormulaEqual, f1, Formula::False());
EXPECT_PRED2(FormulaNotEqual, f1, Formula::True());
const Formula f2{e1_ < e1_prime_}; // false
EXPECT_PRED2(FormulaEqual, f2, Formula::False());
EXPECT_PRED2(FormulaNotEqual, f2, Formula::True());
const Formula f3{e1_ < e3_};
EXPECT_PRED2(FormulaNotEqual, f3, Formula::True());
const Formula f4{e2_ < e3_};
EXPECT_PRED2(FormulaNotEqual, f4, Formula::True());
const Formula f5{x_ < x_ + 5}; // true
EXPECT_PRED2(FormulaEqual, f5, Formula::True());
EXPECT_TRUE(all_of({f3, f4}, is_less_than));
EXPECT_FALSE(any_of({f1, f2, f5}, is_less_than));
const Environment env{{var_x_, 2}, {var_y_, 3}, {var_z_, 3}};
EXPECT_EQ(f3.Evaluate(env), (2 + 3) < (2 + 3));
EXPECT_EQ(f4.Evaluate(env), (2 - 3) < (2 + 3));
EXPECT_EQ((5 + x_ < 3 + y_).to_string(), "((5 + x) < (3 + y))");
}
TEST_F(SymbolicFormulaTest, Gt) {
const Formula f1{e1_ > e1_}; // false
EXPECT_PRED2(FormulaEqual, f1, Formula::False());
EXPECT_PRED2(FormulaNotEqual, f1, Formula::True());
const Formula f2{e1_ > e1_prime_}; // false
EXPECT_PRED2(FormulaEqual, f2, Formula::False());
EXPECT_PRED2(FormulaNotEqual, f2, Formula::True());
const Formula f3{e1_ > e3_};
EXPECT_PRED2(FormulaNotEqual, f3, Formula::True());
const Formula f4{e2_ > e3_};
EXPECT_PRED2(FormulaNotEqual, f4, Formula::True());
const Formula f5{x_ > x_ + 5}; // false
EXPECT_PRED2(FormulaEqual, f5, Formula::False());
EXPECT_TRUE(all_of({f3, f4}, is_greater_than));
EXPECT_FALSE(any_of({f1, f2, f5}, is_greater_than));
const Environment env{{var_x_, 2}, {var_y_, 3}, {var_z_, 3}};
EXPECT_EQ(f3.Evaluate(env), (2 + 3) > (2 + 3));
EXPECT_EQ(f4.Evaluate(env), (2 - 3) > (2 + 3));
EXPECT_EQ((5 + x_ > 3 + y_).to_string(), "((5 + x) > (3 + y))");
}
TEST_F(SymbolicFormulaTest, Leq) {
const Formula f1{e1_ <= e1_}; // true
EXPECT_PRED2(FormulaEqual, f1, Formula::True());
EXPECT_PRED2(FormulaNotEqual, f1, Formula::False());
const Formula f2{e1_ <= e1_prime_}; // true
EXPECT_PRED2(FormulaEqual, f2, Formula::True());
EXPECT_PRED2(FormulaNotEqual, f2, Formula::False());
const Formula f3{e1_ <= e3_};
EXPECT_PRED2(FormulaNotEqual, f3, Formula::True());
const Formula f4{e2_ <= e3_};
EXPECT_PRED2(FormulaNotEqual, f4, Formula::True());
const Formula f5{x_ <= x_ + 5}; // true
EXPECT_PRED2(FormulaEqual, f5, Formula::True());
EXPECT_TRUE(all_of({f3, f4}, is_less_than_or_equal_to));
EXPECT_FALSE(any_of({f1, f2, f5}, is_less_than_or_equal_to));
const Environment env{{var_x_, 2}, {var_y_, 3}, {var_z_, 3}};
EXPECT_EQ(f3.Evaluate(env), (2 + 3) <= (2 + 3));
EXPECT_EQ(f4.Evaluate(env), (2 - 3) <= (2 + 3));
EXPECT_EQ((5 + x_ <= 3 + y_).to_string(), "((5 + x) <= (3 + y))");
}
