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 +844,25 @@
 OpFoldResult CmpIOp::fold(ArrayRef<Attribute> operands) {
   assert(operands.size() == 2 && "cmpi takes two arguments");
 
+  // Operands of the compare are equal.
+  if (lhs() == rhs()) {
+    // 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 +1,101 @@
+// RUN: mlir-opt %s -allow-unregistered-dialect -pass-pipeline='func(canonicalize)' -split-input-file | FileCheck %s
+
+// CHECK-LABEL: test_simplify_sgt
+func @test_simplify_sgt(%arg0: index) -> i1 {
+  %0 = cmpi "sgt", %arg0, %arg0 : index
+  return %0 : i1
+
+  // CHECK-NOT: cmpi
+  // CHECK: [[FALSE:%.+]] = constant false
+  // CHECK: return [[FALSE]] : i1
+}
+
+// CHECK-LABEL: test_simplify_slt
+func @test_simplify_slt(%arg0: index) -> i1 {
+  %0 = cmpi "slt", %arg0, %arg0 : index
+  return %0 : i1
+
+  // CHECK-NOT: cmpi
+  // CHECK: [[FALSE:%.+]] = constant false
+  // CHECK: return [[FALSE]] : i1
+}
+
+// CHECK-LABEL: test_simplify_ugt
+func @test_simplify_ugt(%arg0: index) -> i1 {
+  %0 = cmpi "ugt", %arg0, %arg0 : index
+  return %0 : i1
+
+  // CHECK-NOT: cmpi
+  // CHECK: [[FALSE:%.+]] = constant false
+  // CHECK: return [[FALSE]] : i1
+}
+
+// CHECK-LABEL: test_simplify_ult
+func @test_simplify_ult(%arg0: index) -> i1 {
+  %0 = cmpi "ult", %arg0, %arg0 : index
+  return %0 : i1
+
+  // CHECK-NOT: cmpi
+  // CHECK: [[FALSE:%.+]] = constant false
+  // CHECK: return [[FALSE]] : i1
+}
+
+// CHECK-LABEL: test_simplify_ne
+func @test_simplify_ne(%arg0: index) -> i1 {
+  %0 = cmpi "ne", %arg0, %arg0 : index
+  return %0 : i1
+
+  // CHECK-NOT: cmpi
+  // CHECK: [[FALSE:%.+]] = constant false
+  // CHECK: return [[FALSE]] : i1
+}
+
+// CHECK-LABEL: test_simplify_eq
+func @test_simplify_eq(%arg0: index) -> i1 {
+  %0 = cmpi "eq", %arg0, %arg0 : index
+  return %0 : i1
+
+  // CHECK-NOT: cmpi
+  // CHECK: [[TRUE:%.+]] = constant true
+  // CHECK: return [[TRUE]] : i1
+}
+
+// CHECK-LABEL: test_simplify_sle
+func @test_simplify_sle(%arg0: index) -> i1 {
+  %0 = cmpi "sle", %arg0, %arg0 : index
+  return %0 : i1
+
+  // CHECK-NOT: cmpi
+  // CHECK: [[TRUE:%.+]] = constant true
+  // CHECK: return [[TRUE]] : i1
+}
+
+// CHECK-LABEL: test_simplify_ule
+func @test_simplify_ule(%arg0: index) -> i1 {
+  %0 = cmpi "ule", %arg0, %arg0 : index
+  return %0 : i1
+
+  // CHECK-NOT: cmpi
+  // CHECK: [[TRUE:%.+]] = constant true
+  // CHECK: return [[TRUE]] : i1
+}
+
+// CHECK-LABEL: test_simplify_sge
+func @test_simplify_sge(%arg0: index) -> i1 {
+  %0 = cmpi "sge", %arg0, %arg0 : index
+  return %0 : i1
+
+  // CHECK-NOT: cmpi
+  // CHECK: [[TRUE:%.+]] = constant true
+  // CHECK: return [[TRUE]] : i1
+}
+
+// CHECK-LABEL: test_simplify_uge
+func @test_simplify_uge(%arg0: index) -> i1 {
+  %0 = cmpi "uge", %arg0, %arg0 : index
+  return %0 : i1
+
+  // CHECK-NOT: cmpi
+  // CHECK: [[TRUE:%.+]] = constant true
+  // CHECK: return [[TRUE]] : i1
+}