diff --git a/executable_semantics/ast/BUILD b/executable_semantics/ast/BUILD
index f43f338a3c87..5b2b4052cba3 100644
--- a/executable_semantics/ast/BUILD
+++ b/executable_semantics/ast/BUILD
@@ -17,6 +17,7 @@ cc_library(
         ":function_definition",
         ":member",
         ":struct_definition",
+        "//executable_semantics/interpreter:address",
         "//executable_semantics/interpreter:containers",
     ],
 )
diff --git a/executable_semantics/ast/declaration.h b/executable_semantics/ast/declaration.h
index 2ef89a278a1a..ed4e4dd74a8a 100644
--- a/executable_semantics/ast/declaration.h
+++ b/executable_semantics/ast/declaration.h
@@ -11,6 +11,7 @@
 #include "executable_semantics/ast/function_definition.h"
 #include "executable_semantics/ast/member.h"
 #include "executable_semantics/ast/struct_definition.h"
+#include "executable_semantics/interpreter/address.h"
 #include "executable_semantics/interpreter/dictionary.h"
 
 namespace yy {
@@ -21,7 +22,6 @@ namespace Carbon {
 
 struct Value;
 
-using Address = unsigned int;
 using TypeEnv = Dictionary<std::string, const Value*>;
 using Env = Dictionary<std::string, Address>;
 
diff --git a/executable_semantics/interpreter/BUILD b/executable_semantics/interpreter/BUILD
index e07ece8d6a1c..376392c143e3 100644
--- a/executable_semantics/interpreter/BUILD
+++ b/executable_semantics/interpreter/BUILD
@@ -22,6 +22,7 @@ cc_library(
         "value.h",
     ],
     deps = [
+        ":address",
         ":containers",
         "//common:check",
         "//executable_semantics:tracing_flag",
@@ -33,6 +34,19 @@ cc_library(
     ],
 )
 
