diff --git a/composable_kernel/include/kernel_algorithm/gridwise_convolution_implicit_gemm_v1r3_chwn_cyxk_khwn_padded.hpp b/composable_kernel/include/kernel_algorithm/gridwise_convolution_implicit_gemm_v1r3_chwn_cyxk_khwn_padded.hpp
index 8adc526afd..ad53cd89c3 100644
--- a/composable_kernel/include/kernel_algorithm/gridwise_convolution_implicit_gemm_v1r3_chwn_cyxk_khwn_padded.hpp
+++ b/composable_kernel/include/kernel_algorithm/gridwise_convolution_implicit_gemm_v1r3_chwn_cyxk_khwn_padded.hpp
@@ -47,6 +47,19 @@ template <index_t GridSize,
           index_t OutThreadCopyDataPerAccess_N>
 struct GridwiseConvolutionImplicitGemm_v1r3_chwn_cyxk_khwn_padded
 {
+    static constexpr auto I0  = Number<0>{};
+    static constexpr auto I1  = Number<1>{};
+    static constexpr auto I2  = Number<2>{};
+    static constexpr auto I3  = Number<3>{};
+    static constexpr auto I4  = Number<4>{};
+    static constexpr auto I5  = Number<5>{};
+    static constexpr auto I6  = Number<6>{};
+    static constexpr auto I7  = Number<7>{};
+    static constexpr auto I8  = Number<8>{};
+    static constexpr auto I9  = Number<9>{};
+    static constexpr auto I10 = Number<10>{};
+    static constexpr auto I11 = Number<11>{};
+
 #if 0
     __device__ void Run(const Float* const __restrict__ p_in_global,
                         const Float* const __restrict__ p_wei_global,
@@ -60,11 +73,6 @@ struct GridwiseConvolutionImplicitGemm_v1r3_chwn_cyxk_khwn_padded
                   GemmNPerThreadSubC % NPerThread == 0)),
             "wrong!");
 
-        constexpr auto I0 = Number<0>{};
-        constexpr auto I1 = Number<1>{};
-        constexpr auto I2 = Number<2>{};
-        constexpr auto I3 = Number<3>{};
-
         constexpr auto True  = integral_constant<bool, true>{};
         constexpr auto False = integral_constant<bool, false>{};
 
@@ -487,58 +495,67 @@ struct GridwiseConvolutionImplicitGemm_v1r3_chwn_cyxk_khwn_padded
                         Float* const __restrict__ p_out_global) const
     {
 #if 0
-        constexpr auto tmp = std::tuple<bool>{};
-        constexpr auto flag = std::get<0>(tmp);
-#else
-        constexpr auto a = Tuple<bool, Sequence<1>, index_t>(true, Sequence<1>{}, 99);
+        constexpr auto a = make_tuple(true, Sequence<1>{}, index_t(99));
 
         if(get_thread_local_1d_id() == 0 && get_block_1d_id() == 0)
         {
-            printf("adsas %d\n", a.At(Number<0>{}));
-            print_Sequence("seq", a.At(Number<1>{}));
-            printf("adsas %lu\n", a.At(Number<2>{}));
+            printf("[0] %d\n", a.At(I0));
+            print_Sequence("[1]", a.At(I1));
+            printf("[2] %lu\n", a.At(I2));
         }
 
-        auto b = Tuple<bool, Sequence<1>, index_t>(true, Sequence<1>{}, 99);
+        bool flag = true;
 
-        b.At(Number<0>{}) = false;
+        auto b = make_tuple(flag, Sequence<1>{}, 99);
+
+        b.At(I0) = false;
 
         if(get_thread_local_1d_id() == 0 && get_block_1d_id() == 0)
         {
-            printf("adsas %d\n", b.At(Number<0>{}));
-            print_Sequence("seq", b.At(Number<1>{}));
-            printf("adsas %lu\n", b.At(Number<2>{}));
+            printf("[0] %d\n", b.At(I0));
+            print_Sequence("[1]", b.At(I1));
+            printf("[2] %lu\n", b.At(I2));
+
+            printf("flag %d\n", flag);
         }
 
         if(get_thread_local_1d_id() == 0 && get_block_1d_id() == 0)
         {
-            printf("adsas %d\n",
-                   Tuple<bool, Sequence<1>, index_t>(true, Sequence<1>(), 99).At(Number<0>{}));
-            print_Sequence(
-                "seq", Tuple<bool, Sequence<1>, index_t>(true, Sequence<1>(), 99).At(Number<1>{}));
-            printf("adsas %d\n",
-                   Tuple<bool, Sequence<1>, index_t>(true, Sequence<1>(), 99).At(Number<2>{}));
+            printf("[0] %d\n", make_tuple(true, Sequence<1>(), index_t(99)).At(I0));
+            print_Sequence("[1]", make_tuple(true, Sequence<1>(), index_t(99)).At(I1));
+            printf("[2] %d\n", make_tuple(true, Sequence<1>(), index_t(99)).At(I2));
         }
-#endif
-
-#if 0
-        constexpr auto I0 = Number<0>{};
-        constexpr auto I1 = Number<1>{};
-        constexpr auto I2 = Number<2>{};
-        constexpr auto I3 = Number<3>{};
-
+#elif 1
         // create a native tensor descriptor
-        constexpr auto in_n_c_h_w_global_desc =
+        constexpr auto in_c_h_w_n_global_desc =
             make_NativeTensorDescriptor(InGlobalDesc::GetLengths(), InGlobalDesc::GetStrides());
 
+        constexpr index_t C  = in_c_h_w_n_global_desc.GetLength(I0);
+        constexpr index_t Hi = in_c_h_w_n_global_desc.GetLength(I1);
+        constexpr index_t Wi = in_c_h_w_n_global_desc.GetLength(I2);
+        constexpr index_t N  = in_c_h_w_n_global_desc.GetLength(I3);
+
+        constexpr auto pad_h_w = Pad<Sequence<Hi, Wi>, LowerPads, UpperPads>{};
+        constexpr auto pass_c  = PassThrough<C>{};
+        constexpr auto pass_n  = PassThrough<N>{};
+
+        constexpr auto trans = make_tuple(pass_c, pad_h_w, pass_n);
+        constexpr auto lower_dim_groups =
+            make_tuple(Sequence<0>{}, Sequence<1, 2>{}, Sequence<3>{});
+        constexpr auto upper_dim_groups =
+            make_tuple(Sequence<0>{}, Sequence<1, 2>{}, Sequence<3>{});
+
+        constexpr auto in_c_h_w_n_padded_global_desc = transform_tensor_descriptor(
+            in_c_h_w_n_global_desc, trans, lower_dim_groups, upper_dim_groups);
+
         if(get_thread_local_1d_id() == 0 && get_block_1d_id() == 0)
         {
-            print_tensor_descriptor("in_n_c_h_w_global_desc", in_n_c_h_w_global_desc);
-        }
+            print_tensor_descriptor("in_c_h_w_n_global_desc", in_c_h_w_n_global_desc);
 
-        // transform the tensor descriptor once
-        //
-        // calculate the offset of some entry
+            printf("offset: %lu\n", in_c_h_w_n_global_desc.GetOffset({1, 2, 3, 4}));
+
+            printf("padded offset: %lu\n", in_c_h_w_n_padded_global_desc.GetOffset({1, 4, 5, 4}));
+        }
 #endif
     }
 #endif
diff --git a/composable_kernel/include/tensor_description/ConstantTensorDescriptor.hpp b/composable_kernel/include/tensor_description/ConstantTensorDescriptor.hpp
index 3949652174..b0f6d32ec8 100644
--- a/composable_kernel/include/tensor_description/ConstantTensorDescriptor.hpp
+++ b/composable_kernel/include/tensor_description/ConstantTensorDescriptor.hpp
@@ -178,7 +178,7 @@ struct ConstantTensorDescriptor
         {
             constexpr auto IDim      = IDim_{};
             constexpr index_t stride = PackedStrides::Get(IDim);
-            multi_id.Set(IDim, id / stride);
+            multi_id(IDim)           = id / stride;
             id -= multi_id[IDim] * stride;
         }
     };
@@ -192,7 +192,7 @@ struct ConstantTensorDescriptor
         // calculate index in each of the dimensions in the order of their dimension
         static_for<0, nDim - 1, 1>{}(lambda_GetMultiIndexFrom1dIndex<PackedStrides>(id, multi_id));
 
-        multi_id.Set(Number<nDim - 1>{}, id / PackedStrides::Get(Number<nDim - 1>{}));
+        multi_id(Number<nDim - 1>{}) = id / PackedStrides::Get(Number<nDim - 1>{});
 
         return multi_id;
     }
diff --git a/composable_kernel/include/tensor_description/multi_index_transform.hpp b/composable_kernel/include/tensor_description/multi_index_transform.hpp
index 8812779319..c21f055390 100644
--- a/composable_kernel/include/tensor_description/multi_index_transform.hpp
+++ b/composable_kernel/include/tensor_description/multi_index_transform.hpp
@@ -33,7 +33,7 @@ struct PassThrough
 };
 
 // LowLengths: Sequence<...>
-template <class LowLengths, class LeftPads, class RightPads>
+template <typename LowLengths, typename LeftPads, typename RightPads>
 struct Pad
 {
     static constexpr index_t nDim = LowLengths::GetSize();
@@ -67,7 +67,7 @@ struct Pad
 
 #if 0
 // LowLengths: Sequence<...>
-template <class LowLengths>
+template <typename LowLengths>
 struct Merge
 {
     static constexpr index_t nDimLow = LowLengths::GetSize();
@@ -113,7 +113,7 @@ struct Merge
 #endif
 
 // UpLengths: Sequence<...>
-template <index_t LowLength, class UpLengths>
+template <index_t LowLength, typename UpLengths>
 struct Unmerge
 {
     static constexpr index_t nDimLow = 1;
@@ -161,7 +161,7 @@ struct Unmerge
 // UpLengths: Sequence<...>
 // Coefficients: Sequence<...>
 // idx_low = coefficients[0, ...nDimUp-1] * idx_up[0, ...nDimUp-1] + coefficients[nDimUp]
-template <index_t LowLength, class UpLengths, class Coefficients>
+template <index_t LowLength, typename UpLengths, typename Coefficients>
 struct Embed
 {
     static constexpr index_t nDimLow = 1;
diff --git a/composable_kernel/include/tensor_description/tensor_descriptor.hpp b/composable_kernel/include/tensor_description/tensor_descriptor.hpp
index 4610fc5f74..952b378151 100644
--- a/composable_kernel/include/tensor_description/tensor_descriptor.hpp
+++ b/composable_kernel/include/tensor_description/tensor_descriptor.hpp
@@ -7,12 +7,12 @@
 
 namespace ck {
 
-template <class... NativeDimensions>
+template <typename... NativeDimensions>
 struct NativeTensorDescriptor
 {
     using type                        = NativeTensorDescriptor;
-    static constexpr auto mDimensions = Tuple<NativeDimensions...>{};
-    static constexpr index_t nDim     = mDimensions.GetSize();
+    static constexpr index_t nDim     = sizeof...(NativeDimensions);
+    static constexpr auto mDimensions = make_tuple(NativeDimensions{}...);
 
     using Index = MultiIndex<nDim>;
 
