diff --git a/frontends/pytorch/csrc/builder/ivalue_importer.cpp b/frontends/pytorch/csrc/builder/ivalue_importer.cpp
index 80fe5f7ee..44d41de0e 100644
--- a/frontends/pytorch/csrc/builder/ivalue_importer.cpp
+++ b/frontends/pytorch/csrc/builder/ivalue_importer.cpp
@@ -101,7 +101,8 @@ public:
 private:
   MlirValue rawImportIValue(c10::IValue value);
   MlirValue importModule(torch::jit::Module jitModule);
-  void importMethod(torch::jit::Function *function, MlirBlock nnModuleBody);
+  void importMethod(torch::jit::Function *function, MlirBlock classTypeBody);
+  void importClassType(c10::ClassType *classType);
 
   MlirBlock importBlock;
   MlirContext context;
@@ -111,6 +112,12 @@ private:
   std::unordered_map<c10::IValue, MlirValue, IValueHasher, IValueEq> valueMap;
   // Used to detect potentially aliasing tensors.
   std::unordered_set<c10::StorageImpl *> seenStorageImpls;
+  // The set of ClassType's that have already been imported.
+  //
+  // ClassType's are referenced via their `classType->name()->qualifiedName()`
+  // string (as an MLIR symbol name) so we don't need to keep a map associating
+  // them with the MlirOperation that they import into.
+  std::unordered_set<c10::ClassType *> classTypes;
   // The stack of attribute names we have traversed to reach the current IValue.
   // Used for diagnostics.
   std::vector<std::string> attributeNameStack;
@@ -128,16 +135,25 @@ MlirValue IValueImporter::importModule(torch::jit::Module currentModule) {
   // TODO: Can we do better?
   MlirLocation loc = mlirLocationUnknownGet(context);
 
-  MlirOperation nnModule =
-      createMlirOperation("torch.nn_module", loc,
-                          npcompNnModuleTypeGet(context), mlirRegionCreate());
+  c10::optional<c10::QualifiedName> maybeName = currentModule.type()->name();
+  if (!maybeName) {
+    throw std::invalid_argument("cannot import unnamed module");
+  }
+  std::string moduleTypeName = maybeName->qualifiedName();
+
+  // Ensure the class type has been imported.
+  importClassType(currentModule.type().get());
+
+  MlirOperation nnModule = createMlirOperation(
+      "torch.nn_module", loc,
+      npcompNnModuleTypeGet(context, toMlirStringRef(moduleTypeName)),
+      mlirRegionCreate());
   MlirRegion nnModuleRegion = mlirOperationGetRegion(nnModule, 0);
   mlirRegionAppendOwnedBlock(nnModuleRegion, mlirBlockCreate(0, nullptr));
   MlirBlock nnModuleBody = mlirRegionGetFirstBlock(nnModuleRegion);
 
   if (!rootModuleName.has_value()) {
-    c10::optional<c10::QualifiedName> maybeName = currentModule.type()->name();
-    rootModuleName = maybeName ? maybeName->qualifiedName() : "unnamed module";
+    rootModuleName = moduleTypeName;
   }
 
   const std::vector<c10::IValue> &slots = currentModule._ivalue()->slots();
@@ -151,7 +167,7 @@ MlirValue IValueImporter::importModule(torch::jit::Module currentModule) {
     MlirValue slotValue = importIValue(slots[i]);
     // TODO: Is it necessary to track whether an attribute is a "parameter"?
     createMlirOperationAtEnd(
-        nnModuleBody, "torch.attr", loc, slotValue,
+        nnModuleBody, "torch.slot", loc, slotValue,
         toMlirNamedAttribute(
             "name", mlirStringAttrGet(
                         context, toMlirStringRef(classAttribute.getName()))));
@@ -162,10 +178,6 @@ MlirValue IValueImporter::importModule(torch::jit::Module currentModule) {
     rootModuleName = c10::nullopt;
   }
 
-  for (torch::jit::Function *function : currentModule.type()->methods()) {
-    importMethod(function, nnModuleBody);
-  }
-
   createMlirOperationAtEnd(nnModuleBody, "torch.nn_module_terminator", loc);
   mlirBlockInsertOwnedOperationBefore(
       importBlock, mlirBlockGetTerminator(importBlock), nnModule);
@@ -262,7 +274,7 @@ MlirValue IValueImporter::rawImportIValue(c10::IValue ivalue) {
 }
 
 void IValueImporter::importMethod(torch::jit::Function *function,
-                                  MlirBlock nnModuleBody) {
+                                  MlirBlock classTypeBody) {
   // We make an effort for the func op's symbol name to be useful for debugging,
   // but still clearly non-load-bearing.
   std::string symName =
@@ -275,13 +287,50 @@ void IValueImporter::importMethod(torch::jit::Function *function,
   mlirBlockInsertOwnedOperationBefore(
       importBlock, mlirBlockGetTerminator(importBlock), func);
   createMlirOperationAtEnd(
-      nnModuleBody, "torch.method", mlirLocationUnknownGet(context),
+      classTypeBody, "torch.method", mlirLocationUnknownGet(context),
       toMlirNamedAttribute(
           "name",
           mlirStringAttrGet(context, toMlirStringRef(function->name()))),
       toMlirNamedAttribute("function", mlirFlatSymbolRefAttrGet(
                                            context, toMlirStringRef(symName))));
 }
+
+void IValueImporter::importClassType(c10::ClassType *classType) {
+  if (!classTypes.insert(classType).second) {
+    return;
+  }
+
+  // TODO: Can we do better?
+  MlirLocation loc = mlirLocationUnknownGet(context);
+
+  MlirOperation op = createMlirOperationAtEnd(
+      importBlock, "torch.class_type", loc, mlirRegionCreate(),
+      toMlirNamedAttribute(
+          "sym_name",
+          mlirStringAttrGet(
+              context, toMlirStringRef(classType->name()->qualifiedName()))));
+  MlirRegion region = mlirOperationGetRegion(op, 0);
+  mlirRegionAppendOwnedBlock(region, mlirBlockCreate(0, nullptr));
+  MlirBlock classTypeBody = mlirRegionGetFirstBlock(region);
+
+  for (const c10::ClassAttribute &classAttribute : classType->getAttributes()) {
+    createMlirOperationAtEnd(
+        classTypeBody, "torch.attr", loc,
+        toMlirNamedAttribute(
+            "name", mlirStringAttrGet(
+                        context, toMlirStringRef(classAttribute.getName()))),
+        toMlirNamedAttribute("type",
+                             mlirTypeAttrGet(typeMapper.mapFromTorchType(
+                                 loc, classAttribute.getType()))));
+  }
+
+  for (torch::jit::Function *function : classType->methods()) {
+    importMethod(function, classTypeBody);
+  }
+
+  createMlirOperationAtEnd(classTypeBody, "torch.class_type_terminator", loc);
+}
+
 void torch_mlir::importIValue(c10::IValue ivalue, MlirBlock block,
                               MlirContext context) {
   // When debugging module importing, it can be useful to dump as so:
diff --git a/frontends/pytorch/csrc/builder/torch_to_mlir_utils.cpp b/frontends/pytorch/csrc/builder/torch_to_mlir_utils.cpp
index 8167df8ee..a72656803 100644
--- a/frontends/pytorch/csrc/builder/torch_to_mlir_utils.cpp
+++ b/frontends/pytorch/csrc/builder/torch_to_mlir_utils.cpp
@@ -106,11 +106,19 @@ MlirType TypeMapper::mapFromTorchType(MlirLocation loc,
     return npcompNdArrayTypeGetRanked(dims.size(), dims.data(), elementType);
   }
   case TypeKind::ClassType: {
-    return npcompNnModuleTypeGet(context);
+    auto maybeName = torchType->cast<c10::ClassType>()->name();
+    return npcompNnModuleTypeGet(
+        context, toMlirStringRef(maybeName ? maybeName->qualifiedName()
+                                           : "unnamed class"));
   }
   case TypeKind::FloatType: {
     return mlirF64TypeGet(context);
   }
+  case TypeKind::OptionalType: {
+    return npcompOptionalTypeGet(
+        mapFromTorchType(
+            loc, torchType->cast<c10::OptionalType>()->getElementType()));
+  }
   case TypeKind::IntType: {
     return mlirIntegerTypeGet(context, 64);
   }
@@ -120,6 +128,10 @@ MlirType TypeMapper::mapFromTorchType(MlirLocation loc,
   case TypeKind::BoolType: {
     return npcompBoolTypeGet(context);
   }
+  case TypeKind::ListType: {
+    // TODO: Don't lose the element type information.
+    return npcompListTypeGet(context);
+  }
   default: {
     std::stringstream message;
     message << "unable to map Torch type " << *torchType << " to MLIR type";
diff --git a/frontends/pytorch/test/module_import/list.py b/frontends/pytorch/test/module_import/list.py
index 57fa488c8..f78bec4ff 100644
--- a/frontends/pytorch/test/module_import/list.py
+++ b/frontends/pytorch/test/module_import/list.py
@@ -15,13 +15,16 @@ class TestModule(torch.nn.Module):
     def __init__(self):
         super().__init__()
         self.l = [1, 2]
-
+# CHECK: torch.class_type @[[CLASSTYPE:.*]] {
+# TODO: Don't lose element type.
+# CHECK:   torch.attr "l" : !basicpy.ListType
+# CHECK: }
 # CHECK: %[[N1:.*]] = basicpy.numeric_constant 1 : i64
 # CHECK: %[[N2:.*]] = basicpy.numeric_constant 2 : i64
 # CHECK: %[[LIST:.*]] = basicpy.build_list %[[N1]], %[[N2]] : (i64, i64) -> !basicpy.ListType
 # CHECK: torch.nn_module  {
-# CHECK:   torch.attr "l", %[[LIST]] : !basicpy.ListType
-# CHECK: }
+# CHECK:   torch.slot "l", %[[LIST]] : !basicpy.ListType
+# CHECK: } : !torch.nn.Module<"[[CLASSTYPE]]">
 
 
 test_module = TestModule()
diff --git a/frontends/pytorch/test/module_import/methods-debuggable-ir.py b/frontends/pytorch/test/module_import/methods-debuggable-ir.py
index a39041325..8817a5afc 100644
--- a/frontends/pytorch/test/module_import/methods-debuggable-ir.py
+++ b/frontends/pytorch/test/module_import/methods-debuggable-ir.py
@@ -32,8 +32,8 @@ class TestModule(torch.nn.Module):
 #     the case that the name is `__main__` Torch replaces it with `__torch__` to
 #     avoid collisions.
 
