Index: mlir/lib/IR/Dominance.cpp
===================================================================
--- mlir/lib/IR/Dominance.cpp
+++ mlir/lib/IR/Dominance.cpp
@@ -180,10 +180,9 @@
     b = traverseAncestors(
         b, [&](Block *block) { return block->getParent() == regionA; });
 
-    // If we could not find a valid block b then it is either a not a dominator
-    // or a post dominator.
+    // If we could not find a valid block b then it is a not a dominator.
     if (!b)
-      return IsPostDom;
+      return false;
 
     // Check to see if the ancestor of 'b' is the same block as 'a'.
     if (a == b)
Index: mlir/test/Analysis/test-dominance.mlir
===================================================================
--- mlir/test/Analysis/test-dominance.mlir
+++ mlir/test/Analysis/test-dominance.mlir
@@ -204,4 +204,104 @@
 // CHECK-NEXT: Nearest(4, 2) = 2
 // CHECK-NEXT: Nearest(4, 3) = 4
 // CHECK-NEXT: Nearest(4, 4) = 4
-// CHECK-NEXT: Nearest(4, 5) = 5
\ No newline at end of file
+// CHECK-NEXT: Nearest(4, 5) = 5
+// CHECK-LABEL: --- Block Dominance relationship ---
+// CHECK-NEXT: dominates(0, 0) = true
+// CHECK-NEXT: dominates(0, 1) = true
+// CHECK-NEXT: dominates(0, 2) = true
+// CHECK-NEXT: dominates(0, 3) = true
+// CHECK-NEXT: dominates(0, 4) = true
+// CHECK-NEXT: dominates(0, 5) = true
+// CHECK-NEXT: dominates(0, 6) = false
+// CHECK-NEXT: dominates(1, 0) = false
+// CHECK-NEXT: dominates(1, 1) = true
+// CHECK-NEXT: dominates(1, 2) = true
+// CHECK-NEXT: dominates(1, 3) = true
+// CHECK-NEXT: dominates(1, 4) = true
+// CHECK-NEXT: dominates(1, 5) = true
+// CHECK-NEXT: dominates(1, 6) = false
+// CHECK-NEXT: dominates(2, 0) = false
+// CHECK-NEXT: dominates(2, 1) = false
+// CHECK-NEXT: dominates(2, 2) = true
+// CHECK-NEXT: dominates(2, 3) = true
+// CHECK-NEXT: dominates(2, 4) = true
+// CHECK-NEXT: dominates(2, 5) = false
+// CHECK-NEXT: dominates(2, 6) = false
+// CHECK-NEXT: dominates(3, 0) = false
+// CHECK-NEXT: dominates(3, 1) = false
+// CHECK-NEXT: dominates(3, 2) = false
+// CHECK-NEXT: dominates(3, 3) = true
+// CHECK-NEXT: dominates(3, 4) = false
+// CHECK-NEXT: dominates(3, 5) = false
+// CHECK-NEXT: dominates(3, 6) = false
+// CHECK-NEXT: dominates(4, 0) = false
+// CHECK-NEXT: dominates(4, 1) = false
+// CHECK-NEXT: dominates(4, 2) = false
+// CHECK-NEXT: dominates(4, 3) = true
+// CHECK-NEXT: dominates(4, 4) = true
+// CHECK-NEXT: dominates(4, 5) = false
+// CHECK-NEXT: dominates(4, 6) = false
+// CHECK-NEXT: dominates(5, 0) = false
+// CHECK-NEXT: dominates(5, 1) = false
+// CHECK-NEXT: dominates(5, 2) = false
+// CHECK-NEXT: dominates(5, 3) = false
+// CHECK-NEXT: dominates(5, 4) = false
+// CHECK-NEXT: dominates(5, 5) = true
+// CHECK-NEXT: dominates(5, 6) = false
+// CHECK-NEXT: dominates(6, 0) = true
+// CHECK-NEXT: dominates(6, 1) = true
+// CHECK-NEXT: dominates(6, 2) = true
+// CHECK-NEXT: dominates(6, 3) = true
+// CHECK-NEXT: dominates(6, 4) = true
+// CHECK-NEXT: dominates(6, 5) = true
+// CHECK-NEXT: dominates(6, 6) = true
+// CHECK-LABEL: --- Block PostDominance relationship ---
+// CHECK-NEXT: postdominates(0, 0) = true
+// CHECK-NEXT: postdominates(0, 1) = false
+// CHECK-NEXT: postdominates(0, 2) = false
+// CHECK-NEXT: postdominates(0, 3) = false
+// CHECK-NEXT: postdominates(0, 4) = false
+// CHECK-NEXT: postdominates(0, 5) = false
+// CHECK-NEXT: postdominates(0, 6) = false
+// CHECK-NEXT: postdominates(1, 0) = true
+// CHECK-NEXT: postdominates(1, 1) = true
+// CHECK-NEXT: postdominates(1, 2) = true
+// CHECK-NEXT: postdominates(1, 3) = true
+// CHECK-NEXT: postdominates(1, 4) = true
+// CHECK-NEXT: postdominates(1, 5) = false
+// CHECK-NEXT: postdominates(1, 6) = false
+// CHECK-NEXT: postdominates(2, 0) = false
+// CHECK-NEXT: postdominates(2, 1) = false
+// CHECK-NEXT: postdominates(2, 2) = true
+// CHECK-NEXT: postdominates(2, 3) = true
+// CHECK-NEXT: postdominates(2, 4) = true
+// CHECK-NEXT: postdominates(2, 5) = false
+// CHECK-NEXT: postdominates(2, 6) = false
+// CHECK-NEXT: postdominates(3, 0) = false
+// CHECK-NEXT: postdominates(3, 1) = false
+// CHECK-NEXT: postdominates(3, 2) = false
+// CHECK-NEXT: postdominates(3, 3) = true
+// CHECK-NEXT: postdominates(3, 4) = false
+// CHECK-NEXT: postdominates(3, 5) = false
+// CHECK-NEXT: postdominates(3, 6) = false
+// CHECK-NEXT: postdominates(4, 0) = false
+// CHECK-NEXT: postdominates(4, 1) = false
+// CHECK-NEXT: postdominates(4, 2) = false
+// CHECK-NEXT: postdominates(4, 3) = true
+// CHECK-NEXT: postdominates(4, 4) = true
+// CHECK-NEXT: postdominates(4, 5) = false
+// CHECK-NEXT: postdominates(4, 6) = false
+// CHECK-NEXT: postdominates(5, 0) = true
+// CHECK-NEXT: postdominates(5, 1) = true
+// CHECK-NEXT: postdominates(5, 2) = true
+// CHECK-NEXT: postdominates(5, 3) = true
+// CHECK-NEXT: postdominates(5, 4) = true
+// CHECK-NEXT: postdominates(5, 5) = true
+// CHECK-NEXT: postdominates(5, 6) = false
+// CHECK-NEXT: postdominates(6, 0) = true
+// CHECK-NEXT: postdominates(6, 1) = true
+// CHECK-NEXT: postdominates(6, 2) = true
+// CHECK-NEXT: postdominates(6, 3) = true
+// CHECK-NEXT: postdominates(6, 4) = true
+// CHECK-NEXT: postdominates(6, 5) = true
+// CHECK-NEXT: postdominates(6, 6) = true
Index: mlir/test/lib/Transforms/TestDominance.cpp
===================================================================
--- mlir/test/lib/Transforms/TestDominance.cpp
+++ mlir/test/lib/Transforms/TestDominance.cpp
@@ -17,6 +17,18 @@
 
