diff --git a/mlir/lib/Dialect/StandardOps/IR/Ops.cpp b/mlir/lib/Dialect/StandardOps/IR/Ops.cpp
--- a/mlir/lib/Dialect/StandardOps/IR/Ops.cpp
+++ b/mlir/lib/Dialect/StandardOps/IR/Ops.cpp
@@ -844,6 +844,30 @@
 OpFoldResult CmpIOp::fold(ArrayRef<Attribute> operands) {
   assert(operands.size() == 2 && "cmpi takes two arguments");
 
+  auto lhsOperand = lhs();
+  auto rhsOperand = rhs();
+  if (!lhsOperand || !rhsOperand)
+    return {};
+
+  // Operands of the compare are equal.
+  if (lhsOperand == rhsOperand) {
+    // Cmp Ops which are false when operands are the same.
+    if (getPredicate() == CmpIPredicate::sgt ||
+        getPredicate() == CmpIPredicate::slt ||
+        getPredicate() == CmpIPredicate::ugt ||
+        getPredicate() == CmpIPredicate::ult ||
+        getPredicate() == CmpIPredicate::ne)
+      return IntegerAttr::get(IntegerType::get(1, getContext()), APInt(1, 0));
+
+    // Cmp Ops which are true when operands are the same.
+    if (getPredicate() == CmpIPredicate::eq ||
+        getPredicate() == CmpIPredicate::sle ||
+        getPredicate() == CmpIPredicate::ule ||
+        getPredicate() == CmpIPredicate::sge ||
+        getPredicate() == CmpIPredicate::uge)
+      return IntegerAttr::get(IntegerType::get(1, getContext()), APInt(1, 1));
+  }
+
   auto lhs = operands.front().dyn_cast_or_null<IntegerAttr>();
   auto rhs = operands.back().dyn_cast_or_null<IntegerAttr>();
   if (!lhs || !rhs)
diff --git a/mlir/test/Dialect/Standard/canonicalize.mlir b/mlir/test/Dialect/Standard/canonicalize.mlir
new file mode 100644
--- /dev/null
+++ b/mlir/test/Dialect/Standard/canonicalize.mlir
@@ -0,0 +1,34 @@
+// RUN: mlir-opt %s -allow-unregistered-dialect -pass-pipeline='func(canonicalize)' -split-input-file | FileCheck %s
+func @test_simplify_1(%arg0: memref<?x?xf32>) -> memref<?x10xf32> {
+  %c0 = constant 0 : index
+  %0 = dim %arg0, %c0 : memref<?x?xf32>
+  %c1 = constant 1 : index
+  %1 = dim %arg0, %c1 : memref<?x?xf32>
+  %3 = cmpi "sgt", %0, %0 : index
+  %4 = select %3, %0, %1 : index
+  %5 = alloc(%4) : memref<?x10xf32>
+  return %5 : memref<?x10xf32>
+
+  // CHECK-LABEL: test_simplify_1
+  // CHECK: [[CONST1:%.+]] = constant 1 : index
+  // CHECK: [[DIM2:%.+]] = dim %arg0, [[CONST1]] : memref<?x?xf32>
+  // CHECK-NOT: cmpi "sgt", %0, %0 : index
+  // CHECK: [[RES:%.+]] = alloc([[DIM2]]) : memref<?x10xf32>
+}
+
+func @test_simplify_2(%arg0: memref<?x?xf32>) -> memref<?x10xf32> {
+  %c0 = constant 0 : index
+  %0 = dim %arg0, %c0 : memref<?x?xf32>
+  %c1 = constant 1 : index
+  %1 = dim %arg0, %c1 : memref<?x?xf32>
+  %3 = cmpi "eq", %0, %0 : index
+  %4 = select %3, %0, %1 : index
+  %5 = alloc(%4) : memref<?x10xf32>
+  return %5 : memref<?x10xf32>
+
+  // CHECK-LABEL: test_simplify_2
+  // CHECK: [[CONST0:%.+]] = constant 0 : index
+  // CHECK: [[DIM1:%.+]] = dim %arg0, [[CONST0]] : memref<?x?xf32>
+  // CHECK-NOT: cmpi "sgt", %0, %0 : index
+  // CHECK: [[RES:%.+]] = alloc([[DIM1]]) : memref<?x10xf32>
+}