-# CHECK: func private @__npcomp_priv_fn.__torch__.Submodule.forward
-# CHECK: func private @__npcomp_priv_fn.__torch__.TestModule.forward
+# CHECK-DAG: func private @__npcomp_priv_fn.__torch__.TestModule.forward
+# CHECK=DAG: func private @__npcomp_priv_fn.__torch__.Submodule.forward
 
 
 test_module = TestModule()
diff --git a/frontends/pytorch/test/module_import/methods.py b/frontends/pytorch/test/module_import/methods.py
index 32dfc219d..f070ecd92 100644
--- a/frontends/pytorch/test/module_import/methods.py
+++ b/frontends/pytorch/test/module_import/methods.py
@@ -19,17 +19,22 @@ class TestModule(torch.nn.Module):
 
 # The symbol name of the function is NOT load-bearing and cannot be relied upon.
 
+# CHECK-LABEL:   torch.class_type
+# CHECK-SAME:        @[[CLASSTYPE:.*]] {
+# CHECK:           torch.method "forward", @[[SYMNAME:.*]]
+# CHECK:         }
+
+
 # CHECK-LABEL:   func private
-# CHECK-SAME:                 @[[SYMNAME:.*]](
-# CHECK-SAME:                                 %[[SELF:.*]]: !torch.nn.Module,
+# CHECK-SAME:                 @[[SYMNAME]](
+# CHECK-SAME:                                 %[[SELF:.*]]: !torch.nn.Module<"[[CLASSTYPE]]">,
 # CHECK-SAME:                                 %[[X:.*]]: !numpy.ndarray<*:!numpy.any_dtype>,
 # CHECK-SAME:                                 %[[Y:.*]]: !numpy.ndarray<*:!numpy.any_dtype>) -> !numpy.ndarray<*:!numpy.any_dtype> {
 # CHECK:           %[[RET:.*]] = torch.kernel_call "aten::mul" %[[X]], %[[Y]]
 # CHECK:           return %[[RET]] : !numpy.ndarray<*:!numpy.any_dtype>
 
 # CHECK:         %[[ROOT:.*]] = torch.nn_module  {
-# CHECK:           torch.method "forward", @[[SYMNAME]]
-# CHECK:         }
+# CHECK:         } : !torch.nn.Module<"[[CLASSTYPE]]">
 
 
 test_module = TestModule()
diff --git a/frontends/pytorch/test/module_import/object-identity-torch-bug.py b/frontends/pytorch/test/module_import/object-identity-torch-bug.py
index f6f405c60..fd310a49e 100644
--- a/frontends/pytorch/test/module_import/object-identity-torch-bug.py
+++ b/frontends/pytorch/test/module_import/object-identity-torch-bug.py
@@ -24,8 +24,8 @@ class TestModule(torch.nn.Module):
         # CHECK: %[[L2:.*]] = basicpy.build_list
         # CHECK: %[[L1:.*]] = basicpy.build_list
         # CHECK: torch.nn_module {
-        # CHECK:   torch.attr "l2", %[[L2]]
-        # CHECK:   torch.attr "l1", %[[L1]]
+        # CHECK:   torch.slot "l2", %[[L2]]
+        # CHECK:   torch.slot "l1", %[[L1]]
         self.l2 = self.l1 = [1]
 
     # This can be uncommented when the graph importer supports it.
diff --git a/frontends/pytorch/test/module_import/object-identity.py b/frontends/pytorch/test/module_import/object-identity.py
index d5448a27d..dd930c0ab 100644
--- a/frontends/pytorch/test/module_import/object-identity.py
+++ b/frontends/pytorch/test/module_import/object-identity.py
@@ -16,8 +16,8 @@ class TestModule(torch.nn.Module):
         super().__init__()
         # CHECK: %[[A:.*]] = numpy.create_array_from_tensor
         # CHECK: torch.nn_module {
-        # CHECK:   torch.attr "t1", %[[A]]
-        # CHECK:   torch.attr "t2", %[[A]]
+        # CHECK:   torch.slot "t1", %[[A]]
+        # CHECK:   torch.slot "t2", %[[A]]
         self.t1 = self.t2 = torch.tensor([10., 20.])
 
 
diff --git a/frontends/pytorch/test/module_import/prim.py b/frontends/pytorch/test/module_import/prim.py
index 29ae5f402..578805238 100644
--- a/frontends/pytorch/test/module_import/prim.py
+++ b/frontends/pytorch/test/module_import/prim.py
@@ -18,7 +18,7 @@ class TestModule(torch.nn.Module):
         self.t2 = torch.ones(1)
 
     # CHECK-LABEL:   func{{.*}}TestModule.forward{{.*}}(
-    # CHECK-SAME:         %[[SELF:.*]]: !torch.nn.Module) -> !basicpy.NoneType {
+    # CHECK-SAME:         %[[SELF:.*]]: !torch.nn.Module<"{{.*}}">) -> !basicpy.NoneType {
     def forward(self):
         # CHECK: %[[T2:.*]] = torch.prim.GetAttr %[[SELF]]["t2"]
         # CHECK: torch.prim.SetAttr %[[SELF]]["t1"] = %[[T2]]
@@ -26,7 +26,7 @@ class TestModule(torch.nn.Module):
         # CHECK: torch.prim.CallMethod %[[SELF]]["callee"] (%{{.*}}, %{{.*}})
         self.callee(self.t1, self.t2)
     # CHECK-LABEL:   func{{.*}}TestModule.callee{{.*}}(
-    # CHECK-SAME:         %[[SELF:.*]]: !torch.nn.Module,
+    # CHECK-SAME:         %[[SELF:.*]]: !torch.nn.Module<"{{.*}}">,
     # CHECK-SAME:         %[[X:.*]]: !numpy.ndarray<*:!numpy.any_dtype>,
     # CHECK-SAME:         %[[Y:.*]]: !numpy.ndarray<*:!numpy.any_dtype>
     def callee(self, x, y):
diff --git a/frontends/pytorch/test/module_import/primitives.py b/frontends/pytorch/test/module_import/primitives.py
index b401086ad..f505787da 100644
--- a/frontends/pytorch/test/module_import/primitives.py
+++ b/frontends/pytorch/test/module_import/primitives.py
@@ -17,14 +17,20 @@ class TestModule(torch.nn.Module):
         self.i = 3
         self.f = 42.5
 
+# CHECK: torch.class_type @[[CLASSTYPE:.*]] {
+# CHECK:   torch.attr "training" : !basicpy.BoolType
+# CHECK:   torch.attr "i" : i64
+# CHECK:   torch.attr "f" : f64
+# CHECK: }
 # CHECK: %[[TRUE:.*]] = basicpy.bool_constant true
 # CHECK: %[[N3:.*]] = basicpy.numeric_constant 3 : i64
 # CHECK: %[[N42:.*]] = basicpy.numeric_constant 4.250000e+01 : f64
 # CHECK: %[[MODULE:.*]] = torch.nn_module  {
 # Note: for some reason, Torch always adds a "training" property to all modules.
-# CHECK:   torch.attr "training", %[[TRUE]] : !basicpy.BoolType
-# CHECK:   torch.attr "i", %[[N3]] : i64
-# CHECK:   torch.attr "f", %[[N42]] : f64
+# CHECK:   torch.slot "training", %[[TRUE]] : !basicpy.BoolType
+# CHECK:   torch.slot "i", %[[N3]] : i64
+# CHECK:   torch.slot "f", %[[N42]] : f64
+# CHECK: } : !torch.nn.Module<"[[CLASSTYPE:.*]]">
 
 
 test_module = TestModule()
diff --git a/frontends/pytorch/test/module_import/submodules-select.py b/frontends/pytorch/test/module_import/submodules-select.py
index c6ff7ee1c..088a3c388 100644
--- a/frontends/pytorch/test/module_import/submodules-select.py
+++ b/frontends/pytorch/test/module_import/submodules-select.py
@@ -15,6 +15,8 @@ class Submodule(torch.nn.Module):
     def __init__(self, n):
         super().__init__()
         self.n = n
+    def forward(self):
+       return self.n
 
 class TestModule(torch.nn.Module):
     def __init__(self):
@@ -27,9 +29,9 @@ class TestModule(torch.nn.Module):
         # Modules with the same class can be selected between.
         # CHECK: %[[MOD:.*]] = scf.if
         s = self.s1 if b else self.s2
-        # CHECK: %[[N:.*]] = torch.prim.GetAttr %5["n"]
-        # CHECK: return %[[N]] 
-        return s.n
+        # CHECK: %[[N:.*]] = torch.prim.CallMethod %[[MOD]]["forward"] ()
+        # CHECK: return %[[N]]
+        return s.forward()
 
 
 test_module = TestModule()
diff --git a/frontends/pytorch/test/module_import/submodules.py b/frontends/pytorch/test/module_import/submodules.py
index 3a57c085d..94cfbf9ae 100644
--- a/frontends/pytorch/test/module_import/submodules.py
+++ b/frontends/pytorch/test/module_import/submodules.py
@@ -26,20 +26,20 @@ class TestModule(torch.nn.Module):
 
 # CHECK:         %[[N0:.*]] = basicpy.numeric_constant 0 : i64
 # CHECK:         %[[S0:.*]] = torch.nn_module  {
-# CHECK:           torch.attr "training", %[[T]] : !basicpy.BoolType
-# CHECK:           torch.attr "n", %[[N0]] : i64
+# CHECK:           torch.slot "training", %[[T]] : !basicpy.BoolType
+# CHECK:           torch.slot "n", %[[N0]] : i64
 # CHECK:         }
 
 # CHECK:         %[[N1:.*]] = basicpy.numeric_constant 1 : i64
 # CHECK:         %[[S1:.*]] = torch.nn_module  {
-# CHECK:           torch.attr "training", %[[T]] : !basicpy.BoolType
-# CHECK:           torch.attr "n", %[[N1]] : i64
+# CHECK:           torch.slot "training", %[[T]] : !basicpy.BoolType
+# CHECK:           torch.slot "n", %[[N1]] : i64
 # CHECK:         }
 
