Index: include/llvm/Analysis/LoopInfo.h
===================================================================
--- include/llvm/Analysis/LoopInfo.h
+++ include/llvm/Analysis/LoopInfo.h
@@ -622,7 +622,7 @@
   }
 
   /// Create the loop forest using a stable algorithm.
-  void Analyze(DominatorTreeBase<BlockT> &DomTree);
+  void analyze(const DominatorTreeBase<BlockT> &DomTree);
 
   // Debugging
   void print(raw_ostream &OS) const;
Index: include/llvm/Analysis/LoopInfoImpl.h
===================================================================
--- include/llvm/Analysis/LoopInfoImpl.h
+++ include/llvm/Analysis/LoopInfoImpl.h
@@ -345,7 +345,7 @@
 template<class BlockT, class LoopT>
 static void discoverAndMapSubloop(LoopT *L, ArrayRef<BlockT*> Backedges,
                                   LoopInfoBase<BlockT, LoopT> *LI,
-                                  DominatorTreeBase<BlockT> &DomTree) {
+                                  const DominatorTreeBase<BlockT> &DomTree) {
   typedef GraphTraits<Inverse<BlockT*> > InvBlockTraits;
 
   unsigned NumBlocks = 0;
@@ -468,10 +468,10 @@
 /// insertions per block.
 template<class BlockT, class LoopT>
 void LoopInfoBase<BlockT, LoopT>::
-Analyze(DominatorTreeBase<BlockT> &DomTree) {
+analyze(const DominatorTreeBase<BlockT> &DomTree) {
 
   // Postorder traversal of the dominator tree.
-  DomTreeNodeBase<BlockT>* DomRoot = DomTree.getRootNode();
+  const DomTreeNodeBase<BlockT>* DomRoot = DomTree.getRootNode();
   for (auto DomNode : post_order(DomRoot)) {
 
     BlockT *Header = DomNode->getBlock();
Index: include/llvm/CodeGen/MachineDominators.h
===================================================================
--- include/llvm/CodeGen/MachineDominators.h
+++ include/llvm/CodeGen/MachineDominators.h
@@ -263,6 +263,21 @@
   }
 };
 
+template <> struct GraphTraits<const MachineDomTreeNode *> {
+  typedef const MachineDomTreeNode NodeType;
+  typedef NodeType::const_iterator ChildIteratorType;
+
+  static NodeType *getEntryNode(NodeType *N) {
+    return N;
+  }
+  static inline ChildIteratorType child_begin(NodeType* N) {
+    return N->begin();
+  }
+  static inline ChildIteratorType child_end(NodeType* N) {
+    return N->end();
+  }
+};
+
 template <> struct GraphTraits<MachineDominatorTree*>
   : public GraphTraits<MachineDomTreeNode *> {
   static NodeType *getEntryNode(MachineDominatorTree *DT) {
Index: include/llvm/IR/Dominators.h
===================================================================
--- include/llvm/IR/Dominators.h
+++ include/llvm/IR/Dominators.h
@@ -147,6 +147,31 @@
   }
 };
 
+template <> struct GraphTraits<const DomTreeNode *> {
+  typedef const DomTreeNode NodeType;
+  typedef NodeType::const_iterator ChildIteratorType;
+
+  static NodeType *getEntryNode(NodeType *N) {
+    return N;
+  }
+  static inline ChildIteratorType child_begin(NodeType *N) {
+    return N->begin();
+  }
+  static inline ChildIteratorType child_end(NodeType *N) {
+    return N->end();
+  }
+
+  typedef df_iterator<const DomTreeNode *> nodes_iterator;
+
+  static nodes_iterator nodes_begin(const DomTreeNode *N) {
+    return df_begin(getEntryNode(N));
+  }
+
+  static nodes_iterator nodes_end(const DomTreeNode *N) {
+    return df_end(getEntryNode(N));
+  }
+};
+
 template <> struct GraphTraits<DominatorTree*>
   : public GraphTraits<DomTreeNode*> {
   static NodeType *getEntryNode(DominatorTree *DT) {
Index: lib/Analysis/LoopInfo.cpp
===================================================================
--- lib/Analysis/LoopInfo.cpp
+++ lib/Analysis/LoopInfo.cpp
@@ -675,7 +675,7 @@
   // objects. I don't want to add that kind of complexity until the scope of
   // the problem is better understood.
   LoopInfo LI;
-  LI.Analyze(AM->getResult<DominatorTreeAnalysis>(F));
+  LI.analyze(AM->getResult<DominatorTreeAnalysis>(F));
   return LI;
 }
 
@@ -698,7 +698,7 @@
 
 bool LoopInfoWrapperPass::runOnFunction(Function &) {
   releaseMemory();
-  LI.Analyze(getAnalysis<DominatorTreeWrapperPass>().getDomTree());
+  LI.analyze(getAnalysis<DominatorTreeWrapperPass>().getDomTree());
   return false;
 }
 
Index: lib/CodeGen/MachineLoopInfo.cpp
===================================================================
--- lib/CodeGen/MachineLoopInfo.cpp
+++ lib/CodeGen/MachineLoopInfo.cpp
@@ -37,7 +37,7 @@
 
 bool MachineLoopInfo::runOnMachineFunction(MachineFunction &) {
   releaseMemory();
-  LI.Analyze(getAnalysis<MachineDominatorTree>().getBase());
+  LI.analyze(getAnalysis<MachineDominatorTree>().getBase());
   return false;
 }