test_alias_analysis.cpp

#include <torch/csrc/autograd/generated/variable_factories.h>
#include <torch/csrc/jit/ir/irparser.h>
#include "test/cpp/jit/test_base.h"
#include "torch/csrc/jit/frontend/ir_emitter.h"
#include "torch/csrc/jit/ir/alias_analysis.h"
#include "torch/csrc/jit/runtime/custom_operator.h"
#include "torch/csrc/utils/memory.h"

namespace torch {
namespace jit {

inline c10::AliasAnalysisKind aliasAnalysisFromSchema() {
  return c10::AliasAnalysisKind::FROM_SCHEMA;
}

// Fixture to set up a graph and make assertions clearer
struct TopoMoveTestFixture {
  TopoMoveTestFixture() {
    createGraph();
    aliasDb = torch::make_unique<AliasDb>(graph);
  }

  // Nodes are named after their output.
  // e.g. "a" is an alias for "the node that outputs the value `a`"
  void createGraph() {
    graph = std::make_shared<Graph>();
    createNode("a", {});
    createNode("b", {"a"});
    createNode("c", {});
    createNode("d", {"a", "b"});
    createNode("e", {"c", "b"});
    createNode("f", {"e"});
    createNode("g", {"e"});
    createNode("h", {"g"});
    createNode("i", {"g"});
    createNode("j", {"i"});
    createNode("k", {"i"});
    createNode("l", {"a"});
    createNode("m", {}, {"l"}); // block depends on l
    createNode("n", {"m"});
    createNode("o", {"n"});
    createNode("p", {});
    createNode("q", {});
    createNode("r", {"q"});
    createNode("s", {"q"});

    graph->lint();
  }

  void createNode(
      const std::string& name,
      const std::vector<std::string>& inputNames,
      const std::vector<std::string>& blockInputNames = {}) {
    std::vector<Value*> inputs;
    for (const auto& name_ : inputNames) {
      inputs.push_back(nodes.at(name_)->output());
    }
    auto node = graph->appendNode(graph->create(prim::AutogradZero, inputs));
    node->output()->setDebugName(name);
    nodes[name] = node;

    if (blockInputNames.size() != 0) {
      node->addBlock();
      std::vector<Value*> blockDeps;
      for (const auto& name_ : blockInputNames) {
        blockDeps.push_back(nodes.at(name_)->output());
      }

      auto block = node->blocks().at(0);
      block->appendNode(graph->create(prim::AutogradZero, blockDeps));
    }
  }

  bool moveBeforeTopologicallyValid(
      const std::string& toInsert,
      const std::string& insertPoint) {
    std::function<bool(Node*, Node*)> func =
        [this](Node* toInsert, Node* insertPoint) {
          return aliasDb->moveBeforeTopologicallyValid(toInsert, insertPoint);
        };
    return moveWithChecks(toInsert, insertPoint, func);
  }

  bool moveAfterTopologicallyValid(
      const std::string& toInsert,
      const std::string& insertPoint) {
    std::function<bool(Node*, Node*)> func =
        [this](Node* toInsert, Node* insertPoint) {
          return aliasDb->moveAfterTopologicallyValid(toInsert, insertPoint);
        };
    return moveWithChecks(toInsert, insertPoint, func);
  }

  bool moveWithChecks(
      const std::string& toInsert,
      const std::string& insertPoint,
      std::function<bool(Node*, Node*)> func) {
    auto n = nodes.at(toInsert);
    auto insert = nodes.at(insertPoint);
    bool isAfter = n->isAfter(insert);

    std::vector<Node*> originalOrdering;
    Node* original = isAfter ? n->next() : n->prev();

    auto curNode = original;
    while (curNode != n->owningBlock()->return_node()) {
      originalOrdering.push_back(curNode);
      if (isAfter) {
        curNode = curNode->next();
      } else {
        curNode = curNode->prev();
      }
    }

    const auto couldMove = func(n, insert);
    // Check the graph is okay
    graph->lint();

    // If this is the picture of nodes
    // <some nodes> ... toInsert ... <some more nodes> ... insertPoint
    // ^----------^ check that these nodes haven't moved
    curNode = original;
    size_t idx = 0;
    while (curNode != n->owningBlock()->return_node()) {
      AT_ASSERT(originalOrdering[idx] == curNode);
      if (isAfter) {
        curNode = curNode->next();
      } else {
        curNode = curNode->prev();
      }
      idx++;
    }

    return couldMove;
  }

  void checkPostCondition(
      const std::string& toInsert,
      const std::string& insertPoint,
      bool after) {
    if (after) {
      AT_ASSERT(nodes.at(toInsert)->prev() == nodes.at(insertPoint));
    } else {
      AT_ASSERT(nodes.at(toInsert)->next() == nodes.at(insertPoint));
    }
  }

  std::shared_ptr<Graph> graph;
  std::unique_ptr<AliasDb> aliasDb;
  std::unordered_map<std::string, Node*> nodes;
};

void testTopologicalMove() {
  {
    // Check that we are removing `this`'s deps properly when we need to split
    // `this` and deps (see code for what the hell that means)
    TopoMoveTestFixture fixture;
    AT_ASSERT(fixture.moveBeforeTopologicallyValid("q", "s"));
    fixture.checkPostCondition("q", "s", false);
  }
  // Move after
  {
    // Simple move backward
    TopoMoveTestFixture fixture;
    AT_ASSERT(fixture.moveAfterTopologicallyValid("c", "a"));
    fixture.checkPostCondition("c", "a", true);
  }
  {
    // simple invalid move backward
    TopoMoveTestFixture fixture;
    AT_ASSERT(!fixture.moveAfterTopologicallyValid("d", "a"));
  }
  {
    // doesn't actually move anything
    TopoMoveTestFixture fixture;
    AT_ASSERT(fixture.moveAfterTopologicallyValid("f", "e"));
    fixture.checkPostCondition("f", "e", true);
  }
  {
    // move backward with multiple dependencies
    TopoMoveTestFixture fixture;
    AT_ASSERT(fixture.moveAfterTopologicallyValid("e", "c"));
    fixture.checkPostCondition("e", "c", true);
  }
  {
    // Move backward with non-zero working set
    TopoMoveTestFixture fixture;
    AT_ASSERT(fixture.moveAfterTopologicallyValid("k", "f"));
    fixture.checkPostCondition("k", "f", true);
  }
  {
    // Simple move forward
    TopoMoveTestFixture fixture;
    AT_ASSERT(fixture.moveAfterTopologicallyValid("c", "d"));
    fixture.checkPostCondition("c", "d", true);
  }
  {
    // Move forward with non-zero working set
    TopoMoveTestFixture fixture;
    AT_ASSERT(fixture.moveAfterTopologicallyValid("f", "l"));
    fixture.checkPostCondition("f", "l", true);
  }