 # CHECK:        %[[ROOT:.*]] = torch.nn_module  {
-# CHECK:           torch.attr "training", %[[T]] : !basicpy.BoolType
-# CHECK:           torch.attr "s0", %[[S0]] : !torch.nn.Module
-# CHECK:           torch.attr "s1", %[[S1]] : !torch.nn.Module
+# CHECK:           torch.slot "training", %[[T]] : !basicpy.BoolType
+# CHECK:           torch.slot "s0", %[[S0]] : !torch.nn.Module
+# CHECK:           torch.slot "s1", %[[S1]] : !torch.nn.Module
 # CHECK:         }
 
 
diff --git a/frontends/pytorch/test/module_import/tensors.py b/frontends/pytorch/test/module_import/tensors.py
index af12f4c3d..37a1a3a30 100644
--- a/frontends/pytorch/test/module_import/tensors.py
+++ b/frontends/pytorch/test/module_import/tensors.py
@@ -23,8 +23,8 @@ class TestModule(torch.nn.Module):
 # CHECK:         %[[CT:.*]] = constant dense<1.000000e+00> : tensor<1xf32>
 # CHECK:         %[[T:.*]] = numpy.create_array_from_tensor %[[CT]] : (tensor<1xf32>) -> !numpy.ndarray<*:!numpy.any_dtype>
 # CHECK:         %[[ROOT:.*]] = torch.nn_module  {
-# CHECK:           torch.attr "p", %[[P]] : !numpy.ndarray<*:!numpy.any_dtype>
-# CHECK:           torch.attr "t", %[[T]] : !numpy.ndarray<*:!numpy.any_dtype>
+# CHECK:           torch.slot "p", %[[P]] : !numpy.ndarray<*:!numpy.any_dtype>
+# CHECK:           torch.slot "t", %[[T]] : !numpy.ndarray<*:!numpy.any_dtype>
 # CHECK:         }
 
 
diff --git a/include/npcomp-c/Types.h b/include/npcomp-c/Types.h
index 0a8b679da..e194a71be 100644
--- a/include/npcomp-c/Types.h
+++ b/include/npcomp-c/Types.h
@@ -124,8 +124,18 @@ MlirType npcompTupleTypeGet(MlirContext context);
 /** Checks whether the given type is a torch.nn.Module type */
 int npcompTypeIsANnModule(MlirType t);
 
-/** Gets the singleton torch.nn.Module type. */
-MlirType npcompNnModuleTypeGet(MlirContext context);
+/** Gets the !torch.nn.Module type of the specified class. */
+MlirType npcompNnModuleTypeGet(MlirContext context, MlirStringRef className);
+
+/*============================================================================*/
+/* torch.optional type.                                                       */
+/*============================================================================*/
+
+/** Checks whether the given type is a !torch.optional<T> type */
+int npcompTypeIsAOptional(MlirType t);
+
+/** Gets the !torch.optional<T> type with subtype T. */
+MlirType npcompOptionalTypeGet(MlirType containedType);
 
 #ifdef __cplusplus
 }
diff --git a/include/npcomp/Dialect/Torch/CMakeLists.txt b/include/npcomp/Dialect/Torch/CMakeLists.txt
index f33061b2d..9f57627c3 100644
--- a/include/npcomp/Dialect/Torch/CMakeLists.txt
+++ b/include/npcomp/Dialect/Torch/CMakeLists.txt
@@ -1 +1,2 @@
 add_subdirectory(IR)
+add_subdirectory(Transforms)
diff --git a/include/npcomp/Dialect/Torch/IR/TorchOps.td b/include/npcomp/Dialect/Torch/IR/TorchOps.td
index d6386f8ea..96ba2c3a7 100644
--- a/include/npcomp/Dialect/Torch/IR/TorchOps.td
+++ b/include/npcomp/Dialect/Torch/IR/TorchOps.td
@@ -49,10 +49,11 @@ def Torch_KernelCallOp : Torch_Op<"kernel_call", [
 }
 
 //===----------------------------------------------------------------------===//
-// TorchScript modeling ops.
+// TorchScript `torch.nn.Module` object instantiation ops.
 //===----------------------------------------------------------------------===//
 
 def Torch_NnModuleOp : Torch_Op<"nn_module", [
+    DeclareOpInterfaceMethods<SymbolUserOpInterface>,
     SingleBlockImplicitTerminator<"::mlir::NPCOMP::Torch::NnModuleTerminatorOp">]> {
   let summary = "Constructs a torch.nn.Module";
   let description = [{
@@ -65,15 +66,19 @@ def Torch_NnModuleOp : Torch_Op<"nn_module", [
     Example:
 
     ```mlir
-    %2 = torch.nn_module  {
-      torch.attr "b", %bool_true : !basicpy.BoolType
-      torch.attr "i", %num3_i64 : i64
-      torch.attr "f", %num : f64
-      torch.attr "t", %0 : !numpy.ndarray<*:!numpy.any_dtype>
-      torch.attr "submodule", %1 : !torch.nn.Module
-      torch.method "method", @f
-    }
+    %2 = torch.nn_module {
+      torch.slot "b", %bool_true : !basicpy.BoolType
+      torch.slot "i", %num3_i64 : i64
+      torch.slot "f", %num : f64
+      torch.slot "t", %0 : !numpy.ndarray<*:!numpy.any_dtype>
+      torch.slot "submodule", %1 : !torch.nn.Module
+    } : !torch.nn.Module<"my_class_name">
     ```
+
+    This op is tightly coupled to the `torch.class_type` op named in the
+    `!torch.nn.Module<"my_class_name">` type. Each slot must match precisely
+    with the corresponding `torch.attr` in the `torch.class_type`.
+    See the documentation for `torch.class_type` for information.
   }];
 
   let arguments = (ins);
@@ -81,7 +86,11 @@ def Torch_NnModuleOp : Torch_Op<"nn_module", [
   let regions = (region SizedRegion<1>:$region);
   let verifier = "return ::verify(*this);";
 
-  let assemblyFormat = "$region attr-dict";
+  let assemblyFormat = "$region attr-dict `:` type($result)";
+
+  let extraClassDeclaration = [{
+    StringRef getClassName() { return getType().getClassName(); }
+  }];
 }
 
 def Torch_NnModuleTerminatorOp : Torch_Op<"nn_module_terminator", [Terminator,
@@ -94,13 +103,13 @@ def Torch_NnModuleTerminatorOp : Torch_Op<"nn_module_terminator", [Terminator,
   let assemblyFormat = "attr-dict";
 }
 
-def Torch_AttrOp : Torch_Op<"attr", [
+def Torch_SlotOp : Torch_Op<"slot", [
     HasParent<"::mlir::NPCOMP::Torch::NnModuleOp">]> {
-  let summary = "Define an attribute of a torch.nn.Module";
+  let summary = "Define the value of a slot of a torch.nn.Module";
   let description = [{
-    This op declaratively specifies that the parent torch.nn_module has an
-    attribute `name` with value `value`, which is allowed to be an arbitrary
-    Torch-compatible SSA value, including other torch.nn.Module's.
+    This op specifies that the initial value of the slot `name` of the
+    parent torch.nn_module should be `value`, which is allowed to be an
+    arbitrary Torch-compatible SSA value, including other !torch.nn.Module's.
   }];
 
   let arguments = (ins StrAttr:$name, AnyTorchType:$value);
@@ -111,13 +120,73 @@ def Torch_AttrOp : Torch_Op<"attr", [
   }];
 }
 
+//===----------------------------------------------------------------------===//
+// Modeling of TorchScript class types
+//===----------------------------------------------------------------------===//
+
+def Torch_ClassTypeOp : Torch_Op<"class_type", [
+    Symbol,
+    SingleBlockImplicitTerminator<"::mlir::NPCOMP::Torch::ClassTypeTerminatorOp">]> {
+  let summary = "Constructs a torch.ClassType";
+  let description = [{
+    Declares a class type. Class types are the types used to describe
+    TorchScript `torch.nn.Module`'s. The terminology "class type" is for
+    consistency with TorchScript (a better name in our context might be
+    "nn module subtype"). The `syn_name` of this op is the same string
+    as in the `!torch.nn.Module<"...">` type.
+
+    Example:
+
+    ```mlir
+    // A simple empty torch.class_type, with corresponding torch.nn_module.
+    torch.class_type @empty {}
+    %submodule = torch.nn_module {} : !torch.nn.Module<"empty">
+
+    // A class type with many members.
+    torch.class_type @test {
+      torch.attr "b" : !basicpy.BoolType
+      torch.attr "i" : i64
+      torch.attr "f" : f64
+      torch.attr "t" : !numpy.ndarray<*:!numpy.any_dtype>
+      torch.attr "submodule" : !torch.nn.Module<"empty">
+      torch.method "method", @f
+    }
+    torch.nn_module {
+      // These must match the order and names in the `torch.class_type`.
+      torch.slot "b", %bool_true : !basicpy.BoolType
+      torch.slot "i", %num3_i64 : i64
+      torch.slot "f", %num : f64
+      torch.slot "t", %array : !numpy.ndarray<*:!numpy.any_dtype>
+      torch.slot "submodule", %submodule : !torch.nn.Module<"empty">
+    } : !torch.nn.Module<"test">
+    ```
+  }];
+
+  let arguments = (ins SymbolNameAttr:$sym_name);
+  let results = (outs);
+  let regions = (region SizedRegion<1>:$region);
+  let verifier = "return ::verify(*this);";
+
+  let assemblyFormat = "$sym_name $region attr-dict";
+}
+
+def Torch_ClassTypeTerminatorOp : Torch_Op<"class_type_terminator", [Terminator,
+    HasParent<"::mlir::NPCOMP::Torch::ClassTypeOp">]> {
+  let summary = "Implicit terminator for torch.class_type";
+
+  let arguments = (ins);
+  let results = (outs);
+
+  let assemblyFormat = "attr-dict";
+}
+
 def Torch_MethodOp : Torch_Op<"method", [
-    HasParent<"::mlir::NPCOMP::Torch::NnModuleOp">,
+    HasParent<"::mlir::NPCOMP::Torch::ClassTypeOp">,
     DeclareOpInterfaceMethods<SymbolUserOpInterface>
   ]> {
-  let summary = "Define a method of a torch.nn.Module";
+  let summary = "Declare a method of a torch.class_type";
   let description = [{
-    This op declaratively specifies that the parent torch.nn_module has a
+    This op declaratively specifies that the parent torch.class_type has a
     method `name` which calls `function`. `function` is an unbound function.
     That is, it explicitly takes the torch.nn.Module as a parameter (no implicit
     "self" object).
@@ -131,6 +200,88 @@ def Torch_MethodOp : Torch_Op<"method", [
   }];
 }
 