TEST_F(SymbolicFormulaTest, Geq) {
const Formula f1{e1_ >= e1_}; // true
EXPECT_PRED2(FormulaEqual, f1, Formula::True());
EXPECT_PRED2(FormulaNotEqual, f1, Formula::False());
const Formula f2{e1_ >= e1_prime_}; // true
EXPECT_PRED2(FormulaEqual, f2, Formula::True());
EXPECT_PRED2(FormulaNotEqual, f2, Formula::False());
const Formula f3{e1_ >= e3_};
EXPECT_PRED2(FormulaNotEqual, f3, Formula::True());
const Formula f4{e2_ >= e3_};
EXPECT_PRED2(FormulaNotEqual, f4, Formula::True());
const Formula f5{x_ >= x_ + 5}; // false
EXPECT_PRED2(FormulaEqual, f5, Formula::False());
EXPECT_TRUE(all_of({f3, f4}, is_greater_than_or_equal_to));
EXPECT_FALSE(any_of({f1, f2, f5}, is_greater_than_or_equal_to));
const Environment env{{var_x_, 2}, {var_y_, 3}, {var_z_, 3}};
EXPECT_EQ(f3.Evaluate(env), (2 + 3) >= (2 + 3));
EXPECT_EQ(f4.Evaluate(env), (2 - 3) >= (2 + 3));
EXPECT_EQ((5 + x_ >= 3 + y_).to_string(), "((5 + x) >= (3 + y))");
}
TEST_F(SymbolicFormulaTest, And1) {
EXPECT_PRED2(FormulaEqual, tt_, tt_ && tt_);
EXPECT_PRED2(FormulaEqual, ff_, ff_ && tt_);
EXPECT_PRED2(FormulaEqual, ff_, tt_ && ff_);
EXPECT_PRED2(FormulaEqual, ff_, ff_ && ff_);
EXPECT_PRED2(FormulaEqual, f1_, tt_ && f1_);
EXPECT_PRED2(FormulaEqual, f1_, f1_ && tt_);
EXPECT_PRED2(FormulaEqual, make_conjunction({tt_, f1_, tt_}), f1_);
EXPECT_PRED2(FormulaEqual, make_conjunction({tt_, tt_, ff_}), ff_);
// Checks if flattening works: (f₁ ∧ f₂) ∧ (f₃ ∧ f₄) => f₁ ∧ f₂ ∧ f₃ ∧ f₄.
EXPECT_PRED2(FormulaEqual, make_conjunction({f1_ && f2_, f3_ && f4_}),
make_conjunction({f1_, f2_, f3_, f4_}));
// Empty conjunction = True.
EXPECT_PRED2(FormulaEqual, make_conjunction({}), Formula::True());
}
TEST_F(SymbolicFormulaTest, And2) {
EXPECT_EQ(f_and_.Evaluate(env1_), (1 + 1 > 0) && (1 * 1 < 5));
EXPECT_EQ(f_and_.Evaluate(env2_), (3 + 4 > 0) && (3 * 4 < 5));
EXPECT_EQ(f_and_.Evaluate(env3_), (-2 + -5 > 0) && (-2 * -5 < 5));
EXPECT_EQ(f_and_.Evaluate(env4_), (-1 + -1 > 0) && (-1 * -1 < 5));
EXPECT_EQ((x_ == 3 && y_ == 5).to_string(), "((x == 3) and (y == 5))");
EXPECT_TRUE(is_conjunction(x_ == 3 && y_ == 5));
EXPECT_TRUE(is_nary(x_ == 3 && y_ == 5));
}
TEST_F(SymbolicFormulaTest, And3) {
// Flattening
EXPECT_PRED2(FormulaEqual, f1_ && f2_ && f3_ && f4_,
f1_ && f2_ && f3_ && f4_);
EXPECT_PRED2(FormulaEqual, (f1_ && f2_) && (f3_ && f4_),
f1_ && f2_ && f3_ && f4_);
EXPECT_PRED2(FormulaEqual, f1_ && (f2_ && f3_) && f4_,
f1_ && f2_ && f3_ && f4_);
EXPECT_PRED2(FormulaEqual, f1_ && ((f2_ && f3_) && f4_),
f1_ && f2_ && f3_ && f4_);
// Remove duplicate
EXPECT_PRED2(FormulaEqual, f1_ && f2_ && f1_, f1_ && f2_);
}
TEST_F(SymbolicFormulaTest, And4) {
// Simplification: f && f => f.