  // Move before
  {
    // Simple move forward
    TopoMoveTestFixture fixture;
    AT_ASSERT(fixture.moveBeforeTopologicallyValid("b", "d"));
    fixture.checkPostCondition("b", "d", false);
  }
  {
    // Simple move backward
    TopoMoveTestFixture fixture;
    AT_ASSERT(fixture.moveBeforeTopologicallyValid("c", "a"));
    fixture.checkPostCondition("c", "a", false);
  }
  {
    // doesn't actually move anything
    TopoMoveTestFixture fixture;
    AT_ASSERT(fixture.moveBeforeTopologicallyValid("a", "b"));
    fixture.checkPostCondition("a", "b", false);
  }
  {
    // move forward with deps
    TopoMoveTestFixture fixture;
    AT_ASSERT(fixture.moveBeforeTopologicallyValid("f", "m"));
    fixture.checkPostCondition("f", "m", false);
  }
  {
    // move backward with deps
    TopoMoveTestFixture fixture;
    AT_ASSERT(fixture.moveBeforeTopologicallyValid("l", "f"));
    fixture.checkPostCondition("l", "f", false);
  }

  // check that dependencies in blocks are recognized
  {
    TopoMoveTestFixture fixture;
    AT_ASSERT(!fixture.moveAfterTopologicallyValid("l", "m"));
    AT_ASSERT(!fixture.moveBeforeTopologicallyValid("m", "l"));
    AT_ASSERT(!fixture.moveAfterTopologicallyValid("n", "l"));
    AT_ASSERT(!fixture.moveBeforeTopologicallyValid("l", "n"));
  }

  // Test that moveAfter(n) and moveBefore(n->next()) are not necessarily
  // equivalent. Here, the dependency ordering is n -> o -> p.  So we can't
  // move `n` after `o`, but we can move `n` before `p` (which pushes `o` after
  // `p`)
  {
    TopoMoveTestFixture fixture;
    AT_ASSERT(!fixture.moveAfterTopologicallyValid("n", "o"));
    AT_ASSERT(fixture.moveBeforeTopologicallyValid("o", "p"));
    fixture.checkPostCondition("o", "p", false);
  }
}

namespace {
Node* insertIf(
    Graph& g,
    Value* condValue,
    std::function<std::vector<Value*>()> trueInst,
    std::function<std::vector<Value*>()> falseInst) {
  auto if_ = g.insertNode(g.create(prim::If, 0));
  if_->addInput(condValue); // condition value
  auto trueBlock = if_->addBlock();
  auto falseBlock = if_->addBlock();
  {
    // Mutate in true block
    WithInsertPoint g(trueBlock);
    auto outputs = trueInst();
    for (auto output : outputs) {
      trueBlock->registerOutput(output);
    }
  }
  {
    WithInsertPoint g(falseBlock);
    auto outputs = falseInst();
    for (auto output : outputs) {
      falseBlock->registerOutput(output);
    }
  }

  AT_ASSERT(trueBlock->outputs().size() == falseBlock->outputs().size());
  for (auto output : trueBlock->outputs()) {
    if_->addOutput()->setType(output->type());
  }
  return if_;
}

template <class Exception, class Functor>
inline void expectThrows(Functor&& functor, const char* expectMessageContains) {
  try {
    std::forward<Functor>(functor)();
  } catch (const Exception& e) {
    if (std::string(e.what()).find(expectMessageContains) ==
        std::string::npos) {
      AT_ERROR(
          "Expected error message to contain \"",
          expectMessageContains,
          "\" but error message was: ",
          e.what());
    }
    return;
  }
  AT_ERROR(
      "Expected to throw exception containing \"",
      expectMessageContains,
      "\" but didn't throw");
}

} // namespace

void testAliasAnalysis() {
  {
    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    auto b = graph->addInput();

    // addsB = b + b
    // c = a + b
    // a += b
    // d = c + c
    auto addsB = graph->insert(aten::add, {b, b});
    auto c = graph->insert(aten::add, {a, b});
    auto aMut = graph->insert(aten::add_, {a, b});
    auto d = graph->insert(aten::add, {c, c});

    graph->lint();

    AliasDb aliasDb(graph);
    // Can't move past a mutation of a used value
    AT_ASSERT(!aliasDb.moveAfterTopologicallyValid(c->node(), aMut->node()));
    AT_ASSERT(aliasDb.moveAfterTopologicallyValid(d->node(), c->node()));

    // b should alias to a (since they are both inputs)
    AT_ASSERT(
        !aliasDb.moveAfterTopologicallyValid(addsB->node(), aMut->node()));
    AT_ASSERT(aliasDb.moveAfterTopologicallyValid(addsB->node(), c->node()));

    graph->lint();
  }

  {
    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    auto b = graph->addInput();

    auto constant = graph->insertConstant(1);
    auto fresh = graph->insert(aten::rand, {constant});
    auto usesB = graph->insert(aten::add, {b, fresh});
    auto aliasesB = graph->insert(aten::select, {a, constant, constant});
    auto mutatesAliasOfB = graph->insert(aten::add_, {aliasesB, fresh});
    graph->insert(aten::add, {fresh, aliasesB});
    graph->lint();

    AliasDb aliasDb(graph);
    AT_ASSERT(!aliasDb.moveAfterTopologicallyValid(
        aliasesB->node(), mutatesAliasOfB->node()));
    AT_ASSERT(!aliasDb.moveAfterTopologicallyValid(
        usesB->node(), mutatesAliasOfB->node()));
  }

  {
    // Test moves across side effectful nodes
    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    auto print1 = graph->insertNode(graph->create(prim::Print, {a}, 0));
    WithInsertPoint guard(print1);
    auto print2 = graph->insertNode(graph->create(prim::Print, {a, a}, 0));
    AliasDb aliasDb(graph);

    // def foo(a):
    //  print2(a, a)
    //  print1(a)

    // test moving across each other
    AT_ASSERT(!aliasDb.moveAfterTopologicallyValid(print2, print1));
    AT_ASSERT(!aliasDb.moveBeforeTopologicallyValid(print1, print2));

    // test moving where they already are
    AT_ASSERT(aliasDb.moveBeforeTopologicallyValid(print2, print1));
    AT_ASSERT(aliasDb.moveAfterTopologicallyValid(print1, print2));

    graph->insertNode(graph->create(prim::MakeTestTensor, {}, 1));
    AliasDb aliasDb2(graph);