+def Torch_AttrOp : Torch_Op<"attr", [
+    HasParent<"::mlir::NPCOMP::Torch::ClassTypeOp">
+  ]> {
+  let summary = "Declare an attribute of a torch.class_type";
+  let description = [{
+    This op declaratively specifies that torch.nn.Module's of the parent
+    torch.class_type must have an attribute `name` of type `type`.
+  }];
+
+  let arguments = (ins StrAttr:$name, TypeAttr:$type);
+  let results = (outs);
+
+  let assemblyFormat = [{
+    $name `:` $type attr-dict
+  }];
+}
+
+//===----------------------------------------------------------------------===//
+// Global slot ops
+//===----------------------------------------------------------------------===//
+// TODO: Should these be in a separate dialect?
+// At this point, they are fairly specific to torch types, but their get/set
+// semantics follow Python.
+//===----------------------------------------------------------------------===//
+
+def Torch_GlobalSlotOp : Torch_Op<"global_slot", [
+    Symbol,
+    IsolatedFromAbove,
+  ]> {
+  let summary = "A slot with global storage";
+  let description = [{
+    Represents a slot with global storage. The slot semantics are the same
+    as Python's: getting or setting a slot is done by object identity.
+  }];
+
+  let arguments = (ins SymbolNameAttr:$sym_name, TypeAttr:$typeBound);
+  let results = (outs);
+
+
+  let assemblyFormat = [{
+    $sym_name attr-dict `:` $typeBound
+  }];
+
+  let extraClassDeclaration = [{
+    // The name of the function, which, for semantic correctness, must be called
+    // exactly once and this call must be done before any other calls into
+    // the module.
+    // TODO: Avoid load-bearing names.
+    // We could replace this with an op that marks the function as initializer.
+    static constexpr StringRef getGlobalSlotInitializerFuncName() {
+      return "__torch_global_slot_initializer";
+    }
+  }];
+}
+
+def Torch_GlobalSlotGetOp : Torch_Op<"global_slot.get", []> {
+  let summary = "Get the value stored in a torch.global_slot";
+
+  let arguments = (ins
+    FlatSymbolRefAttr:$slot
+  );
+  let results = (outs AnyTorchType:$result);
+
+  let assemblyFormat = [{
+    $slot attr-dict `:` type($result)
+  }];
+}
+
+def Torch_GlobalSlotSetOp : Torch_Op<"global_slot.set", []> {
+  let summary = "Set the value stored in a torch.global_slot";
+
+  let arguments = (ins
+    FlatSymbolRefAttr:$slot,
+    AnyTorchType:$value
+  );
+  let results = (outs);
+
+  let assemblyFormat = [{
+    $slot `=` $value attr-dict `:` type($value)
+  }];
+}
+
 //===----------------------------------------------------------------------===//
 // TorchScript `prim::` ops.
 //===----------------------------------------------------------------------===//
@@ -142,7 +293,7 @@ def Torch_PrimGetAttrOp : Torch_Op<"prim.GetAttr", []> {
   let results = (outs AnyTorchType:$result);
 
   let assemblyFormat = [{
-    $receiver `[` $name `]` attr-dict `:` type($result)
+    $receiver `[` $name `]` attr-dict `:` type($receiver) `->` type($result)
   }];
 }
 
@@ -157,7 +308,7 @@ def Torch_PrimSetAttrOp : Torch_Op<"prim.SetAttr", []> {
   let results = (outs);
 
   let assemblyFormat = [{
-    $receiver `[` $name `]` `=` $value attr-dict `:` type($value)
+    $receiver `[` $name `]` `=` $value attr-dict `:` type($receiver) `,` type($value)
   }];
 }
 
@@ -172,7 +323,7 @@ def Torch_PrimCallMethodOp : Torch_Op<"prim.CallMethod", []> {
   let results = (outs AnyTorchType:$result);
 
   let assemblyFormat = [{
-    $receiver `[` $name `]` `(` $operands `)` attr-dict `:` type($operands) `->` type($result)
+    $receiver `[` $name `]` `(` $operands `)` attr-dict `:` type($receiver) `,` functional-type($operands, $result)
   }];
 }
 
diff --git a/include/npcomp/Dialect/Torch/IR/TorchTypes.td b/include/npcomp/Dialect/Torch/IR/TorchTypes.td
index 0a72d2644..9dab6fc41 100644
--- a/include/npcomp/Dialect/Torch/IR/TorchTypes.td
+++ b/include/npcomp/Dialect/Torch/IR/TorchTypes.td
@@ -22,9 +22,62 @@ class Torch_Type<string name, string typeMnemonic> : TypeDef<Torch_Dialect, name
 def Torch_NnModuleType : Torch_Type<"NnModule", "nn.Module"> {
   let summary = "torch.nn.Module";
   let description = [{
+    Represents an instance of a `torch.nn.Module` with the given `className`.
+  }];
+  let parameters = (ins StringRefParameter<"class name">:$className);
+
+  let printer = [{
+    $_printer << "nn.Module<\"";
+    llvm::printEscapedString(getImpl()->className, $_printer.getStream());
+    $_printer << "\">";
+  }];
+
+  let parser = [{
+    if (parser.parseLess())
+      return Type();
+    StringRef className;
+    if ($_parser.parseOptionalString(&className))
+      return Type();
+    if ($_parser.parseGreater())
+      return Type();
+    return get($_ctxt, className);
   }];
 }
 
+// TODO: It feels like this should be something more general.
+// However, to do that, we need to agree on construction operations
+// and the valid MLIR representations of the "None" state.
+//
+// For now, we only need it as a stand-in type to allow importing
+// the `_is_full_backward_hook` optional bool type that Torch puts on
+// all classes.
+def Torch_OptionalType : Torch_Type<"Optional", "optional"> {
+  let summary = "!torch.optional<T>";
+  let description = [{
+  }];
+  let parameters = (ins "::mlir::Type":$containedType);
+
+  let printer = [{
+    $_printer << "optional<" << getImpl()->containedType << ">";
+  }];
+
+  let parser = [{
+    if (parser.parseLess())
+      return Type();
+    Type containedType;
+    if ($_parser.parseType(containedType))
+      return Type();
+    if ($_parser.parseGreater())
+      return Type();
+    return get($_ctxt, containedType);
+  }];
+
+  let builders = [
+    TypeBuilderWithInferredContext<(ins "::mlir::Type":$containedType), [{
+      return Base::get(containedType.getContext(), containedType);
+    }]>
+  ];
+}
 
 //===----------------------------------------------------------------------===//
 // Type predicates
diff --git a/include/npcomp/Dialect/Torch/Transforms/CMakeLists.txt b/include/npcomp/Dialect/Torch/Transforms/CMakeLists.txt
new file mode 100644
index 000000000..a55778059
--- /dev/null
+++ b/include/npcomp/Dialect/Torch/Transforms/CMakeLists.txt
@@ -0,0 +1,5 @@
+set(LLVM_TARGET_DEFINITIONS Passes.td)
+mlir_tablegen(Passes.h.inc -gen-pass-decls)
+add_public_tablegen_target(NPCOMPTorchPassIncGen)
+
+add_mlir_doc(Passes -gen-pass-doc NPCOMPTorchTransforms ./)
diff --git a/include/npcomp/Dialect/Torch/Transforms/Passes.h b/include/npcomp/Dialect/Torch/Transforms/Passes.h
new file mode 100644
index 000000000..12016e5fa
--- /dev/null
+++ b/include/npcomp/Dialect/Torch/Transforms/Passes.h
@@ -0,0 +1,30 @@
+//===------------------------------------------------------------*- C++ -*-===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef NPCOMP_DIALECT_TORCH_TRANSFORMS_PASSES_H
+#define NPCOMP_DIALECT_TORCH_TRANSFORMS_PASSES_H
+
+#include "mlir/Pass/Pass.h"
+
+#include <memory>
+
+namespace mlir {
+namespace NPCOMP {
+namespace Torch {
+
+std::unique_ptr<OperationPass<ModuleOp>> createGlobalizeObjectGraphPass();
+
+} // namespace Torch
+
+/// Registers all Torch transformation passes.
+void registerTorchPasses();
+
+} // namespace NPCOMP
+} // namespace mlir
+
+#endif // NPCOMP_DIALECT_TORCH_TRANSFORMS_PASSES_H
diff --git a/include/npcomp/Dialect/Torch/Transforms/Passes.td b/include/npcomp/Dialect/Torch/Transforms/Passes.td
new file mode 100644
index 000000000..ab427fd37
--- /dev/null
+++ b/include/npcomp/Dialect/Torch/Transforms/Passes.td
@@ -0,0 +1,65 @@
+//===-- Passes.td - Pass definition file -------------------*- tablegen -*-===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef NPCOMP_TORCH_PASSES
+#define NPCOMP_TORCH_PASSES
+
+include "mlir/Pass/PassBase.td"
+
+def GlobalizeObjectGraph : Pass<"torch-globalize-object-graph", "ModuleOp"> {
+  let summary = "Converts TorchScript object graphs to a globalized form";
+  let constructor = "mlir::NPCOMP::Torch::createGlobalizeObjectGraphPass()";
+  let description = [{
+    This pass converts a subset of possible TorchScript modules into a
+    more restrictive lower-level form that strips away the need to be
+    concerned with instances of !torch.nn.Module<...> type. Specifically,
+    the object graph is flattened into a set of discrete globals
+    (`torch.global_slot`) that hold the program state.
+
+    The overarching goal is for a strict correspondence between the original
+    `torch.nn.Module` (call it `root`) that the user `torch.jit.script`'ed, and
+    the public interface of the resulting MLIR module. Specifically:
+      - The call `root.encoder.forward(...)` in Python corresponds to invoking
+        the `func @encoder.forward` on the resulting MLIR module.
+      - The data member access `root.decoder.ids_to_strings_table` in Python
+        corresponds to accessing the
+        `torch.global_slot @decoder.ids_to_strings_table` on the resulting
+        MLIR module.
+    In effect, the entire MLIR module corresponds to an instance of the `root`
+    object. This matches with the intuitive behavior desired for deployment:
+    When the MLIR module (or, more likely, a compiled artifact derived from it)
+    is loaded in a deployed environment, it is equivalent to recreating the
+    original `root` object.
+
+    This pass performs a complete change of the externally visible calling
+    convention of the MLIR module for a graph of objects and methods to a
+    fixed set of globals and functions.
+
+    Of course, only a subset of programs can be transformed, and this pass fails
+    with an error if the conditions are violated.
+
+    Specifically, the restrictions are:
+    - There must be a unique torch.nn_module that is not the value of a slot
+      of any other torch.nn_module
+      - Rationale: Allows us to have a notion of a unique "root" op, which is
+        used to define linkage. This also matches how TorchScript imports in
+        practice (`torch.jit.script` imports a single root object).
+    - There must be exactly one instance of each torch.class_type. Equivalently,
+      Every torch.nn_module must have a distinct type.
+      - Rationale: This guarantee precludes things like selecting between
+        multiple modules dynamically at runtime, which would require indirecting
+        between the separate storage of each instance.
+    - All torch.nn_module's must be reachable by a unique path from the root
+      - Rationale: Eliminates possibility of potentially exponential number of
+        paths. Or worse, infinite number of paths when considering cyclic
+        object graphs. Also as of Feb 2021, TorchScript won't import into
+        this form (it has a bug related to the identity of submodules).
+  }];
+}
+
+#endif // NPCOMP_TORCH_PASSES
diff --git a/lib/CAPI/Types.cpp b/lib/CAPI/Types.cpp
index b24660a96..6aa626619 100644
--- a/lib/CAPI/Types.cpp
+++ b/lib/CAPI/Types.cpp
@@ -156,7 +156,21 @@ int npcompTypeIsANnModule(MlirType t) {
   return unwrap(t).isa<Torch::NnModuleType>();
 }
 
