diff --git a/.github/workflow/ci.yml b/.github/workflows/ci.yml
similarity index 100%
rename from .github/workflow/ci.yml
rename to .github/workflows/ci.yml
diff --git a/src/ir/array_ref.h b/src/ir/array_ref.h
new file mode 100644
index 0000000..a08685a
--- /dev/null
+++ b/src/ir/array_ref.h
@@ -0,0 +1,186 @@
+// Copyright (c) ONNX Project Contributors
+
+/*
+ * SPDX-License-Identifier: Apache-2.0
+ */
+
+// ATTENTION: The code in this file is highly EXPERIMENTAL.
+// Adventurous users should note that the APIs will probably change.
+
+//===--- ArrayRef.h - Array Reference Wrapper -------------------*- C++ -*-===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+
+// ONNX: modified from llvm::ArrayRef.
+// removed llvm-specific functionality
+// removed some implicit const -> non-const conversions that rely on
+// complicated std::enable_if meta-programming
+// removed a bunch of slice variants for simplicity...
+
+#pragma once
+#include <assert.h>
+
+#include <array>
+#include <vector>
+
+namespace my_ai_training::ir {
+/// ArrayRef - Represent a constant reference to an array (0 or more elements
+/// consecutively in memory), i.e. a start pointer and a length.  It allows
+/// various APIs to take consecutive elements easily and conveniently.
+///
+/// This class does not own the underlying data, it is expected to be used in
+/// situations where the data resides in some other buffer, whose lifetime
+/// extends past that of the ArrayRef. For this reason, it is not in general
+/// safe to store an ArrayRef.
+///
+/// This is intended to be trivially copyable, so it should be passed by
+/// value.
+template <typename T>
+class ArrayRef {
+ public:
+  typedef const T* iterator;
+  typedef const T* const_iterator;
+  typedef size_t size_type;
+
+  typedef std::reverse_iterator<iterator> reverse_iterator;
+
+ private:
+  /// The start of the array, in an external buffer.
+  const T* Data;
+
+  /// The number of elements.
+  size_type Length;
+
+ public:
+  /// @name Constructors
+  /// @{
+
+  /// Construct an empty ArrayRef.
+  /*implicit*/ ArrayRef() : Data(nullptr), Length(0) {}
+
+  /// Construct an ArrayRef from a single element.
+  /*implicit*/ ArrayRef(const T& OneElt) : Data(&OneElt), Length(1) {}
+
+  /// Construct an ArrayRef from a pointer and length.
+  /*implicit*/ ArrayRef(const T* data, size_t length)
+      : Data(data), Length(length) {}
+
+  /// Construct an ArrayRef from a range.
+  ArrayRef(const T* begin, const T* end) : Data(begin), Length(end - begin) {}
+
+  /// Construct an ArrayRef from a std::vector.
+  template <typename A>
+  /*implicit*/ ArrayRef(const std::vector<T, A>& Vec)
+      : Data(Vec.data()), Length(Vec.size()) {}
+
+  /// Construct an ArrayRef from a std::array
+  template <size_t N>
+  /*implicit*/ constexpr ArrayRef(const std::array<T, N>& Arr)
+      : Data(Arr.data()), Length(N) {}
+
+  /// Construct an ArrayRef from a C array.
+  template <size_t N>
+  /*implicit*/ constexpr ArrayRef(const T (&Arr)[N]) : Data(Arr), Length(N) {}
+
+  /// Construct an ArrayRef from a std::initializer_list.
+  /*implicit*/ ArrayRef(const std::initializer_list<T>& Vec)
+      : Data(Vec.begin() == Vec.end() ? (T*)nullptr : Vec.begin()),
+        Length(Vec.size()) {}
+
+  /// @}
+  /// @name Simple Operations
+  /// @{
+
+  iterator begin() const { return Data; }
+  iterator end() const { return Data + Length; }
+
+  reverse_iterator rbegin() const { return reverse_iterator(end()); }
+  reverse_iterator rend() const { return reverse_iterator(begin()); }
+
+  /// empty - Check if the array is empty.
+  bool empty() const { return Length == 0; }
+
+  const T* data() const { return Data; }
+
+  /// size - Get the array size.
+  size_t size() const { return Length; }
+
+  /// front - Get the first element.