for (const Formula& f :
{b1_, b2_, tt_, ff_, f1_, f2_, f3_, f4_, f_eq_, f_neq_, f_lt_, f_lte_,
f_gt_, f_gte_, f_and_, f_or_, not_f_or_, f_forall_}) {
EXPECT_PRED2(FormulaEqual, f && f, f);
}
}
TEST_F(SymbolicFormulaTest, And5) {
// Flatten and removing duplicates. This is the example mentioned in
// symbolic_formula.h file:
// (f1 && f2) && f1 => f1 && f2
// f1 && (f2 && f1) => f1 && f2
EXPECT_PRED2(FormulaEqual, (f1_ && f2_) && f1_, f1_ && f2_);
EXPECT_PRED2(FormulaEqual, f1_ && (f2_ && f1_), f1_ && f2_);
EXPECT_PRED2(FormulaEqual, (f1_ && f2_) && f1_, f1_ && (f2_ && f1_));
}
TEST_F(SymbolicFormulaTest, AndWithBooleanVariableOperator) {
// Checks if operator&& works Boolean variables as expected.
const Formula f1{var_b1_ && var_b2_};
ASSERT_TRUE(is_conjunction(f1));
EXPECT_EQ(get_operands(f1).count(b1_), 1);
EXPECT_EQ(get_operands(f1).count(b2_), 1);
const Formula f2{var_b1_ && (y_ > 0)};
ASSERT_TRUE(is_conjunction(f2));
EXPECT_EQ(get_operands(f2).count(b1_), 1);
const Formula f3{(x_ > 0) && var_b2_};
ASSERT_TRUE(is_conjunction(f3));
EXPECT_EQ(get_operands(f3).count(b2_), 1);
}
TEST_F(SymbolicFormulaTest, AndWithBooleanVariableEvaluate) {
// Checks the evaluations of conjunctive formulas with Boolean variables.
const Formula f{b1_ && b2_};
const Environment env1{{var_b1_, true}, {var_b2_, true}};
const Environment env2{{var_b1_, true}, {var_b2_, false}};
const Environment env3{{var_b1_, false}, {var_b2_, true}};
const Environment env4{{var_b1_, false}, {var_b2_, false}};
EXPECT_TRUE(f.Evaluate(env1));
EXPECT_FALSE(f.Evaluate(env2));
EXPECT_FALSE(f.Evaluate(env3));
EXPECT_FALSE(f.Evaluate(env4));
}
TEST_F(SymbolicFormulaTest, Or1) {
EXPECT_PRED2(FormulaEqual, tt_, tt_ || tt_);
EXPECT_PRED2(FormulaEqual, tt_, ff_ || tt_);
EXPECT_PRED2(FormulaEqual, tt_, tt_ || ff_);
EXPECT_PRED2(FormulaEqual, ff_, ff_ || ff_);
EXPECT_PRED2(FormulaEqual, f1_, ff_ || f1_);
EXPECT_PRED2(FormulaEqual, f1_, f1_ || ff_);
EXPECT_PRED2(FormulaEqual, make_disjunction({ff_, f1_, ff_}), f1_);
EXPECT_PRED2(FormulaEqual, make_disjunction({ff_, ff_, tt_}), tt_);
// Checks if flattening works: (f₁ ∨ f₂) ∨ (f₃ ∨ f₄) => f₁ ∨ f₂ ∨ f₃ ∨ f₄.