-/** Gets the singleton torch.nn.Module type. */
-MlirType npcompNnModuleTypeGet(MlirContext context) {
-  return wrap(Torch::NnModuleType::get(unwrap(context)));
+/** Gets the torch.nn.Module type of the specified class. */
+MlirType npcompNnModuleTypeGet(MlirContext context, MlirStringRef className) {
+  return wrap(Torch::NnModuleType::get(unwrap(context), unwrap(className)));
+}
+
+/*============================================================================*/
+/* torch.optional type.                                                       */
+/*============================================================================*/
+
+/** Checks whether the given type is a !torch.optional<T> type */
+int npcompTypeIsAOptional(MlirType t) {
+  return unwrap(t).isa<Torch::OptionalType>();
+}
+
+/** Gets the !torch.optional<T> type with subtype T. */
+MlirType npcompOptionalTypeGet(MlirType containedType) {
+  return wrap(Torch::OptionalType::get(unwrap(containedType)));
 }
diff --git a/lib/Dialect/Torch/CMakeLists.txt b/lib/Dialect/Torch/CMakeLists.txt
index f33061b2d..9f57627c3 100644
--- a/lib/Dialect/Torch/CMakeLists.txt
+++ b/lib/Dialect/Torch/CMakeLists.txt
@@ -1 +1,2 @@
 add_subdirectory(IR)
+add_subdirectory(Transforms)
diff --git a/lib/Dialect/Torch/IR/TorchDialect.cpp b/lib/Dialect/Torch/IR/TorchDialect.cpp
index 89c903898..08e93b570 100644
--- a/lib/Dialect/Torch/IR/TorchDialect.cpp
+++ b/lib/Dialect/Torch/IR/TorchDialect.cpp
@@ -10,6 +10,7 @@
 #include "mlir/IR/DialectImplementation.h"
 #include "npcomp/Dialect/Torch/IR/TorchOps.h"
 #include "npcomp/Dialect/Torch/IR/TorchTypes.h"
+#include "llvm/ADT/StringExtras.h"
 #include "llvm/ADT/TypeSwitch.h"
 
 using namespace mlir;
diff --git a/lib/Dialect/Torch/IR/TorchOps.cpp b/lib/Dialect/Torch/IR/TorchOps.cpp
index 017b3b66b..92a749de1 100644
--- a/lib/Dialect/Torch/IR/TorchOps.cpp
+++ b/lib/Dialect/Torch/IR/TorchOps.cpp
@@ -14,6 +14,7 @@
 #include "npcomp/Dialect/Basicpy/IR/BasicpyOps.h"
 #include "npcomp/Dialect/Numpy/IR/NumpyDialect.h"
 #include "npcomp/Dialect/Numpy/IR/NumpyOps.h"
+#include "llvm/ADT/StringMap.h"
 
 using namespace mlir;
 using namespace mlir::NPCOMP;
@@ -49,8 +50,23 @@ KernelMetadata KernelCallOp::getTorchKernelMetadata() {
 LogicalResult MethodOp::verifySymbolUses(SymbolTableCollection &symbolTable) {
   auto func = symbolTable.lookupNearestSymbolFrom<FuncOp>(*this, function());
   if (!func)
-    return emitError() << "'" << function()
+    return emitError() << "'@" << function()
                        << "' does not reference a valid function";
+  if (func.getVisibility() != SymbolTable::Visibility::Private)
+    return emitError() << "'@" << function()
+                       << "' must reference a private function";
+  if (func.isDeclaration())
+    return emitError() << "'@" << function()
+                       << "' must reference a function that is defined (not "
+                          "merely declared)";
+  auto expectedReceiverArgType = NnModuleType::get(
+      getContext(), getOperation()->getParentOfType<ClassTypeOp>().getName());
+  if (func.getType().getNumInputs() == 0 ||
+      func.getType().getInput(0) != expectedReceiverArgType) {
+    return emitError() << "the referenced function '" << function()
+                       << "' must have a first argument of type "
+                       << expectedReceiverArgType;
+  }
   return success();
 }
 
@@ -60,8 +76,82 @@ LogicalResult MethodOp::verifySymbolUses(SymbolTableCollection &symbolTable) {
 
 static LogicalResult verify(NnModuleOp op) {
   for (Operation &child : *op.getBody())
-    if (!isa<AttrOp, MethodOp, NnModuleTerminatorOp>(&child))
-      return child.emitOpError() << "is not allowed inside `torch.nn_module`";
+    if (!isa<SlotOp, NnModuleTerminatorOp>(&child))
+      return child.emitOpError() << "is not allowed inside 'torch.nn_module'";
+  return success();
+}
+
+// PyTorch has a well-developed notion of subtyping.
+//
+// This is a restricted subset of it.
+//
+// TODO: Flesh this out.
+bool isValidSubtype(Type subtype, Type type) {
+  if (subtype == type)
+    return true;
+  if (auto optional = type.dyn_cast<OptionalType>())
+    return subtype == optional.getContainedType() ||
+           subtype.isa<Basicpy::NoneType>();
+  return false;
+}
+
+LogicalResult NnModuleOp::verifySymbolUses(SymbolTableCollection &symbolTable) {
+  auto classType =
+      symbolTable.lookupNearestSymbolFrom<ClassTypeOp>(*this, getClassName());
+  if (!classType)
+    return emitError() << "'" << getClassName()
+                       << "' does not reference a valid class type";
+
+  auto attrs = llvm::to_vector<6>(getBody()->getOps<SlotOp>());
+  auto attrDefs = llvm::to_vector<6>(classType.getBody()->getOps<AttrOp>());
+  if (attrs.size() != attrDefs.size())
+    return emitError() << "number of 'torch.slot's in a 'torch.nn_module' must "
+                          "match number of 'torch.attr's in "
+                          "the corresponding 'torch.class_type'";
+  for (int i = 0, e = attrs.size(); i != e; i++) {
+    SlotOp attr = attrs[i];
+    AttrOp attrDef = attrDefs[i];
+    if (!isValidSubtype(attr.value().getType(), attrDef.type()) ||
+        attr.name() != attrDef.name()) {
+      return attr.emitOpError()
+          .append("is expected to match type and name of '",
+                  attrDef.getOperation(), "'")
+          .attachNote(attrDef.getLoc())
+          .append("see torch.attr at corresponding index ", i, " here");
+    }
+  }
+
+  return success();
+}
+
+//===----------------------------------------------------------------------===//
+// ClassTypeOp
+//===----------------------------------------------------------------------===//
+
+static LogicalResult verify(ClassTypeOp op) {
+  llvm::StringMap<Operation *> namesToOps;
+  for (Operation &child : op.getBody()->without_terminator()) {
+    if (!isa<AttrOp, MethodOp>(&child))
+      return child.emitOpError() << "is not allowed inside `torch.class_type`";
+    StringRef name;
+    if (auto attr = dyn_cast<AttrOp>(child))
+      name = attr.name();
+    else
+      name = cast<MethodOp>(child).name();
+    auto itAndWasInserted = namesToOps.insert({name, &child});
+    auto it = itAndWasInserted.first;
+    bool wasInserted = itAndWasInserted.second;
+    if (!wasInserted) {
+      auto diag = op.emitOpError().append(
+          "has duplicate attr/method with name '", name, "'");
+      diag.attachNote(it->second->getLoc())
+          .append("see first conflicting attr/method here");
+      diag.attachNote(child.getLoc())
+          .append("see second conflicting attr/method here");
+      return failure();
+    }
+  }
+
   return success();
 }
 