+  const T& front() const {
+    assert(!empty());
+    return Data[0];
+  }
+
+  /// back - Get the last element.
+  const T& back() const {
+    assert(!empty());
+    return Data[Length - 1];
+  }
+
+  /// equals - Check for element-wise equality.
+  bool equals(ArrayRef RHS) const {
+    if (Length != RHS.Length) return false;
+    return std::equal(begin(), end(), RHS.begin());
+  }
+
+  /// slice(n, m) - Chop off the first N elements of the array, and keep M
+  /// elements in the array.
+  ArrayRef<T> slice(size_t N, size_t M) const {
+    assert(N + M <= size() && "Invalid specifier");
+    return ArrayRef<T>(data() + N, M);
+  }
+
+  /// slice(n) - Chop off the first N elements of the array.
+  ArrayRef<T> slice(size_t N) const { return slice(N, size() - N); }
+
+  /// @}
+  /// @name Operator Overloads
+  /// @{
+  const T& operator[](size_t Index) const {
+    assert(Index < Length && "Invalid index!");
+    return Data[Index];
+  }
+
+  /// Vector compatibility
+  const T& at(size_t Index) const {
+    assert(Index < Length && "Invalid index!");
+    return Data[Index];
+  }
+
+  /// Disallow accidental assignment from a temporary.
+  ///
+  /// The declaration here is extra complicated so that "arrayRef = {}"
+  /// continues to select the move assignment operator.
+  template <typename U>
+  typename std::enable_if<std::is_same<U, T>::value, ArrayRef<T>>::type&
+  operator=(U&& Temporary) = delete;
+
+  /// Disallow accidental assignment from a temporary.
+  ///
+  /// The declaration here is extra complicated so that "arrayRef = {}"
+  /// continues to select the move assignment operator.
+  template <typename U>
+  typename std::enable_if<std::is_same<U, T>::value, ArrayRef<T>>::type&
+  operator=(std::initializer_list<U>) = delete;
+
+  /// @}
+  /// @name Expensive Operations
+  /// @{
+  std::vector<T> vec() const { return std::vector<T>(Data, Data + Length); }
+
+  /// @}
+  /// @name Conversion operators
+  /// @{
+  operator std::vector<T>() const {
+    return std::vector<T>(Data, Data + Length);
+  }
+
+  /// @}
+};
+
+}  // namespace my_ai_training::ir
diff --git a/src/ir/graph_node_list.h b/src/ir/graph_node_list.h
new file mode 100644
index 0000000..2841b02
--- /dev/null
+++ b/src/ir/graph_node_list.h
@@ -0,0 +1,158 @@
+#pragma once
+
+#include "ir/assertions.h"
+
+namespace my_ai_training::ir {
+
+// Intrusive doubly linked lists with sane reverse iterators.
+// The header file is named graph_node_list.h because it is ONLY
+// used for Graph's Node lists, and if you want to use it for other
+// things, you will have to do some refactoring.
+//
+// At the moment, the templated type T must support a few operations:
+//
+//  - It must have a field: T* next_in_graph[2] = { nullptr, nullptr };
+//    which are used for the intrusive linked list pointers.
+//
+//  - It must have a method 'destroy()', which removes T from the
+//    list and frees a T.
+//
+// In practice, we are only using it with Node and const Node.  'destroy()'
+// needs to be renegotiated if you want to use this somewhere else.
+//
+// Besides the benefits of being intrusive, unlike std::list, these lists handle
+// forward and backward iteration uniformly because we require a
+// "before-first-element" sentinel.  This means that reverse iterators
+// physically point to the element they logically point to, rather than
+// the off-by-one behavior for all standard library reverse iterators.