@@ -20,7 +20,7 @@ struct NativeTensorDescriptor
 
     struct lambda_GetLength
     {
-        template <class IDim>
+        template <typename IDim>
         __host__ __device__ constexpr auto operator()(IDim) const
         {
             return GetLength(IDim{});
@@ -34,7 +34,7 @@ struct NativeTensorDescriptor
 
     struct lambda_GetStride
     {
-        template <class IDim>
+        template <typename IDim>
         __host__ __device__ constexpr auto operator()(IDim) const
         {
             return GetStride(IDim{});
@@ -49,16 +49,16 @@ struct NativeTensorDescriptor
     template <index_t IDim>
     __host__ __device__ static constexpr auto GetLength(Number<IDim>)
     {
-        return mDimensions.Get(Number<IDim>{}).GetLength();
+        return mDimensions.At(Number<IDim>{}).GetLength();
     }
 
     template <index_t IDim>
     __host__ __device__ static constexpr auto GetStride(Number<IDim>)
     {
-        return mDimensions.Get(Number<IDim>{}).GetStride();
+        return mDimensions.At(Number<IDim>{}).GetStride();
     }
 
-    __host__ __device__ static constexpr index_t GetOffset(Index idx)
+    __host__ __device__ static constexpr index_t GetOffset(const Index& idx)
     {
         index_t offset = 0;
 
@@ -67,7 +67,7 @@ struct NativeTensorDescriptor
         return offset;
     }
 
-    __host__ __device__ static constexpr index_t GetOffsetDiff(Index idx_diff)
+    __host__ __device__ static constexpr index_t GetOffsetDiff(const Index& idx_diff)
     {
         index_t offset_diff = 0;
 
@@ -96,28 +96,65 @@ struct NativeTensorDescriptor
     }
 };
 
-#if 0
 // LowerTensorDescriptor
-// Transforms: std::tuple<DimensionTransforms...>
-// LowerDimensionIds: std::tuple<Sequence<...>>
-// UpperDimensionIds: std::tuple<Sequence<...>>
-template <class LowTensorDescriptor, class Transforms, class LowDimensionIds, class UpDimensionIds>
+// Transforms: Tuple<DimensionTransforms...>
+// LowerDimensionIds: Tuple<Sequence<...>>
+// UpperDimensionIds: Tuple<Sequence<...>>
+template <typename LowTensorDescriptor,
+          typename Transforms,
+          typename LowDimensionIds,
+          typename UpDimensionIds>
 struct TransformedTensorDescriptor
 {
-    using type                       = TransformedTensorDescriptor;
-    static constexpr index_t nDimUp  = GetUpperNumOfDimension();
-    static constexpr index_t nDimLow = GetLowerNumOfDimension();
+    using type                          = TransformedTensorDescriptor;
+    static constexpr index_t nTransform = Transforms::Size();
 
-    static constexpr index_t nTransform = Transforms::GetSize();
+    struct lambda_merge_sequences
+    {
+        template <typename... Seqs>
+        __host__ __device__ constexpr auto operator()(Seqs... seqs) const
+        {
+            return merge_sequences(seqs...);
+        }
+    };
+
+    __host__ __device__ static constexpr auto GetNumOfLowerDimension()
+    {
+        // Here, we assume all lower-dimensions are active
+        // TODO: sanity-check all lower-dimension are indeed active
+
+        using duplicated_low_active_dims =
+            decltype(unpack(lambda_merge_sequences{}, LowDimensionIds{}));
+
+        using low_active_dims = typename sequence_unique_sort<duplicated_low_active_dims,
+                                                              math::less<index_t>,
+                                                              math::equal<index_t>>::type;
+
+        return low_active_dims::Size();
+    }
+
+    __host__ __device__ static constexpr auto GetNumOfUpperDimension()
+    {
+        using duplicated_up_active_dims =
+            decltype(unpack(lambda_merge_sequences{}, UpDimensionIds{}));
+
+        using up_active_dims = typename sequence_unique_sort<duplicated_up_active_dims,
+                                                             math::less<index_t>,
+                                                             math::equal<index_t>>::type;
+
+        return up_active_dims::Size();
+    }
+
+    static constexpr index_t nDimUp  = GetNumOfUpperDimension();
+    static constexpr index_t nDimLow = GetNumOfLowerDimension();
 
     using UpperIndex = MultiIndex<nDimUp>;
     using LowerIndex = MultiIndex<nDimLow>;
 
-    __host__ __device__ static constexpr TransformedTensorDescriptor()
+    __host__ __device__ constexpr TransformedTensorDescriptor()
     {
-        static_assert(nTransform == Transforms::GetSize() &&
-                          nTransform == LowDimensionIds::GetSize() &&
-                          nTransform == UpDimensionIds::GetSize(),
+        static_assert(nTransform == Transforms::Size() && nTransform == LowDimensionIds::Size() &&
+                          nTransform == UpDimensionIds::Size(),
                       "wrong! # of transformations not the same");
 
         // TODO: sanity check: LowDimensionIds should include all low-dimensions,
@@ -128,33 +165,17 @@ struct TransformedTensorDescriptor
         //   a low-dimension should be associated with only one transformation
     }
 
-    __host__ __device__ static constexpr auto GetNumOfLowerDimension()
-    {
-        // Here, we assume all lower-dimensions are active
-        // TODO: sanity-check all lower-dimension are indeed active
-        constexpr auto low_active_dims = unique_sort_sequence(
-            merge_tuple_of_sequences(LowDimensionIds{}), math::less<index_t>{});
-
-        return low_active_dims.GetSize();
-    }
-
-    __host__ __device__ static constexpr auto GetNumOfUpperDimension()
-    {
-        constexpr auto up_active_dims =
-            unique_sort_sequence(merge_tuple_of_sequences(UpDimensionIds{}), math::less<index_t>{});
-        return up_active_dims.GetSize();
-    }
-
     __host__ __device__ static constexpr auto GetNumOfDimension()
     {
         return GetNumOfUpperDimension();
     }
 
-    __host__ __device__ static constexpr auto GetLengths()
+#if 0
+    __host__ __device__ static constexpr auto GetUpperLengths()
     {
         struct lambda_get_upper_lengths
         {
-            template <class Transform>
+            template <typename Transform>
             __host__ __device__ constexpr auto operator()(Transform tran) const
             {
                 return tran.GetUpperLengths();
@@ -173,6 +194,7 @@ struct TransformedTensorDescriptor
 
         using sort_dimension_ids =
             sequence_unique_sort<decltype(all_upper_dimension_ids), math::less<index_t>>;
+
         constexpr auto sorted_upper_dimension_ids = typename sort_dimension_ids::type;
         constexpr auto sorted2unsorted_map = typename sort_dimension_ids::sorted2unsorted_map_type;
 
@@ -182,46 +204,48 @@ struct TransformedTensorDescriptor
         return sorted_upper_lengths;
     }
 
+    __host__ __device__ static constexpr auto GetLengths() { return GetUpperLengths(); }
+#endif
+
     __host__ __device__ static constexpr auto GetLowerTensorDescriptor()
     {
         return LowTensorDescriptor{};
     }
 
-    __host__ __device__ static constexpr index_t GetLowerIndex(UpperIndex idx_up)
+    __host__ __device__ static constexpr LowerIndex GetLowerIndex(const UpperIndex& idx_up)
     {
         LowerIndex idx_low;
 
         static_for<0, nTransform, 1>{}([&](auto itran) {
-            constexpr auto tran = Transforms::Get(itran);
+            constexpr auto tran = Transforms{}.At(itran);
 
-            constexpr auto idx_low_part = pick_array_element(idx_low, LowDimensionIds::Get(itran));
-            constexpr auto idx_up_part  = pick_array_element(idx_up, UpDimensionIds::Get(itran));
+            auto idx_low_part      = pick_array_element(idx_low, LowDimensionIds{}.At(itran));
+            const auto idx_up_part = pick_array_element(idx_up, UpDimensionIds{}.At(itran));
 
             // this assume each lower (single) index is only assocaited with one transformation,
             //   which is required for index transformation, and has been checked during constructor
             //   of TransformedTensorDescriptor
-            idx_low_part = tran.GetLowerIndex(idx_up_part);
+            idx_low_part = tran.GetLowerIndex(to_array(idx_up_part));
         });
 
         return idx_low;
     }
 
-    __host__ __device__ static constexpr index_t GetLowerIndexDiff(UpperIndex idx_up_diff,
-                                                                   LowerIndex idx_low_old)
+    __host__ __device__ static constexpr LowerIndex GetLowerIndexDiff(const UpperIndex& idx_up_diff,
+                                                                      const LowerIndex& idx_low_old)
     {
         LowerIndex idx_low_diff;
 
         static_for<0, nTransform, 1>{}([&](auto itran) {
-            constexpr auto tran = Transforms::Get(itran);
+            constexpr auto tran = Transforms::At(itran);
 
-            constexpr auto idx_up_diff_part =
-                pick_array_element(idx_up_diff, UpDimensionIds::Get(itran));
+            const auto idx_up_diff_part =
+                pick_array_element(idx_up_diff, UpDimensionIds::At(itran));
 
-            constexpr auto idx_low_diff_part =
-                pick_array_element(idx_low_diff, LowDimensionIds::Get(itran));
+            auto idx_low_diff_part = pick_array_element(idx_low_diff, LowDimensionIds::At(itran));
 
-            constexpr auto idx_low_old_part =
-                pick_array_element(idx_low_old, LowDimensionIds::Get(itran));
+            const auto idx_low_old_part =
+                pick_array_element(idx_low_old, LowDimensionIds::At(itran));
 
             // this assume each lower (single) index is associated with only one transformation,
             //   which is required for index transformation, and has been checked during constructor
@@ -232,13 +256,14 @@ struct TransformedTensorDescriptor
         return idx_low_diff;
     }
 
-    __host__ __device__ static constexpr index_t GetOffset(UpperIndex idx_up)
+    __host__ __device__ static constexpr index_t GetOffset(const UpperIndex& idx_up)
     {
         return GetLowerTensorDescriptor().GetOffset(GetLowerIndex(idx_up));
     }
 
+#if 0
     template <index_t IDim>
-    __host__ __device__ static constexpr bool IsLinearDimension(Number<IDim>);
+    __host__ __device__ static constexpr bool IsLinearDimension(Number<IDim>)
     {
         // not implemented
     }
@@ -257,8 +282,8 @@ struct TransformedTensorDescriptor
     {
         // not implemented
     }
-};
 #endif
+};
 
 template <index_t... Lengths, index_t... Strides>
 __host__ __device__ constexpr auto make_NativeTensorDescriptor(Sequence<Lengths...>,
@@ -267,15 +292,28 @@ __host__ __device__ constexpr auto make_NativeTensorDescriptor(Sequence<Lengths.
     return NativeTensorDescriptor<NativeDimension<Lengths, Strides>...>{};
 }
 