    // def foo(a):
    //  print2(a, a)
    //  non_side_effectful = makeTestTensor()
    //  print1(a)

    // test moving with a side effectful node between
    AT_ASSERT(!aliasDb2.moveAfterTopologicallyValid(print2, print1));
    AT_ASSERT(!aliasDb2.moveBeforeTopologicallyValid(print2, print1));
    AT_ASSERT(!aliasDb2.moveAfterTopologicallyValid(print1, print2));
    AT_ASSERT(!aliasDb2.moveBeforeTopologicallyValid(print1, print2));
  }

  {
    // Test moves across inner blocks

    // a = rand(1)
    // b = rand(1)
    // if True:
    //   a.add_(b)
    // c = a + b
    auto graph = std::make_shared<Graph>();
    auto constant = graph->insertConstant(1);
    auto a = graph->insert(aten::rand, {constant});
    auto b = graph->insert(aten::rand, {constant});

    auto if_ = insertIf(
        *graph,
        constant,
        [&]() -> std::vector<Value*> {
          auto aMut = graph->insert(aten::add_, {a, b});
          return {aMut};
        },
        [&]() -> std::vector<Value*> { return {a}; });

    auto c = graph->insert(aten::add, {a, b});

    graph->lint();

    // we should not be able to move `c` before the if statement, since it
    // may write to `a`.
    AliasDb aliasDb(graph);
    ASSERT_FALSE(aliasDb.moveBeforeTopologicallyValid(c->node(), if_));
  }

  // test none value does not have writers
  {{auto graph = std::make_shared<Graph>();
  std::unordered_map<std::string, Value*> vmap;
  parseIR(
      R"IR(
    graph():
      %opt : Tensor? = prim::Constant()
      %out : Tensor = prim::unchecked_unwrap_optional(%opt)
      %ret.2 : Tensor = aten::div(%out, %out, %out)
      return (%opt, %out, %ret.2)
      )IR",
      &*graph,
      vmap);

  AliasDb aliasDb(graph);
  AT_ASSERT(!aliasDb.hasWriters(vmap["opt"]->node()));
}
} // namespace jit

// test safeToIntroduceAliasingRelationship
{
  auto graph = std::make_shared<Graph>();
  std::unordered_map<std::string, Value*> vmap;
  parseIR(
      R"IR(
  graph(%x : Tensor):
      %3 : int = prim::Constant[value=1]()
      %2 : int = prim::Constant[value=0]()
      %b : Tensor = aten::add(%x, %2, %3)
      %c : Tensor = aten::add(%x, %2, %3)
      %d : Tensor = aten::add(%x, %2, %3)
      %e : Tensor = aten::add(%x, %2, %3)
      %f : Tensor[] = prim::ListConstruct(%e)
      %14 : (Tensor, Tensor) = prim::TupleConstruct(%b, %c)
      return (%14)
    )IR",
      &*graph,
      vmap);

  AliasDb aliasDb(graph);
  // x, b, c escape scope, so we can't introduce an aliasing relationship
  TORCH_INTERNAL_ASSERT(
      !aliasDb.safeToChangeAliasingRelationship(vmap["x"], vmap["b"]));
  TORCH_INTERNAL_ASSERT(
      !aliasDb.safeToChangeAliasingRelationship(vmap["b"], vmap["x"]));
  TORCH_INTERNAL_ASSERT(
      !aliasDb.safeToChangeAliasingRelationship(vmap["b"], vmap["c"]));
  TORCH_INTERNAL_ASSERT(
      !aliasDb.safeToChangeAliasingRelationship(vmap["c"], vmap["b"]));

  // e aliases the wildcard set because it's contained in a list
  TORCH_INTERNAL_ASSERT(
      !aliasDb.safeToChangeAliasingRelationship(vmap["e"], vmap["x"]));
  TORCH_INTERNAL_ASSERT(
      !aliasDb.safeToChangeAliasingRelationship(vmap["x"], vmap["e"]));

  // d is a temporary with no writers, safe to change aliasing relationship here
  TORCH_INTERNAL_ASSERT(
      aliasDb.safeToChangeAliasingRelationship(vmap["c"], vmap["d"]));
  TORCH_INTERNAL_ASSERT(
      aliasDb.safeToChangeAliasingRelationship(vmap["d"], vmap["c"]));
}
} // namespace torch

void testWriteTracking() {
  RegisterOperators reg({Operator(
      "prim::creates_alias(Tensor(a) x) -> Tensor(a)",
      [](Stack* s) {},
      aliasAnalysisFromSchema())});
  const auto creates_alias = Symbol::fromQualString("prim::creates_alias");
  {
    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    auto b = graph->addInput();

    // aten::add(%b, %b)
    // aten::add_(%a, %b)
    // foo::creates_alias(%a)
    auto pureNode = graph->insert(aten::add, {b, b})->node();
    auto writingNode = graph->insert(aten::add_, {a, b})->node();
    auto node3 = graph->insert(creates_alias, {a})->node();
    auto aAlias = node3->output();

    graph->lint();

    AliasDb aliasDb(graph);
    ASSERT_TRUE(aliasDb.mayAlias(aAlias, a));
    ASSERT_TRUE(aliasDb.mayAlias(a, b));
    ASSERT_FALSE(
        aliasDb.writesToAlias(pureNode, std::unordered_set<const Value*>{a}));
    ASSERT_FALSE(
        aliasDb.writesToAlias(pureNode, std::unordered_set<const Value*>{b}));
    ASSERT_TRUE(aliasDb.writesToAlias(
        writingNode, std::unordered_set<const Value*>{a}));
    ASSERT_TRUE(aliasDb.writesToAlias(
        writingNode, std::unordered_set<const Value*>{a, b}));
    ASSERT_TRUE(aliasDb.writesToAlias(
        writingNode, std::unordered_set<const Value*>{aAlias}));
  }
  {
    auto graph = std::make_shared<Graph>();
    parseIR(
        R"IR(
  graph(%x: Tensor):
    %b : Tensor = aten::relu_(%x)
    return (%b)
    )IR",
        &*graph);
    auto node_iter = graph->block()->nodes().begin();
    auto relu = *node_iter;
    AliasDb aliasDb(graph);
    AT_ASSERT(aliasDb.isMutable(relu));
  }
  {
    auto graph = std::make_shared<Graph>();
    parseIR(
        R"IR(
  graph(%x: Tensor, %y : Tensor):
    %b : Tensor = aten::mul(%x, %y)
    return (%b)
    )IR",
        &*graph);
    auto node_iter = graph->block()->nodes().begin();
    auto mul = *node_iter;
    AliasDb aliasDb(graph);
    AT_ASSERT(!aliasDb.isMutable(mul));
  }
  {
    auto graph = std::make_shared<Graph>();
    std::unordered_map<std::string, Value*> vmap;
    parseIR(
        R"IR(
  graph(%x: Tensor, %y : Tensor):
    %c1 : int = prim::Constant[value=1]()
    %b : Tensor = aten::add_(%x, %y, %c1)
    return (%b)
    )IR",
        &*graph,
        vmap);
    auto add = vmap["b"]->node();
    AliasDb aliasDb(graph);
    AT_ASSERT(aliasDb.hasWriters(add));
    AT_ASSERT(aliasDb.isMutable(add));
  }
}