+
+static constexpr size_t kNextDirection = 0;
+static constexpr size_t kPrevDirection = 1;
+
+template <typename T>
+struct generic_graph_node_list;
+
+template <typename T>
+struct generic_graph_node_list_iterator;
+
+struct Node;
+using graph_node_list = generic_graph_node_list<Node>;
+using const_graph_node_list = generic_graph_node_list<const Node>;
+using graph_node_list_iterator = generic_graph_node_list_iterator<Node>;
+using const_graph_node_list_iterator =
+    generic_graph_node_list_iterator<const Node>;
+
+template <typename T>
+struct generic_graph_node_list_iterator final {
+  generic_graph_node_list_iterator() : cur(nullptr), d(kNextDirection) {}
+  generic_graph_node_list_iterator(T* cur, size_t d) : cur(cur), d(d) {}
+  T* operator*() const { return cur; }
+  T* operator->() const { return cur; }
+  generic_graph_node_list_iterator& operator++() {
+    ONNX_ASSERT(cur);
+    cur = cur->next_in_graph[d];
+    return *this;
+  }
+  generic_graph_node_list_iterator operator++(int) {
+    generic_graph_node_list_iterator old = *this;
+    ++(*this);
+    return old;
+  }
+  generic_graph_node_list_iterator& operator--() {
+    ONNX_ASSERT(cur);
+    cur = cur->next_in_graph[reverseDir()];
+    return *this;
+  }
+  generic_graph_node_list_iterator operator--(int) {
+    generic_graph_node_list_iterator old = *this;
+    --(*this);
+    return old;
+  }
+
+  // erase cur without invalidating this iterator
+  // named differently from destroy so that ->/. bugs do not
+  // silently cause the wrong one to be called.
+  // iterator will point to the previous entry after call
+  void destroyCurrent() {
+    T* n = cur;
+    cur = cur->next_in_graph[reverseDir()];
+    n->destroy();
+  }
+  generic_graph_node_list_iterator reverse() {
+    return generic_graph_node_list_iterator(cur, reverseDir());
+  }
+
+ private:
+  size_t reverseDir() {
+    return d == kNextDirection ? kPrevDirection : kNextDirection;
+  }
+  T* cur;
+  size_t d;  // direction 0 is forward 1 is reverse, see next_in_graph
+};
+
+template <typename T>
+struct generic_graph_node_list final {
+  using iterator = generic_graph_node_list_iterator<T>;
+  using const_iterator = generic_graph_node_list_iterator<const T>;
+  generic_graph_node_list_iterator<T> begin() {
+    return generic_graph_node_list_iterator<T>(head->next_in_graph[d], d);
+  }
+  generic_graph_node_list_iterator<const T> begin() const {
+    return generic_graph_node_list_iterator<const T>(head->next_in_graph[d], d);
+  }
+  generic_graph_node_list_iterator<T> end() {
+    return generic_graph_node_list_iterator<T>(head, d);
+  }
+  generic_graph_node_list_iterator<const T> end() const {
+    return generic_graph_node_list_iterator<const T>(head, d);
+  }
+  generic_graph_node_list_iterator<T> rbegin() { return reverse().begin(); }
+  generic_graph_node_list_iterator<const T> rbegin() const {
+    return reverse().begin();
+  }
+  generic_graph_node_list_iterator<T> rend() { return reverse().end(); }
+  generic_graph_node_list_iterator<const T> rend() const {
+    return reverse().end();
+  }
+  generic_graph_node_list reverse() {
+    return generic_graph_node_list(
+        head, d == kNextDirection ? kPrevDirection : kNextDirection);
+  }
+  const generic_graph_node_list reverse() const {
+    return generic_graph_node_list(
+        head, d == kNextDirection ? kPrevDirection : kNextDirection);
+  }
+  generic_graph_node_list(T* head, size_t d) : head(head), d(d) {}
+
+ private:
+  T* head;
+  size_t d;
+};
+
+template <typename T>
+static inline bool operator==(generic_graph_node_list_iterator<T> a,
+                              generic_graph_node_list_iterator<T> b) {
+  return *a == *b;
+}
+
+template <typename T>
+static inline bool operator!=(generic_graph_node_list_iterator<T> a,
+                              generic_graph_node_list_iterator<T> b) {
+  return *a != *b;
+}
+
+}  // namespace my_ai_training::ir
+
+namespace std {
+
+template <typename T>
+struct iterator_traits<
+    my_ai_training::ir::generic_graph_node_list_iterator<T>> {
+  using difference_type = int64_t;
+  using value_type = T*;
+  using pointer = T**;
+  using reference = T*&;
+  using iterator_category = bidirectional_iterator_tag;
+};
+
+}  // namespace std
diff --git a/src/ir/ir.h b/src/ir/ir.h
index b07f4e3..fde37e6 100644
--- a/src/ir/ir.h
+++ b/src/ir/ir.h
@@ -16,7 +16,10 @@
 #include <utility>
 #include <vector>
 
+#include "ir/array_ref.h"
 #include "ir/assertions.h"
+#include "ir/graph_node_list.h"
+#include "ir/interned_strings.h"
 
 #define MY_AI_TRAINING_DISALLOW_COPY_AND_ASSIGN(TypeName) \
   TypeName(const TypeName&) = delete;                     \
@@ -24,6 +27,16 @@
 
 namespace my_ai_training::ir {
 
+namespace {  // internal/private API
+
+std::string toVarName(size_t i) {
+  std::ostringstream oss;
+  oss << "_v_" << i;
+  return oss.str();
+}
+
+}  // namespace
+
 struct Graph;
 
 struct Node;
@@ -86,6 +99,215 @@ static inline const char* toString(AttributeKind kind) {
   return names[int(kind)];
 }
 
+// Each use is represented by this type, see Node::uses()
+// 'user' is the consumer of the value, offset is the index into
+// 'user's input this where the produces will be found.