-template <class Lengths>
+template <typename Lengths>
 __host__ __device__ constexpr auto make_NativeTensorDescriptor_packed(Lengths)
 {
-    constexpr index_t strides = reverse_inclusive_scan_sequence(
-                                    Lengths::PopFront(), math::multiplies<index_t>{}, Number<1>{})
-                                    .PushBack(Number<1>{});
+    constexpr auto strides = reverse_inclusive_scan_sequence(
+                                 Lengths::PopFront(), math::multiplies<index_t>{}, Number<1>{})
+                                 .PushBack(Number<1>{});
 
     return make_NativeTensorDescriptor(Lengths{}, strides);
 }
 
+template <typename LowTensorDescriptor,
+          typename Transforms,
+          typename LowDimensionIds,
+          typename UpDimensionIds>
+__host__ __device__ constexpr auto
+    transform_tensor_descriptor(LowTensorDescriptor, Transforms, LowDimensionIds, UpDimensionIds)
+{
+    return TransformedTensorDescriptor<LowTensorDescriptor,
+                                       Transforms,
+                                       LowDimensionIds,
+                                       UpDimensionIds>{};
+}
+
 } // namespace ck
 #endif
diff --git a/composable_kernel/include/tensor_description/tensor_descriptor_helper.hpp b/composable_kernel/include/tensor_description/tensor_descriptor_helper.hpp
index f1f662f772..04009a740c 100644
--- a/composable_kernel/include/tensor_description/tensor_descriptor_helper.hpp
+++ b/composable_kernel/include/tensor_description/tensor_descriptor_helper.hpp
@@ -6,7 +6,7 @@
 
 namespace ck {
 
-template <class... NativeDimensions>
+template <typename... NativeDimensions>
 __host__ __device__ void print_tensor_descriptor(const char* s,
                                                  NativeTensorDescriptor<NativeDimensions...> desc)
 {
diff --git a/composable_kernel/include/utility/Array.hpp b/composable_kernel/include/utility/Array.hpp
index 8b94d46b83..1cc8d4d0d6 100644
--- a/composable_kernel/include/utility/Array.hpp
+++ b/composable_kernel/include/utility/Array.hpp
@@ -6,48 +6,78 @@
 
 namespace ck {
 
-template <class TData, index_t NSize>
+template <typename TData, index_t NSize>
 struct Array
 {
-    using Type      = Array<TData, NSize>;
+    using type      = Array<TData, NSize>;
     using data_type = TData;
 
-    static constexpr index_t nSize = NSize;
+    index_t mData[NSize];
 
-    index_t mData[nSize];
+    __host__ __device__ explicit constexpr Array() {}
 
-    template <class... Xs>
-    __host__ __device__ constexpr Array(Xs... xs) : mData{static_cast<TData>(xs)...}
+    template <typename X, typename... Xs>
+    __host__ __device__ explicit constexpr Array(X x, Xs... xs)
+        : mData{static_cast<TData>(x), static_cast<TData>(xs)...}
     {
+        static_assert(sizeof...(Xs) + 1 == NSize, "wrong! size");
     }
 
-    __host__ __device__ static constexpr index_t GetSize() { return NSize; }
-
-    template <index_t I>
-    __host__ __device__ constexpr TData operator[](Number<I>) const
+#if 0
+    template <typename T>
+    __host__ __device__ explicit constexpr Array(const T& x)
     {
-        return mData[I];
-    }
+        static_assert(T::Size() == NSize, "wrong! size");
 
-    __host__ __device__ constexpr TData operator[](index_t i) const { return mData[i]; }
+        static_for<0, NSize, 1>{}([&](auto i){
+           mData[i] = x.At(i); 
+        })
+    }
+#endif
+
+    __host__ __device__ static constexpr index_t Size() { return NSize; }
+
+    __host__ __device__ static constexpr index_t GetSize() { return Size(); }
 
     template <index_t I>
-    __host__ __device__ TData& operator()(Number<I>)
-    {
-        return mData[I];
-    }
-
-    __host__ __device__ TData& operator()(index_t i) { return mData[i]; }
-
-    template <index_t I>
-    __host__ __device__ constexpr void Set(Number<I>, TData x)
+    __host__ __device__ constexpr const TData& At(Number<I>) const
     {
         static_assert(I < NSize, "wrong!");
 
-        mData[I] = x;
+        return mData[I];
     }
 
-    __host__ __device__ constexpr void Set(index_t I, TData x) { mData[I] = x; }
+    template <index_t I>
+    __host__ __device__ constexpr TData& At(Number<I>)
+    {
+        static_assert(I < NSize, "wrong!");
+
+        return mData[I];
+    }
+
+    __host__ __device__ constexpr const TData& At(index_t i) const { return mData[i]; }
+
+    __host__ __device__ constexpr TData& At(index_t i) { return mData[i]; }
+
+    template <typename I>
+    __host__ __device__ constexpr const TData& operator[](I i) const
+    {
+        return At(i);
+    }
+
+    template <typename I>
+    __host__ __device__ constexpr TData& operator()(I i)
+    {
+        return At(i);
+    }
+
+    template <typename T>
+    __host__ __device__ constexpr type& operator=(const T& x)
+    {
+        static_for<0, Size(), 1>{}([&](auto i) { operator()(i) = x[i]; });
+
+        return *this;
+    }
 
     struct lambda_PushBack // emulate constexpr lambda
     {
@@ -63,7 +93,7 @@ struct Array
         template <index_t I>
         __host__ __device__ constexpr void operator()(Number<I>) const
         {
-            new_array.Set(Number<I>{}, old_array[I]);
+            new_array(Number<I>{}) = old_array[I];
         }
     };
 
@@ -73,71 +103,98 @@ struct Array
 
         static_for<0, NSize, 1>{}(lambda_PushBack(*this, new_array));
 
-        new_array.Set(Number<NSize>{}, x);
+        new_array(Number<NSize>{}) = x;
 
         return new_array;
     }
 };
 
-// A: Array
+// Arr: Array
 // Picks: Sequence<...>
-template <class Arr, class Picks>
+template <typename Arr, typename Picks>
 struct ArrayElementPicker
 {
+    using type      = ArrayElementPicker;
     using data_type = typename Arr::data_type;
 
-    __host__ __device__ constexpr ArrayElementPicker(Arr& array) : mData{array}
+    __host__ __device__ constexpr ArrayElementPicker() = delete;
+
+    __host__ __device__ explicit constexpr ArrayElementPicker(Arr& array) : mArray{array}
     {
         constexpr index_t imax =
             accumulate_on_sequence(Picks{}, math::maxer<index_t>{}, Number<0>{});
 
-        static_assert(imax < Picks::GetSize(), "wrong! exceeding max id");
+        static_assert(imax < Arr::Size(), "wrong! exceeding # array element");
     }
 
-    __host__ __device__ static constexpr index_t GetSize() { return Picks::GetSize(); }
+    __host__ __device__ static constexpr auto Size() { return Picks::Size(); }
 
     template <index_t I>
-    __host__ __device__ constexpr data_type operator[](Number<I>) const
+    __host__ __device__ constexpr const data_type& At(Number<I>) const
     {
-        constexpr auto IP = Picks::Get(Number<I>{});
-        return mData[IP];
-    }
+        static_assert(I < Size(), "wrong!");
 
-    __host__ __device__ constexpr data_type operator[](index_t i) const
-    {
-        constexpr index_t ip = Picks{}[i];
-        return mData[ip];
+        constexpr auto IP = Picks{}[I];
+        return mArray[IP];
     }
 
     template <index_t I>
-    __host__ __device__ data_type& operator()(Number<I>)
+    __host__ __device__ constexpr data_type& At(Number<I>)
     {
-        constexpr auto IP = Picks::Get(Number<I>{});
-        return mData[IP];
+        static_assert(I < Size(), "wrong!");
+
+        constexpr auto IP = Picks{}[I];
+        return mArray(IP);
     }
 
-    __host__ __device__ data_type& operator()(index_t i)
+    template <typename I>
+    __host__ __device__ constexpr const data_type& operator[](I i) const
     {
-        constexpr index_t ip = Picks{}[i];
-        return mData[ip];
+        return At(i);
     }
 
-    Arr& mData;
+    template <typename I>
+    __host__ __device__ constexpr data_type& operator()(I i)
+    {
+        return At(i);
+    }
+
+    template <typename T>
+    __host__ __device__ constexpr type& operator=(const T& a)
+    {
+        static_for<0, Size(), 1>{}([&](auto i) { operator()(i) = a[i]; });
+
+        return *this;
+    }
+
+    Arr& mArray;
 };
 
-template <class Arr, class Picks>
+template <typename Arr, typename Picks>
 __host__ __device__ constexpr auto pick_array_element(Arr& a, Picks)
 {
     return ArrayElementPicker<Arr, Picks>(a);
 }
 
+#if 1
+template <typename T>
+__host__ __device__ constexpr auto to_array(const T& x)
+{
+    Array<typename T::data_type, T::Size()> y;
+
+    static_for<0, T::Size(), 1>{}([&](auto i) { y.At(i) = x.At(i); });
+
+    return y;
+}
+#endif
+
 template <index_t... Is>
 __host__ __device__ constexpr auto sequence2array(Sequence<Is...>)
 {
     return Array<index_t, sizeof...(Is)>{Is...};
 }
 
-template <class TData, index_t NSize>
+template <typename TData, index_t NSize>
 __host__ __device__ constexpr auto make_zero_array()
 {
     constexpr auto zero_sequence = typename uniform_sequence_gen<NSize, 0>::type{};
@@ -145,7 +202,7 @@ __host__ __device__ constexpr auto make_zero_array()
     return zero_array;
 }
 
-template <class TData, index_t NSize, index_t... IRs>
+template <typename TData, index_t NSize, index_t... IRs>
 __host__ __device__ constexpr auto reorder_array_given_new2old(const Array<TData, NSize>& old_array,
                                                                Sequence<IRs...> /*new2old*/)
 {
@@ -156,7 +213,7 @@ __host__ __device__ constexpr auto reorder_array_given_new2old(const Array<TData
     return Array<TData, NSize>{old_array[IRs]...};
 }
 
-template <class TData, index_t NSize, class MapOld2New>
+template <typename TData, index_t NSize, typename MapOld2New>
 struct lambda_reorder_array_given_old2new
 {
     const Array<TData, NSize>& old_array;
@@ -173,13 +230,13 @@ struct lambda_reorder_array_given_old2new
     {
         TData old_data = old_array[IOldDim];
 