+cc_library(
+    name = "field_path",
+    hdrs = ["field_path.h"],
+)
+
+cc_library(
+    name = "address",
+    hdrs = ["address.h"],
+    deps = [
+        ":field_path",
+    ],
+)
+
 cc_library(
     name = "containers",
     srcs = [
diff --git a/executable_semantics/interpreter/address.h b/executable_semantics/interpreter/address.h
new file mode 100644
index 000000000000..f8b19714928d
--- /dev/null
+++ b/executable_semantics/interpreter/address.h
@@ -0,0 +1,68 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+#ifndef EXECUTABLE_SEMANTICS_INTERPRETER_ADDRESS_H_
+#define EXECUTABLE_SEMANTICS_INTERPRETER_ADDRESS_H_
+
+#include <cstdint>
+#include <iostream>
+#include <string>
+#include <vector>
+
+#include "executable_semantics/interpreter/field_path.h"
+
+namespace Carbon {
+
+// An Address represents a memory address in the Carbon virtual machine.
+// Addresses are used to access values stored in a Heap, and are obtained
+// from a Heap (or by deriving them from other Addresses).
+class Address {
+ public:
+  Address(const Address&) = default;
+  Address(Address&&) = default;
+  auto operator=(const Address&) -> Address& = default;
+  auto operator=(Address&&) -> Address& = default;
+
+  // Returns true if the two addresses refer to the same memory location.
+  friend auto operator==(const Address& lhs, const Address& rhs) -> bool {
+    return lhs.index == rhs.index;
+  }
+
+  friend auto operator!=(const Address& lhs, const Address& rhs) -> bool {
+    return !(lhs == rhs);
+  }
+
+  // Prints a human-readable representation of `a` to `out`.
+  //
+  // Currently, that representation consists of an integer index identifying
+  // the whole memory allocation, and an optional FieldPath specifying a
+  // particular field within that allocation.
+  friend auto operator<<(std::ostream& out, const Address& a) -> std::ostream& {
+    out << "Address(" << a.index << ")" << a.field_path;
+    return out;
+  }
+
+  // If *this represents the address of an object with a field named
+  // `field_name`, this method returns the address of that field.
+  auto SubobjectAddress(std::string field_name) const -> Address {
+    Address result = *this;
+    result.field_path.Append(std::move(field_name));
+    return result;
+  }
+
+ private:
+  // The representation of Address describes how to locate an object within
+  // the Heap, so its implementation details are tied to the implementation
+  // details of the Heap.
+  friend class Heap;
+
+  explicit Address(uint64_t index) : index(index) {}
+
+  uint64_t index;
+  FieldPath field_path;
+};
+
+}  // namespace Carbon
+
+#endif  // EXECUTABLE_SEMANTICS_INTERPRETER_ADDRESS_H_
diff --git a/executable_semantics/interpreter/field_path.h b/executable_semantics/interpreter/field_path.h
new file mode 100644
index 000000000000..926f5eb2df5c
--- /dev/null
+++ b/executable_semantics/interpreter/field_path.h
@@ -0,0 +1,64 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+#ifndef EXECUTABLE_SEMANTICS_INTERPRETER_FIELD_PATH_H_
+#define EXECUTABLE_SEMANTICS_INTERPRETER_FIELD_PATH_H_
+
+#include <ostream>
+#include <string>
+#include <vector>
+
+namespace Carbon {
+
+// Given some initial Value, a FieldPath identifies a sub-Value within it,
+// in much the same way that a file path identifies a file within some
+// directory. FieldPaths are relative rather than absolute: the initial
+// Value is specified by the context in which the FieldPath is used, not
+// by the FieldPath itself.
+//
+// A FieldPath consists of a series of steps, which specify how to
+// incrementally navigate from a Value to one of its fields. Currently
+// there is only one kind of step, a string specifying a child field by name,
+// but that may change as Carbon develops. Note that an empty FieldPath
+// refers to the initial Value itself.
+class FieldPath {
+ public:
+  // Constructs an empty FieldPath.
+  FieldPath() = default;
+
+  // Constructs a FieldPath consisting of a single step.
+  explicit FieldPath(std::string name) : components({std::move(name)}) {}
+
+  FieldPath(const FieldPath&) = default;
+  FieldPath(FieldPath&&) = default;
+  auto operator=(const FieldPath&) -> FieldPath& = default;
+  auto operator=(FieldPath&&) -> FieldPath& = default;
+
+  // Returns whether *this is empty.
+  auto IsEmpty() const -> bool { return components.empty(); }
+
+  // Appends `name` to the end of *this.
+  auto Append(std::string name) -> void {
+    components.push_back(std::move(name));
+  }
+
+  friend auto operator<<(std::ostream& out, const FieldPath& path)
+      -> std::ostream& {
+    for (const std::string& component : path.components) {
+      out << "." << component;
+    }
+    return out;
+  }
+
+ private:
+  // The representation of FieldPath describes how to locate a Value within
+  // another Value, so its implementation details are tied to the implementation
+  // details of Value.
+  friend struct Value;
+  std::vector<std::string> components;
+};
+
+}  // namespace Carbon
+
+#endif  // EXECUTABLE_SEMANTICS_INTERPRETER_FIELD_PATH_H_
diff --git a/executable_semantics/interpreter/interpreter.cpp b/executable_semantics/interpreter/interpreter.cpp
index a3d1d0d3e3aa..f5bf744483ea 100644
--- a/executable_semantics/interpreter/interpreter.cpp
+++ b/executable_semantics/interpreter/interpreter.cpp
@@ -26,7 +26,6 @@ State* state = nullptr;
 auto PatternMatch(const Value* pat, const Value* val, Env,
                   std::list<std::string>*, int) -> std::optional<Env>;
 auto Step() -> void;
-auto GetMember(const Value* v, const std::string& f, int line_num) -> Address;
 //
 // Auxiliary Functions
 //
@@ -37,27 +36,27 @@ auto Heap::AllocateValue(const Value* v) -> Address {
   // Consider whether to include a copy of the input v in this function
   // or to leave it up to the caller.
   CHECK(v != nullptr);
-  Address a = values_.size();
+  Address a(values_.size());
   values_.push_back(v);
   alive_.push_back(true);
   return a;
 }
 
-auto Heap::Read(Address a, int line_num) -> const Value* {
+auto Heap::Read(const Address& a, int line_num) -> const Value* {
   this->CheckAlive(a, line_num);
-  return values_[a];
+  return values_[a.index]->GetField(a.field_path, line_num);
 }
 
-auto Heap::Write(Address a, const Value* v, int line_num) -> void {
+auto Heap::Write(const Address& a, const Value* v, int line_num) -> void {
   CHECK(v != nullptr);
   this->CheckAlive(a, line_num);
-  values_[a] = v;
+  values_[a.index] = values_[a.index]->SetField(a.field_path, v, line_num);
 }
 
-void Heap::CheckAlive(Address address, int line_num) {
-  if (!alive_[address]) {
+void Heap::CheckAlive(const Address& address, int line_num) {
+  if (!alive_[address.index]) {
     std::cerr << line_num << ": undefined behavior: access to dead value ";
-    PrintValue(values_[address], std::cerr);
+    PrintValue(values_[address.index], std::cerr);
     std::cerr << std::endl;
     exit(-1);
   }
@@ -68,21 +67,16 @@ auto CopyVal(const Value* val, int line_num) -> const Value* {
     case ValKind::TupleValue: {
       std::vector<TupleElement> elements;
       for (const TupleElement& element : val->GetTupleValue().elements) {
-        const Value* new_element =
-            CopyVal(state->heap.Read(element.address, line_num), line_num);
-        Address new_address = state->heap.AllocateValue(new_element);
-        elements.push_back({.name = element.name, .address = new_address});
+        elements.push_back(
+            {.name = element.name, .value = CopyVal(element.value, line_num)});
       }
       return Value::MakeTupleValue(std::move(elements));
     }
     case ValKind::AlternativeValue: {
-      const Value* arg = CopyVal(
-          state->heap.Read(val->GetAlternativeValue().argument, line_num),
-          line_num);
-      Address argument_address = state->heap.AllocateValue(arg);
+      const Value* arg = CopyVal(val->GetAlternativeValue().argument, line_num);
       return Value::MakeAlternativeValue(val->GetAlternativeValue().alt_name,
                                          val->GetAlternativeValue().choice_name,
-                                         argument_address);
+                                         arg);
     }
     case ValKind::StructValue: {
       const Value* inits = CopyVal(val->GetStructValue().inits, line_num);
@@ -128,28 +122,10 @@ auto CopyVal(const Value* val, int line_num) -> const Value* {
   }
 }
 