diff --git a/lib/Dialect/Torch/Transforms/CMakeLists.txt b/lib/Dialect/Torch/Transforms/CMakeLists.txt
new file mode 100644
index 000000000..b49e56794
--- /dev/null
+++ b/lib/Dialect/Torch/Transforms/CMakeLists.txt
@@ -0,0 +1,19 @@
+add_npcomp_conversion_library(NPCOMPTorchPasses
+  Passes.cpp
+  GlobalizeObjectGraph.cpp
+
+  ADDITIONAL_HEADER_DIRS
+  ${PROJECT_SOURCE_DIR}/include/npcomp/Dialect/Torch/Transforms
+
+  DEPENDS
+  NPCOMPTorchPassIncGen
+
+  LINK_COMPONENTS
+  Core
+
+  LINK_LIBS PUBLIC
+  MLIRIR
+  MLIRPass
+  NPCOMPTorchDialect
+  NPCOMPBasicpyDialect
+)
diff --git a/lib/Dialect/Torch/Transforms/GlobalizeObjectGraph.cpp b/lib/Dialect/Torch/Transforms/GlobalizeObjectGraph.cpp
new file mode 100644
index 000000000..6ee787386
--- /dev/null
+++ b/lib/Dialect/Torch/Transforms/GlobalizeObjectGraph.cpp
@@ -0,0 +1,340 @@
+//===- GlobalizeObjectGraph.cpp ----------------------------------*- C++-*-===//
+//
+// This file is licensed 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 "PassDetail.h"
+
+#include "mlir/Dialect/StandardOps/IR/Ops.h"
+#include "mlir/IR/BlockAndValueMapping.h"
+#include "mlir/IR/Builders.h"
+#include "mlir/IR/BuiltinOps.h"
+#include "npcomp/Dialect/Basicpy/IR/BasicpyDialect.h"
+#include "npcomp/Dialect/Torch/IR/TorchDialect.h"
+#include "npcomp/Dialect/Torch/IR/TorchOps.h"
+#include "npcomp/Dialect/Torch/Transforms/Passes.h"
+#include "llvm/ADT/MapVector.h"
+
+using namespace mlir;
+using namespace mlir::NPCOMP;
+using namespace mlir::NPCOMP::Torch;
+
+namespace {
+// See the pass documentation for `torch-globalize-object-graph`.
+class ObjectGraphGlobalizer {
+public:
+  ObjectGraphGlobalizer(ModuleOp module);
+  LogicalResult globalizeObjectGraph();
+
+private:
+  FailureOr<NnModuleOp> findRootNnModule();
+  LogicalResult checkSingleInstanceOfEachClass();
+  LogicalResult recursivelyTraverseClassType(ClassTypeOp classType);
+  void createInitializerFunc();
+  LogicalResult rewriteMethods();
+  void removeObjectGraph();
+
+  ModuleOp module;
+  SymbolTable symbolTable;
+  OpBuilder globalBuilder;
+  // The stack of attribute names we have traversed during our recursive
+  // traversal of the class/object hierarchy.
+  //
+  // Linkage names are calculated based on the set of attribute names traversed
+  // from the root class/module in the program.
+  SmallVector<std::string> nameStack;
+
+  // Sometimes it is natural to want a map keyed on torch.attr ops or torch.slot
+  // ops. However, usually it is better to keep a map keyed on an ClassTypeOp
+  // + attr name since frequently that is all one has access to and it
+  // would be tedious to scan the body of the ClassTypeOp for the torch.attr
+  // with the corresponding name.
+  using AttrOfClass =
+      std::pair</*ClassTypeOp*/ Operation *, /*attr name*/ StringRef>;
+  // The initial value associated with an attribute of a class.
+  // Since we only allow a single instance of a class, this is equivalent to
+  // the initial value of the unique slot corresponding to that attr.
+  DenseMap<AttrOfClass, Value> slotInitialValues;
+  // The inverse map of `slotInitialValues`.
+  // Many attributes can have the same initial value, so the value type
+  // is a vector.
+  DenseMap<Value, std::vector<AttrOfClass>> slotInitialValuesInverseMap;
+
+  // The torch.global_slot corresponding to each torch.attr/torch.slot.
+  DenseMap<AttrOfClass, GlobalSlotOp> globalSlotForAttr;
+  // The linkage name (value) for the function with symbol name (key).
+  DenseMap<StringRef, std::string> methodLinkageNames;
+
+  // The set of class types that have already been processed.
+  // Used for diagnostics.
+  // The map value is the original path from the root that we found it at.
+  DenseMap</*ClassTypeOp*/ Operation *, std::string> seenClassTypes;
+};
+} // namespace
+
+ObjectGraphGlobalizer::ObjectGraphGlobalizer(ModuleOp module)
+    : module(module), symbolTable(module),
+      globalBuilder(module.getBodyRegion()) {}
+
+LogicalResult ObjectGraphGlobalizer::globalizeObjectGraph() {
+  // We require there to be a unique root !torch.nn.Module.
+  FailureOr<NnModuleOp> maybeRootNnModule = findRootNnModule();
+  if (failed(maybeRootNnModule))
+    return failure();
+  NnModuleOp rootNnModule = *maybeRootNnModule;
+  if (!rootNnModule)
+    return module.emitError()
+           << "module does not contain a root torch.nn_module";
+
+  // We require one instance of each class. That is, there is a single
+  // torch.nn_module for each torch.class_type.
+  if (failed(checkSingleInstanceOfEachClass()))
+    return failure();
+
+  for (NnModuleOp nnModule : module.getOps<NnModuleOp>()) {
+    auto classType = symbolTable.lookup<ClassTypeOp>(nnModule.getClassName());
+    for (auto slot : nnModule.getOps<SlotOp>()) {
+      AttrOfClass attrOfClass = {classType, slot.name()};
+      slotInitialValues[attrOfClass] = slot.value();
+      slotInitialValuesInverseMap[slot.value()].push_back(attrOfClass);
+    }
+  }
+
+  // Recursively traverse the class hierarchy, globalizing slots and
+  // tracking linkage names for methods.
+  auto rootClassType =
+      symbolTable.lookup<ClassTypeOp>(rootNnModule.getClassName());
+  if (failed(recursivelyTraverseClassType(rootClassType)))
+    return failure();
+
+  // Move all slot initial values into an initializer func.
+  createInitializerFunc();
+
+  // Rewrite torch.prim.GetAttr/torch.prim.SetAttr/torch.prim.CallMethod.
+  if (failed(rewriteMethods()))
+    return failure();
+
+  // Now that all we have finished converting to the new form, remove
+  // the original object graph.
+  removeObjectGraph();
+
+  return success();
+}
+
+FailureOr<NnModuleOp> ObjectGraphGlobalizer::findRootNnModule() {
+  NnModuleOp rootNnModule;
+  for (NnModuleOp op : module.getOps<NnModuleOp>()) {
+    if (!op.use_empty())
+      continue;
+    if (rootNnModule) {
+      op.emitError()
+          .append("found more than one root module (module that is not a "
+                  "child of any other module)")
+          .attachNote(rootNnModule.getLoc())
+          .append("see other root module here");
+      return failure();
+    }
+    rootNnModule = op;
+  }
+  return rootNnModule;
+}
+
+LogicalResult ObjectGraphGlobalizer::checkSingleInstanceOfEachClass() {
+  llvm::MapVector</*ClassTypeOp*/ Operation *, std::vector<NnModuleOp>>
+      classInstances;
+  for (NnModuleOp op : module.getOps<NnModuleOp>()) {
+    auto classType = symbolTable.lookup<ClassTypeOp>(op.getClassName());
+    classInstances[classType].push_back(op);
+  }
+  for (auto &p : classInstances) {
+    ClassTypeOp classType = cast<ClassTypeOp>(p.first);
+    ArrayRef<NnModuleOp> instances = p.second;
+    if (instances.size() > 1) {
+      // TODO: Improve this diagnostic based on user use cases.
+      // This is a user-facing diagnostic that enforces key invariants to
+      // our TorchScript subset.
+      auto diag = classType.emitError(
+          "class type has more than one instance: the current TorchScript "
+          "supported subset only allows single instances");
+      for (NnModuleOp instance : instances) {
+        diag.attachNote(instance.getLoc()) << "see instance here";
+      }
+      return failure();
+    }
+  }
+  return success();
+}
+
+LogicalResult
+ObjectGraphGlobalizer::recursivelyTraverseClassType(ClassTypeOp classType) {
+  std::string pathToClassFromRoot = llvm::join(nameStack, ".");
+  if (!seenClassTypes.insert({classType, pathToClassFromRoot}).second) {
+    return classType.emitError()
+           << "reachable by multiple paths from root object: '<root>."
+           << seenClassTypes[classType] << "' and '<root>."
+           << pathToClassFromRoot << "'";
+  }
+
+  // For each attr, create a global slot for it.
+  for (auto attr : classType.getOps<AttrOp>()) {
+    nameStack.push_back(attr.name().str());
+    if (auto type = attr.type().dyn_cast<NnModuleType>()) {
+      recursivelyTraverseClassType(
+          symbolTable.lookup<ClassTypeOp>(type.getClassName()));
+    } else {
+      auto linkageName = llvm::join(nameStack, ".");
+      auto globalSlot = globalBuilder.create<GlobalSlotOp>(
+          attr->getLoc(), linkageName, TypeAttr::get(attr.type()));
+      AttrOfClass attrOfClass = {classType, attr.name()};
+      assert(globalSlotForAttr.find(attrOfClass) == globalSlotForAttr.end());
+      globalSlotForAttr[attrOfClass] = globalSlot;
+    }
+    nameStack.pop_back();
+  }
+  // For each method, track the linkage name it will eventually have.
+  for (auto method : classType.getOps<MethodOp>()) {
+    nameStack.push_back(method.name().str());
+    auto linkageName = llvm::join(nameStack, ".");
+    nameStack.pop_back();
+    if (!methodLinkageNames.insert({method.function(), linkageName}).second)
+      method.emitError() << "unbound function shared by multiple methods";
+  }
+  return success();
+}
+
+void ObjectGraphGlobalizer::createInitializerFunc() {
+  auto loc = module.getLoc();
+  auto func = globalBuilder.create<FuncOp>(
+      loc, GlobalSlotOp::getGlobalSlotInitializerFuncName(),
+      globalBuilder.getFunctionType({}, {}));
+  OpBuilder builder(func.getContext());
+  Block *body = builder.createBlock(&func.getBody());
+
+  SmallVector<Operation *> opsToMove;
+  for (Operation &op : llvm::make_early_inc_range(*module.getBody())) {
+    if (isa<ClassTypeOp, NnModuleOp, GlobalSlotOp, FuncOp, ModuleTerminatorOp>(
+            &op))
+      continue;
+    op.moveBefore(body, body->end());
+    for (Value result : llvm::make_early_inc_range(op.getResults())) {
+      auto it = slotInitialValuesInverseMap.find(result);
+      if (it == slotInitialValuesInverseMap.end())
+        continue;
+      for (AttrOfClass attrOfClass : it->second) {
+        GlobalSlotOp globalSlot = globalSlotForAttr[attrOfClass];
+        OpBuilder::atBlockEnd(body).create<GlobalSlotSetOp>(
+            globalSlot.getLoc(), globalSlot.sym_name(), result);
+      }
+    }
+  }
+
+  builder.create<ReturnOp>(loc);
+}
+
+LogicalResult ObjectGraphGlobalizer::rewriteMethods() {
+  DenseMap<AttrOfClass, StringRef> linkageNames;
+  for (auto classType : module.getOps<ClassTypeOp>()) {
+    for (auto method : classType.getOps<MethodOp>()) {
+      auto it = methodLinkageNames.find(method.function());
+      if (it == methodLinkageNames.end())
+        continue;
+      linkageNames[{classType, method.name()}] = it->second;
+    }
+  }
+  // We only handle a small subset of ops that conform with the set of
+  // assumptions that allow us to globalize the object graph. Anything that
+  // tries to treat modules as bona-fide objects and not just namespaces
+  // of methods with a single instance of the corresponding type just gets
+  // arbitrarily tricky to rewrite. E.g. what if the user creates a list
+  // of modules, or there is an scf.if selecting between modules, etc.
+  auto rewriteOpWithNnModuleTypeOperand = [&](Operation *op) {
+    if (auto primSetAttr = dyn_cast<PrimSetAttrOp>(op)) {
+      auto classType = symbolTable.lookup<ClassTypeOp>(
+          primSetAttr.receiver().getType().cast<NnModuleType>().getClassName());
+      auto globalSlot = globalSlotForAttr[{classType, primSetAttr.name()}];
+      OpBuilder(primSetAttr)
+          .create<GlobalSlotSetOp>(primSetAttr.getLoc(), globalSlot.sym_name(),
+                                   primSetAttr.value());
+      primSetAttr.erase();
+    }
+    if (auto primGetAttr = dyn_cast<PrimGetAttrOp>(op)) {
+      auto classType = symbolTable.lookup<ClassTypeOp>(
+          primGetAttr.receiver().getType().cast<NnModuleType>().getClassName());
+      auto globalSlot = globalSlotForAttr[{classType, primGetAttr.name()}];
+      auto globalSlotGet = OpBuilder(primGetAttr)
+                               .create<GlobalSlotGetOp>(primGetAttr.getLoc(),
+                                                        primGetAttr.getType(),
+                                                        globalSlot.sym_name());
+      primGetAttr.replaceAllUsesWith(globalSlotGet.getOperation());
+      primGetAttr.erase();
+    }
+    if (auto primCallMethod = dyn_cast<PrimCallMethodOp>(op)) {
+      auto classType = symbolTable.lookup<ClassTypeOp>(primCallMethod.receiver()
+                                                           .getType()
+                                                           .cast<NnModuleType>()
+                                                           .getClassName());
+      StringRef linkageName = linkageNames[{classType, primCallMethod.name()}];
+      auto call = OpBuilder(primCallMethod)
+                      .create<CallOp>(primCallMethod.getLoc(), linkageName,
+                                      primCallMethod.getType(),
+                                      primCallMethod.operands());
+      primCallMethod.replaceAllUsesWith(call);
+      primCallMethod.erase();
+    }
+  };
+  for (auto classType : module.getOps<ClassTypeOp>()) {
+    for (auto method : classType.getOps<MethodOp>()) {
+      auto it = methodLinkageNames.find(method.function());
+      if (it == methodLinkageNames.end())
+        continue;
+      FuncOp func = symbolTable.lookup<FuncOp>(method.function());
+      func.setVisibility(SymbolTable::Visibility::Public);
+      func.setName(it->second);
+      func.walk(rewriteOpWithNnModuleTypeOperand);
+      SmallVector<unsigned> argsToErase;
+      for (auto arg : llvm::enumerate(func.getArguments())) {
+        if (!arg.value().getType().isa<NnModuleType>())
+          continue;
+        if (!arg.value().use_empty()) {
+          // TODO: Improve this based on real user use cases.
+          // This is a diagnostic that users will hit if they do not conform to
+          // the supported subset of TorchScript.
+          auto diag = func.emitError().append(
+              "func argument at index ", arg.index(),
+              " has uses that were not able to be converted");
+          for (Operation *user : arg.value().getUsers())
+            diag.attachNote(user->getLoc()).append("see user here");
+          return failure();
+        }
+        argsToErase.push_back(arg.index());
+      }
+      func.eraseArguments(argsToErase);
+    }
+  }
+  return success();
+}
+
+void ObjectGraphGlobalizer::removeObjectGraph() {
+  for (Operation &op : llvm::make_early_inc_range(*module.getBody())) {
+    if (isa<ClassTypeOp, NnModuleOp>(op))
+      op.erase();
+  }
+}
+
+namespace {
+class GlobalizeObjectGraphPass
+    : public GlobalizeObjectGraphBase<GlobalizeObjectGraphPass> {
+  void runOnOperation() override {
+    if (failed(ObjectGraphGlobalizer(getOperation()).globalizeObjectGraph()))
+      return signalPassFailure();
+  }
+};
+} // namespace
+
+std::unique_ptr<OperationPass<ModuleOp>>
+mlir::NPCOMP::Torch::createGlobalizeObjectGraphPass() {
+  return std::make_unique<GlobalizeObjectGraphPass>();
+}
diff --git a/lib/Dialect/Torch/Transforms/PassDetail.h b/lib/Dialect/Torch/Transforms/PassDetail.h
new file mode 100644
index 000000000..af5f9744f
--- /dev/null
+++ b/lib/Dialect/Torch/Transforms/PassDetail.h
@@ -0,0 +1,25 @@
+//===- PassDetail.h - Pass details ------------------------------*- C++ -*-===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef NPCOMP_DIALECT_TORCH_TRANSFORMS_PASSDETAIL_H
+#define NPCOMP_DIALECT_TORCH_TRANSFORMS_PASSDETAIL_H
+
+#include "mlir/Pass/Pass.h"
+
+namespace mlir {
+namespace NPCOMP {
+namespace Torch {
+
+#define GEN_PASS_CLASSES
+#include "npcomp/Dialect/Torch/Transforms/Passes.h.inc"
+
+} // namespace Torch
+} // namespace NPCOMP
+} // end namespace mlir
+
+#endif // NPCOMP_DIALECT_TORCH_TRANSFORMS_PASSDETAIL_H
diff --git a/lib/Dialect/Torch/Transforms/Passes.cpp b/lib/Dialect/Torch/Transforms/Passes.cpp
new file mode 100644
index 000000000..fa6594e53
--- /dev/null
+++ b/lib/Dialect/Torch/Transforms/Passes.cpp
@@ -0,0 +1,20 @@
+//===----------------------------------------------------------------------===//
+//
+// 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 "npcomp/Dialect/Torch/Transforms/Passes.h"
+
+//===----------------------------------------------------------------------===//
+// Pass registration
+//===----------------------------------------------------------------------===//
+
+namespace {
+#define GEN_PASS_REGISTRATION
+#include "npcomp/Dialect/Torch/Transforms/Passes.h.inc"
+} // end namespace
+
+void mlir::NPCOMP::registerTorchPasses() { ::registerPasses(); }
diff --git a/lib/InitAll.cpp b/lib/InitAll.cpp
index dd9a67021..231d740ac 100644
--- a/lib/InitAll.cpp
+++ b/lib/InitAll.cpp
@@ -21,6 +21,7 @@
 #include "npcomp/Dialect/TCP/IR/TCPDialect.h"
 #include "npcomp/Dialect/TCP/Transforms/Passes.h"
 #include "npcomp/Dialect/Torch/IR/TorchDialect.h"
+#include "npcomp/Dialect/Torch/Transforms/Passes.h"
 #include "npcomp/Typing/Transforms/Passes.h"
 