EXPECT_PRED2(FormulaEqual, make_disjunction({f1_ || f2_, f3_ || f4_}),
make_disjunction({f1_, f2_, f3_, f4_}));
// Empty disjunction = False.
EXPECT_PRED2(FormulaEqual, make_disjunction({}), Formula::False());
}
TEST_F(SymbolicFormulaTest, Or2) {
EXPECT_EQ(f_or_.Evaluate(env1_), (1 + 1 > 0) || (1 * 1 < 5));
EXPECT_EQ(f_or_.Evaluate(env2_), (3 + 4 > 0) || (3 * 4 < 5));
EXPECT_EQ(f_or_.Evaluate(env3_), (-2 + -5 > 0) || (-2 * -5 < 5));
EXPECT_EQ(f_or_.Evaluate(env4_), (-1 + -1 > 0) || (-1 * -1 < 5));
EXPECT_EQ((x_ == 3 || y_ == 5).to_string(), "((x == 3) or (y == 5))");
EXPECT_TRUE(is_disjunction(x_ == 3 || y_ == 5));
EXPECT_TRUE(is_nary(x_ == 3 || y_ == 5));
}
TEST_F(SymbolicFormulaTest, Or3) {
// Flattening
EXPECT_PRED2(FormulaEqual, f1_ || f2_ || f3_ || f4_,
f1_ || f2_ || f3_ || f4_);
EXPECT_PRED2(FormulaEqual, (f1_ || f2_) || (f3_ || f4_),
f1_ || f2_ || f3_ || f4_);
EXPECT_PRED2(FormulaEqual, f1_ || (f2_ || f3_) || f4_,
f1_ || f2_ || f3_ || f4_);
EXPECT_PRED2(FormulaEqual, f1_ || ((f2_ || f3_) || f4_),
f1_ || f2_ || f3_ || f4_);
// Remove duplicate
EXPECT_PRED2(FormulaEqual, f1_ || f2_ || f1_, f1_ || f2_);
}
TEST_F(SymbolicFormulaTest, Or4) {
// Simplification: f || f => f.
for (const Formula& f :
{b1_, b2_, tt_, ff_, f1_, f2_, f3_, f4_, f_eq_, f_neq_, f_lt_, f_lte_,
f_gt_, f_gte_, f_and_, f_or_, not_f_or_, f_forall_}) {
EXPECT_PRED2(FormulaEqual, f || f, f);
}
}
TEST_F(SymbolicFormulaTest, Or5) {
// Flatten and removing duplicates. This is a disjunctive version of the
// example mentioned in symbolic_formula.h file:
// (f1 || f2) || f1 => f1 || f2
// f1 || (f2 || f1) => f1 || f2
EXPECT_PRED2(FormulaEqual, (f1_ || f2_) || f1_, f1_ || f2_);
EXPECT_PRED2(FormulaEqual, f1_ || (f2_ || f1_), f1_ || f2_);
EXPECT_PRED2(FormulaEqual, (f1_ || f2_) || f1_, f1_ || (f2_ || f1_));
}
TEST_F(SymbolicFormulaTest, OrWithBooleanVariableOperator) {
// Checks if operator|| works with Boolean variables as expected.
const Formula f1{var_b1_ || var_b2_};
ASSERT_TRUE(is_disjunction(f1));
EXPECT_EQ(get_operands(f1).count(b1_), 1);
EXPECT_EQ(get_operands(f1).count(b2_), 1);
const Formula f2{var_b1_ || (y_ > 0)};
ASSERT_TRUE(is_disjunction(f2));
EXPECT_EQ(get_operands(f2).count(b1_), 1);
const Formula f3{(x_ > 0) || var_b2_};
ASSERT_TRUE(is_disjunction(f3));
EXPECT_EQ(get_operands(f3).count(b2_), 1);
}
TEST_F(SymbolicFormulaTest, OrWithBooleanVariableEvaluate) {
// Checks the evaluations of disjunctive formulas with Boolean variables.