-        constexpr index_t INewDim = MapOld2New::Get(Number<IOldDim>{});
+        constexpr index_t INewDim = MapOld2New::At(Number<IOldDim>{});
 
-        new_array.Set(Number<INewDim>{}, old_data);
+        new_array(Number<INewDim>{}) = old_data;
     }
 };
 
-template <class TData, index_t NSize, index_t... IRs>
+template <typename TData, index_t NSize, index_t... IRs>
 __host__ __device__ constexpr auto reorder_array_given_old2new(const Array<TData, NSize>& old_array,
                                                                Sequence<IRs...> /*old2new*/)
 {
@@ -195,7 +252,7 @@ __host__ __device__ constexpr auto reorder_array_given_old2new(const Array<TData
     return new_array;
 }
 
-template <class TData, index_t NSize, class ExtractSeq>
+template <typename TData, index_t NSize, typename ExtractSeq>
 __host__ __device__ constexpr auto extract_array(const Array<TData, NSize>& old_array, ExtractSeq)
 {
     Array<TData, ExtractSeq::GetSize()> new_array;
@@ -204,12 +261,13 @@ __host__ __device__ constexpr auto extract_array(const Array<TData, NSize>& old_
 
     static_assert(new_size <= NSize, "wrong! too many extract");
 
-    static_for<0, new_size, 1>{}([&](auto I) { new_array(I) = old_array[ExtractSeq::Get(I)]; });
+    static_for<0, new_size, 1>{}([&](auto I) { new_array(I) = old_array[ExtractSeq::At(I)]; });
 
     return new_array;
 }
 
-template <class F, class X, class Y, class Z> // emulate constepxr lambda for array math
+template <typename F, typename X, typename Y, typename Z> // emulate constepxr lambda for array
+// math
 struct lambda_array_math
 {
     const F& f;
@@ -226,13 +284,12 @@ struct lambda_array_math
     __host__ __device__ constexpr void operator()(Number<IDim_>) const
     {
         constexpr auto IDim = Number<IDim_>{};
-
-        z.Set(IDim, f(x[IDim], y[IDim]));
+        z(IDim)             = f(x[IDim], y[IDim]);
     }
 };
 
 // Array = Array + Array
-template <class TData, index_t NSize>
+template <typename TData, index_t NSize>
 __host__ __device__ constexpr auto operator+(Array<TData, NSize> a, Array<TData, NSize> b)
 {
     Array<TData, NSize> result;
@@ -247,7 +304,7 @@ __host__ __device__ constexpr auto operator+(Array<TData, NSize> a, Array<TData,
 }
 
 // Array = Array - Array
-template <class TData, index_t NSize>
+template <typename TData, index_t NSize>
 __host__ __device__ constexpr auto operator-(Array<TData, NSize> a, Array<TData, NSize> b)
 {
     Array<TData, NSize> result;
@@ -262,7 +319,7 @@ __host__ __device__ constexpr auto operator-(Array<TData, NSize> a, Array<TData,
 }
 
 // Array += Array
-template <class TData, index_t NSize>
+template <typename TData, index_t NSize>
 __host__ __device__ constexpr auto operator+=(Array<TData, NSize>& a, Array<TData, NSize> b)
 {
     a = a + b;
@@ -270,14 +327,14 @@ __host__ __device__ constexpr auto operator+=(Array<TData, NSize>& a, Array<TDat
 }
 
 // Array -= Array
-template <class TData, index_t NSize>
+template <typename TData, index_t NSize>
 __host__ __device__ constexpr auto operator-=(Array<TData, NSize>& a, Array<TData, NSize> b)
 {
     a = a - b;
     return a;
 }
 // Array = Array + Sequence
-template <class TData, index_t NSize, index_t... Is>
+template <typename TData, index_t NSize, index_t... Is>
 __host__ __device__ constexpr auto operator+(Array<TData, NSize> a, Sequence<Is...> b)
 {
     static_assert(sizeof...(Is) == NSize, "wrong! size not the same");
@@ -294,7 +351,7 @@ __host__ __device__ constexpr auto operator+(Array<TData, NSize> a, Sequence<Is.
 }
 
 // Array = Array - Sequence
-template <class TData, index_t NSize, index_t... Is>
+template <typename TData, index_t NSize, index_t... Is>
 __host__ __device__ constexpr auto operator-(Array<TData, NSize> a, Sequence<Is...> b)
 {
     static_assert(sizeof...(Is) == NSize, "wrong! size not the same");
@@ -311,7 +368,7 @@ __host__ __device__ constexpr auto operator-(Array<TData, NSize> a, Sequence<Is.
 }
 
 // Array = Array * Sequence
-template <class TData, index_t NSize, index_t... Is>
+template <typename TData, index_t NSize, index_t... Is>
 __host__ __device__ constexpr auto operator*(Array<TData, NSize> a, Sequence<Is...> b)
 {
     static_assert(sizeof...(Is) == NSize, "wrong! size not the same");
@@ -328,7 +385,7 @@ __host__ __device__ constexpr auto operator*(Array<TData, NSize> a, Sequence<Is.
 }
 
 // Array = Sequence - Array
-template <class TData, index_t NSize, index_t... Is>
+template <typename TData, index_t NSize, index_t... Is>
 __host__ __device__ constexpr auto operator-(Sequence<Is...> a, Array<TData, NSize> b)
 {
     static_assert(sizeof...(Is) == NSize, "wrong! size not the same");
@@ -344,7 +401,7 @@ __host__ __device__ constexpr auto operator-(Sequence<Is...> a, Array<TData, NSi
     return result;
 }
 
-template <class TData, index_t NSize, class Reduce>
+template <typename TData, index_t NSize, typename Reduce>
 __host__ __device__ constexpr TData
 accumulate_on_array(const Array<TData, NSize>& a, Reduce f, TData init)
 {
@@ -357,89 +414,5 @@ accumulate_on_array(const Array<TData, NSize>& a, Reduce f, TData init)
     return result;
 }
 
-template <class T, index_t NSize>
-__host__ __device__ void print_Array(const char* s, Array<T, NSize> a)
-{
-    constexpr index_t nsize = a.GetSize();
-
-    static_assert(nsize > 0 && nsize <= 10, "wrong!");
-
-    static_if<nsize == 1>{}([&](auto) { printf("%s size %u, {%u}\n", s, nsize, a[0]); });
-
-    static_if<nsize == 2>{}([&](auto) { printf("%s size %u, {%u %u}\n", s, nsize, a[0], a[1]); });
-
-    static_if<nsize == 3>{}(
-        [&](auto) { printf("%s size %u, {%u %u %u}\n", s, nsize, a[0], a[1], a[2]); });
-
-    static_if<nsize == 4>{}(
-        [&](auto) { printf("%s size %u, {%u %u %u %u}\n", s, nsize, a[0], a[1], a[2], a[3]); });
-
-    static_if<nsize == 5>{}([&](auto) {
-        printf("%s size %u, {%u %u %u %u %u}\n", s, nsize, a[0], a[1], a[2], a[3], a[4]);
-    });
-
-    static_if<nsize == 6>{}([&](auto) {
-        printf("%s size %u, {%u %u %u %u %u %u}\n", s, nsize, a[0], a[1], a[2], a[3], a[4], a[5]);
-    });
-
-    static_if<nsize == 7>{}([&](auto) {
-        printf("%s size %u, {%u %u %u %u %u %u %u}\n",
-               s,
-               nsize,
-               a[0],
-               a[1],
-               a[2],
-               a[3],
-               a[4],
-               a[5],
-               a[6]);
-    });
-
-    static_if<nsize == 8>{}([&](auto) {
-        printf("%s size %u, {%u %u %u %u %u %u %u %u}\n",
-               s,
-               nsize,
-               a[0],
-               a[1],
-               a[2],
-               a[3],
-               a[4],
-               a[5],
-               a[6],
-               a[7]);
-    });
-
-    static_if<nsize == 9>{}([&](auto) {
-        printf("%s size %u, {%u %u %u %u %u %u %u %u %u}\n",
-               s,
-               nsize,
-               a[0],
-               a[1],
-               a[2],
-               a[3],
-               a[4],
-               a[5],
-               a[6],
-               a[7],
-               a[8]);
-    });
-
-    static_if<nsize == 10>{}([&](auto) {
-        printf("%s size %u, {%u %u %u %u %u %u %u %u %u %u}\n",
-               s,
-               nsize,
-               a[0],
-               a[1],
-               a[2],
-               a[3],
-               a[4],
-               a[5],
-               a[6],
-               a[7],
-               a[8],
-               a[9]);
-    });
-}
-
 } // namespace ck
 #endif
diff --git a/composable_kernel/include/utility/Sequence.hpp b/composable_kernel/include/utility/Sequence.hpp
index 3abdceda16..b9327bdd81 100644
--- a/composable_kernel/include/utility/Sequence.hpp
+++ b/composable_kernel/include/utility/Sequence.hpp
@@ -12,22 +12,22 @@ struct static_for;
 template <index_t...>
 struct Sequence;
 
-template <class Seq, index_t I>
+template <typename Seq, index_t I>
 struct sequence_split;
 
-template <class>
+template <typename>
 struct sequence_reverse;
 
-template <class>
+template <typename>
 struct sequence_map_inverse;
 
-template <class>
+template <typename>
 struct is_valid_sequence_map;
 
 template <index_t I, index_t... Is>
 __host__ __device__ constexpr auto sequence_pop_front(Sequence<I, Is...>);
 
-template <class Seq>
+template <typename Seq>
 __host__ __device__ constexpr auto sequence_pop_back(Seq);
 
 template <index_t... Is>
@@ -38,9 +38,11 @@ struct Sequence
 
     static constexpr index_t mSize = sizeof...(Is);
 
-    __host__ __device__ static constexpr auto GetSize() { return Number<mSize>{}; }
+    __host__ __device__ static constexpr auto Size() { return Number<mSize>{}; }
 
-    __host__ __device__ static constexpr index_t GetImpl(index_t I)
+    __host__ __device__ static constexpr auto GetSize() { return Size(); }
+
+    __host__ __device__ static constexpr index_t At(index_t I)
     {
         // the last dummy element is to prevent compiler complain about empty array, when mSize = 0
         const index_t mData[mSize + 1] = {Is..., 0};
@@ -48,23 +50,24 @@ struct Sequence
     }
 
     template <index_t I>
-    __host__ __device__ static constexpr auto Get(Number<I>)
+    __host__ __device__ static constexpr auto At(Number<I>)
     {
         static_assert(I < mSize, "wrong! I too large");
 
-        return Number<GetImpl(Number<I>{})>{};
+        return Number<At(I)>{};
     }
 
-    __host__ __device__ static constexpr auto Get(index_t I) { return GetImpl(I); }
-
     template <index_t I>
-    __host__ __device__ constexpr auto operator[](Number<I>) const
+    __host__ __device__ static constexpr auto Get(Number<I>)
     {
-        return Get(Number<I>{});
+        return At(Number<I>{});
     }
 