-void Heap::DeallocateSubObjects(const Value* val) {
-  switch (val->tag()) {
-    case ValKind::AlternativeValue:
-      Deallocate(val->GetAlternativeValue().argument);
-      break;
-    case ValKind::StructValue:
-      DeallocateSubObjects(val->GetStructValue().inits);
-      break;
-    case ValKind::TupleValue:
-      for (const TupleElement& element : val->GetTupleValue().elements) {
-        Deallocate(element.address);
-      }
-      break;
-    default:
-      break;
-  }
-}
-
-void Heap::Deallocate(Address address) {
-  if (alive_[address]) {
-    alive_[address] = false;
-    DeallocateSubObjects(values_[address]);
+void Heap::Deallocate(const Address& address) {
+  CHECK(address.field_path.IsEmpty());
+  if (alive_[address.index]) {
+    alive_[address.index] = false;
   } else {
     std::cerr << "runtime error, deallocating an already dead value"
               << std::endl;
@@ -187,17 +163,17 @@ void PrintStack(Stack<Frame*> ls, std::ostream& out) {
 }
 
 void Heap::PrintHeap(std::ostream& out) {
-  for (Address i = 0; i < values_.size(); ++i) {
-    PrintAddress(i, out);
+  for (size_t i = 0; i < values_.size(); ++i) {
+    PrintAddress(Address(i), out);
     out << ", ";
   }
 }
 
-auto Heap::PrintAddress(Address a, std::ostream& out) -> void {
-  if (!alive_[a]) {
+auto Heap::PrintAddress(const Address& a, std::ostream& out) -> void {
+  if (!alive_[a.index]) {
     out << "!!";
   }
-  PrintValue(values_[a], out);
+  PrintValue(values_[a.index], out);
 }
 
 auto CurrentEnv(State* state) -> Env {
@@ -392,8 +368,7 @@ void CallFunction(int line_num, std::vector<const Value*> operas,
       const Value* arg = CopyVal(operas[1], line_num);
       const Value* av = Value::MakeAlternativeValue(
           operas[0]->GetAlternativeConstructorValue().alt_name,
-          operas[0]->GetAlternativeConstructorValue().choice_name,
-          state->heap.AllocateValue(arg));
+          operas[0]->GetAlternativeConstructorValue().choice_name, arg);
       Frame* frame = state->stack.Top();
       frame->todo.Push(Action::MakeValAction(av));
       break;
@@ -430,8 +405,7 @@ void CreateTuple(Frame* frame, Action* act, const Expression* exp) {
   auto f = exp->GetTupleLiteral().fields.begin();
 