+struct Use final {
+  Use(Node* user, size_t offset) : user(user), offset(offset) {}
+  Node* user;
+  size_t offset;
+};
+
+static inline bool operator==(const Use& a, const Use& b) {
+  return a.user == b.user && a.offset == b.offset;
+}
+
+// the list types are intentionally simple, but we type-def
+// them here so if we need to change them, refactoring will be easier
+using node_list = std::vector<Node*>;
+using value_list = std::vector<Value*>;
+using use_list = std::vector<Use>;
+using NodeKind = Symbol;
+
+struct Value final {
+  MY_AI_TRAINING_DISALLOW_COPY_AND_ASSIGN(Value);
+  Value(Node* node, size_t offset);
+  Value(Value&&) = default;
+  Value& operator=(Value&&) = default;
+  ~Value() = default;
+
+ private:
+  friend struct Node;
+  friend struct Graph;
+  Node* node_;
+  size_t offset_;
+  size_t unique_ = 0;  // unique id
+  size_t stage_ = 0;   // 0-forward, 1-backward, 2-double-backward,...
+  use_list uses_in_current_graph_;
+  bool has_unique_name_;
+  std::string unique_name_;
+  int32_t elem_type_;
+  bool has_sizes_;
+  std::vector<Dimension> sizes_;
+
+ public:
+  Value* setElemType(int32_t elem_type) {
+    elem_type_ = elem_type;
+    return this;
+  }
+
+  int32_t elemType() const { return elem_type_; }
+
+  bool has_sizes() const { return has_sizes_; }
+
+  Value* setSizes(std::vector<Dimension> sizes) {
+    has_sizes_ = true;
+    sizes_ = std::move(sizes);
+    return this;
+  }
+
+  Value* wipeSizes() {
+    has_sizes_ = false;
+    sizes_ = std::vector<Dimension>();
+    return this;
+  }
+
+  const std::vector<Dimension>& sizes() const { return sizes_; }
+
+  size_t unique() const { return unique_; }
+
+  bool has_unique_name() const { return has_unique_name_; }
 
+  std::string uniqueName() const {
+    if (has_unique_name()) return unique_name_;
+    return toVarName(unique());
+  }
+
+  Value* setUniqueName(const std::string& name,
+                       bool rename_subgraph_captured_nodes = true);
+  Value* setStage(size_t s) {
+    stage_ = s;
+    return this;
+  }
+  size_t stage() const { return stage_; }
+  Node* node() { return node_; }
+  size_t offset() const { return offset_; }
+  const Node* node() const { return node_; }
+  Graph* owningGraph();
+  const Graph* owningGraph() const;
+  // TODO: make this more const correct
+  const use_list uses() const;
+
+  // Replaces all uses of this node with 'newValue'.