-    // make sure I is constepxr if you want a constexpr return type
-    __host__ __device__ constexpr index_t operator[](index_t I) const { return GetImpl(I); }
+    template <typename I>
+    __host__ __device__ constexpr auto operator[](I i) const
+    {
+        return At(i);
+    }
 
     template <index_t... IRs>
     __host__ __device__ static constexpr auto ReorderGivenNew2Old(Sequence<IRs...> /*new2old*/)
@@ -74,14 +77,14 @@ struct Sequence
 
         static_assert(is_valid_sequence_map<Sequence<IRs...>>::value, "wrong! invalid reorder map");
 
-        return Sequence<Type::Get(Number<IRs>{})...>{};
+        return Sequence<Type::At(Number<IRs>{})...>{};
     }
 
     // MapOld2New is Sequence<...>
-    template <class MapOld2New>
+    template <typename MapOld2New>
     __host__ __device__ static constexpr auto ReorderGivenOld2New(MapOld2New)
     {
-        static_assert(MapOld2New::GetSize() == GetSize(),
+        static_assert(MapOld2New::Size() == Size(),
                       "wrong! reorder map should have the same size as Sequence to be rerodered");
 
         static_assert(is_valid_sequence_map<MapOld2New>::value, "wrong! invalid reorder map");
@@ -97,13 +100,13 @@ struct Sequence
     __host__ __device__ static constexpr auto Front()
     {
         static_assert(mSize > 0, "wrong!");
-        return Get(Number<0>{});
+        return At(Number<0>{});
     }
 
     __host__ __device__ static constexpr auto Back()
     {
         static_assert(mSize > 0, "wrong!");
-        return Get(Number<mSize - 1>{});
+        return At(Number<mSize - 1>{});
     }
 
     __host__ __device__ static constexpr auto PopFront() { return sequence_pop_front(Type{}); }
@@ -137,19 +140,19 @@ struct Sequence
     template <index_t... Ns>
     __host__ __device__ static constexpr auto Extract(Number<Ns>...)
     {
-        return Sequence<Type::Get(Number<Ns>{})...>{};
+        return Sequence<Type::At(Number<Ns>{})...>{};
     }
 
     template <index_t... Ns>
     __host__ __device__ static constexpr auto Extract(Sequence<Ns...>)
     {
-        return Sequence<Type::Get(Number<Ns>{})...>{};
+        return Sequence<Type::At(Number<Ns>{})...>{};
     }
 
     template <index_t I, index_t X>
     __host__ __device__ static constexpr auto Modify(Number<I>, Number<X>)
     {
-        static_assert(I < GetSize(), "wrong!");
+        static_assert(I < Size(), "wrong!");
 
         using seq_split          = sequence_split<Type, I>;
         constexpr auto seq_left  = typename seq_split::SeqType0{};
@@ -158,7 +161,7 @@ struct Sequence
         return seq_left.PushBack(Number<X>{}).PushBack(seq_right);
     }
 
-    template <class F>
+    template <typename F>
     __host__ __device__ static constexpr auto Transform(F f)
     {
         return Sequence<f(Is)...>{};
@@ -166,8 +169,11 @@ struct Sequence
 };
 
 // merge sequence
-template <class, class>
-struct sequence_merge;
+template <typename Seq, typename... Seqs>
+struct sequence_merge
+{
+    using type = typename sequence_merge<Seq, typename sequence_merge<Seqs...>::type>::type;
+};
 
 template <index_t... Xs, index_t... Ys>
 struct sequence_merge<Sequence<Xs...>, Sequence<Ys...>>
@@ -175,8 +181,14 @@ struct sequence_merge<Sequence<Xs...>, Sequence<Ys...>>
     using type = Sequence<Xs..., Ys...>;
 };
 
+template <typename Seq>
+struct sequence_merge<Seq>
+{
+    using type = Seq;
+};
+
 // generate sequence
-template <index_t IBegin, index_t NRemain, class F>
+template <index_t IBegin, index_t NRemain, typename F>
 struct sequence_gen_impl
 {
     static constexpr index_t NRemainLeft  = NRemain / 2;
@@ -188,20 +200,20 @@ struct sequence_gen_impl
                                 typename sequence_gen_impl<IMiddle, NRemainRight, F>::type>::type;
 };
 
-template <index_t I, class F>
+template <index_t I, typename F>
 struct sequence_gen_impl<I, 1, F>
 {
     static constexpr index_t Is = F{}(Number<I>{});
     using type                  = Sequence<Is>;
 };
 
-template <index_t I, class F>
+template <index_t I, typename F>
 struct sequence_gen_impl<I, 0, F>
 {
     using type = Sequence<>;
 };
 
-template <index_t NSize, class F>
+template <index_t NSize, typename F>
 struct sequence_gen
 {
     using type = typename sequence_gen_impl<0, NSize, F>::type;
@@ -235,10 +247,10 @@ struct uniform_sequence_gen
 };
 
 // reverse inclusive scan (with init) sequence
-template <class, class, index_t>
+template <typename, typename, index_t>
 struct sequence_reverse_inclusive_scan;
 
-template <index_t I, index_t... Is, class Reduce, index_t Init>
+template <index_t I, index_t... Is, typename Reduce, index_t Init>
 struct sequence_reverse_inclusive_scan<Sequence<I, Is...>, Reduce, Init>
 {
     using old_scan = typename sequence_reverse_inclusive_scan<Sequence<Is...>, Reduce, Init>::type;
@@ -248,23 +260,23 @@ struct sequence_reverse_inclusive_scan<Sequence<I, Is...>, Reduce, Init>
     using type = typename sequence_merge<Sequence<new_reduce>, old_scan>::type;
 };
 
-template <index_t I, class Reduce, index_t Init>
+template <index_t I, typename Reduce, index_t Init>
 struct sequence_reverse_inclusive_scan<Sequence<I>, Reduce, Init>
 {
     using type = Sequence<Reduce{}(I, Init)>;
 };
 
-template <class Reduce, index_t Init>
+template <typename Reduce, index_t Init>
 struct sequence_reverse_inclusive_scan<Sequence<>, Reduce, Init>
 {
     using type = Sequence<>;
 };
 
 // split sequence
-template <class Seq, index_t I>
+template <typename Seq, index_t I>
 struct sequence_split
 {
-    static constexpr index_t NSize = Seq{}.GetSize();
+    static constexpr index_t NSize = Seq{}.Size();
 
     using range0 = typename arithmetic_sequence_gen<0, I, 1>::type;
     using range1 = typename arithmetic_sequence_gen<I, NSize, 1>::type;
@@ -274,10 +286,10 @@ struct sequence_split
 };
 
 // reverse sequence
-template <class Seq>
+template <typename Seq>
 struct sequence_reverse
 {
-    static constexpr index_t NSize = Seq{}.GetSize();
+    static constexpr index_t NSize = Seq{}.Size();
 
     using seq_split = sequence_split<Seq, NSize / 2>;
     using type      = typename sequence_merge<
@@ -297,19 +309,102 @@ struct sequence_reverse<Sequence<I0, I1>>
     using type = Sequence<I1, I0>;
 };
 
-template <class Seq, class Compare>
+template <typename Seq, typename Compare>
 struct sequence_sort
 {
-    // not implemented
+    template <typename SeqLeft, typename SeqRight, typename MergedSeq, typename Comp>
+    struct sorted_sequence_merge_impl
+    {
+        static constexpr bool pick_left     = SeqLeft::Front() < SeqRight::Front();
+        static constexpr index_t next_value = pick_left ? SeqLeft::Front() : SeqRight::Front();
+
+        using new_merged_seq = decltype(MergedSeq::PushBack(Number<next_value>{}));
+
+        using new_left_seq =
+            typename conditional<pick_left, decltype(SeqLeft::PopFront()), SeqLeft>::type;
+        using new_right_seq =
+            typename conditional<pick_left, SeqRight, decltype(SeqRight::PopFront())>::type;
+
+        using type =
+            typename sorted_sequence_merge_impl<new_left_seq, new_right_seq, new_merged_seq, Comp>::
+                type;
+    };
+
+    template <typename SeqLeft, typename MergedSeq, typename Comp>
+    struct sorted_sequence_merge_impl<SeqLeft, Sequence<>, MergedSeq, Comp>
+    {
+        using type = typename sequence_merge<MergedSeq, SeqLeft>::type;
+    };
+
+    template <typename SeqRight, typename MergedSeq, typename Comp>
+    struct sorted_sequence_merge_impl<Sequence<>, SeqRight, MergedSeq, Comp>
+    {
+        using type = typename sequence_merge<MergedSeq, SeqRight>::type;
+    };
+
+    template <typename Seq0, typename Seq1, typename Comp>
+    struct sorted_sequence_merge
+    {
+        using type = typename sorted_sequence_merge_impl<Seq0, Seq1, Sequence<>, Comp>::type;
+    };
+
+    using split          = sequence_split<Seq, Seq::Size() / 2>;
+    using unsorted_left  = typename split::SeqType0;
+    using unsorted_right = typename split::SeqType1;
+
+    using sorted_left  = typename sequence_sort<unsorted_left, Compare>::type;
+    using sorted_right = typename sequence_sort<unsorted_right, Compare>::type;
+
+    using type = typename sorted_sequence_merge<sorted_left, sorted_right, Compare>::type;
 };
 
-template <class Seq, class Compare>
+template <index_t X, index_t Y, typename Compare>
+struct sequence_sort<Sequence<X, Y>, Compare>
+{
+    static constexpr bool x_first = Compare{}(X, Y);
+
+    using type = typename conditional<x_first, Sequence<X, Y>, Sequence<Y, X>>::type;
+};
+
+template <index_t X, typename Compare>
+struct sequence_sort<Sequence<X>, Compare>
+{
+    using type = Sequence<X>;
+};
+
+template <typename Seq, typename Less, typename Equal>
 struct sequence_unique_sort
 {
-    // not implemented
+    template <typename WorkInputSeq, typename WorkOutputSeq, typename Eq>
+    struct sorted_sequence_uniquify_impl
+    {
+        static constexpr index_t new_value = WorkInputSeq::Front();
+        using new_work_input_seq           = decltype(WorkInputSeq::PopFront());
+
+        using new_working_output_seq =
+            typename conditional<new_value == WorkOutputSeq::Back(),
+                                 WorkOutputSeq,
+                                 decltype(WorkOutputSeq::PopBack(Number<new_value>{}))>::type;
+    };
+
+    template <typename WorkInputSeq, typename Eq>
+    struct sorted_sequence_uniquify_impl<WorkInputSeq, Sequence<>, Eq>
+    {
+        using type = WorkInputSeq;
+    };
+
+    template <typename SortedSeq, typename Eq>
+    struct sorted_sequence_uniquify
+    {
+        using type = typename sorted_sequence_uniquify_impl<SortedSeq, Sequence<>, Eq>::type;
+    };
+
+    using sorted_seq = typename sequence_sort<Seq, Less>::type;
+
+    using type = typename sorted_sequence_uniquify<sorted_seq, Equal>::type;
 };
 