   for (auto i = act->results.begin(); i != act->results.end(); ++i, ++f) {
-    Address a = state->heap.AllocateValue(*i);  // copy?
-    elements.push_back({.name = f->name, .address = a});
+    elements.push_back({.name = f->name, .value = *i});
   }
   const Value* tv = Value::MakeTupleValue(std::move(elements));
   frame->todo.Pop(1);
@@ -462,17 +436,19 @@ auto PatternMatch(const Value* p, const Value* v, Env values,
                       << std::endl;
             exit(-1);
           }
-          for (const TupleElement& element : p->GetTupleValue().elements) {
-            auto a = FindTupleField(element.name, v);
-            if (a == std::nullopt) {
-              std::cerr << "runtime error: field " << element.name << "not in ";
+          for (const TupleElement& pattern_element :
+               p->GetTupleValue().elements) {
+            const Value* value_field =
+                v->GetTupleValue().FindField(pattern_element.name);
+            if (value_field == nullptr) {
+              std::cerr << "runtime error: field " << pattern_element.name
+                        << "not in ";
               PrintValue(v, std::cerr);
               std::cerr << std::endl;
               exit(-1);
             }
             std::optional<Env> matches = PatternMatch(
-                state->heap.Read(element.address, line_num),
-                state->heap.Read(*a, line_num), values, vars, line_num);
+                pattern_element.value, value_field, values, vars, line_num);
             if (!matches) {
               return std::nullopt;
             }
@@ -497,9 +473,8 @@ auto PatternMatch(const Value* p, const Value* v, Env values,
             return std::nullopt;
           }
           std::optional<Env> matches = PatternMatch(
-              state->heap.Read(p->GetAlternativeValue().argument, line_num),
-              state->heap.Read(v->GetAlternativeValue().argument, line_num),
-              values, vars, line_num);
+              p->GetAlternativeValue().argument,
+              v->GetAlternativeValue().argument, values, vars, line_num);
           if (!matches) {
             return std::nullopt;
           }
@@ -553,16 +528,18 @@ void PatternAssignment(const Value* pat, const Value* val, int line_num) {
                       << std::endl;
             exit(-1);
           }
-          for (const TupleElement& element : pat->GetTupleValue().elements) {
-            auto a = FindTupleField(element.name, val);
-            if (a == std::nullopt) {
-              std::cerr << "runtime error: field " << element.name << "not in ";
+          for (const TupleElement& pattern_element :
+               pat->GetTupleValue().elements) {
+            const Value* value_field =
+                val->GetTupleValue().FindField(pattern_element.name);
+            if (value_field == nullptr) {
+              std::cerr << "runtime error: field " << pattern_element.name
+                        << "not in ";
               PrintValue(val, std::cerr);
               std::cerr << std::endl;
               exit(-1);
             }
-            PatternAssignment(state->heap.Read(element.address, line_num),
-                              state->heap.Read(*a, line_num), line_num);
+            PatternAssignment(pattern_element.value, value_field, line_num);
           }
           break;
         }
@@ -586,10 +563,8 @@ void PatternAssignment(const Value* pat, const Value* val, int line_num) {
             std::cerr << "internal error in pattern assignment" << std::endl;
             exit(-1);
           }
-          PatternAssignment(
-              state->heap.Read(pat->GetAlternativeValue().argument, line_num),
-              state->heap.Read(val->GetAlternativeValue().argument, line_num),
-              line_num);
+          PatternAssignment(pat->GetAlternativeValue().argument,
+                            val->GetAlternativeValue().argument, line_num);
           break;
         }
         default:
@@ -641,17 +616,17 @@ void StepLvalue() {
       if (act->pos == 0) {
         //    { {e.f :: C, E, F} :: S, H}
         // -> { e :: [].f :: C, E, F} :: S, H}
-        frame->todo.Push(Action::MakeExpressionAction(
-            exp->GetFieldAccessExpression().aggregate));
+        frame->todo.Push(
+            Action::MakeLValAction(exp->GetFieldAccessExpression().aggregate));
         act->pos++;
       } else {
         //    { v :: [].f :: C, E, F} :: S, H}
         // -> { { &v.f :: C, E, F} :: S, H }
-        const Value* str = act->results[0];
-        Address a = GetMember(str, exp->GetFieldAccessExpression().field,
-                              exp->line_num);
+        Address aggregate = act->results[0]->GetPointerValue();
+        Address field =
+            aggregate.SubobjectAddress(exp->GetFieldAccessExpression().field);
         frame->todo.Pop(1);
-        frame->todo.Push(Action::MakeValAction(Value::MakePointerValue(a)));
+        frame->todo.Push(Action::MakeValAction(Value::MakePointerValue(field)));
       }
       break;
     }
@@ -660,7 +635,7 @@ void StepLvalue() {
         //    { {e[i] :: C, E, F} :: S, H}
         // -> { e :: [][i] :: C, E, F} :: S, H}
         frame->todo.Push(
-            Action::MakeExpressionAction(exp->GetIndexExpression().aggregate));
+            Action::MakeLValAction(exp->GetIndexExpression().aggregate));
         act->pos++;
       } else if (act->pos == 1) {
         frame->todo.Push(
@@ -669,17 +644,11 @@ void StepLvalue() {
       } else if (act->pos == 2) {
         //    { v :: [][i] :: C, E, F} :: S, H}
         // -> { { &v[i] :: C, E, F} :: S, H }
-        const Value* tuple = act->results[0];
+        Address aggregate = act->results[0]->GetPointerValue();
         std::string f = std::to_string(ToInteger(act->results[1]));
-        auto a = FindTupleField(f, tuple);
-        if (a == std::nullopt) {
-          std::cerr << "runtime error: field " << f << "not in ";
-          PrintValue(tuple, std::cerr);
-          std::cerr << std::endl;
-          exit(-1);
-        }
+        Address field = aggregate.SubobjectAddress(f);
         frame->todo.Pop(1);
-        frame->todo.Push(Action::MakeValAction(Value::MakePointerValue(*a)));
+        frame->todo.Push(Action::MakeValAction(Value::MakePointerValue(field)));
       }
       break;
     }
@@ -767,16 +736,15 @@ void StepExp() {
             //    { { v :: [][i] :: C, E, F} :: S, H}
             // -> { { v_i :: C, E, F} : S, H}
             std::string f = std::to_string(ToInteger(act->results[1]));
-            auto a = FindTupleField(f, tuple);
-            if (a == std::nullopt) {
+            const Value* field = tuple->GetTupleValue().FindField(f);
+            if (field == nullptr) {
               std::cerr << "runtime error, field " << f << " not in ";
               PrintValue(tuple, std::cerr);
               std::cerr << std::endl;
               exit(-1);
             }
             frame->todo.Pop(1);
-            const Value* element = state->heap.Read(*a, exp->line_num);
-            frame->todo.Push(Action::MakeValAction(element));
+            frame->todo.Push(Action::MakeValAction(field));
             break;
           }
           default:
@@ -825,12 +793,10 @@ void StepExp() {
       } else {
         //    { { v :: [].f :: C, E, F} :: S, H}
         // -> { { v_f :: C, E, F} : S, H}
-        Address element =
-            GetMember(act->results[0], exp->GetFieldAccessExpression().field,
-                      exp->line_num);
+        const Value* element = act->results[0]->GetField(
+            FieldPath(exp->GetFieldAccessExpression().field), exp->line_num);
         frame->todo.Pop(1);
-        frame->todo.Push(
-            Action::MakeValAction(state->heap.Read(element, exp->line_num)));
+        frame->todo.Push(Action::MakeValAction(element));
       }
       break;
     }
@@ -1293,55 +1259,14 @@ void StepStmt() {
       std::vector<Frame*> paused;
       do {
         paused.push_back(state->stack.Pop());
-      } while (!paused.back()->IsContinuation());
+      } while (paused.back()->continuation == std::nullopt);
       // Update the continuation with the paused stack.
-      state->heap.Write(paused.back()->continuation,
+      state->heap.Write(*paused.back()->continuation,
                         Value::MakeContinuationValue(paused), stmt->line_num);
       break;
   }
 }
 
