diff --git a/lib/Dialect/Poly/BUILD b/lib/Dialect/Poly/BUILD
index 0651282..c1c36f7 100644
--- a/lib/Dialect/Poly/BUILD
+++ b/lib/Dialect/Poly/BUILD
@@ -8,12 +8,14 @@ td_library(
     name = "td_files",
     srcs = [
         "PolyDialect.td",
+        "PolyOps.td",
         "PolyTypes.td",
     ],
     includes = ["@heir//include"],
     deps = [
         # the base mlir target for defining operations and dialects in tablegen
         "@llvm-project//mlir:OpBaseTdFiles",
+        "@llvm-project//mlir:BuiltinDialectTdFiles",
         "@llvm-project//mlir:SideEffectInterfacesTdFiles",
     ],
 )
@@ -80,7 +82,10 @@ gentbl_cc_library(
 
 cc_library(
     name = "Poly",
-    srcs = ["PolyDialect.cpp"],
+    srcs = [
+        "PolyDialect.cpp",
+        "PolyOps.cpp",
+    ],
     hdrs = [
         "PolyDialect.h",
         "PolyOps.h",
@@ -90,6 +95,7 @@ cc_library(
         ":dialect_inc_gen",
         ":ops_inc_gen",
         ":types_inc_gen",
+        "@llvm-project//mlir:Dialect",
         "@llvm-project//mlir:IR",
         "@llvm-project//mlir:Support",
     ],
diff --git a/lib/Dialect/Poly/PolyDialect.cpp b/lib/Dialect/Poly/PolyDialect.cpp
index 1529c97..291cb12 100644
--- a/lib/Dialect/Poly/PolyDialect.cpp
+++ b/lib/Dialect/Poly/PolyDialect.cpp
@@ -2,8 +2,8 @@
 
 #include "lib/Dialect/Poly/PolyOps.h"
 #include "lib/Dialect/Poly/PolyTypes.h"
-#include "llvm/include/llvm/ADT/TypeSwitch.h"
 #include "mlir/include/mlir/IR/Builders.h"
+#include "llvm/include/llvm/ADT/TypeSwitch.h"
 
 #include "lib/Dialect/Poly/PolyDialect.cpp.inc"
 #define GET_TYPEDEF_CLASSES
@@ -26,6 +26,14 @@ void PolyDialect::initialize() {
       >();
 }
 
+Operation *PolyDialect::materializeConstant(OpBuilder &builder, Attribute value,
+                                            Type type, Location loc) {
+  auto coeffs = dyn_cast<DenseIntElementsAttr>(value);
+  if (!coeffs)
+    return nullptr;
+  return builder.create<ConstantOp>(loc, type, coeffs);
+}
+
 } // namespace poly
 } // namespace tutorial
 } // namespace mlir
diff --git a/lib/Dialect/Poly/PolyDialect.td b/lib/Dialect/Poly/PolyDialect.td
index f00e35f..c0214dd 100644
--- a/lib/Dialect/Poly/PolyDialect.td
+++ b/lib/Dialect/Poly/PolyDialect.td
@@ -14,6 +14,7 @@ def Poly_Dialect : Dialect {
   let cppNamespace = "::mlir::tutorial::poly";
 