void testContainerAliasing() {
  {
    auto graph = std::make_shared<Graph>();
    std::unordered_map<std::string, Value*> vmap;
    parseIR(
        R"IR(
  graph(%inp: Tensor[]):
    %x : str = prim::Constant[value="a"]()
    %y : Tensor = prim::Constant()
    %z : Tensor = prim::Constant()
    %a : (Tensor) = prim::TupleConstruct(%y)
    %b : Dict(str, Tensor) = prim::DictConstruct(%x, %y)
    %c : Tensor[] = prim::ListConstruct(%y)
    return (%a, %b, %c)
    )IR",
        &*graph,
        vmap);

    auto str_output = vmap["x"];
    auto ten_output = vmap["y"];
    auto local_var = vmap["z"];
    AliasDb aliasDb(graph);

    AT_ASSERT(graph->outputs().size() == 3);
    for (auto out : graph->outputs()) {
      AT_ASSERT(aliasDb.mayContainAlias(ten_output, out));
      AT_ASSERT(!aliasDb.mayContainAlias(local_var, out));
    }

    AT_ASSERT(aliasDb.mayContainAlias(ten_output, graph->inputs()));
    AT_ASSERT(!aliasDb.mayContainAlias(local_var, graph->inputs()));

    AT_ASSERT(aliasDb.mayContainAlias({ten_output}, graph->outputs()));
    AT_ASSERT(!aliasDb.mayContainAlias(str_output, graph->outputs()));
  }

  {
    auto graph = std::make_shared<Graph>();
    parseIR(
        R"IR(
  graph():
    %x : str = prim::Constant[value="a"]()
    %y : int = prim::Constant[value=1]()
    %a : (int) = prim::TupleConstruct(%y)
    %b : Dict(str, int) = prim::DictConstruct(%x, %y)
    %c : int[] = prim::ListConstruct(%y)
    return (%a, %b, %c)
    )IR",
        &*graph);

    auto node_iter = graph->block()->nodes().begin();
    node_iter++; // string
    Node* int_node = *node_iter++;
    AliasDb aliasDb(graph);

    AT_ASSERT(graph->outputs().size() == 3);
    // primitive values don't need to alias container
    for (auto out : graph->outputs()) {
      AT_ASSERT(!aliasDb.mayContainAlias(int_node->output(), out));
    }
  }

  // Test input aliasing
  {
    auto graph = std::make_shared<Graph>();
    parseIR(
        R"IR(
  graph(%x: Tensor, %y: Tensor):
    %a : (Tensor) = prim::TupleConstruct(%x)
    return (%a)
    )IR",
        &*graph);

    auto node_iter = graph->block()->nodes().begin();
    auto tuple_node = *node_iter;
    AliasDb aliasDb(graph);

    for (auto input : graph->inputs()) {
      AT_ASSERT(aliasDb.mayContainAlias(input, tuple_node->output()));
    }
    AT_ASSERT(aliasDb.mayContainAlias(graph->inputs(), graph->outputs()));
  }

  // Test tuple that doesn't come from construct
  {
    auto graph = std::make_shared<Graph>();
    parseIR(
        R"IR(
graph(%x : int,
      %y : Tensor,
      %z : Tensor):
  %3 : int = prim::Constant[value=1]()
  %4 : bool = aten::eq(%x, %3)
  %a : (Tensor) = prim::If(%4)
    block0():
      %a.1 : (Tensor) = prim::TupleConstruct(%y)
      -> (%a.1)
    block1():
      %a.2 : (Tensor) = prim::TupleConstruct(%z)
      -> (%a.2)
  return (%a)
 )IR",
        &*graph);

    AliasDb aliasDb(graph);

    for (auto input : graph->inputs()) {
      if (input->type() == IntType::get()) {
        continue;
      }

      AT_ASSERT(aliasDb.mayContainAlias(input, graph->outputs().at(0)));
    }
  }

  // test nested types
  {
    auto graph = std::make_shared<Graph>();
    parseIR(
        R"IR(
graph():
  %a : Tensor = prim::MakeTestTensor()
  %a_list : Tensor[] = prim::ListConstruct(%a)
  %b : Tensor = prim::MakeTestTensor()
  %b_list : Tensor[] = prim::ListConstruct(%b)
  %13 : (Tensor[], Tensor[]) = prim::TupleConstruct(%a_list, %b_list)
  return (%13)
)IR",
        &*graph);
    AliasDb aliasDb(graph);
    auto g_output = graph->outputs().at(0);
    auto list_2 = g_output->node()->inputs().at(0);
    auto list_1 = g_output->node()->inputs().at(1);

    // TODO FIX assume conservatively for now
    AT_ASSERT(aliasDb.mayContainAlias(list_1, list_2));
    AT_ASSERT(aliasDb.mayContainAlias(list_2, list_1));

    AT_ASSERT(aliasDb.mayContainAlias(list_1, g_output));
    AT_ASSERT(aliasDb.mayContainAlias(list_2, g_output));
  }

  // simple example
  {
    auto graph = std::make_shared<Graph>();
    parseIR(
        R"IR(
graph():
  %0 : Tensor = prim::Constant()
  %1 : Tensor = prim::Constant()
  %13 : (Tensor) = prim::TupleConstruct(%0)
  return (%13)
)IR",
        &*graph);
    AliasDb aliasDb(graph);

    auto node_iter = graph->block()->nodes().begin();
    auto first_ten = *node_iter++;
    auto second_ten = *node_iter++;
    auto tup_node = *node_iter;