-auto GetMember(const Value* v, const std::string& f, int line_num) -> Address {
-  switch (v->tag()) {
-    case ValKind::StructValue: {
-      auto a = FindTupleField(f, v->GetStructValue().inits);
-      if (a == std::nullopt) {
-        std::cerr << "runtime error, member " << f << " not in ";
-        PrintValue(v, std::cerr);
-        std::cerr << std::endl;
-        exit(-1);
-      }
-      return *a;
-    }
-    case ValKind::TupleValue: {
-      auto a = FindTupleField(f, v);
-      if (a == std::nullopt) {
-        std::cerr << "field " << f << " not in ";
-        PrintValue(v, std::cerr);
-        std::cerr << std::endl;
-        exit(-1);
-      }
-      return *a;
-    }
-    case ValKind::ChoiceType: {
-      if (FindInVarValues(f, v->GetChoiceType().alternatives) == nullptr) {
-        std::cerr << "alternative " << f << " not in ";
-        PrintValue(v, std::cerr);
-        std::cerr << std::endl;
-        exit(-1);
-      }
-      auto ac =
-          Value::MakeAlternativeConstructorValue(f, v->GetChoiceType().name);
-      return state->heap.AllocateValue(ac);
-    }
-    default:
-      std::cerr << "field access not allowed for value ";
-      PrintValue(v, std::cerr);
-      std::cerr << std::endl;
-      exit(-1);
-  }
-}
-
 // State transition.
 void Step() {
   Frame* frame = state->stack.Top();
diff --git a/executable_semantics/interpreter/interpreter.h b/executable_semantics/interpreter/interpreter.h
index d6608d1d60fd..87a2fa507a2b 100644
--- a/executable_semantics/interpreter/interpreter.h
+++ b/executable_semantics/interpreter/interpreter.h
@@ -47,16 +47,10 @@ struct Frame {
   Stack<Action*> todo;
   // If this frame is the bottom frame of a continuation, then it stores
   // the address of the continuation.
-  // Otherwise the `continuation` field is the sentinel UINT_MAX.
-  Address continuation;
-  // Returns whether this frame is the bottom frame of a continuation.
-  auto IsContinuation() -> bool { return continuation != UINT_MAX; }
+  std::optional<Address> continuation;
 
   Frame(std::string n, Stack<Scope*> s, Stack<Action*> c)
-      : name(std::move(std::move(n))),
-        scopes(s),
-        todo(c),
-        continuation(UINT_MAX) {}
+      : name(std::move(std::move(n))), scopes(s), todo(c), continuation() {}
 };
 
 // A Heap represents the abstract machine's dynamically allocated memory.
@@ -70,30 +64,27 @@ class Heap {
 
   // Returns the value at the given address in the heap after
   // checking that it is alive.
-  auto Read(Address a, int line_num) -> const Value*;
+  auto Read(const Address& a, int line_num) -> const Value*;
 
   // Writes the given value at the address in the heap after
   // checking that the address is alive.
-  auto Write(Address a, const Value* v, int line_num) -> void;
+  auto Write(const Address& a, const Value* v, int line_num) -> void;
 
   // Put the given value on the heap and mark it as alive.
   auto AllocateValue(const Value* v) -> Address;
 