const Formula f{b1_ || b2_};
const Environment env1{{var_b1_, true}, {var_b2_, true}};
const Environment env2{{var_b1_, true}, {var_b2_, false}};
const Environment env3{{var_b1_, false}, {var_b2_, true}};
const Environment env4{{var_b1_, false}, {var_b2_, false}};
EXPECT_TRUE(f.Evaluate(env1));
EXPECT_TRUE(f.Evaluate(env2));
EXPECT_TRUE(f.Evaluate(env3));
EXPECT_FALSE(f.Evaluate(env4));
}
TEST_F(SymbolicFormulaTest, Not1) {
EXPECT_PRED2(FormulaEqual, ff_, !tt_);
EXPECT_PRED2(FormulaEqual, tt_, !ff_);
EXPECT_PRED2(FormulaEqual, tt_, !(!tt_));
EXPECT_PRED2(FormulaEqual, ff_, !(!ff_));
EXPECT_PRED2(FormulaEqual, !(x_ == 5), !(x_ == 5));
EXPECT_PRED2(FormulaNotEqual, !(x_ == 5), !(x_ == 6));
}
TEST_F(SymbolicFormulaTest, Not2) {
EXPECT_EQ(not_f_or_.Evaluate(env1_), !((1 + 1 > 0) || (1 * 1 < 5)));
EXPECT_EQ(not_f_or_.Evaluate(env2_), !((3 + 4 > 0) || (3 * 4 < 5)));
EXPECT_EQ(not_f_or_.Evaluate(env3_), !((-2 + -5 > 0) || (-2 * -5 < 5)));
EXPECT_EQ(not_f_or_.Evaluate(env4_), !((-1 + -1 > 0) || (-1 * -1 < 5)));
EXPECT_EQ((!(x_ == 5)).to_string(), "!((x == 5))");
EXPECT_TRUE(is_negation(!(x_ == 5)));
}
// Tests if `!(!f)` is simplified into `f` for all formulas in
// SymbolicFormulaTest.
TEST_F(SymbolicFormulaTest, DoubleNegationSimplification) {
const vector<Formula> collection{b1_, b2_, tt_, ff_, f1_,
f2_, f3_, f4_, f_eq_, f_neq_,
f_lt_, f_lte_, f_gt_, f_gte_, f_and_,
f_or_, not_f_or_, f_forall_, f_isnan_};
vector<Formula> negated_collection{collection.size()};
transform(collection.cbegin(), collection.cend(), negated_collection.begin(),
[](const Formula& f) { return !f; });
for (size_t i = 0; i < collection.size(); ++i) {
EXPECT_PRED2(FormulaEqual, collection[i], !(negated_collection[i]));
}
}
TEST_F(SymbolicFormulaTest, NotWithBooleanVariableOperator) {
// Checks if operator! works with Boolean variables as expected.
const Formula f{!var_b1_};
EXPECT_TRUE(is_negation(f));
ASSERT_TRUE(is_variable(get_operand(f)));
EXPECT_PRED2(VarEqual, get_variable(get_operand(f)), var_b1_);
}
TEST_F(SymbolicFormulaTest, NotWithBooleanVariableEvaluate) {
// Checks the evaluations of negation formulas with a Boolean variable.