 #include "npcomp/Conversion/Passes.h"
@@ -47,5 +48,6 @@ void mlir::NPCOMP::registerAllPasses() {
   mlir::NPCOMP::registerNumpyPasses();
   mlir::NPCOMP::registerTCFPasses();
   mlir::NPCOMP::registerTCPPasses();
+  mlir::NPCOMP::registerTorchPasses();
   mlir::NPCOMP::registerTypingPasses();
 }
diff --git a/test/Dialect/Torch/globalize-object-graph-error.mlir b/test/Dialect/Torch/globalize-object-graph-error.mlir
new file mode 100644
index 000000000..c659c0768
--- /dev/null
+++ b/test/Dialect/Torch/globalize-object-graph-error.mlir
@@ -0,0 +1,63 @@
+// RUN: npcomp-opt -torch-globalize-object-graph -verify-diagnostics -split-input-file %s
+
+torch.class_type @c1 {}
+torch.class_type @c2 {}
+
+// expected-note @+1 {{see other root module here}}
+torch.nn_module {} : !torch.nn.Module<"c1">
+// expected-error @+1 {{found more than one root module (module that is not a child of any other module)}}
+torch.nn_module {} : !torch.nn.Module<"c2">
+
+// -----
+
+// expected-error @+1 {{class type has more than one instance: the current TorchScript supported subset only allows single instances}}
+torch.class_type @child {}
+torch.class_type @parent {
+    torch.attr "m1" : !torch.nn.Module<"child">
+    torch.attr "m2" : !torch.nn.Module<"child">
+}
+
+// expected-note @+1 {{see instance here}}
+%0 = torch.nn_module {} : !torch.nn.Module<"child">
+// expected-note @+1 {{see instance here}}
+%1 = torch.nn_module {} : !torch.nn.Module<"child">
+
+%root = torch.nn_module {
+    torch.slot "m1", %0 : !torch.nn.Module<"child">
+    torch.slot "m2", %1 : !torch.nn.Module<"child">
+} : !torch.nn.Module<"parent">
+
+// -----
+
+torch.class_type @c {
+  torch.method "f", @f
+}
+// expected-error @+1 {{func argument at index 1 has uses that were not able to be converted}}
+func private @f(%arg0: !torch.nn.Module<"c">, %arg1: !torch.nn.Module<"c">) {
+  // expected-note @+1 {{see user here}}
+  %0 = basicpy.build_list %arg1 : (!torch.nn.Module<"c">) -> !basicpy.ListType
+  return
+}
+
+torch.nn_module {} : !torch.nn.Module<"c">
+
+// -----
+
+// expected-error @+1 {{reachable by multiple paths from root object: '<root>.m' and '<root>.m2'}}
+torch.class_type @child {
+  torch.attr "float" : f64
+}
+torch.class_type @parent {
+  torch.attr "m" : !torch.nn.Module<"child">
+  torch.attr "m2" : !torch.nn.Module<"child">
+
+}
+
+%c42 = std.constant 42.0 : f64
+%child = torch.nn_module {
+  torch.slot "float", %c42 : f64
+} : !torch.nn.Module<"child">
+%parent = torch.nn_module {
+  torch.slot "m", %child : !torch.nn.Module<"child">
+  torch.slot "m2", %child : !torch.nn.Module<"child">
+} : !torch.nn.Module<"parent">
diff --git a/test/Dialect/Torch/globalize-object-graph-methods.mlir b/test/Dialect/Torch/globalize-object-graph-methods.mlir
new file mode 100644
index 000000000..755635fad
--- /dev/null
+++ b/test/Dialect/Torch/globalize-object-graph-methods.mlir
@@ -0,0 +1,39 @@
+// RUN: npcomp-opt -torch-globalize-object-graph -split-input-file %s | FileCheck %s
+
+torch.class_type @c {
+  torch.attr "float" : f64
+  torch.method "test_get", @test_get
+  torch.method "test_set", @test_set
+  torch.method "test_call", @test_call
+}
+
+// CHECK-LABEL:   func @test_get() -> f64 {
+// CHECK:           %[[V:.*]] = torch.global_slot.get @float : f64
+// CHECK:           return %[[V]] : f64
+func private @test_get(%arg0: !torch.nn.Module<"c">) -> f64 {
+  %0 = torch.prim.GetAttr %arg0["float"] : !torch.nn.Module<"c"> -> f64
+  return %0 : f64
+}
+
+// CHECK-LABEL:   func @test_set(
+// CHECK-SAME:                   %[[A:.*]]: f64) {
+// CHECK:           torch.global_slot.set @float = %[[A]] : f64
+// CHECK:           return
+func private @test_set(%arg0: !torch.nn.Module<"c">, %arg1: f64) {
+  torch.prim.SetAttr %arg0["float"] = %arg1 : !torch.nn.Module<"c">, f64
+  return
+}
+
+// CHECK-LABEL:   func @test_call(
+// CHECK-SAME:                    %[[A:.*]]: f64) -> f64 {
+// CHECK:           %[[V:.*]] = call @test_call(%[[A]]) : (f64) -> f64
+// CHECK:           return %[[V]] : f64
+func private @test_call(%arg0: !torch.nn.Module<"c">, %arg1: f64) -> f64 {
+  %0 = torch.prim.CallMethod %arg0["test_call"] (%arg1) : !torch.nn.Module<"c">, (f64) -> f64
+  return %0 : f64
+}
+
+%c42 = std.constant 42.0 : f64
+torch.nn_module {
+  torch.slot "float", %c42 : f64
+} : !torch.nn.Module<"c">
diff --git a/test/Dialect/Torch/globalize-object-graph-submodules.mlir b/test/Dialect/Torch/globalize-object-graph-submodules.mlir
new file mode 100644
index 000000000..544640b4d
--- /dev/null
+++ b/test/Dialect/Torch/globalize-object-graph-submodules.mlir
@@ -0,0 +1,25 @@
+// RUN: npcomp-opt -torch-globalize-object-graph -split-input-file %s | FileCheck %s
+
+// Check that linkage names consist of the dotted path from the root. 
+
+// CHECK-LABEL:   torch.global_slot @m.float : f64
+
+// CHECK-LABEL:   func @__torch_global_slot_initializer() {
+// CHECK:           %[[C42:.*]] = constant 4.200000e+01 : f64
+// CHECK:           torch.global_slot.set @m.float = %[[C42]] : f64
+// CHECK:           return
+
+torch.class_type @child {
+  torch.attr "float" : f64
+}
+torch.class_type @parent {
+  torch.attr "m" : !torch.nn.Module<"child">
+}
+
+%c42 = std.constant 42.0 : f64
+%child = torch.nn_module {
+  torch.slot "float", %c42 : f64
+} : !torch.nn.Module<"child">
+%parent = torch.nn_module {
+  torch.slot "m", %child : !torch.nn.Module<"child">
+} : !torch.nn.Module<"parent">
diff --git a/test/Dialect/Torch/globalize-object-graph.mlir b/test/Dialect/Torch/globalize-object-graph.mlir
new file mode 100644
index 000000000..0e51d0141
--- /dev/null
+++ b/test/Dialect/Torch/globalize-object-graph.mlir
@@ -0,0 +1,63 @@
+// RUN: npcomp-opt -torch-globalize-object-graph -split-input-file %s | FileCheck %s
+
+// Basic case.
+
+// CHECK-LABEL:   torch.global_slot @b : !basicpy.BoolType
+// CHECK:         torch.global_slot @i : i64
+// CHECK:         torch.global_slot @f : f64
+// CHECK:         torch.global_slot @a : !numpy.ndarray<*:!numpy.any_dtype>
+
+// CHECK-LABEL:   func @__torch_global_slot_initializer() {
+// CHECK:           %[[CB:.*]] = basicpy.bool_constant true
+// CHECK:           torch.global_slot.set @b = %[[CB]] : !basicpy.BoolType
+// CHECK:           %[[CI:.*]] = basicpy.numeric_constant 3 : i64
+// CHECK:           torch.global_slot.set @i = %[[CI]] : i64
+// CHECK:           %[[CF:.*]] = basicpy.numeric_constant 4.250000e+01 : f64
+// CHECK:           torch.global_slot.set @f = %[[CF]] : f64
+// CHECK:           %[[C:.*]] = constant dense<1.000000e+00> : tensor<1xf32>
+// CHECK:           %[[CA:.*]] = numpy.create_array_from_tensor %[[C]] : (tensor<1xf32>) -> !numpy.ndarray<*:!numpy.any_dtype>
+// CHECK:           torch.global_slot.set @a = %[[CA]] : !numpy.ndarray<*:!numpy.any_dtype>
+// CHECK:           return
+
+torch.class_type @c {
+  torch.attr "b" : !basicpy.BoolType
+  torch.attr "i" : i64
+  torch.attr "f" : f64
+  torch.attr "a" : !numpy.ndarray<*:!numpy.any_dtype>
+}
+
+%bool_true = basicpy.bool_constant true
+%i = basicpy.numeric_constant 3 : i64
+%f = basicpy.numeric_constant 4.250000e+01 : f64
+%cst = constant dense<1.000000e+00> : tensor<1xf32>
+%a = numpy.create_array_from_tensor %cst : (tensor<1xf32>) -> !numpy.ndarray<*:!numpy.any_dtype>
+torch.nn_module {
+  torch.slot "b", %bool_true : !basicpy.BoolType
+  torch.slot "i", %i : i64
+  torch.slot "f", %f : f64
+  torch.slot "a", %a : !numpy.ndarray<*:!numpy.any_dtype>
+} : !torch.nn.Module<"c">
+
+// -----
+
+// Same SSA value used as initializer for multiple slots.
+
+// CHECK-LABEL:   torch.global_slot @b1 : !basicpy.BoolType
+// CHECK-LABEL:   torch.global_slot @b2 : !basicpy.BoolType
+// CHECK-LABEL:   func @__torch_global_slot_initializer() {
+// CHECK:           %[[TRUE:.*]] = basicpy.bool_constant true
+// CHECK:           torch.global_slot.set @b1 = %[[TRUE]] : !basicpy.BoolType
+// CHECK:           torch.global_slot.set @b2 = %[[TRUE]] : !basicpy.BoolType
+// CHECK:           return
+// CHECK:         }
+
+torch.class_type @c {
+  torch.attr "b1" : !basicpy.BoolType
+  torch.attr "b2" : !basicpy.BoolType
+}
+
+%bool_true = basicpy.bool_constant true
+torch.nn_module {
+  torch.slot "b1", %bool_true : !basicpy.BoolType
+  torch.slot "b2", %bool_true : !basicpy.BoolType
+} : !torch.nn.Module<"c">
diff --git a/test/Dialect/Torch/invalid.mlir b/test/Dialect/Torch/invalid.mlir
index cd518d8e8..dcaf8e36e 100644
--- a/test/Dialect/Torch/invalid.mlir
+++ b/test/Dialect/Torch/invalid.mlir
@@ -2,14 +2,98 @@
 