   // Marks the object at this address, and all of its sub-objects, as dead.
-  auto Deallocate(Address address) -> void;
+  auto Deallocate(const Address& address) -> void;
 
   // Print the value at the given address to the stream `out`.
-  auto PrintAddress(Address a, std::ostream& out) -> void;
+  auto PrintAddress(const Address& a, std::ostream& out) -> void;
 
   // Print all the values on the heap to the stream `out`.
   auto PrintHeap(std::ostream& out) -> void;
 
  private:
   // Signal an error if the address is no longer alive.
-  void CheckAlive(Address address, int line_num);
-
-  // Marks all sub-objects of this value as dead.
-  void DeallocateSubObjects(const Value* val);
+  void CheckAlive(const Address& address, int line_num);
 
   std::vector<const Value*> values_;
   std::vector<bool> alive_;
diff --git a/executable_semantics/interpreter/typecheck.cpp b/executable_semantics/interpreter/typecheck.cpp
index 47c583f91474..d1d29b05ed18 100644
--- a/executable_semantics/interpreter/typecheck.cpp
+++ b/executable_semantics/interpreter/typecheck.cpp
@@ -70,10 +70,8 @@ auto ReifyType(const Value* t, int line_num) -> const Expression* {
     case ValKind::TupleValue: {
       std::vector<FieldInitializer> args;
       for (const TupleElement& field : t->GetTupleValue().elements) {
-        args.push_back(
-            {.name = field.name,
-             .expression = ReifyType(state->heap.Read(field.address, line_num),
-                                     line_num)});
+        args.push_back({.name = field.name,
+                        .expression = ReifyType(field.value, line_num)});
       }
       return Expression::MakeTupleLiteral(0, args);
     }
@@ -169,15 +167,14 @@ auto TypeCheckExp(const Expression* e, TypeEnv types, Env values,
         case ValKind::TupleValue: {
           auto i = ToInteger(InterpExp(values, e->GetIndexExpression().offset));
           std::string f = std::to_string(i);
-          std::optional<Address> field_address = FindTupleField(f, t);
-          if (field_address == std::nullopt) {
+          const Value* field_t = t->GetTupleValue().FindField(f);
+          if (field_t == nullptr) {
             std::cerr << e->line_num << ": compilation error, field " << f
                       << " is not in the tuple ";
             PrintValue(t, std::cerr);
             std::cerr << std::endl;
             exit(-1);
           }
-          auto field_t = state->heap.Read(*field_address, e->line_num);
           auto new_e = Expression::MakeIndexExpression(
               e->line_num, res.exp, Expression::MakeIntLiteral(e->line_num, i));
           return TCResult(new_e, field_t, res.types);
@@ -217,16 +214,13 @@ auto TypeCheckExp(const Expression* e, TypeEnv types, Env values,
                       << " but got " << arg->name << std::endl;
             exit(-1);
           }
-          arg_expected = state->heap.Read(
-              expected->GetTupleValue().elements[i].address, e->line_num);
+          arg_expected = expected->GetTupleValue().elements[i].value;
         }
         auto arg_res = TypeCheckExp(arg->expression, new_types, values,
                                     arg_expected, context);
         new_types = arg_res.types;
         new_args.push_back({.name = arg->name, .expression = arg_res.exp});
-        arg_types.push_back(
-            {.name = arg->name,
-             .address = state->heap.AllocateValue(arg_res.type)});
+        arg_types.push_back({.name = arg->name, .value = arg_res.type});
       }
       auto tuple_e = Expression::MakeTupleLiteral(e->line_num, new_args);
       auto tuple_t = Value::MakeTupleValue(std::move(arg_types));
@@ -264,9 +258,7 @@ auto TypeCheckExp(const Expression* e, TypeEnv types, Env values,
             if (e->GetFieldAccessExpression().field == field.name) {
               auto new_e = Expression::MakeFieldAccessExpression(
                   e->line_num, res.exp, e->GetFieldAccessExpression().field);
-              return TCResult(new_e,
-                              state->heap.Read(field.address, e->line_num),
-                              res.types);
+              return TCResult(new_e, field.value, res.types);
             }
           }
           std::cerr << e->line_num << ": compilation error, struct "
@@ -777,8 +769,7 @@ auto StructDeclaration::TopLevel(TypeCheckContext& tops) const -> void {
   tops.values.Set(Name(), a);  // Is this obsolete?
   std::vector<TupleElement> field_types;
   for (const auto& [field_name, field_value] : st->GetStructType().fields) {
-    field_types.push_back({.name = field_name,
-                           .address = state->heap.AllocateValue(field_value)});
+    field_types.push_back({.name = field_name, .value = field_value});
   }
   auto fun_ty = Value::MakeFunctionType(
       Value::MakeTupleValue(std::move(field_types)), st);
diff --git a/executable_semantics/interpreter/value.cpp b/executable_semantics/interpreter/value.cpp
index a5f01c09f7bf..8a097ebf8824 100644
--- a/executable_semantics/interpreter/value.cpp
+++ b/executable_semantics/interpreter/value.cpp
@@ -97,15 +97,13 @@ auto FieldsEqual(const VarValues& ts1, const VarValues& ts2) -> bool {
   }
 }
 