+  //
+  // Given:   %3 = f(%1, %2)
+  //          %4 = g(%3)
+  //          %5 = h(%3, %3)
+  // Execute: %3.replaceAllUsesWith(%6)
+  // Result:  %3 = f(%1, %2)
+  //          %4 = g(%6)
+  //          %5 = h(%6, %6)
+  void replaceAllUsesWith(Value* newValue);
+
+  Value* copyMetadata(Value* from) {
+    setElemType(from->elemType());
+    setSizes(from->sizes());
+    if (from->has_unique_name()) {
+      setUniqueName(from->uniqueName());
+    }
+    return this;
+  }
+};
+
+struct Node {
+  MY_AI_TRAINING_DISALLOW_COPY_AND_ASSIGN(Node);
+  friend struct Graph;
+  friend struct Value;
+  friend graph_node_list;
+  friend const_graph_node_list;
+  friend graph_node_list_iterator;
+  friend const_graph_node_list_iterator;
+
+ private:
+  // each node but Return/Param
+  // is associated with exactly one place in the node list...
+  // of the graph_
+  // this circular is a doubly-linked list, the Return node is used as the
+  // sentinel for the beginning and end of the list such that the list never has
+  // null pointers next_in_graph[0] is next pointer next_in_graph[1] is prev
+  // pointer using an array to allow the same iterator class for forward and
+  // reverse node lists This list represents a topological sort
+
+  Node* next_in_graph[2] = {nullptr, nullptr};
+  Node*& next() { return next_in_graph[kNextDirection]; }
+  Node*& prev() { return next_in_graph[kPrevDirection]; }
+  Node* const& next() const { return next_in_graph[kNextDirection]; }
+  Node* const& prev() const { return next_in_graph[kPrevDirection]; }
+
+  const NodeKind kind_;
+  std::vector<Value*> inputs_;
+  std::vector<Value*> outputs_;
+  Graph* graph_;
+  size_t stage_;
+  bool has_name_;
+  std::string name_;
+  bool has_domain_;
+  std::string domain_;
+  bool has_doc_string_;
+  std::string doc_string_;
+  bool has_overload_;
+  std::string overload_;
+
+ protected:
+  Node(Graph* graph_, NodeKind kind_);  // defined after graph
+
+ public:
+  bool has_name() const { return has_name_; }
+  const std::string& name() const { return name_; }
+  void setName(std::string name) {
+    has_name_ = true;
+    name_ = std::move(name);
+  }
+  bool has_domain() const { return has_domain_; }
+  const std::string& domain() const { return domain_; }
+  void setDomain(std::string domain) {
+    has_domain_ = true;
+    domain_ = std::move(domain);
+  }
+  bool has_overload() const { return has_overload_; }
+  const std::string& overload() const { return overload_; }
+  void setOverload(std::string overload) {
+    has_overload_ = true;
+    overload_ = std::move(overload);
+  }
+  bool has_doc_string() const { return has_doc_string_; }
+  const std::string& docString() const { return doc_string_; }
+  void setDocString(std::string doc_string) {
+    has_doc_string_ = true;
+    doc_string_ = std::move(doc_string);
+  }
+  NodeKind kind() const { return kind_; }
+  Graph* owningGraph() { return graph_; }
+  const Graph* owningGraph() const { return graph_; }
+  size_t stage() const { return stage_; }
+  Node* setStage(size_t s) {
+    stage_ = s;
+    return this;
+  }
+  // NB: This returns an ArrayRef; that means that it will
+  // get invalidated if you resize inputs (e.g., using addInput)
+  // We can't return a std::vector<Node*>& because there's no
+  // way to soundly cast to std::vector<const Node*> (an insane
+  // implementation of std::vector could make this representationally
+  // different.)
+  ArrayRef<Value*> inputs() { return inputs_; }
+  ArrayRef<const Value*> inputs() const {
+    // Vectors are not convertible in const-ness of elements, but
+    // raw pointers are.
+    return {inputs_.data(), inputs_.size()};
+  }
+  // NB: This returns an ArrayRef; that means that it will
+  // get invalidated if you resize inputs (e.g., using addInput)
+  // We can't return a std::vector<Node*>& because there's no
+  // way to soundly cast to std::vector<const Node*> (an insane
+  // implementation of std::vector could make this representationally
+  // different.)
+  ArrayRef<Value*> outputs() { return outputs_; }
+  ArrayRef<const Value*> outputs() const {
+    // Vectors are not convertible in const-ness of elements, but
+    // raw pointers are.
+    return {outputs_.data(), outputs_.size()};
+  }
+};
 
 }  // namespace my_ai_training::ir