 // -----
 
-torch.nn_module {
-  // expected-error @+1 {{'func' op is not allowed inside `torch.nn_module`}}
+torch.class_type @c {}
+%0 = torch.nn_module {
+  // expected-error @+1 {{'func' op is not allowed inside 'torch.nn_module'}}
+  func @f()
+} : !torch.nn.Module<"c">
+
+// -----
+
+torch.class_type @c {}
+%c0 = constant 0 : i64
+// expected-error @+1 {{number of 'torch.slot's in a 'torch.nn_module' must match number of 'torch.attr's in the corresponding 'torch.class_type'}}
+%0 = torch.nn_module {
+  torch.slot "f", %c0 : i64
+} : !torch.nn.Module<"c">
+
+// -----
+
+torch.class_type @c {
+  // expected-note @+1 {{see torch.attr at corresponding index 0 here}}
+  torch.attr "g" : i64
+}
+%c0 = constant 0 : i64
+%0 = torch.nn_module {
+  // expected-error @+1 {{'torch.slot' op is expected to match type and name of 'torch.attr "g" : i64'}}
+  torch.slot "f", %c0 : i64
+} : !torch.nn.Module<"c">
+
+// -----
+
+torch.class_type @c {
+  // expected-error @+1 {{'func' op is not allowed inside `torch.class_type`}}
   func @f()
 }
 
 // -----
 
-torch.nn_module {
-  // expected-error @+1 {{'invalidSym' does not reference a valid function}}
+// expected-error @+1 {{has duplicate attr/method with name 'a'}}
+torch.class_type @c {
+  // expected-note @+1 {{see first conflicting attr/method here}}
+  torch.attr "a" : i64
+  // expected-note @+1 {{see second conflicting attr/method here}}
+  torch.attr "a" : i64
+}
+
+// -----
+
+torch.class_type @c {
+  // expected-error @+1 {{'@invalidSym' does not reference a valid function}}
   torch.method "f", @invalidSym
 }
+
+// -----
+
+torch.class_type @c {
+  // expected-error @+1 {{'@f' must reference a private function}}
+  torch.method "f", @f
+}
+
+func @f(%arg0: !torch.nn.Module<"c">) {
+  return
+}
+
+// -----
+
+torch.class_type @c {
+  // expected-error @+1 {{'@f' must reference a function that is defined (not merely declared)}}
+  torch.method "f", @f
+}
+
+func private @f(%arg0: !torch.nn.Module<"c">)
+
+// -----
+
+func private @f() {
+  return
+}
+torch.class_type @c {
+  // expected-error @+1 {{the referenced function 'f' must have a first argument of type '!torch.nn.Module<"c">'}}
+  torch.method "f", @f
+}
+
+// -----
+
+func private @f(!torch.nn.Module<"other_c">) {
+  return
+}
+torch.class_type @c {
+  // expected-error @+1 {{the referenced function 'f' must have a first argument of type '!torch.nn.Module<"c">'}}
+  torch.method "f", @f
+}
+
+// -----
+
+// expected-error @+1 {{'a' does not reference a valid class type}}
+%m = torch.nn_module {} : !torch.nn.Module<"a">
diff --git a/test/Dialect/Torch/ops.mlir b/test/Dialect/Torch/ops.mlir
index ae003ac8e..16d610c7a 100644
--- a/test/Dialect/Torch/ops.mlir
+++ b/test/Dialect/Torch/ops.mlir
@@ -14,16 +14,28 @@ func @kernel_call(%arg0 : si32, %arg1 : tensor<3x4xf32>) -> tensor<*xf32> {
 %num = basicpy.numeric_constant 4.250000e+01 : f64
 %cst = constant dense<1.000000e+00> : tensor<1xf32>
 %array = numpy.create_array_from_tensor %cst : (tensor<1xf32>) -> !numpy.ndarray<*:!numpy.any_dtype>
-func @f(%arg0: !torch.nn.Module) {
+%none = basicpy.singleton : !basicpy.NoneType
+func private @f(%arg0: !torch.nn.Module<"test">) {
   return
 }
-%submodule = torch.nn_module {}
 
-torch.nn_module {
-  torch.attr "b", %bool_true : !basicpy.BoolType
-  torch.attr "i", %num3_i64 : i64
-  torch.attr "f", %num : f64
-  torch.attr "t", %array : !numpy.ndarray<*:!numpy.any_dtype>
-  torch.attr "submodule", %submodule : !torch.nn.Module
+torch.class_type @empty {}
+%submodule = torch.nn_module {} : !torch.nn.Module<"empty">
+
+torch.class_type @test {
+  torch.attr "b" : !basicpy.BoolType
+  torch.attr "i" : i64
+  torch.attr "f" : f64
+  torch.attr "t" : !numpy.ndarray<*:!numpy.any_dtype>
+  torch.attr "submodule" : !torch.nn.Module<"empty">
+  torch.attr "ob" : !torch.optional<!basicpy.BoolType>
   torch.method "method", @f
 }
+torch.nn_module {
+  torch.slot "b", %bool_true : !basicpy.BoolType
+  torch.slot "i", %num3_i64 : i64
+  torch.slot "f", %num : f64
+  torch.slot "t", %array : !numpy.ndarray<*:!numpy.any_dtype>
+  torch.slot "submodule", %submodule : !torch.nn.Module<"empty">
+  torch.slot "ob", %none : !basicpy.NoneType
+} : !torch.nn.Module<"test">