const Formula f{!b1_};
const Environment env1{{var_b1_, true}};
const Environment env2{{var_b1_, false}};
EXPECT_FALSE(f.Evaluate(env1));
EXPECT_TRUE(f.Evaluate(env2));
}
TEST_F(SymbolicFormulaTest, Forall1) {
const Formula f1{forall({var_x_, var_y_}, x_ == y_)};
const Formula f2{forall({var_x_, var_y_}, x_ == y_)};
const Formula f3{forall({var_x_, var_y_}, x_ > y_)};
EXPECT_PRED2(FormulaEqual, f1, f2);
EXPECT_PRED2(FormulaNotEqual, f1, f3);
EXPECT_PRED2(FormulaNotEqual, f2, f3);
EXPECT_TRUE(all_of({f1, f2, f3}, is_forall));
}
TEST_F(SymbolicFormulaTest, Forall2) {
const Formula f1{forall({var_x_, var_y_}, x_ == y_)};
EXPECT_THROW(f1.Evaluate(), runtime_error);
}
TEST_F(SymbolicFormulaTest, PSD_Exception) {
auto non_square = Eigen::Matrix<Expression, 2, 3>::Zero().eval();
EXPECT_THROW(positive_semidefinite(non_square), runtime_error);
Eigen::Matrix<Expression, 3, 3> m;
// clang-format off
m << 1.0, 2.0, 3.0,
4.0, 5.0, 6.0,
7.0, 8.0, 9.0;
// clang-format on
// m is not symmetric.
EXPECT_THROW(positive_semidefinite(m), runtime_error);
// positive_semidefinite only takes Eigen::Lower and Eigen::Upper.
EXPECT_THROW(positive_semidefinite(m, Eigen::UnitDiag), runtime_error);
EXPECT_THROW(positive_semidefinite(m, Eigen::ZeroDiag), runtime_error);
EXPECT_THROW(positive_semidefinite(m, Eigen::UnitLower), runtime_error);
EXPECT_THROW(positive_semidefinite(m, Eigen::UnitUpper), runtime_error);
EXPECT_THROW(positive_semidefinite(m, Eigen::StrictlyLower), runtime_error);
EXPECT_THROW(positive_semidefinite(m, Eigen::StrictlyUpper), runtime_error);
EXPECT_THROW(positive_semidefinite(m, Eigen::SelfAdjoint), runtime_error);
EXPECT_THROW(positive_semidefinite(m, Eigen::Symmetric), runtime_error);
}
TEST_F(SymbolicFormulaTest, PSD_GetFreeVariables) {
const Variables vars1{f_psd_static_2x2_.GetFreeVariables()};
EXPECT_EQ(vars1.size(), 2);
EXPECT_TRUE(vars1.include(var_x_));
EXPECT_TRUE(vars1.include(var_y_));
const Variables vars2{f_psd_dynamic_2x2_.GetFreeVariables()};
EXPECT_EQ(vars2.size(), 2);
EXPECT_TRUE(vars2.include(var_x_));
EXPECT_TRUE(vars2.include(var_y_));
const Variables vars3{f_psd_static_3x3_.GetFreeVariables()};
EXPECT_EQ(vars3.size(), 3);
EXPECT_TRUE(vars3.include(var_x_));
EXPECT_TRUE(vars3.include(var_y_));
EXPECT_TRUE(vars3.include(var_z_));
}
TEST_F(SymbolicFormulaTest, PSD_EqualTo) {
EXPECT_TRUE(f_psd_static_2x2_.EqualTo(f_psd_static_2x2_));
EXPECT_FALSE(f_psd_static_2x2_.EqualTo(f_psd_dynamic_2x2_));
EXPECT_FALSE(f_psd_static_2x2_.EqualTo(f_psd_static_3x3_));