    AT_ASSERT(aliasDb.mayContainAlias(first_ten->output(), tup_node->output()));
    AT_ASSERT(
        !aliasDb.mayContainAlias(second_ten->output(), tup_node->output()));

    std::vector<Value*> first_st = {first_ten->output()};
    std::vector<Value*> second_st = {second_ten->output()};
    std::vector<Value*> tup_st = {tup_node->output()};
    AT_ASSERT(aliasDb.mayContainAlias(first_st, tup_st));
    AT_ASSERT(!aliasDb.mayContainAlias(first_st, second_st));
    AT_ASSERT(!aliasDb.mayContainAlias(second_st, tup_st));
  }
  {
    auto graph = std::make_shared<Graph>();
    std::unordered_map<std::string, Value*> vmap;
    parseIR(
        R"IR(
  graph():
    %x : str = prim::Constant[value="a"]()
    %y : Tensor = prim::Constant()
    %c : Tensor[] = prim::ListConstruct(%y)
    %d : Tensor[] = prim::ListConstruct(%y)
    return (%c, %d)
    )IR",
        &*graph,
        vmap);

    AliasDb aliasDb(graph);
    auto x = vmap["x"];
    auto c = vmap["c"];
    AT_ASSERT(!aliasDb.mayContainAlias(x, c));
    AT_ASSERT(!aliasDb.mayContainAlias(c, x));

    auto d = vmap["d"];

    AT_ASSERT(aliasDb.mayContainAlias(d, c));
    AT_ASSERT(aliasDb.mayContainAlias(c, d));
  }
  {
    // Test list container aliasing
    auto graph = std::make_shared<Graph>();
    std::unordered_map<std::string, Value*> vmap;
    parseIR(
        R"IR(
graph():
  %0 : int = prim::Constant[value=2]()
  %1 : int = prim::Constant[value=3]()
  %2 : int[] = prim::ListConstruct(%0, %1)
  %x : Tensor = prim::MakeTestTensor()
  %12 : int[] = prim::ListConstruct(%0, %1)
  %y : Tensor = prim::MakeTestTensor()
  %22 : int[] = prim::ListConstruct(%0, %1)
  %z : Tensor = prim::MakeTestTensor()
  %32 : int[] = prim::ListConstruct(%0, %1)
  %fresh : Tensor = prim::MakeTestTensor()
  %foo : Tensor[] = prim::ListConstruct(%x, %y)
  %43 : Tensor[] = aten::append(%foo, %z)
  return ()
)IR",
        graph.get(),
        vmap);
    AliasDb aliasDb(graph);
    auto x = vmap["x"];
    auto y = vmap["y"];
    auto z = vmap["z"];
    // Tensors x, y, and z went into a list, so they all may alias each other.
    ASSERT_TRUE(aliasDb.mayAlias(x, y));
    ASSERT_TRUE(aliasDb.mayAlias(y, z));
    ASSERT_TRUE(aliasDb.mayAlias(x, z));

    // But we know `fresh` didn't go into a list, so x, y, and z should not
    // alias it.
    auto fresh = vmap["fresh"];
    ASSERT_FALSE(aliasDb.mayAlias(x, fresh));
    ASSERT_FALSE(aliasDb.mayAlias(y, fresh));
    ASSERT_FALSE(aliasDb.mayAlias(z, fresh));
  }
  {
    // test "conservative" analysis writes to the inside of a container.
    auto ops = torch::RegisterOperators(
        "custom::conservative", [](torch::List<at::Tensor> in) { return in; });

    auto graph = std::make_shared<Graph>();
    std::unordered_map<std::string, Value*> vmap;
    parseIR(
        R"IR(
graph():
  %0 : int = prim::Constant[value=2]()
  %1 : int = prim::Constant[value=3]()
  %2 : int[] = prim::ListConstruct(%0, %1)
  %11 : Tensor = prim::MakeTestTensor()
  %12 : Tensor[] = prim::ListConstruct(%11)
  %out : Tensor[] = custom::conservative(%12)
  %ret.2 : Tensor = aten::div(%11, %11)
  return ()
)IR",
        graph.get(),
        vmap);
    AliasDb aliasDb(graph);
    auto conservativeOp = vmap["out"]->node();
    auto tensor = vmap["11"];
    ASSERT_TRUE(aliasDb.writesToAlias(conservativeOp, ValueSet{tensor}));
  }
  {
    auto ops = torch::RegisterOperators().op(
        "uses::list",
        torch::RegisterOperators::options()
            .catchAllKernel([](torch::List<at::Tensor> in) {
              return torch::rand({2, 3});
            })
            .aliasAnalysis(AliasAnalysisKind::PURE_FUNCTION));
    // Write to the inside of a list. Check that we can't reorder a
    // print across it.
    auto graph = std::make_shared<Graph>();
    std::unordered_map<std::string, Value*> vmap;
    parseIR(
        R"IR(
graph():
  %35 : int = prim::Constant[value=1]()
  %0 : int = prim::Constant[value=2]()
  %1 : int = prim::Constant[value=3]()
  %23 : int = prim::Constant[value=0]()
  %2 : int[] = prim::ListConstruct(%0, %1)
  %11 : Tensor = prim::MakeTestTensor()
  %12 : int[] = prim::ListConstruct(%0, %1)
  %21 : Tensor = prim::MakeTestTensor()
  %l : Tensor[] = prim::ListConstruct(%11, %21)
  %24 : Tensor = aten::select(%l, %23)
  %25 : int[] = prim::ListConstruct(%0, %1)
  %34 : Tensor = prim::MakeTestTensor()
  %36 : Tensor = aten::add_(%24, %34, %35)
  %37 : Tensor = uses::list(%l)
  return (%37)
)IR",
        graph.get(),
        vmap);
    AliasDb aliasDb(graph);
    auto listUse = vmap["37"]->node();
    auto internalWrite = vmap["36"]->node();
    ASSERT_FALSE(aliasDb.moveBeforeTopologicallyValid(listUse, internalWrite));
  }
  {
    // The same as above, but with a nested list
    auto ops = torch::RegisterOperators().op(
        "uses::list",
        torch::RegisterOperators::options()
            .catchAllKernel([](torch::List<at::Tensor> in) {
              return torch::rand({2, 3});
            })
            .aliasAnalysis(AliasAnalysisKind::PURE_FUNCTION));
    // Write to the inside of a list. Check that we can't reorder a
    // print across it.
    auto graph = std::make_shared<Graph>();
    std::unordered_map<std::string, Value*> vmap;
    parseIR(
        R"IR(
graph():
  %38 : int = prim::Constant[value=1]()
  %0 : int = prim::Constant[value=2]()
  %1 : int = prim::Constant[value=3]()
  %24 : int = prim::Constant[value=0]()
  %2 : int[] = prim::ListConstruct(%0, %1)
  %11 : Tensor = prim::MakeTestTensor()
  %12 : int[] = prim::ListConstruct(%0, %1)
  %21 : Tensor = prim::MakeTestTensor()
  %l : Tensor[] = prim::ListConstruct(%11, %21)
  %25 : Tensor = aten::select(%l, %24)
  %27 : Tensor = aten::select(%25, %24, %24)
  %28 : int[] = prim::ListConstruct(%0, %1)
  %37 : Tensor = prim::MakeTestTensor()
  %39 : Tensor = aten::add_(%27, %37, %38)
  %40 : Tensor = uses::list(%l)
  return (%40)
)IR",
        graph.get(),
        vmap);
    AliasDb aliasDb(graph);
    auto listUse = vmap["40"]->node();
    auto internalWrite = vmap["39"]->node();
    ASSERT_FALSE(aliasDb.moveBeforeTopologicallyValid(listUse, internalWrite));
  }
}

