clang/unittests/Analysis/FlowSensitive/SolverTest.cpp

//===- unittests/Analysis/FlowSensitive/SolverTest.cpp --------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#include <utility>

#include "TestingSupport.h"
#include "clang/Analysis/FlowSensitive/Formula.h"
#include "clang/Analysis/FlowSensitive/Solver.h"
#include "clang/Analysis/FlowSensitive/WatchedLiteralsSolver.h"
#include "llvm/ADT/ArrayRef.h"
#include "gmock/gmock.h"
#include "gtest/gtest.h"

namespace {

using namespace clang;
using namespace dataflow;

using test::ConstraintContext;
using testing::_;
using testing::AnyOf;
using testing::Pair;
using testing::UnorderedElementsAre;

constexpr auto AssignedTrue = Solver::Result::Assignment::AssignedTrue;
constexpr auto AssignedFalse = Solver::Result::Assignment::AssignedFalse;

// Checks if the conjunction of `Vals` is satisfiable and returns the
// corresponding result.
Solver::Result solve(llvm::ArrayRef<const Formula *> Vals) {
  return WatchedLiteralsSolver().solve(Vals);
}

MATCHER(unsat, "") {
  return arg.getStatus() == Solver::Result::Status::Unsatisfiable;
}
MATCHER_P(sat, SolutionMatcher,
          "is satisfiable, where solution " +
              (testing::DescribeMatcher<
                  llvm::DenseMap<Atom, Solver::Result::Assignment>>(
                  SolutionMatcher))) {
  if (arg.getStatus() != Solver::Result::Status::Satisfiable)
    return false;
  auto Solution = *arg.getSolution();
  return testing::ExplainMatchResult(SolutionMatcher, Solution,
                                     result_listener);
}

TEST(SolverTest, Var) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();

  // X
  EXPECT_THAT(solve({X}),
              sat(UnorderedElementsAre(Pair(X->getAtom(), AssignedTrue))));
}

TEST(SolverTest, NegatedVar) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto NotX = Ctx.neg(X);

  // !X
  EXPECT_THAT(solve({NotX}),
              sat(UnorderedElementsAre(Pair(X->getAtom(), AssignedFalse))));
}

TEST(SolverTest, UnitConflict) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto NotX = Ctx.neg(X);

  // X ^ !X
  EXPECT_THAT(solve({X, NotX}), unsat());
}

TEST(SolverTest, DistinctVars) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto NotY = Ctx.neg(Y);

  // X ^ !Y
  EXPECT_THAT(solve({X, NotY}),
              sat(UnorderedElementsAre(Pair(X->getAtom(), AssignedTrue),
                                       Pair(Y->getAtom(), AssignedFalse))));
}

TEST(SolverTest, DoubleNegation) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto NotX = Ctx.neg(X);
  auto NotNotX = Ctx.neg(NotX);

  // !!X ^ !X
  EXPECT_THAT(solve({NotNotX, NotX}), unsat());
}

TEST(SolverTest, NegatedDisjunction) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto XOrY = Ctx.disj(X, Y);
  auto NotXOrY = Ctx.neg(XOrY);

  // !(X v Y) ^ (X v Y)
  EXPECT_THAT(solve({NotXOrY, XOrY}), unsat());
}

TEST(SolverTest, NegatedConjunction) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto XAndY = Ctx.conj(X, Y);
  auto NotXAndY = Ctx.neg(XAndY);

  // !(X ^ Y) ^ (X ^ Y)
  EXPECT_THAT(solve({NotXAndY, XAndY}), unsat());
}

TEST(SolverTest, DisjunctionSameVarWithNegation) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto NotX = Ctx.neg(X);
  auto XOrNotX = Ctx.disj(X, NotX);

  // X v !X
  EXPECT_THAT(solve({XOrNotX}), sat(_));
}

TEST(SolverTest, DisjunctionSameVar) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto XOrX = Ctx.disj(X, X);