EXPECT_FALSE(f_psd_dynamic_2x2_.EqualTo(f_psd_static_2x2_));
EXPECT_TRUE(f_psd_dynamic_2x2_.EqualTo(f_psd_dynamic_2x2_));
EXPECT_FALSE(f_psd_dynamic_2x2_.EqualTo(f_psd_static_3x3_));
EXPECT_FALSE(f_psd_static_3x3_.EqualTo(f_psd_static_2x2_));
EXPECT_FALSE(f_psd_static_3x3_.EqualTo(f_psd_dynamic_2x2_));
EXPECT_TRUE(f_psd_static_3x3_.EqualTo(f_psd_static_3x3_));
}
TEST_F(SymbolicFormulaTest, PSD_Evaluate) {
EXPECT_THROW(f_psd_static_2x2_.Evaluate(), runtime_error);
EXPECT_THROW(f_psd_dynamic_2x2_.Evaluate(), runtime_error);
EXPECT_THROW(f_psd_static_3x3_.Evaluate(), runtime_error);
}
TEST_F(SymbolicFormulaTest, GetFreeVariables) {
const Formula f1{x_ + y_ > 0};
const Formula f2{y_ * z_ < 5};
const Formula f_or{f1 || f2};
const Formula f_forall{forall({var_x_, var_y_}, f_or)};
const Variables vars1{f1.GetFreeVariables()}; // {x_, y_}
EXPECT_EQ(vars1.size(), 2u);
EXPECT_TRUE(vars1.include(var_x_));
EXPECT_TRUE(vars1.include(var_y_));
const Variables vars2{f2.GetFreeVariables()}; // {y_, z_}
EXPECT_EQ(vars2.size(), 2u);
EXPECT_TRUE(vars2.include(var_y_));
EXPECT_TRUE(vars2.include(var_z_));
const Variables vars3{f_or.GetFreeVariables()}; // {x_, y_, z_}
EXPECT_EQ(vars3.size(), 3u);
EXPECT_TRUE(vars3.include(var_x_));
EXPECT_TRUE(vars3.include(var_y_));
EXPECT_TRUE(vars3.include(var_z_));
const Variables vars4{f_forall.GetFreeVariables()}; // {z_}
EXPECT_EQ(vars4.size(), 1u);
EXPECT_TRUE(vars4.include(var_z_));
const Variables vars5{(!f1).GetFreeVariables()}; // {x_, y_}
EXPECT_EQ(vars5.size(), 2u);
EXPECT_TRUE(vars5.include(var_x_));
EXPECT_TRUE(vars5.include(var_y_));
}
TEST_F(SymbolicFormulaTest, ToString) {
EXPECT_EQ(f1_.to_string(), "((x + y) > 0)");
EXPECT_EQ(f2_.to_string(), "((x * y) < 5)");
EXPECT_EQ(f_or_.to_string(), "(((x + y) > 0) or ((x * y) < 5))");
EXPECT_EQ(f_forall_.to_string(),
"forall({x, y}. (((x + y) > 0) or ((x * y) < 5)))");
EXPECT_EQ(f_isnan_.to_string(), "isnan(NaN)");
}
TEST_F(SymbolicFormulaTest, IsTrue) {
EXPECT_TRUE(is_true(tt_));
EXPECT_FALSE(any_of({ff_, f_eq_, f_neq_, f_lt_, f_lte_, f_gt_, f_gte_, f_and_,
f_or_, not_f_or_, f_forall_, f_isnan_, f_psd_static_2x2_,
f_psd_dynamic_2x2_, f_psd_static_3x3_},
is_true));
}
TEST_F(SymbolicFormulaTest, IsFalse) {
EXPECT_TRUE(is_false(ff_));
EXPECT_FALSE(any_of({tt_, f_eq_, f_neq_, f_lt_, f_lte_, f_gt_, f_gte_, f_and_,
f_or_, not_f_or_, f_forall_, f_isnan_, f_psd_static_2x2_,
f_psd_dynamic_2x2_, f_psd_static_3x3_},
is_false));
}
TEST_F(SymbolicFormulaTest, IsEqualTo) {