void testWildcards() {
  RegisterOperators reg({Operator(
                             "prim::returns_wildcard(Tensor a) -> Tensor(*)",
                             [](Stack* stack) {},
                             aliasAnalysisFromSchema()),
                         Operator(
                             "prim::writes(Tensor(z!) a) -> Tensor(a)",
                             [](Stack* stack) {},
                             aliasAnalysisFromSchema())});
  const auto returns_wildcard =
      Symbol::fromQualString("prim::returns_wildcard");
  const auto writes = Symbol::fromQualString("prim::writes");

  auto graph = std::make_shared<Graph>();
  const auto a = graph->addInput();

  const auto constant = graph->insertConstant(1);
  const auto fresh = graph->insert(aten::rand, {constant});
  const auto fresh2 = graph->insert(aten::rand, {constant});
  const auto wildcard = graph->insert(returns_wildcard, {fresh});

  {
    graph->lint();
    AliasDb aliasDb(graph);

    ASSERT_FALSE(aliasDb.mayAlias(a, fresh));
    ASSERT_FALSE(aliasDb.mayAlias(wildcard, fresh));
    ASSERT_TRUE(aliasDb.mayAlias(wildcard, a));
    ASSERT_FALSE(aliasDb.mayAlias(ValueSet{wildcard}, ValueSet{}));
    ASSERT_FALSE(aliasDb.hasWriters(wildcard->node()));
  }

  graph->insert(writes, {fresh2})->node();
  {
    graph->lint();
    AliasDb aliasDb(graph);
    ASSERT_FALSE(aliasDb.hasWriters(wildcard->node()));
  }

  const auto wildcardWrite = graph->insert(writes, {wildcard})->node();
  {
    graph->lint();
    AliasDb aliasDb(graph);
    // Test writes to wildcards
    ASSERT_FALSE(aliasDb.writesToAlias(
        wildcardWrite, std::unordered_set<const Value*>{fresh}));
    ASSERT_FALSE(aliasDb.writesToAlias(
        wildcardWrite, std::unordered_set<const Value*>{fresh2}));
    ASSERT_TRUE(aliasDb.writesToAlias(
        wildcardWrite, std::unordered_set<const Value*>{a}));
    ASSERT_TRUE(aliasDb.hasWriters(wildcard->node()));
  }

  // test that wildcards are correctly divided by type
  {
    auto graph = std::make_shared<Graph>();
    std::unordered_map<std::string, Value*> vmap;
    parseIR(
        R"IR(
  graph(%ten_list : Tensor[], %int_list : int[], %opt_ten_list : Tensor[]?):
    %ten : Tensor = prim::Constant()
    %4 : Tensor[] = aten::append(%ten_list, %ten)
    %ten_ten_list : Tensor[][] = prim::Constant()
    %int_int_list : int[][] = prim::Constant()
    return ()
    )IR",
        &*graph,
        vmap);
    AliasDb aliasDb(graph);
    auto opt_ten_list = vmap["opt_ten_list"];
    auto ten_list = vmap["ten_list"];
    auto int_list = vmap["int_list"];
    AT_ASSERT(!aliasDb.hasWriters(int_list));
    AT_ASSERT(aliasDb.hasWriters(opt_ten_list));
    AT_ASSERT(aliasDb.hasWriters(ten_list));
    AT_ASSERT(!aliasDb.mayContainAlias(int_list, opt_ten_list));
    AT_ASSERT(aliasDb.mayContainAlias(ten_list, opt_ten_list));
    AT_ASSERT(aliasDb.mayAlias(ten_list, opt_ten_list));

    auto list_of_tensor_lists = vmap["ten_ten_list"];
    AT_ASSERT(aliasDb.mayContainAlias(ten_list, list_of_tensor_lists));
    AT_ASSERT(aliasDb.mayContainAlias(ten_list, vmap["ten"]));

    AT_ASSERT(
        !aliasDb.mayContainAlias(vmap["int_int_list"], list_of_tensor_lists));
  }

  // test invariant container aliasing
  // the containers of different type cannot alias each other,
  // however they may contain elements which alias each other
  {
    auto graph = std::make_shared<Graph>();
    std::unordered_map<std::string, Value*> vmap;
    parseIR(
        R"IR(
  graph(%ten_list : Tensor[], %ten_opt_list : Tensor?[]):
    %ten : Tensor = prim::Constant()
    %4 : Tensor[] = aten::append(%ten_list, %ten)
    return ()
    )IR",
        &*graph,
        vmap);
    AliasDb aliasDb(graph);
    auto ten_opt_list = vmap["ten_opt_list"];
    auto ten_list = vmap["ten_list"];
    AT_ASSERT(!aliasDb.hasWriters(ten_opt_list));
    AT_ASSERT(aliasDb.hasWriters(ten_list));
    AT_ASSERT(aliasDb.mayContainAlias(ten_list, ten_opt_list));
    AT_ASSERT(!aliasDb.mayAlias(ten_list, ten_opt_list));
  }

  {
    auto graph = std::make_shared<Graph>();
    std::unordered_map<std::string, Value*> vmap;
    parseIR(
        R"IR(
  graph(%float_3D : Float(*, *, *), %float_2D : Float(*, *)):
    return ()
    )IR",
        &*graph,
        vmap);
    AliasDb aliasDb(graph);
    AT_ASSERT(aliasDb.mayAlias(vmap["float_3D"], vmap["float_2D"]));
  }