  // X v X
  EXPECT_THAT(solve({XOrX}), sat(_));
}

TEST(SolverTest, ConjunctionSameVarsConflict) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto NotX = Ctx.neg(X);
  auto XAndNotX = Ctx.conj(X, NotX);

  // X ^ !X
  EXPECT_THAT(solve({XAndNotX}), unsat());
}

TEST(SolverTest, ConjunctionSameVar) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto XAndX = Ctx.conj(X, X);

  // X ^ X
  EXPECT_THAT(solve({XAndX}), sat(_));
}

TEST(SolverTest, PureVar) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto NotX = Ctx.neg(X);
  auto NotXOrY = Ctx.disj(NotX, Y);
  auto NotY = Ctx.neg(Y);
  auto NotXOrNotY = Ctx.disj(NotX, NotY);

  // (!X v Y) ^ (!X v !Y)
  EXPECT_THAT(solve({NotXOrY, NotXOrNotY}),
              sat(UnorderedElementsAre(Pair(X->getAtom(), AssignedFalse),
                                       Pair(Y->getAtom(), _))));
}

TEST(SolverTest, MustAssumeVarIsFalse) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto XOrY = Ctx.disj(X, Y);
  auto NotX = Ctx.neg(X);
  auto NotXOrY = Ctx.disj(NotX, Y);
  auto NotY = Ctx.neg(Y);
  auto NotXOrNotY = Ctx.disj(NotX, NotY);

  // (X v Y) ^ (!X v Y) ^ (!X v !Y)
  EXPECT_THAT(solve({XOrY, NotXOrY, NotXOrNotY}),
              sat(UnorderedElementsAre(Pair(X->getAtom(), AssignedFalse),
                                       Pair(Y->getAtom(), AssignedTrue))));
}

TEST(SolverTest, DeepConflict) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto XOrY = Ctx.disj(X, Y);
  auto NotX = Ctx.neg(X);
  auto NotXOrY = Ctx.disj(NotX, Y);
  auto NotY = Ctx.neg(Y);
  auto NotXOrNotY = Ctx.disj(NotX, NotY);
  auto XOrNotY = Ctx.disj(X, NotY);

  // (X v Y) ^ (!X v Y) ^ (!X v !Y) ^ (X v !Y)
  EXPECT_THAT(solve({XOrY, NotXOrY, NotXOrNotY, XOrNotY}), unsat());
}

TEST(SolverTest, IffIsEquivalentToDNF) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto NotX = Ctx.neg(X);
  auto NotY = Ctx.neg(Y);
  auto XIffY = Ctx.iff(X, Y);
  auto XIffYDNF = Ctx.disj(Ctx.conj(X, Y), Ctx.conj(NotX, NotY));
  auto NotEquivalent = Ctx.neg(Ctx.iff(XIffY, XIffYDNF));

  // !((X <=> Y) <=> ((X ^ Y) v (!X ^ !Y)))
  EXPECT_THAT(solve({NotEquivalent}), unsat());
}

TEST(SolverTest, IffSameVars) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto XEqX = Ctx.iff(X, X);

  // X <=> X
  EXPECT_THAT(solve({XEqX}), sat(_));
}

TEST(SolverTest, IffDistinctVars) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto XEqY = Ctx.iff(X, Y);

  // X <=> Y
  EXPECT_THAT(
      solve({XEqY}),
      sat(AnyOf(UnorderedElementsAre(Pair(X->getAtom(), AssignedTrue),
                                     Pair(Y->getAtom(), AssignedTrue)),
                UnorderedElementsAre(Pair(X->getAtom(), AssignedFalse),
                                     Pair(Y->getAtom(), AssignedFalse)))));
}

TEST(SolverTest, IffWithUnits) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto XEqY = Ctx.iff(X, Y);

  // (X <=> Y) ^ X ^ Y
  EXPECT_THAT(solve({XEqY, X, Y}),
              sat(UnorderedElementsAre(Pair(X->getAtom(), AssignedTrue),
                                       Pair(Y->getAtom(), AssignedTrue))));
}

TEST(SolverTest, IffWithUnitsConflict) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto XEqY = Ctx.iff(X, Y);
  auto NotY = Ctx.neg(Y);