-auto FindTupleField(const std::string& name, const Value* tuple)
-    -> std::optional<Address> {
-  CHECK(tuple->tag() == ValKind::TupleValue);
-  for (const TupleElement& element : tuple->GetTupleValue().elements) {
+auto TupleValue::FindField(const std::string& name) const -> const Value* {
+  for (const TupleElement& element : elements) {
     if (element.name == name) {
-      return element.address;
+      return element.value;
     }
   }
-  return std::nullopt;
+  return nullptr;
 }
 
 auto Value::MakeIntValue(int i) -> const Value* {
@@ -148,7 +146,7 @@ auto Value::MakeTupleValue(std::vector<TupleElement> elements) -> const Value* {
 }
 
 auto Value::MakeAlternativeValue(std::string alt_name, std::string choice_name,
-                                 Address argument) -> const Value* {
+                                 const Value* argument) -> const Value* {
   auto* v = new Value();
   v->value = AlternativeValue({.alt_name = std::move(alt_name),
                                .choice_name = std::move(choice_name),
@@ -246,6 +244,106 @@ auto Value::MakeChoiceType(std::string name, VarValues alts) -> const Value* {
   return v;
 }
 
+namespace {
+
+auto GetMember(const Value* v, const std::string& f, int line_num)
+    -> const Value* {
+  switch (v->tag()) {
+    case ValKind::StructValue: {
+      const Value* field =
+          v->GetStructValue().inits->GetTupleValue().FindField(f);
+      if (field == nullptr) {
+        std::cerr << "runtime error, member " << f << " not in ";
+        PrintValue(v, std::cerr);
+        std::cerr << std::endl;
+        exit(-1);
+      }
+      return field;
+    }
+    case ValKind::TupleValue: {
+      const Value* field = v->GetTupleValue().FindField(f);
+      if (field == nullptr) {
+        std::cerr << "field " << f << " not in ";
+        PrintValue(v, std::cerr);
+        std::cerr << std::endl;
+        exit(-1);
+      }
+      return field;
+    }
+    case ValKind::ChoiceType: {
+      if (FindInVarValues(f, v->GetChoiceType().alternatives) == nullptr) {
+        std::cerr << "alternative " << f << " not in ";
+        PrintValue(v, std::cerr);
+        std::cerr << std::endl;
+        exit(-1);
+      }
+      return Value::MakeAlternativeConstructorValue(f, v->GetChoiceType().name);
+    }
+    default:
+      std::cerr << "field access not allowed for value ";
+      PrintValue(v, std::cerr);
+      std::cerr << std::endl;
+      exit(-1);
+  }
+}
+
+}  // namespace
+
+auto Value::GetField(const FieldPath& path, int line_num) const
+    -> const Value* {
+  const Value* value = this;
+  for (const std::string& field : path.components) {
+    value = GetMember(value, field, line_num);
+  }
+  return value;
+}
+
+namespace {
+
+auto SetFieldImpl(const Value* value,
+                  std::vector<std::string>::const_iterator path_begin,
+                  std::vector<std::string>::const_iterator path_end,
+                  const Value* field_value, int line_num) -> const Value* {
+  if (path_begin == path_end) {
+    return field_value;
+  }
+  switch (value->tag()) {
+    case ValKind::StructValue: {
+      return SetFieldImpl(value->GetStructValue().inits, path_begin, path_end,
+                          field_value, line_num);
+    }
+    case ValKind::TupleValue: {
+      std::vector<TupleElement> elements = value->GetTupleValue().elements;
+      auto it = std::find_if(elements.begin(), elements.end(),
+                             [path_begin](const TupleElement& element) {
+                               return element.name == *path_begin;
+                             });
+      if (it == elements.end()) {
+        std::cerr << "field " << *path_begin << " not in ";
+        PrintValue(value, std::cerr);
+        std::cerr << std::endl;
+        exit(-1);
+      }
+      it->value = SetFieldImpl(it->value, path_begin + 1, path_end, field_value,
+                               line_num);
+      return Value::MakeTupleValue(elements);
+    }
+    default:
+      std::cerr << "field access not allowed for value ";
+      PrintValue(value, std::cerr);
+      std::cerr << std::endl;
+      exit(-1);
+  }
+}
+
+}  // namespace
+
+auto Value::SetField(const FieldPath& path, const Value* field_value,
+                     int line_num) const -> const Value* {
+  return SetFieldImpl(this, path.components.begin(), path.components.end(),
+                      field_value, line_num);
+}
+
 auto PrintValue(const Value* val, std::ostream& out) -> void {
   switch (val->tag()) {
     case ValKind::AlternativeConstructorValue: {
@@ -261,7 +359,7 @@ auto PrintValue(const Value* val, std::ostream& out) -> void {
     case ValKind::AlternativeValue: {
       out << "alt " << val->GetAlternativeValue().choice_name << "."
           << val->GetAlternativeValue().alt_name << " ";
-      state->heap.PrintAddress(val->GetAlternativeValue().argument, out);
+      PrintValue(val->GetAlternativeValue().argument, out);
       break;
     }
     case ValKind::StructValue: {
@@ -280,7 +378,7 @@ auto PrintValue(const Value* val, std::ostream& out) -> void {
         }
 