  {
    auto graph = std::make_shared<Graph>();
    std::unordered_map<std::string, Value*> vmap;
    parseIR(
        R"IR(
  graph(%float_3D_list : Float(*, *, *)[], %float_2D_list : Float(*, *)[], %ten: Tensor):
    return ()
    )IR",
        &*graph,
        vmap);
    AliasDb aliasDb(graph);
    AT_ASSERT(aliasDb.mayAlias(vmap["float_3D_list"], vmap["float_2D_list"]));
    AT_ASSERT(aliasDb.mayContainAlias(vmap["float_3D_list"], vmap["ten"]));
    AT_ASSERT(aliasDb.mayContainAlias(vmap["float_2D_list"], vmap["ten"]));
  }
}

void testMemoryDAG() {
  auto graph = std::make_shared<Graph>();
  const Value* aValue = graph->addInput();
  const Value* bValue = graph->addInput();
  const Value* cValue = graph->addInput();
  const Value* dValue = graph->addInput();
  const Value* eValue = graph->addInput();
  const Value* fValue = graph->addInput();
  const Value* gValue = graph->addInput();

  {
    // a <- b <- c
    //      b <- d
    // a <- e
    // f <- e
    // g is by itself
    auto t = std::make_unique<MemoryDAGBuilder>();
    auto a = t->makeFreshValue(aValue);
    auto b = t->makeFreshValue(bValue);
    auto c = t->makeFreshValue(cValue);
    auto d = t->makeFreshValue(dValue);
    auto e = t->makeFreshValue(eValue);
    auto f = t->makeFreshValue(fValue);
    auto g = t->makeFreshValue(gValue);
    t->makePointerTo(b, a);
    t->makePointerTo(c, b);
    t->makePointerTo(d, b);
    t->makePointerTo(e, a);
    t->makePointerTo(e, f);

    auto dag = std::make_unique<MemoryDAG>(std::move(t));

    /**
     * Test mayAlias()
     */
    // Values should alias themselves
    ASSERT_TRUE(dag->mayAlias(a, a));
    ASSERT_TRUE(dag->mayAlias(g, g));

    // Values that point to the same location should alias
    ASSERT_TRUE(dag->mayAlias(a, b));
    ASSERT_TRUE(dag->mayAlias(a, c));
    ASSERT_TRUE(dag->mayAlias(c, d));

    // e may point to a OR f
    ASSERT_TRUE(dag->mayAlias(e, a));
    ASSERT_TRUE(dag->mayAlias(e, f));
    // But a and f don't alias
    ASSERT_FALSE(dag->mayAlias(a, f));
  }
  {
    // x(y) -> x contains y

    // b(a)
    // c(a)
    auto t = std::make_unique<MemoryDAGBuilder>();
    auto a = t->makeFreshValue(aValue);
    auto b = t->makeFreshValue(bValue);
    t->addToContainedElements(a, b);

    auto c = t->makeFreshValue(cValue);
    t->addToContainedElements(a, c);

    auto dag = std::make_unique<MemoryDAG>(std::move(t));
    AT_ASSERT(dag->mayContainAlias(a, b));
    AT_ASSERT(dag->mayContainAlias(b, a));

    AT_ASSERT(dag->mayContainAlias(a, c));
    AT_ASSERT(dag->mayContainAlias(c, a));

    AT_ASSERT(dag->mayContainAlias(b, c));
    AT_ASSERT(dag->mayContainAlias(c, b));

    // containers contain an element in themselves
    AT_ASSERT(dag->mayContainAlias(b, b));
    AT_ASSERT(dag->mayContainAlias(c, c));
    AT_ASSERT(dag->mayContainAlias(a, a));
  }
  {
    // b(a)
    // c(a)
    // d(b(a))
    auto t = std::make_unique<MemoryDAGBuilder>();
    auto a = t->makeFreshValue(aValue);
    auto b = t->makeFreshValue(bValue);
    t->addToContainedElements(a, b);

    auto c = t->makeFreshValue(cValue);
    t->addToContainedElements(a, c);

    auto d = t->makeFreshValue(dValue);
    t->addToContainedElements(b, d);

    auto dag = std::make_unique<MemoryDAG>(std::move(t));
    AT_ASSERT(dag->mayContainAlias(b, d));
    AT_ASSERT(dag->mayContainAlias(d, b));

    AT_ASSERT(dag->mayContainAlias(c, d));
    AT_ASSERT(dag->mayContainAlias(d, c));

    AT_ASSERT(dag->mayContainAlias(a, d));
  }
  {
    // f(e)
    auto t = std::make_unique<MemoryDAGBuilder>();
    auto a = t->makeFreshValue(aValue);
    auto b = t->makeFreshValue(bValue);
    t->addToContainedElements(a, b);

    auto c = t->makeFreshValue(cValue);
    t->addToContainedElements(a, c);

    auto d = t->makeFreshValue(dValue);
    t->addToContainedElements(b, d);

    auto f = t->makeFreshValue(aValue);
    auto e = t->makeFreshValue(bValue);

    t->addToContainedElements(f, e);

    auto dag = std::make_unique<MemoryDAG>(std::move(t));
    for (auto elem : {a, b, c, d}) {
      AT_ASSERT(!dag->mayContainAlias(f, elem));
      AT_ASSERT(!dag->mayContainAlias(e, elem));
    }
  }
}

void testAliasRegistration() {
  {
    auto registry = torch::RegisterOperators().op(
        "foo::rand1",
        torch::RegisterOperators::options()
            .catchAllKernel([](at::Tensor) -> at::Tensor {
              return at::rand({2, 2});
            })
            .aliasAnalysis(AliasAnalysisKind::CONSERVATIVE));
    const auto rand_op = Symbol::fromQualString("foo::rand1");
    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    auto b = graph->insert(rand_op, {a});
    AliasDb aliasDb(graph);
    // Conservatively we assume there is a reference
    ASSERT_TRUE(aliasDb.mayAlias(a, b));
  }
  {
    auto registry = torch::RegisterOperators().op(
        "foo::rand2(Tensor arg1) -> Tensor",
        torch::RegisterOperators::options()
            .catchAllKernel([](at::Tensor) -> at::Tensor {
              return at::rand({2, 2});
            })
            .aliasAnalysis(AliasAnalysisKind::CONSERVATIVE));
    const auto rand_op = Symbol::fromQualString("foo::rand2");
    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    auto b = graph->insert(rand_op, {a});
    AliasDb aliasDb(graph);
    // Conservatively we assume there is a reference
    ASSERT_TRUE(aliasDb.mayAlias(a, b));
  }
  {
    auto registry = torch::RegisterOperators().op(
        "foo::rand3(Tensor(a) arg1) -> Tensor(b)",
        torch::RegisterOperators::options()
            .catchAllKernel([](at::Tensor) -> at::Tensor {
              return at::rand({2, 2});
            })
            .aliasAnalysis(AliasAnalysisKind::CONSERVATIVE));

    const auto rand_op = Symbol::fromQualString("foo::rand3");
    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    graph->insert(rand_op, {a});