   let useDefaultTypePrinterParser = 1;
+  let hasConstantMaterializer = 1;
 }
 
 #endif  // LIB_DIALECT_POLY_POLYDIALECT_TD_
diff --git a/lib/Dialect/Poly/PolyOps.cpp b/lib/Dialect/Poly/PolyOps.cpp
new file mode 100644
index 0000000..b54b117
--- /dev/null
+++ b/lib/Dialect/Poly/PolyOps.cpp
@@ -0,0 +1,66 @@
+#include "lib/Dialect/Poly/PolyOps.h"
+
+#include "mlir/Dialect/CommonFolders.h"
+#include "llvm/Support/Debug.h"
+
+namespace mlir {
+namespace tutorial {
+namespace poly {
+
+OpFoldResult ConstantOp::fold(ConstantOp::FoldAdaptor adaptor) {
+  return adaptor.getCoefficients();
+}
+
+OpFoldResult AddOp::fold(AddOp::FoldAdaptor adaptor) {
+  return constFoldBinaryOp<IntegerAttr, APInt>(
+      adaptor.getOperands(), [&](APInt a, APInt b) { return a + b; });
+}
+
+OpFoldResult SubOp::fold(SubOp::FoldAdaptor adaptor) {
+  return constFoldBinaryOp<IntegerAttr, APInt>(
+      adaptor.getOperands(), [&](APInt a, APInt b) { return a - b; });
+}
+
+OpFoldResult MulOp::fold(MulOp::FoldAdaptor adaptor) {
+  auto lhs = dyn_cast<DenseIntElementsAttr>(adaptor.getOperands()[0]);
+  auto rhs = dyn_cast<DenseIntElementsAttr>(adaptor.getOperands()[1]);
+
+  if (!lhs || !rhs)
+    return nullptr;
+
+  auto degree = getResult().getType().cast<PolynomialType>().getDegreeBound();
+  auto maxIndex = lhs.size() + rhs.size() - 1;
+
+  SmallVector<APInt, 8> result;
+  result.reserve(maxIndex);
+  for (int i = 0; i < maxIndex; ++i) {
+    result.push_back(APInt((*lhs.begin()).getBitWidth(), 0));
+  }
+
+  int i = 0;
+  for (auto lhsIt = lhs.value_begin<APInt>(); lhsIt != lhs.value_end<APInt>();
+       ++lhsIt) {
+    int j = 0;
+    for (auto rhsIt = rhs.value_begin<APInt>(); rhsIt != rhs.value_end<APInt>();
+         ++rhsIt) {
+      // index is modulo degree because poly's semantics are defined modulo x^N = 1.
+      result[(i + j) % degree] += *rhsIt * (*lhsIt);
+      ++j;
+    }
+    ++i;
+  }
+
+  return DenseIntElementsAttr::get(
+      RankedTensorType::get(static_cast<int64_t>(result.size()),
+                            IntegerType::get(getContext(), 32)),
+      result);
+}
+
+OpFoldResult FromTensorOp::fold(FromTensorOp::FoldAdaptor adaptor) {
+  // Returns null if the cast failed, which corresponds to a failed fold.
+  return dyn_cast<DenseIntElementsAttr>(adaptor.getInput());
+}
+
+} // namespace poly
+} // namespace tutorial
+} // namespace mlir
diff --git a/lib/Dialect/Poly/PolyOps.td b/lib/Dialect/Poly/PolyOps.td
index 5755f03..f5e1dcd 100644
--- a/lib/Dialect/Poly/PolyOps.td
+++ b/lib/Dialect/Poly/PolyOps.td
@@ -3,6 +3,8 @@
 
 include "PolyDialect.td"
 include "PolyTypes.td"
+include "mlir/IR/BuiltinAttributes.td"
+include "mlir/IR/OpBase.td"
 include "mlir/Interfaces/SideEffectInterfaces.td"
 
 // Type constraint for poly binop arguments: polys, vectors of polys, or
@@ -13,6 +15,7 @@ class Poly_BinOp<string mnemonic> : Op<Poly_Dialect, mnemonic, [Pure, Elementwis
   let arguments = (ins PolyOrContainer:$lhs, PolyOrContainer:$rhs);
   let results = (outs PolyOrContainer:$output);
   let assemblyFormat = "$lhs `,` $rhs attr-dict `:` `(` type($lhs) `,` type($rhs) `)` `->` type($output)";
+  let hasFolder = 1;
 }
 
 def Poly_AddOp : Poly_BinOp<"add"> {
@@ -32,6 +35,7 @@ def Poly_FromTensorOp : Op<Poly_Dialect, "from_tensor", [Pure]> {
   let arguments = (ins TensorOf<[AnyInteger]>:$input);
   let results = (outs Polynomial:$output);
   let assemblyFormat = "$input attr-dict `:` type($input) `->` type($output)";
+  let hasFolder = 1;
 }
 
 def Poly_EvalOp : Op<Poly_Dialect, "eval"> {
@@ -41,5 +45,13 @@ def Poly_EvalOp : Op<Poly_Dialect, "eval"> {
   let assemblyFormat = "$input `,` $point attr-dict `:` `(` type($input) `,` type($point) `)` `->` type($output)";
 }
 
+def Poly_ConstantOp : Op<Poly_Dialect, "constant", [Pure, ConstantLike]> {
+  let summary = "Define a constant polynomial via an attribute.";
+  let arguments = (ins AnyIntElementsAttr:$coefficients);
+  let results = (outs Polynomial:$output);
+  let assemblyFormat = "$coefficients attr-dict `:` type($output)";
+  let hasFolder = 1;
+}
+
 
