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 BoolAttr::get(false, getContext());
+
+    // 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 BoolAttr::get(true, getContext());
+  }
+
   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 +1,100 @@
+// RUN: mlir-opt %s -allow-unregistered-dialect -pass-pipeline='func(canonicalize)' -split-input-file | FileCheck %s
+func @test_simplify_sgt(%arg0: index, %arg1 : index, %arg2 : index) -> index {
+  %0 = cmpi "sgt", %arg0, %arg0 : index
+  %1 = select %0, %arg1, %arg2 : index
+  return %1 : index
+
+  // CHECK-LABEL: test_simplify_sgt
+  // CHECK-NOT: cmpi "sgt", %arg0, %arg0 : index
+  // CHECK: return %arg2 : index
+}
+
+func @test_simplify_slt(%arg0: index, %arg1 : index, %arg2 : index) -> index {
+  %0 = cmpi "slt", %arg0, %arg0 : index
+  %1 = select %0, %arg1, %arg2 : index
+  return %1 : index
+
+  // CHECK-LABEL: test_simplify_slt
+  // CHECK-NOT: cmpi "slt", %arg0, %arg0 : index
+  // CHECK: return %arg2 : index
+}
+
+func @test_simplify_ugt(%arg0: index, %arg1 : index, %arg2 : index) -> index {
+  %0 = cmpi "ugt", %arg0, %arg0 : index
+  %1 = select %0, %arg1, %arg2 : index
+  return %1 : index
+
+  // CHECK-LABEL: test_simplify_ugt
+  // CHECK-NOT: cmpi "ugt", %arg0, %arg0 : index
+  // CHECK: return %arg2 : index
+}
+
+func @test_simplify_ult(%arg0: index, %arg1 : index, %arg2 : index) -> index {
+  %0 = cmpi "ult", %arg0, %arg0 : index
+  %1 = select %0, %arg1, %arg2 : index
+  return %1 : index
+
+  // CHECK-LABEL: test_simplify_ult
+  // CHECK-NOT: cmpi "ult", %arg0, %arg0 : index
+  // CHECK: return %arg2 : index
+}
+
+func @test_simplify_ne(%arg0: index, %arg1 : index, %arg2 : index) -> index {
+  %0 = cmpi "ne", %arg0, %arg0 : index
+  %1 = select %0, %arg1, %arg2 : index
+  return %1 : index
+
+  // CHECK-LABEL: test_simplify_ne
+  // CHECK-NOT: cmpi "ne", %arg0, %arg0 : index
+  // CHECK: return %arg2 : index
+}
+
+func @test_simplify_eq(%arg0: index, %arg1 : index, %arg2 : index) -> index {
+  %0 = cmpi "eq", %arg0, %arg0 : index
+  %1 = select %0, %arg1, %arg2 : index
+  return %1 : index
+
+  // CHECK-LABEL: test_simplify_eq
+  // CHECK-NOT: cmpi "eq", %arg0, %arg0 : index
+  // CHECK: return %arg1 : index
+}
+
+func @test_simplify_sle(%arg0: index, %arg1 : index, %arg2 : index) -> index {
+  %0 = cmpi "sle", %arg0, %arg0 : index
+  %1 = select %0, %arg1, %arg2 : index
+  return %1 : index
+
+  // CHECK-LABEL: test_simplify_sle
+  // CHECK-NOT: cmpi "sle", %arg0, %arg0 : index
+  // CHECK: return %arg1 : index
+}
+
+func @test_simplify_ule(%arg0: index, %arg1 : index, %arg2 : index) -> index {
+  %0 = cmpi "ule", %arg0, %arg0 : index
+  %1 = select %0, %arg1, %arg2 : index
+  return %1 : index
+
+  // CHECK-LABEL: test_simplify_ule
+  // CHECK-NOT: cmpi "ule", %arg0, %arg0 : index
+  // CHECK: return %arg1 : index
+}
+
+func @test_simplify_sge(%arg0: index, %arg1 : index, %arg2 : index) -> index {
+  %0 = cmpi "sge", %arg0, %arg0 : index
+  %1 = select %0, %arg1, %arg2 : index
+  return %1 : index
+
+  // CHECK-LABEL: test_simplify_sge
+  // CHECK-NOT: cmpi "sge", %arg0, %arg0 : index
+  // CHECK: return %arg1 : index
+}
+
+func @test_simplify_uge(%arg0: index, %arg1 : index, %arg2 : index) -> index {
+  %0 = cmpi "uge", %arg0, %arg0 : index
+  %1 = select %0, %arg1, %arg2 : index
+  return %1 : index
+
+  // CHECK-LABEL: test_simplify_uge
+  // CHECK-NOT: cmpi "uge", %arg0, %arg0 : index
+  // CHECK: return %arg1 : index
+}