 using namespace mlir;
 
+/// Overloaded helper to call the right function based on whether we are testing
+/// dominance or post-dominance.
+static bool dominatesOrPostDominates(DominanceInfo &dominanceInfo, Block *a,
+                                     Block *b) {
+  return dominanceInfo.dominates(a, b);
+}
+
+static bool dominatesOrPostDominates(PostDominanceInfo &dominanceInfo, Block *a,
+                                     Block *b) {
+  return dominanceInfo.postDominates(a, b);
+}
+
 namespace {
 
 /// Helper class to print dominance information.
@@ -34,7 +46,8 @@
 
   /// Prints dominance information of all blocks.
   template <typename DominanceT>
-  void printDominance(DominanceT &dominanceInfo) {
+  void printDominance(DominanceT &dominanceInfo,
+                      bool printCommonDominatorInfo) {
     DenseSet<Block *> parentVisited;
     operation->walk([&](Operation *op) {
       Block *block = op->getBlock();
@@ -46,15 +59,28 @@
         Block *nestedBlock = nested->getBlock();
         if (!visited.insert(nestedBlock).second)
           return;
-        llvm::errs() << "Nearest(" << blockIds[block] << ", "
-                     << blockIds[nestedBlock] << ") = ";
-        Block *dom =
-            dominanceInfo.findNearestCommonDominator(block, nestedBlock);
-        if (dom)
-          llvm::errs() << blockIds[dom];
-        else
-          llvm::errs() << "<no dom>";
-        llvm::errs() << "\n";
+        if (printCommonDominatorInfo) {
+          llvm::errs() << "Nearest(" << blockIds[block] << ", "
+                       << blockIds[nestedBlock] << ") = ";
+          Block *dom =
+              dominanceInfo.findNearestCommonDominator(block, nestedBlock);
+          if (dom)
+            llvm::errs() << blockIds[dom];
+          else
+            llvm::errs() << "<no dom>";
+          llvm::errs() << "\n";
+        } else {
+          if (std::is_same<DominanceInfo, DominanceT>::value)
+            llvm::errs() << "dominates(";
+          else
+            llvm::errs() << "postdominates(";
+          llvm::errs() << blockIds[block] << ", " << blockIds[nestedBlock]
+                       << ") = ";
+          if (dominatesOrPostDominates(dominanceInfo, block, nestedBlock))
+            llvm::errs() << "true\n";
+          else
+            llvm::errs() << "false\n";
+        }
       });
     });
   }
@@ -72,10 +98,21 @@
 
     // Print dominance information.
     llvm::errs() << "--- DominanceInfo ---\n";
-    dominanceTest.printDominance(getAnalysis<DominanceInfo>());
+    dominanceTest.printDominance(getAnalysis<DominanceInfo>(),
+                                 /*printCommonDominatorInfo=*/true);
 
     llvm::errs() << "--- PostDominanceInfo ---\n";
-    dominanceTest.printDominance(getAnalysis<PostDominanceInfo>());
+    dominanceTest.printDominance(getAnalysis<PostDominanceInfo>(),
+                                 /*printCommonDominatorInfo=*/true);
+
+    // Print dominance relationship between blocks.
+    llvm::errs() << "--- Block Dominance relationship ---\n";
+    dominanceTest.printDominance(getAnalysis<DominanceInfo>(),
+                                 /*printCommonDominatorInfo=*/false);
+
+    llvm::errs() << "--- Block PostDominance relationship ---\n";
+    dominanceTest.printDominance(getAnalysis<PostDominanceInfo>(),
+                                 /*printCommonDominatorInfo=*/false);
   }
 };