         out << element.name << " = ";
-        state->heap.PrintAddress(element.address, out);
+        PrintValue(element.value, out);
       }
       out << ")";
       break;
@@ -364,9 +462,8 @@ auto TypeEqual(const Value* t1, const Value* t2) -> bool {
             t2->GetTupleValue().elements[i].name) {
           return false;
         }
-        if (!TypeEqual(
-                state->heap.Read(t1->GetTupleValue().elements[i].address, 0),
-                state->heap.Read(t2->GetTupleValue().elements[i].address, 0))) {
+        if (!TypeEqual(t1->GetTupleValue().elements[i].value,
+                       t2->GetTupleValue().elements[i].value)) {
           return false;
         }
       }
@@ -401,8 +498,7 @@ static auto FieldsValueEqual(const std::vector<TupleElement>& ts1,
     if (iter == ts2.end()) {
       return false;
     }
-    if (!ValueEqual(state->heap.Read(element.address, line_num),
-                    state->heap.Read(iter->address, line_num), line_num)) {
+    if (!ValueEqual(element.value, iter->value, line_num)) {
       return false;
     }
   }
diff --git a/executable_semantics/interpreter/value.h b/executable_semantics/interpreter/value.h
index 82c03d0e6368..dd398ba85f7f 100644
--- a/executable_semantics/interpreter/value.h
+++ b/executable_semantics/interpreter/value.h
@@ -7,34 +7,31 @@
 
 #include <list>
 #include <optional>
+#include <string>
 #include <variant>
 #include <vector>
 
 #include "executable_semantics/ast/statement.h"
+#include "executable_semantics/interpreter/address.h"
+#include "executable_semantics/interpreter/field_path.h"
 #include "executable_semantics/interpreter/stack.h"
 
 namespace Carbon {
 
 struct Value;
-using Address = unsigned int;
 using VarValues = std::list<std::pair<std::string, const Value*>>;
 
 auto FindInVarValues(const std::string& field, const VarValues& inits)
     -> const Value*;
 auto FieldsEqual(const VarValues& ts1, const VarValues& ts2) -> bool;
 
-// Finds the field in `*tuple` named `name`, and returns its address, or
-// nullopt if there is no such field. `*tuple` must be a tuple value.
-auto FindTupleField(const std::string& name, const Value* tuple)
-    -> std::optional<Address>;
-
 // A TupleElement represents the value of a single tuple field.
 struct TupleElement {
   // The field name.
   std::string name;
 
-  // Location of the field's value.
-  Address address;
+  // The field's value.
+  const Value* value;
 };
 
 enum class ValKind {
@@ -99,12 +96,16 @@ struct AlternativeValue {
   static constexpr ValKind Kind = ValKind::AlternativeValue;
   std::string alt_name;
   std::string choice_name;
-  Address argument;
+  const Value* argument;
 };
 
 struct TupleValue {
   static constexpr ValKind Kind = ValKind::TupleValue;
   std::vector<TupleElement> elements;
+
+  // Returns the value of the field named `name` in this tuple, or
+  // null if there is no such field.
+  auto FindField(const std::string& name) const -> const Value*;
 };
 
 struct BindingPlaceholderValue {
@@ -177,8 +178,8 @@ struct Value {
       -> const Value*;
   static auto MakeTupleValue(std::vector<TupleElement> elts) -> const Value*;
   static auto MakeAlternativeValue(std::string alt_name,
-                                   std::string choice_name, Address argument)
-      -> const Value*;
+                                   std::string choice_name,
+                                   const Value* argument) -> const Value*;
   static auto MakeAlternativeConstructorValue(std::string alt_name,
                                               std::string choice_name)
       -> const Value*;
@@ -218,6 +219,15 @@ struct Value {
     return std::visit([](const auto& t) { return t.Kind; }, value);
   }
 
+  // Returns the sub-Value specified by `path`, which must be a valid field
+  // path for *this.
+  auto GetField(const FieldPath& path, int line_num) const -> const Value*;
+
+  // Returns a copy of *this, but with the sub-Value specified by `path`
+  // set to `field_value`. `path` must be a valid field path for *this.
+  auto SetField(const FieldPath& path, const Value* field_value,
+                int line_num) const -> const Value*;
+
  private:
   std::variant<IntValue, FunctionValue, PointerValue, BoolValue, StructValue,
                AlternativeValue, TupleValue, IntType, BoolType, TypeType,