    // Registration time is okay, but throw exception when fetch from
    // registration.
    expectThrows<c10::Error>(
        [&graph] { AliasDb aliasDb(graph); },
        "Tried to register operator foo::rand3(Tensor(a) arg1) -> (Tensor(b)) with aliasing information in the schema but without AliasAnalysisKind::FROM_SCHEMA");
  }
  {
    auto registry = torch::RegisterOperators().op(
        "foo::rand4(Tensor(a) arg1) -> Tensor(a)",
        torch::RegisterOperators::options()
            .catchAllKernel([](at::Tensor) -> at::Tensor {
              return at::rand({2, 2});
            })
            .aliasAnalysis(AliasAnalysisKind::CONSERVATIVE));
    const auto rand_op = Symbol::fromQualString("foo::rand4");
    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    graph->insert(rand_op, {a});

    // Registration time is okay, but throw exception when fetch from
    // registration.
    expectThrows<c10::Error>(
        [&graph] { AliasDb aliasDb(graph); },
        "Tried to register operator foo::rand4(Tensor(a) arg1) -> (Tensor(a)) with aliasing information in the schema but without AliasAnalysisKind::FROM_SCHEMA");
  }
  {
    expectThrows<c10::Error>(
        [] {
          torch::RegisterOperators().op(
              "foo::rand5",
              torch::RegisterOperators::options()
                  .catchAllKernel([](at::Tensor) -> at::Tensor {
                    return at::rand({2, 2});
                  })
                  .aliasAnalysis(AliasAnalysisKind::FROM_SCHEMA));
        },
        "Tried to register operator foo::rand5(Tensor _0) -> (Tensor _0) with AliasAnalysisKind::FROM_SCHEMA, but the schema is inferred");
  }
  {
    auto registry = torch::RegisterOperators().op(
        "foo::rand6(Tensor arg1) -> Tensor",
        torch::RegisterOperators::options()
            .catchAllKernel([](at::Tensor) -> at::Tensor {
              return at::rand({2, 2});
            })
            .aliasAnalysis(AliasAnalysisKind::FROM_SCHEMA));
    const auto rand_op = Symbol::fromQualString("foo::rand6");
    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    auto b = graph->insert(rand_op, {a});
    AliasDb aliasDb(graph);
    // The schema doesn't contain alias information, which means it's pure
    // (meh!)
    ASSERT_FALSE(aliasDb.mayAlias(a, b));
  }
  {
    auto registry = torch::RegisterOperators().op(
        "foo::rand7(Tensor(a) arg1) -> Tensor(a)",
        torch::RegisterOperators::options()
            .catchAllKernel([](at::Tensor t) -> at::Tensor { return t * 2; })
            .aliasAnalysis(AliasAnalysisKind::FROM_SCHEMA));
    const auto rand_op = Symbol::fromQualString("foo::rand7");

    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    auto b = graph->insert(rand_op, {a});
    AliasDb aliasDb(graph);
    // The schema has an alias reference
    ASSERT_TRUE(aliasDb.mayAlias(a, b));
  }
  {
    auto registry = torch::RegisterOperators().op(
        "foo::rand8(Tensor(a) arg1) -> Tensor(b)",
        torch::RegisterOperators::options()
            .catchAllKernel([](at::Tensor t) -> at::Tensor { return t * 2; })
            .aliasAnalysis(AliasAnalysisKind::FROM_SCHEMA));
    const auto rand_op = Symbol::fromQualString("foo::rand8");
    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    auto b = graph->insert(rand_op, {a});
    AliasDb aliasDb(graph);
    // The schema does not have an alias reference
    ASSERT_FALSE(aliasDb.mayAlias(a, b));
  }
  {
    auto registry = torch::RegisterOperators().op(
        "foo::rand9",
        torch::RegisterOperators::options()
            .catchAllKernel([](at::Tensor) -> at::Tensor {
              return at::rand({2, 2});
            })
            .aliasAnalysis(AliasAnalysisKind::PURE_FUNCTION));
    const auto rand_op = Symbol::fromQualString("foo::rand9");
    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    auto b = graph->insert(rand_op, {a});
    AliasDb aliasDb(graph);
    // The schema is pure, there cannot be any alias
    ASSERT_FALSE(aliasDb.mayAlias(a, b));
  }
  {
    auto registry = torch::RegisterOperators().op(
        "foo::rand10(Tensor arg1) -> Tensor",
        torch::RegisterOperators::options()
            .catchAllKernel([](at::Tensor) -> at::Tensor {
              return at::rand({2, 2});
            })
            .aliasAnalysis(AliasAnalysisKind::PURE_FUNCTION));
    const auto rand_op = Symbol::fromQualString("foo::rand10");
    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    auto b = graph->insert(rand_op, {a});
    AliasDb aliasDb(graph);
    // The schema is pure, there cannot be any alias
    ASSERT_FALSE(aliasDb.mayAlias(a, b));
  }
  {
    auto registry = torch::RegisterOperators().op(
        "foo::rand11(Tensor(a) arg1) -> Tensor(a)",
        torch::RegisterOperators::options()
            .catchAllKernel([](at::Tensor t) -> at::Tensor { return t * 2; })
            .aliasAnalysis(AliasAnalysisKind::PURE_FUNCTION));
    const auto rand_op = Symbol::fromQualString("foo::rand11");
    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    graph->insert(rand_op, {a});

    // Registration time is okay, but throw exception when fetch from
    // registration.
    expectThrows<c10::Error>(
        [&graph] { AliasDb aliasDb(graph); },
        "Tried to register operator foo::rand11(Tensor(a) arg1) -> (Tensor(a)) with aliasing information in the schema but without AliasAnalysisKind::FROM_SCHEMA");
  }
  {
    auto registry = torch::RegisterOperators().op(
        "foo::rand12(Tensor(a) arg1) -> Tensor(b)",
        torch::RegisterOperators::options()
            .catchAllKernel([](at::Tensor t) -> at::Tensor { return t * 2; })
            .aliasAnalysis(AliasAnalysisKind::PURE_FUNCTION));
    const auto rand_op = Symbol::fromQualString("foo::rand12");
    auto graph = std::make_shared<Graph>();
    auto a = graph->addInput();
    graph->insert(rand_op, {a});

    // Registration time is okay, but throw exception when fetch from
    // registration.
    expectThrows<c10::Error>(
        [&graph] { AliasDb aliasDb(graph); },
        "Tried to register operator foo::rand12(Tensor(a) arg1) -> (Tensor(b)) with aliasing information in the schema but without AliasAnalysisKind::FROM_SCHEMA");
  }
}

} // namespace jit
} // namespace torch