diff --git a/mlir/include/mlir/Dialect/StandardOps/IR/Ops.td b/mlir/include/mlir/Dialect/StandardOps/IR/Ops.td
--- a/mlir/include/mlir/Dialect/StandardOps/IR/Ops.td
+++ b/mlir/include/mlir/Dialect/StandardOps/IR/Ops.td
@@ -1027,6 +1027,8 @@
 
   let hasFolder = 1;
 
+  let hasCanonicalizer = 1;
+
   let assemblyFormat = "$predicate `,` $lhs `,` $rhs attr-dict `:` type($lhs)";
 }
 
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
@@ -853,6 +853,52 @@
   return IntegerAttr::get(IntegerType::get(1, getContext()), APInt(1, val));
 }
 
+namespace {
+/// cmpi <predicate> %op %op
+///   -> {0/1}
+struct SimplifyCmpIOpWithIdenticalOperands : public OpRewritePattern<CmpIOp> {
+  using OpRewritePattern<CmpIOp>::OpRewritePattern;
+
+  LogicalResult matchAndRewrite(CmpIOp cmpIOp,
+                                PatternRewriter &rewriter) const override {
+    auto loc = cmpIOp.getLoc();
+    Value replacement = nullptr;
+
+    // Operands of the compare are equal.
+    if (cmpIOp.getOperands()[0] == cmpIOp.getOperands()[1]) {
+      // Cmp Ops which are false when operands are the same.
+      if (cmpIOp.getPredicate() == CmpIPredicate::sgt ||
+          cmpIOp.getPredicate() == CmpIPredicate::slt ||
+          cmpIOp.getPredicate() == CmpIPredicate::ugt ||
+          cmpIOp.getPredicate() == CmpIPredicate::ult ||
+          cmpIOp.getPredicate() == CmpIPredicate::ne)
+        replacement = rewriter.create<ConstantOp>(
+            loc, rewriter.getIntegerAttr(rewriter.getIndexType(), 0));
+
+      // Cmp Ops which are true when operands are the same.
+      if (cmpIOp.getPredicate() == CmpIPredicate::eq ||
+          cmpIOp.getPredicate() == CmpIPredicate::sle ||
+          cmpIOp.getPredicate() == CmpIPredicate::ule ||
+          cmpIOp.getPredicate() == CmpIPredicate::sge ||
+          cmpIOp.getPredicate() == CmpIPredicate::uge)
+        replacement = rewriter.create<ConstantOp>(
+            loc, rewriter.getIntegerAttr(rewriter.getIndexType(), 1));
+    }
+
+    if (!replacement)
+      return failure();
+
+    rewriter.replaceOp(cmpIOp, replacement);
+    return success();
+  }
+};
+} // end namespace
+
+void CmpIOp::getCanonicalizationPatterns(
+    OwningRewritePatternList &results, MLIRContext *context) {
+  results.insert<SimplifyCmpIOpWithIdenticalOperands>(context);
+}
+
 //===----------------------------------------------------------------------===//
 // CmpFOp
 //===----------------------------------------------------------------------===//
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 +1,32 @@
+// 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: [[DIM2:%.+]] = dim %arg0, %c1 : 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: [[DIM1:%.+]] = dim %arg0, %c0 : memref<?x?xf32>
+  // CHECK-NOT: cmpi "sgt", %0, %0 : index
+  // CHECK: [[RES:%.+]] = alloc([[DIM1]]) : memref<?x10xf32>
+}