-template <class Seq>
+template <typename Seq>
 struct is_valid_sequence_map
 {
     // not implemented yet, always return true
@@ -317,36 +412,35 @@ struct is_valid_sequence_map
 
     // TODO: add proper check for is_valid, something like:
     // static constexpr bool value =
-    //     is_same<typename arithmetic_sequence_gen<0, Seq::GetSize(), 1>::type,
+    //     is_same<typename arithmetic_sequence_gen<0, Seq::Size(), 1>::type,
     //             typename sequence_sort<Seq>::SortedSeqType>{};
 };
 
-template <class X2Y, class WorkingY2X, index_t XBegin, index_t XRemain>
+template <typename X2Y, typename WorkingY2X, index_t XBegin, index_t XRemain>
 struct sequence_map_inverse_impl
 {
     private:
-    static constexpr auto new_y2x =
-        WorkingY2X::Modify(X2Y::Get(Number<XBegin>{}), Number<XBegin>{});
+    static constexpr auto new_y2x = WorkingY2X::Modify(X2Y::At(Number<XBegin>{}), Number<XBegin>{});
 
     public:
     using type =
         typename sequence_map_inverse_impl<X2Y, decltype(new_y2x), XBegin + 1, XRemain - 1>::type;
 };
 
-template <class X2Y, class WorkingY2X, index_t XBegin>
+template <typename X2Y, typename WorkingY2X, index_t XBegin>
 struct sequence_map_inverse_impl<X2Y, WorkingY2X, XBegin, 0>
 {
     using type = WorkingY2X;
 };
 
-template <class X2Y>
+template <typename X2Y>
 struct sequence_map_inverse
 {
     using type =
         typename sequence_map_inverse_impl<X2Y,
-                                           typename uniform_sequence_gen<X2Y::GetSize(), 0>::type,
+                                           typename uniform_sequence_gen<X2Y::Size(), 0>::type,
                                            0,
-                                           X2Y::GetSize()>::type;
+                                           X2Y::Size()>::type;
 };
 
 template <index_t... Xs, index_t... Ys>
@@ -457,20 +551,26 @@ __host__ __device__ constexpr auto sequence_pop_front(Sequence<I, Is...>)
     return Sequence<Is...>{};
 }
 
-template <class Seq>
+template <typename Seq>
 __host__ __device__ constexpr auto sequence_pop_back(Seq)
 {
-    static_assert(Seq::GetSize() > 0, "wrong! cannot pop an empty Sequence!");
+    static_assert(Seq::Size() > 0, "wrong! cannot pop an empty Sequence!");
     return sequence_pop_front(Seq::Reverse()).Reverse();
 }
 
-template <class F, index_t... Xs>
+template <typename F, index_t... Xs>
 __host__ __device__ constexpr auto transform_sequences(F f, Sequence<Xs...>)
 {
     return Sequence<f(Xs)...>{};
 }
 
-template <class F, index_t... Xs, index_t... Ys>
+template <typename... Seqs>
+__host__ __device__ constexpr auto merge_sequences(Seqs...)
+{
+    return typename sequence_merge<Seqs...>::type{};
+}
+
+template <typename F, index_t... Xs, index_t... Ys>
 __host__ __device__ constexpr auto transform_sequences(F f, Sequence<Xs...>, Sequence<Ys...>)
 {
     static_assert(Sequence<Xs...>::mSize == Sequence<Ys...>::mSize, "Dim not the same");
@@ -478,7 +578,7 @@ __host__ __device__ constexpr auto transform_sequences(F f, Sequence<Xs...>, Seq
     return Sequence<f(Xs, Ys)...>{};
 }
 
-template <class F, index_t... Xs, index_t... Ys, index_t... Zs>
+template <typename F, index_t... Xs, index_t... Ys, index_t... Zs>
 __host__ __device__ constexpr auto
 transform_sequences(F f, Sequence<Xs...>, Sequence<Ys...>, Sequence<Zs...>)
 {
@@ -489,19 +589,19 @@ transform_sequences(F f, Sequence<Xs...>, Sequence<Ys...>, Sequence<Zs...>)
     return Sequence<f(Xs, Ys, Zs)...>{};
 }
 
-template <class Seq, class Reduce, index_t Init>
+template <typename Seq, typename Reduce, index_t Init>
 __host__ __device__ constexpr auto reverse_inclusive_scan_sequence(Seq, Reduce, Number<Init>)
 {
     return typename sequence_reverse_inclusive_scan<Seq, Reduce, Init>::type{};
 }
 
-template <class Seq, class Reduce, index_t Init>
+template <typename Seq, typename Reduce, index_t Init>
 __host__ __device__ constexpr auto inclusive_scan_sequence(Seq, Reduce, Number<Init>)
 {
     return reverse_inclusive_scan_sequence(Seq{}.Reverse(), Reduce{}, Number<Init>{}).Reverse();
 }
 
-template <class Seq, class Reduce>
+template <typename Seq, typename Reduce>
 struct lambda_accumulate_on_sequence
 {
     const Reduce& f;
@@ -512,14 +612,14 @@ struct lambda_accumulate_on_sequence
     {
     }
 
-    template <class IDim>
+    template <typename IDim>
     __host__ __device__ constexpr index_t operator()(IDim) const
     {
-        return result = f(result, Seq::Get(IDim{}));
+        return result = f(result, Seq::At(IDim{}));
     }
 };
 
-template <class Seq, class Reduce, index_t Init>
+template <typename Seq, typename Reduce, index_t Init>
 __host__ __device__ constexpr index_t
 accumulate_on_sequence(Seq, Reduce f, Number<Init> /*initial_value*/)
 {
@@ -530,41 +630,5 @@ accumulate_on_sequence(Seq, Reduce f, Number<Init> /*initial_value*/)
     return result;
 }
 
-template <index_t... Xs>
-__host__ __device__ void print_Sequence(const char* s, Sequence<Xs...>)
-{
-    constexpr index_t nsize = Sequence<Xs...>::GetSize();
-
-    static_assert(nsize <= 10, "wrong!");
-
-    static_if<nsize == 0>{}([&](auto) { printf("%s size %u, {}\n", s, nsize, Xs...); });
-
-    static_if<nsize == 1>{}([&](auto) { printf("%s size %u, {%u}\n", s, nsize, Xs...); });
-
-    static_if<nsize == 2>{}([&](auto) { printf("%s size %u, {%u %u}\n", s, nsize, Xs...); });
-
-    static_if<nsize == 3>{}([&](auto) { printf("%s size %u, {%u %u %u}\n", s, nsize, Xs...); });
-
-    static_if<nsize == 4>{}([&](auto) { printf("%s size %u, {%u %u %u %u}\n", s, nsize, Xs...); });
-
-    static_if<nsize == 5>{}(
-        [&](auto) { printf("%s size %u, {%u %u %u %u %u}\n", s, nsize, Xs...); });
-
-    static_if<nsize == 6>{}(
-        [&](auto) { printf("%s size %u, {%u %u %u %u %u %u}\n", s, nsize, Xs...); });
-
-    static_if<nsize == 7>{}(
-        [&](auto) { printf("%s size %u, {%u %u %u %u %u %u %u}\n", s, nsize, Xs...); });
-
-    static_if<nsize == 8>{}(
-        [&](auto) { printf("%s size %u, {%u %u %u %u %u %u %u %u}\n", s, nsize, Xs...); });
-
-    static_if<nsize == 9>{}(
-        [&](auto) { printf("%s size %u, {%u %u %u %u %u %u %u %u %u}\n", s, nsize, Xs...); });
-
-    static_if<nsize == 10>{}(
-        [&](auto) { printf("%s size %u, {%u %u %u %u %u %u %u %u %u %u}\n", s, nsize, Xs...); });
-}
-
 } // namespace ck
 #endif
diff --git a/composable_kernel/include/utility/array_helper.hpp b/composable_kernel/include/utility/array_helper.hpp
new file mode 100644
index 0000000000..55f022be7d
--- /dev/null
+++ b/composable_kernel/include/utility/array_helper.hpp
@@ -0,0 +1,93 @@
+#ifndef CK_ARRAY_HELPER_HPP
+#define CK_ARRAY_HELPER_HPP
+
+#include "Array.hpp"
+
+namespace ck {
+
+template <typename T, index_t NSize>
+__host__ __device__ void print_Array(const char* s, Array<T, NSize> a)
+{
+    constexpr index_t nsize = a.GetSize();
+
+    static_assert(nsize > 0 && nsize <= 10, "wrong!");
+
+    static_if<nsize == 1>{}([&](auto) { printf("%s size %u, {%u}\n", s, nsize, a[0]); });
+
+    static_if<nsize == 2>{}([&](auto) { printf("%s size %u, {%u %u}\n", s, nsize, a[0], a[1]); });
+
+    static_if<nsize == 3>{}(
+        [&](auto) { printf("%s size %u, {%u %u %u}\n", s, nsize, a[0], a[1], a[2]); });
+
+    static_if<nsize == 4>{}(
+        [&](auto) { printf("%s size %u, {%u %u %u %u}\n", s, nsize, a[0], a[1], a[2], a[3]); });
+
+    static_if<nsize == 5>{}([&](auto) {
+        printf("%s size %u, {%u %u %u %u %u}\n", s, nsize, a[0], a[1], a[2], a[3], a[4]);
+    });
+
+    static_if<nsize == 6>{}([&](auto) {
+        printf("%s size %u, {%u %u %u %u %u %u}\n", s, nsize, a[0], a[1], a[2], a[3], a[4], a[5]);
+    });
+
+    static_if<nsize == 7>{}([&](auto) {
+        printf("%s size %u, {%u %u %u %u %u %u %u}\n",
+               s,
+               nsize,
+               a[0],
+               a[1],
+               a[2],
+               a[3],
+               a[4],
+               a[5],
+               a[6]);
+    });
+
+    static_if<nsize == 8>{}([&](auto) {
+        printf("%s size %u, {%u %u %u %u %u %u %u %u}\n",
+               s,
+               nsize,
+               a[0],
+               a[1],
+               a[2],
+               a[3],
+               a[4],
+               a[5],
+               a[6],
+               a[7]);
+    });
+
+    static_if<nsize == 9>{}([&](auto) {
+        printf("%s size %u, {%u %u %u %u %u %u %u %u %u}\n",
+               s,
+               nsize,
+               a[0],
+               a[1],
+               a[2],
+               a[3],
+               a[4],
+               a[5],
+               a[6],
+               a[7],
+               a[8]);
+    });
+
+    static_if<nsize == 10>{}([&](auto) {
+        printf("%s size %u, {%u %u %u %u %u %u %u %u %u %u}\n",
+               s,
+               nsize,
+               a[0],
+               a[1],
+               a[2],
+               a[3],
+               a[4],
+               a[5],
+               a[6],
+               a[7],
+               a[8],
+               a[9]);
+    });
+}
+
+} // namespace ck
+#endif
\ No newline at end of file
diff --git a/composable_kernel/include/utility/common_header.hpp b/composable_kernel/include/utility/common_header.hpp
index a1ec782c9a..902e78f25c 100644
--- a/composable_kernel/include/utility/common_header.hpp
+++ b/composable_kernel/include/utility/common_header.hpp
@@ -4,14 +4,19 @@
 #include "config.hpp"
 #include "utility.hpp"
 #include "integral_constant.hpp"
+#include "number.hpp"
+#include "type.hpp"
 #include "tuple.hpp"
 #include "math.hpp"
 #include "vector_type.hpp"
 #include "Sequence.hpp"
+#include "sequence_helper.hpp"
 #include "Array.hpp"
+#include "array_helper.hpp"
 #include "functional.hpp"
 #include "functional2.hpp"
 #include "functional3.hpp"
+#include "functional4.hpp"
 