 #endif  // LIB_DIALECT_POLY_POLYOPS_TD_
diff --git a/tests/poly_canonicalize.mlir b/tests/poly_canonicalize.mlir
new file mode 100644
index 0000000..8d8636a
--- /dev/null
+++ b/tests/poly_canonicalize.mlir
@@ -0,0 +1,13 @@
+// RUN: tutorial-opt --canonicalize %s | FileCheck %s
+
+// CHECK-LABEL: @test_simple
+func.func @test_simple() -> !poly.poly<10> {
+  // CHECK: poly.constant dense<[2, 4, 6]>
+  // CHECK-NEXT: return
+  %0 = arith.constant dense<[1, 2, 3]> : tensor<3xi32>
+  %p0 = poly.from_tensor %0 : tensor<3xi32> -> !poly.poly<10>
+  %2 = poly.add %p0, %p0 : (!poly.poly<10>, !poly.poly<10>) -> !poly.poly<10>
+  %3 = poly.mul %p0, %p0 : (!poly.poly<10>, !poly.poly<10>) -> !poly.poly<10>
+  %4 = poly.add %2, %3 : (!poly.poly<10>, !poly.poly<10>) -> !poly.poly<10>
+  return %2 : !poly.poly<10>
+}
diff --git a/tests/poly_syntax.mlir b/tests/poly_syntax.mlir
index 29515b2..0eb66b3 100644
--- a/tests/poly_syntax.mlir
+++ b/tests/poly_syntax.mlir
@@ -31,6 +31,12 @@ module {
     // CHECK: poly.add
     %9 = poly.add %7, %4 : (tensor<2x!poly.poly<10>>, !poly.poly<10>) -> tensor<2x!poly.poly<10>>
 
+    // CHECK: poly.constant
+    %10 = poly.constant dense<[2, 3, 4]> : tensor<3xi32> : !poly.poly<10>
+    %11 = poly.constant dense<[2, 3, 4]> : tensor<3xi8> : !poly.poly<10>
+    %12 = poly.constant dense<"0x020304"> : tensor<3xi8> : !poly.poly<10>
+    %13 = poly.constant dense<4> : tensor<100xi32> : !poly.poly<10>
+
     return %4 : !poly.poly<10>
   }
 }
diff --git a/tests/sccp.mlir b/tests/sccp.mlir
new file mode 100644
index 0000000..39b3a24
--- /dev/null
+++ b/tests/sccp.mlir
@@ -0,0 +1,35 @@
+// RUN: tutorial-opt -pass-pipeline="builtin.module(func.func(sccp))" %s | FileCheck %s
+
+// Note how sscp creates new constants for the computed values,
+// though it does not remove the dead code.
+
+// CHECK-LABEL: @test_arith_sccp
+// CHECK-NEXT: %[[v0:.*]] = arith.constant 63 : i32
+// CHECK-NEXT: %[[v1:.*]] = arith.constant 49 : i32
+// CHECK-NEXT: %[[v2:.*]] = arith.constant 14 : i32
+// CHECK-NEXT: %[[v3:.*]] = arith.constant 8 : i32
+// CHECK-NEXT: %[[v4:.*]] = arith.constant 7 : i32
+// CHECK-NEXT: return %[[v2]] : i32
+func.func @test_arith_sccp() -> i32 {
+  %0 = arith.constant 7 : i32
+  %1 = arith.constant 8 : i32
+  %2 = arith.addi %0, %0 : i32
+  %3 = arith.muli %0, %0 : i32
+  %4 = arith.addi %2, %3 : i32
+  return %2 : i32
+}
+
+// CHECK-LABEL: @test_poly_sccp
+func.func @test_poly_sccp() -> !poly.poly<10> {
+  %0 = arith.constant dense<[1, 2, 3]> : tensor<3xi32>
+  %p0 = poly.from_tensor %0 : tensor<3xi32> -> !poly.poly<10>
+  // CHECK: poly.constant dense<[2, 8, 20, 24, 18]>
+  // CHECK: poly.constant dense<[1, 4, 10, 12, 9]>
+  // CHECK: poly.constant dense<[1, 2, 3]>
+  // CHECK-NOT: poly.mul
+  // CHECK-NOT: poly.add
+  %2 = poly.mul %p0, %p0 : (!poly.poly<10>, !poly.poly<10>) -> !poly.poly<10>
+  %3 = poly.mul %p0, %p0 : (!poly.poly<10>, !poly.poly<10>) -> !poly.poly<10>
+  %4 = poly.add %2, %3 : (!poly.poly<10>, !poly.poly<10>) -> !poly.poly<10>
+  return %2 : !poly.poly<10>
+}