  // (X <=> Y) ^ X  !Y
  EXPECT_THAT(solve({XEqY, X, NotY}), unsat());
}

TEST(SolverTest, IffTransitiveConflict) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto Z = Ctx.atom();
  auto XEqY = Ctx.iff(X, Y);
  auto YEqZ = Ctx.iff(Y, Z);
  auto NotX = Ctx.neg(X);

  // (X <=> Y) ^ (Y <=> Z) ^ Z ^ !X
  EXPECT_THAT(solve({XEqY, YEqZ, Z, NotX}), unsat());
}

TEST(SolverTest, DeMorgan) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto Z = Ctx.atom();
  auto W = Ctx.atom();

  // !(X v Y) <=> !X ^ !Y
  auto A = Ctx.iff(Ctx.neg(Ctx.disj(X, Y)), Ctx.conj(Ctx.neg(X), Ctx.neg(Y)));

  // !(Z ^ W) <=> !Z v !W
  auto B = Ctx.iff(Ctx.neg(Ctx.conj(Z, W)), Ctx.disj(Ctx.neg(Z), Ctx.neg(W)));

  // A ^ B
  EXPECT_THAT(solve({A, B}), sat(_));
}

TEST(SolverTest, RespectsAdditionalConstraints) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto XEqY = Ctx.iff(X, Y);
  auto NotY = Ctx.neg(Y);

  // (X <=> Y) ^ X ^ !Y
  EXPECT_THAT(solve({XEqY, X, NotY}), unsat());
}

TEST(SolverTest, ImplicationIsEquivalentToDNF) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto XImpliesY = Ctx.impl(X, Y);
  auto XImpliesYDNF = Ctx.disj(Ctx.neg(X), Y);
  auto NotEquivalent = Ctx.neg(Ctx.iff(XImpliesY, XImpliesYDNF));

  // !((X => Y) <=> (!X v Y))
  EXPECT_THAT(solve({NotEquivalent}), unsat());
}

TEST(SolverTest, ImplicationConflict) {
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto *XImplY = Ctx.impl(X, Y);
  auto *XAndNotY = Ctx.conj(X, Ctx.neg(Y));

  // X => Y ^ X ^ !Y
  EXPECT_THAT(solve({XImplY, XAndNotY}), unsat());
}

TEST(SolverTest, LowTimeoutResultsInTimedOut) {
  WatchedLiteralsSolver solver(10);
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto Z = Ctx.atom();
  auto W = Ctx.atom();

  // !(X v Y) <=> !X ^ !Y
  auto A = Ctx.iff(Ctx.neg(Ctx.disj(X, Y)), Ctx.conj(Ctx.neg(X), Ctx.neg(Y)));

  // !(Z ^ W) <=> !Z v !W
  auto B = Ctx.iff(Ctx.neg(Ctx.conj(Z, W)), Ctx.disj(Ctx.neg(Z), Ctx.neg(W)));

  // A ^ B
  EXPECT_EQ(solver.solve({A, B}).getStatus(), Solver::Result::Status::TimedOut);
}

TEST(SolverTest, ReachedLimitsReflectsTimeouts) {
  WatchedLiteralsSolver solver(10);
  ConstraintContext Ctx;
  auto X = Ctx.atom();
  auto Y = Ctx.atom();
  auto Z = Ctx.atom();
  auto W = Ctx.atom();

  // !(X v Y) <=> !X ^ !Y
  auto A = Ctx.iff(Ctx.neg(Ctx.disj(X, Y)), Ctx.conj(Ctx.neg(X), Ctx.neg(Y)));

  // !(Z ^ W) <=> !Z v !W
  auto B = Ctx.iff(Ctx.neg(Ctx.conj(Z, W)), Ctx.disj(Ctx.neg(Z), Ctx.neg(W)));

  // A ^ B
  ASSERT_EQ(solver.solve({A, B}).getStatus(), Solver::Result::Status::TimedOut);
  EXPECT_TRUE(solver.reachedLimit());
}

} // namespace