 #if CK_USE_AMD_INLINE_ASM
 #include "amd_inline_asm.hpp"
diff --git a/composable_kernel/include/utility/functional.hpp b/composable_kernel/include/utility/functional.hpp
index e1f6b004ce..a22f8b2435 100644
--- a/composable_kernel/include/utility/functional.hpp
+++ b/composable_kernel/include/utility/functional.hpp
@@ -3,9 +3,11 @@
 
 #include "integral_constant.hpp"
 #include "Sequence.hpp"
+#include "type.hpp"
 
 namespace ck {
 
+// TODO: right? wrong?
 struct forwarder
 {
     template <typename T>
@@ -17,7 +19,7 @@ struct forwarder
 
 struct swallow
 {
-    template <class... Ts>
+    template <typename... Ts>
     __host__ __device__ constexpr swallow(Ts&&...)
     {
     }
@@ -32,7 +34,7 @@ struct static_if<true>
 {
     using Type = static_if<true>;
 
-    template <class F>
+    template <typename F>
     __host__ __device__ constexpr auto operator()(F f) const
     {
         // This is a trick for compiler:
@@ -43,7 +45,7 @@ struct static_if<true>
         return Type{};
     }
 
-    template <class F>
+    template <typename F>
     __host__ __device__ static constexpr auto Else(F)
     {
         return Type{};
@@ -55,13 +57,13 @@ struct static_if<false>
 {
     using Type = static_if<false>;
 
-    template <class F>
+    template <typename F>
     __host__ __device__ constexpr auto operator()(F) const
     {
         return Type{};
     }
 
-    template <class F>
+    template <typename F>
     __host__ __device__ static constexpr auto Else(F f)
     {
         // This is a trick for compiler:
@@ -73,5 +75,23 @@ struct static_if<false>
     }
 };
 
+template <bool predicate, class X, class Y>
+struct conditional;
+
+template <class X, class Y>
+struct conditional<true, X, Y>
+{
+    using type = X;
+};
+
+template <class X, class Y>
+struct conditional<false, X, Y>
+{
+    using type = Y;
+};
+
+template <bool predicate, class X, class Y>
+using conditional_t = typename conditional<predicate, X, Y>::type;
+
 } // namespace ck
 #endif
diff --git a/composable_kernel/include/utility/functional2.hpp b/composable_kernel/include/utility/functional2.hpp
index 52e96b90f5..df10ca1f25 100644
--- a/composable_kernel/include/utility/functional2.hpp
+++ b/composable_kernel/include/utility/functional2.hpp
@@ -6,6 +6,8 @@
 
 namespace ck {
 
+namespace detail {
+
 template <class>
 struct static_for_impl;
 
@@ -19,6 +21,8 @@ struct static_for_impl<Sequence<Is...>>
     }
 };
 
+} // namespace detail
+
 // F signature: F(Number<Iter>)
 template <index_t NBegin, index_t NEnd, index_t Increment>
 struct static_for
@@ -33,7 +37,8 @@ struct static_for
     template <class F>
     __host__ __device__ constexpr void operator()(F f) const
     {
-        static_for_impl<typename arithmetic_sequence_gen<NBegin, NEnd, Increment>::type>{}(f);
+        detail::static_for_impl<typename arithmetic_sequence_gen<NBegin, NEnd, Increment>::type>{}(
+            f);
     }
 };
 
diff --git a/composable_kernel/include/utility/functional3.hpp b/composable_kernel/include/utility/functional3.hpp
index f1c21d7f59..540938fd10 100644
--- a/composable_kernel/include/utility/functional3.hpp
+++ b/composable_kernel/include/utility/functional3.hpp
@@ -8,20 +8,7 @@
 
 namespace ck {
 
-template <class>
-struct is_static : integral_constant<bool, false>
-{
-};
-
-template <class T, T X>
-struct is_static<integral_constant<T, X>> : integral_constant<bool, true>
-{
-};
-
-template <index_t... Is>
-struct is_static<Sequence<Is...>> : integral_constant<bool, true>
-{
-};
+namespace detail {
 
 // RemainLengths: Sequence<...>
 // Orders: Sequence<...>
@@ -58,29 +45,6 @@ struct static_ford_impl<Sequence<>, Orders>
     }
 };
 
-// Lengths is Sequence<...>, it is the length of each dimension for N-dimensional loop
-// Orders is Sequence<...>, it is the order of dimension in which static_ford will loop over each
-// dimension
-template <class Lengths,
-          class Orders = typename arithmetic_sequence_gen<0, Lengths::GetSize(), 1>::type>
-struct static_ford
-{
-    __host__ __device__ constexpr static_ford()
-    {
-        static_assert(Lengths::GetSize() > 0, "wrong! Lengths is empty");
-        static_assert(Lengths::GetSize() == Orders::GetSize(), "wrong! inconsistent size");
-    }
-
-    // F signature: F(Sequence<...> multi_id)
-    // multi_id is the unordered multi-index
-    template <class F>
-    __host__ __device__ constexpr void operator()(F f) const
-    {
-        constexpr auto ordered_lengths = Lengths::ReorderGivenNew2Old(Orders{});
-        static_ford_impl<decltype(ordered_lengths), Orders>{}(f, Sequence<>{});
-    }
-};
-
 // RemainLengths: Sequence<...>
 // Orders: Sequence<...>
 template <class RemainLengths, class Orders>
@@ -117,6 +81,31 @@ struct ford_impl<Sequence<>, Orders>
     }
 };
 
+} // namespace detail
+
+// Lengths is Sequence<...>, it is the length of each dimension for N-dimensional loop
+// Orders is Sequence<...>, it is the order of dimension in which static_ford will loop over each
+// dimension
+template <class Lengths,
+          class Orders = typename arithmetic_sequence_gen<0, Lengths::GetSize(), 1>::type>
+struct static_ford
+{
+    __host__ __device__ constexpr static_ford()
+    {
+        static_assert(Lengths::GetSize() > 0, "wrong! Lengths is empty");
+        static_assert(Lengths::GetSize() == Orders::GetSize(), "wrong! inconsistent size");
+    }
+
+    // F signature: F(Sequence<...> multi_id)
+    // multi_id is the unordered multi-index
+    template <class F>
+    __host__ __device__ constexpr void operator()(F f) const
+    {
+        constexpr auto ordered_lengths = Lengths::ReorderGivenNew2Old(Orders{});
+        detail::static_ford_impl<decltype(ordered_lengths), Orders>{}(f, Sequence<>{});
+    }
+};
+
 // Lengths is Sequence<...>, it is the length of each dimension for N-dimensional loop
 // Orders is Sequence<...>, it is the order of dimension in which ford will loop over each
 // dimension
@@ -139,7 +128,8 @@ struct ford
 
         for(index_t i = 0; i < ordered_lengths.Front(); ++i)
         {
-            ford_impl<decltype(ordered_lengths.PopFront()), Orders>{}(f, Array<index_t, 1>{i});
+            detail::ford_impl<decltype(ordered_lengths.PopFront()), Orders>{}(f,
+                                                                              Array<index_t, 1>{i});
         }
     }
 };
diff --git a/composable_kernel/include/utility/functional4.hpp b/composable_kernel/include/utility/functional4.hpp
new file mode 100644
index 0000000000..2cbc94ea8b
--- /dev/null
+++ b/composable_kernel/include/utility/functional4.hpp
@@ -0,0 +1,34 @@
+#ifndef CK_FUNCTIONAL4_HPP
+#define CK_FUNCTIONAL4_HPP
+
+#include "Sequence.hpp"
+#include "tuple.hpp"
+#include "Array.hpp"
+
+namespace ck {
+
+namespace detail {
+
+template <typename Indices>
+struct unpack_impl;
+
+template <index_t... Is>
+struct unpack_impl<Sequence<Is...>>
+{
+    template <typename F, typename X>
+    __host__ __device__ constexpr auto operator()(F f, const X& x) const
+    {
+        return f(x.At(Number<Is>{})...);
+    }
+};
+
+} // namespace detail
+
+template <typename F, typename X>
+__host__ __device__ constexpr auto unpack(F f, const X& x)
+{
+    return detail::unpack_impl<typename arithmetic_sequence_gen<0, X::Size(), 1>::type>{}(f, x);
+}
+
+} // namespace ck
+#endif
diff --git a/composable_kernel/include/utility/integral_constant.hpp b/composable_kernel/include/utility/integral_constant.hpp
index cae52ebe3a..14f3df894b 100644
--- a/composable_kernel/include/utility/integral_constant.hpp
+++ b/composable_kernel/include/utility/integral_constant.hpp
@@ -13,54 +13,5 @@ struct integral_constant
     __host__ __device__ constexpr value_type operator()() const noexcept { return value; }
 };
 
-template <class X, class Y>
-struct is_same : public integral_constant<bool, false>
-{
-};
-
-template <class X>
-struct is_same<X, X> : public integral_constant<bool, true>
-{
-};
-
-template <class T>
-using remove_cv_t = typename std::remove_cv<T>::type;
-
-template <index_t N>
-using Number = integral_constant<index_t, N>;
-
-template <index_t X, index_t Y>
-__host__ __device__ constexpr auto operator+(Number<X>, Number<Y>)
-{
-    return Number<X + Y>{};
-}
-
-template <index_t X, index_t Y>
-__host__ __device__ constexpr auto operator-(Number<X>, Number<Y>)
-{
-    static_assert(Y <= X, "wrong!");
-    return Number<X - Y>{};
-}
-
-template <index_t X, index_t Y>
-__host__ __device__ constexpr auto operator*(Number<X>, Number<Y>)
-{
-    return Number<X * Y>{};
-}
-
-template <index_t X, index_t Y>
-__host__ __device__ constexpr auto operator/(Number<X>, Number<Y>)
-{
-    static_assert(Y > 0, "wrong!");
-    return Number<X / Y>{};
-}
-
-template <index_t X, index_t Y>
-__host__ __device__ constexpr auto operator%(Number<X>, Number<Y>)
-{
-    static_assert(Y > 0, "wrong!");
-    return Number<X % Y>{};
-}
-
 } // namespace ck
 #endif
diff --git a/composable_kernel/include/utility/math.hpp b/composable_kernel/include/utility/math.hpp
index 9e987df11f..7d7252cd4d 100644
--- a/composable_kernel/include/utility/math.hpp
+++ b/composable_kernel/include/utility/math.hpp
@@ -104,6 +104,18 @@ __host__ __device__ constexpr T lcm(T x, Ts... xs)
     return max(x, xs...);
 }
 