EXPECT_TRUE(is_equal_to(f_eq_));
EXPECT_FALSE(any_of({tt_, ff_, f_neq_, f_lt_, f_lte_, f_gt_, f_gte_, f_and_,
f_or_, not_f_or_, f_forall_, f_isnan_, f_psd_static_2x2_,
f_psd_dynamic_2x2_, f_psd_static_3x3_},
is_equal_to));
}
TEST_F(SymbolicFormulaTest, IsNotEqualTo) {
EXPECT_TRUE(is_not_equal_to(f_neq_));
EXPECT_FALSE(any_of({tt_, ff_, f_eq_, f_lt_, f_lte_, f_gt_, f_gte_, f_and_,
f_or_, not_f_or_, f_forall_, f_isnan_, f_psd_static_2x2_,
f_psd_dynamic_2x2_, f_psd_static_3x3_},
is_not_equal_to));
}
TEST_F(SymbolicFormulaTest, IsLessThan) {
EXPECT_TRUE(is_less_than(f_lt_));
EXPECT_FALSE(any_of({tt_, ff_, f_eq_, f_neq_, f_lte_, f_gt_, f_gte_, f_and_,
f_or_, not_f_or_, f_forall_, f_isnan_, f_psd_static_2x2_,
f_psd_dynamic_2x2_, f_psd_static_3x3_},
is_less_than));
}
TEST_F(SymbolicFormulaTest, IsLessThanOrEqualTo) {
EXPECT_TRUE(is_less_than_or_equal_to(f_lte_));
EXPECT_FALSE(any_of({tt_, ff_, f_eq_, f_neq_, f_lt_, f_gt_, f_gte_, f_and_,
f_or_, not_f_or_, f_forall_, f_isnan_, f_psd_static_2x2_,
f_psd_dynamic_2x2_, f_psd_static_3x3_},
is_less_than_or_equal_to));
}
TEST_F(SymbolicFormulaTest, IsGreaterThan) {
EXPECT_TRUE(is_greater_than(f_gt_));
EXPECT_FALSE(any_of({tt_, ff_, f_eq_, f_neq_, f_lt_, f_lte_, f_gte_, f_and_,
f_or_, not_f_or_, f_forall_, f_isnan_, f_psd_static_2x2_,
f_psd_dynamic_2x2_, f_psd_static_3x3_},
is_greater_than));
}
TEST_F(SymbolicFormulaTest, IsGreaterThanOrEqualTo) {
EXPECT_TRUE(is_greater_than_or_equal_to(f_gte_));
EXPECT_FALSE(any_of({tt_, ff_, f_eq_, f_neq_, f_lt_, f_lte_, f_gt_, f_and_,
f_or_, not_f_or_, f_forall_, f_isnan_, f_psd_static_2x2_,
f_psd_dynamic_2x2_, f_psd_static_3x3_},
is_greater_than_or_equal_to));
}
TEST_F(SymbolicFormulaTest, IsRelational) {
EXPECT_TRUE(
all_of({f_eq_, f_neq_, f_lt_, f_lte_, f_gt_, f_gte_}, is_relational));
EXPECT_FALSE(
any_of({tt_, ff_, f_and_, f_or_, not_f_or_, f_forall_, f_isnan_,
f_psd_static_2x2_, f_psd_dynamic_2x2_, f_psd_static_3x3_},
is_relational));
}
TEST_F(SymbolicFormulaTest, IsConjunction) {
EXPECT_TRUE(is_conjunction(f_and_));
EXPECT_FALSE(any_of({tt_, ff_, f_eq_, f_neq_, f_lt_, f_lte_, f_gt_, f_gte_,
f_or_, not_f_or_, f_forall_, f_isnan_, f_psd_static_2x2_,
f_psd_dynamic_2x2_, f_psd_static_3x3_},
is_conjunction));
}
TEST_F(SymbolicFormulaTest, IsDisjunction) {
EXPECT_TRUE(is_disjunction(f_or_));
EXPECT_FALSE(
any_of({tt_, ff_, f_eq_, f_neq_, f_lt_, f_lte_, f_gt_, f_gte_, f_and_,
not_f_or_, f_forall_, f_isnan_, f_psd_static_2x2_,
f_psd_dynamic_2x2_, f_psd_static_3x3_},
is_disjunction));
}