+template <class T>
+struct equal
+{
+    __host__ __device__ constexpr bool operator()(T x, T y) const { return x == y; }
+};
+
+template <class T>
+struct less
+{
+    __host__ __device__ constexpr bool operator()(T x, T y) const { return x < y; }
+};
+
 } // namespace math
 } // namspace ck
 
diff --git a/composable_kernel/include/utility/number.hpp b/composable_kernel/include/utility/number.hpp
new file mode 100644
index 0000000000..f8c5643694
--- /dev/null
+++ b/composable_kernel/include/utility/number.hpp
@@ -0,0 +1,44 @@
+#ifndef CK_NUMBER_HPP
+#define CK_NUMBER_HPP
+
+#include "integral_constant.hpp"
+
+namespace ck {
+
+template <index_t N>
+using Number = integral_constant<index_t, N>;
+
+template <index_t X, index_t Y>
+__host__ __device__ constexpr auto operator+(Number<X>, Number<Y>)
+{
+    return Number<X + Y>{};
+}
+
+template <index_t X, index_t Y>
+__host__ __device__ constexpr auto operator-(Number<X>, Number<Y>)
+{
+    static_assert(Y <= X, "wrong!");
+    return Number<X - Y>{};
+}
+
+template <index_t X, index_t Y>
+__host__ __device__ constexpr auto operator*(Number<X>, Number<Y>)
+{
+    return Number<X * Y>{};
+}
+
+template <index_t X, index_t Y>
+__host__ __device__ constexpr auto operator/(Number<X>, Number<Y>)
+{
+    static_assert(Y > 0, "wrong!");
+    return Number<X / Y>{};
+}
+
+template <index_t X, index_t Y>
+__host__ __device__ constexpr auto operator%(Number<X>, Number<Y>)
+{
+    static_assert(Y > 0, "wrong!");
+    return Number<X % Y>{};
+}
+} // namespace ck
+#endif
diff --git a/composable_kernel/include/utility/sequence_helper.hpp b/composable_kernel/include/utility/sequence_helper.hpp
new file mode 100644
index 0000000000..c499d6e9a2
--- /dev/null
+++ b/composable_kernel/include/utility/sequence_helper.hpp
@@ -0,0 +1,46 @@
+#ifndef CK_SEQUENCE_HELPER_HPP
+#define CK_SEQUENCE_HELPER_HPP
+
+#include "Sequence.hpp"
+
+namespace ck {
+
+template <index_t... Xs>
+__host__ __device__ void print_Sequence(const char* s, Sequence<Xs...>)
+{
+    constexpr index_t nsize = Sequence<Xs...>::Size();
+
+    static_assert(nsize <= 10, "wrong!");
+
+    static_if<nsize == 0>{}([&](auto) { printf("%s size %u, {}\n", s, nsize, Xs...); });
+
+    static_if<nsize == 1>{}([&](auto) { printf("%s size %u, {%u}\n", s, nsize, Xs...); });
+
+    static_if<nsize == 2>{}([&](auto) { printf("%s size %u, {%u %u}\n", s, nsize, Xs...); });
+
+    static_if<nsize == 3>{}([&](auto) { printf("%s size %u, {%u %u %u}\n", s, nsize, Xs...); });
+
+    static_if<nsize == 4>{}([&](auto) { printf("%s size %u, {%u %u %u %u}\n", s, nsize, Xs...); });
+
+    static_if<nsize == 5>{}(
+        [&](auto) { printf("%s size %u, {%u %u %u %u %u}\n", s, nsize, Xs...); });
+
+    static_if<nsize == 6>{}(
+        [&](auto) { printf("%s size %u, {%u %u %u %u %u %u}\n", s, nsize, Xs...); });
+
+    static_if<nsize == 7>{}(
+        [&](auto) { printf("%s size %u, {%u %u %u %u %u %u %u}\n", s, nsize, Xs...); });
+
+    static_if<nsize == 8>{}(
+        [&](auto) { printf("%s size %u, {%u %u %u %u %u %u %u %u}\n", s, nsize, Xs...); });
+
+    static_if<nsize == 9>{}(
+        [&](auto) { printf("%s size %u, {%u %u %u %u %u %u %u %u %u}\n", s, nsize, Xs...); });
+
+    static_if<nsize == 10>{}(
+        [&](auto) { printf("%s size %u, {%u %u %u %u %u %u %u %u %u %u}\n", s, nsize, Xs...); });
+}
+
+} // namespace ck
+
+#endif
diff --git a/composable_kernel/include/utility/tuple.hpp b/composable_kernel/include/utility/tuple.hpp
index 019430cd92..3fa9d0fccd 100644
--- a/composable_kernel/include/utility/tuple.hpp
+++ b/composable_kernel/include/utility/tuple.hpp
@@ -2,6 +2,7 @@
 #define CK_TUPLE_HPP
 
 #include "integral_constant.hpp"
+#include "type.hpp"
 #include "Sequence.hpp"
 
 namespace ck {
@@ -16,6 +17,8 @@ struct TupleElementKey
 template <typename Key, typename Data>
 struct TupleElement
 {
+    __host__ __device__ explicit constexpr TupleElement() : mData() {}
+
     template <typename T>
     __host__ __device__ explicit constexpr TupleElement(T&& v) : mData(static_cast<T&&>(v))
     {
@@ -48,6 +51,12 @@ struct TupleImpl;
 template <index_t... Is, typename... Xs>
 struct TupleImpl<Sequence<Is...>, Xs...> : TupleElement<TupleElementKey<Is>, Xs>...
 {
+#if 1
+    __host__ __device__ explicit constexpr TupleImpl() : TupleElement<TupleElementKey<Is>, Xs>()...
+    {
+    }
+#endif
+
     template <typename... Ys>
     __host__ __device__ explicit constexpr TupleImpl(Ys&&... ys)
         : TupleElement<TupleElementKey<Is>, Xs>(static_cast<Ys&&>(ys))...
@@ -97,5 +106,28 @@ struct Tuple : detail::TupleImpl<typename arithmetic_sequence_gen<0, sizeof...(X
     }
 };
 
+template <typename... Xs>
+__host__ __device__ constexpr auto make_tuple(Xs&&... xs)
+{
+    return Tuple<remove_cv_t<remove_reference_t<Xs>>...>(std::forward<Xs>(xs)...);
+}
+
+namespace detail {
+
+template <typename X, typename F, index_t... Is>
+__host__ __device__ constexpr auto transpose_tuple_impl(X& x, F f, Sequence<Is...>)
+{
+    return make_tuple(f(x.At(Number<Is>{}))...);
+}
+
+} // namespace detail
+
+template <typename X, typename F>
+__host__ __device__ constexpr auto transpose_tuple(X& x, F f)
+{
+    return detail::transpose_tuple_impl(
+        x, f, typename arithmetic_sequence_gen<0, X::Size(), 1>::type{});
+}
+
 } // namespace ck
 #endif
diff --git a/composable_kernel/include/utility/type.hpp b/composable_kernel/include/utility/type.hpp
new file mode 100644
index 0000000000..98a4640027
--- /dev/null
+++ b/composable_kernel/include/utility/type.hpp
@@ -0,0 +1,41 @@
+#ifndef CK_TYPE_HPP
+#define CK_TYPE_HPP
+
+#include "integral_constant.hpp"
+#include "Sequence.hpp"
+
+namespace ck {
+
+template <typename X, typename Y>
+struct is_same : public integral_constant<bool, false>
+{
+};
+
+template <typename X>
+struct is_same<X, X> : public integral_constant<bool, true>
+{
+};
+
+template <typename>
+struct is_static : integral_constant<bool, false>
+{
+};
+
+template <typename T, T X>
+struct is_static<integral_constant<T, X>> : integral_constant<bool, true>
+{
+};
+
+template <index_t... Is>
+struct is_static<Sequence<Is...>> : integral_constant<bool, true>
+{
+};
+
+template <typename T>
+using remove_reference_t = typename std::remove_reference<T>::type;
+
+template <typename T>
+using remove_cv_t = typename std::remove_cv<T>::type;
+
+} // namespace ck
+#endif
diff --git a/driver/include/device_convolution_implicit_gemm_v1_chwn_cyxk_khwn_padded.hpp b/driver/include/device_convolution_implicit_gemm_v1_chwn_cyxk_khwn_padded.hpp
index 9649caea0a..857924db25 100644
--- a/driver/include/device_convolution_implicit_gemm_v1_chwn_cyxk_khwn_padded.hpp
+++ b/driver/include/device_convolution_implicit_gemm_v1_chwn_cyxk_khwn_padded.hpp
@@ -115,8 +115,12 @@ void device_convolution_implicit_gemm_v1_chwn_cyxk_khwn_padded(InDesc,
     constexpr index_t OutThreadCopyDataPerAccess_N = 4;
 #endif
 
+#if 0 // debug
     constexpr index_t GridSize =
         (N / NPerBlock) * (K / KPerBlock) * (Ho / HoPerBlock) * (Wo / WoPerBlock);
+#else
+    constexpr index_t GridSize = 1;
+#endif
 
     printf("%s: BlockSize %u, GridSize %u \n", __func__, BlockSize, GridSize);
 
diff --git a/driver/src/driver.cpp b/driver/src/driver.cpp
index 7304647362..e25426d812 100644
--- a/driver/src/driver.cpp
+++ b/driver/src/driver.cpp
@@ -73,19 +73,19 @@ int main(int argc, char* argv[])
     using namespace ck;
 
 #if 1
-    constexpr index_t N  = 64;
-    constexpr index_t C  = 1536;
-    constexpr index_t HI = 8;
-    constexpr index_t WI = 8;
-    constexpr index_t K  = 256;
+    constexpr index_t N  = 10;
+    constexpr index_t C  = 10;
+    constexpr index_t HI = 10;
+    constexpr index_t WI = 10;
+    constexpr index_t K  = 10;
     constexpr index_t Y  = 1;
     constexpr index_t X  = 1;
 
     using ConvStrides   = Sequence<1, 1>;
     using ConvDilations = Sequence<1, 1>;
 
-    constexpr index_t HPad = 0;
-    constexpr index_t WPad = 0;
+    constexpr index_t HPad = 2;
+    constexpr index_t WPad = 2;
 #elif 1
     // 3x3, 34x34
     constexpr index_t N  = 64;