diff --git a/src/include/units/dimension.h b/src/include/units/dimension.h
index 31eaf8bb..47039cae 100644
--- a/src/include/units/dimension.h
+++ b/src/include/units/dimension.h
@@ -27,23 +27,42 @@
 
 namespace std::experimental::units {
 
-  // dim_id
+  struct base_dimension {
+    const char* name;
+  };
 
-  template<int UniqueValue>
-  using dim_id = std::integral_constant<int, UniqueValue>;
+  constexpr bool operator==(const base_dimension& lhs, const base_dimension& rhs)
+  {
+    const char* p1 = lhs.name;
+    const char* p2 = rhs.name;
+    for(; (*p1 != '\0') && (*p2 != '\0'); ++p1, (void)++p2) {
+      if(*p1 != *p2) return false;
+    }
+    return *p1 == *p2;
+  }
 
-  // dim_id_less
+  constexpr bool operator<(const base_dimension& lhs, const base_dimension& rhs)
+  {
+    const char* p1 = lhs.name;
+    const char* p2 = rhs.name;
+    for(; (*p1 != '\0') && (*p2 != '\0'); ++p1, (void)++p2) {
+      if(*p1 < *p2) return true;
+      if(*p2 < *p1) return false;
+    }
+    return (*p1 == '\0') && (*p2 != '\0');
+  }
 
-  template<typename D1, typename D2>
-  struct dim_id_less : std::bool_constant<D1::value < D2::value> {
+  // base_dimension_less
+
+  template<const base_dimension& D1, const base_dimension& D2>
+  struct base_dimension_less : std::bool_constant<D1 < D2> {
   };
 
   // exp
 
-  template<typename BaseDimension, int Value>  // todo: to be replaced with fixed_string when supported by the compilers
-  // template<fixed_string BaseDimension, int Value>
+  template<const base_dimension& BaseDimension, int Value>
   struct exp {
-    using dimension = BaseDimension;
+    static constexpr const base_dimension& dimension = BaseDimension;
     static constexpr int value = Value;
   };
 
@@ -52,8 +71,8 @@ namespace std::experimental::units {
     template<typename T>
     inline constexpr bool is_exp = false;
 
-    template<typename BaseDim, int Value>
-    inline constexpr bool is_exp<exp<BaseDim, Value>> = true;
+    template<const base_dimension& BaseDimension, int Value>
+    inline constexpr bool is_exp<exp<BaseDimension, Value>> = true;
   }  // namespace detail
 
   template<typename T>
@@ -62,7 +81,7 @@ namespace std::experimental::units {
   // exp_dim_id_less
 
   template<Exponent E1, Exponent E2>
-  struct exp_dim_id_less : dim_id_less<typename E1::dimension, typename E2::dimension> {
+  struct exp_less : base_dimension_less<E1::dimension, E2::dimension> {
   };
 
   // exp_invert
@@ -70,7 +89,7 @@ namespace std::experimental::units {
   template<Exponent E>
   struct exp_invert;
 
-  template<typename BaseDimension, int Value>
+  template<const base_dimension& BaseDimension, int Value>
   struct exp_invert<exp<BaseDimension, Value>> {
     using type = exp<BaseDimension, -Value>;
   };
@@ -138,7 +157,7 @@ namespace std::experimental::units {
       using type = conditional<std::is_same_v<rest, dimension<>>, dimension<E1>, type_list_push_front<rest, E1>>;
     };
 
-    template<typename D, int V1, int V2, typename... ERest>
+    template<const base_dimension& D, int V1, int V2, typename... ERest>
     struct dim_consolidate<dimension<exp<D, V1>, exp<D, V2>, ERest...>> {
       using type = conditional<V1 + V2 == 0, dim_consolidate_t<dimension<ERest...>>,
                                dim_consolidate_t<dimension<exp<D, V1 + V2>, ERest...>>>;
@@ -148,7 +167,7 @@ namespace std::experimental::units {
 
   template<Exponent... Es>
   struct make_dimension {
-    using type = detail::dim_consolidate_t<type_list_sort<dimension<Es...>, exp_dim_id_less>>;
+    using type = detail::dim_consolidate_t<type_list_sort<dimension<Es...>, exp_less>>;
   };
 
   template<Exponent... Es>
@@ -156,7 +175,7 @@ namespace std::experimental::units {
 
   template<Dimension D1, Dimension D2>
   struct merge_dimension {
-    using type = detail::dim_consolidate_t<type_list_merge_sorted<D1, D2, exp_dim_id_less>>;
+    using type = detail::dim_consolidate_t<type_list_merge_sorted<D1, D2, exp_less>>;
   };
 
   template<Dimension D1, Dimension D2>
diff --git a/src/include/units/base_dimensions.h b/src/include/units/dimensions/base_dimensions.h
similarity index 73%
rename from src/include/units/base_dimensions.h
rename to src/include/units/dimensions/base_dimensions.h
index 2d71c329..6b6db449 100644
--- a/src/include/units/base_dimensions.h
+++ b/src/include/units/dimensions/base_dimensions.h
@@ -26,14 +26,12 @@
 
 namespace std::experimental::units {
 
-  // todo: to be replaced with fixed_string when supported by the compilers
-
-  struct base_dim_length : dim_id<0> {};
-  struct base_dim_mass : dim_id<1> {};
-  struct base_dim_time : dim_id<2> {};
-  struct base_dim_current : dim_id<3> {};
-  struct base_dim_temperature : dim_id<4> {};
-  struct base_dim_substance : dim_id<5> {};
-  struct base_dim_luminous_intensity : dim_id<6> {};
+  inline constexpr base_dimension base_dim_length{"length"};
+  inline constexpr base_dimension base_dim_mass{"mass"};
+  inline constexpr base_dimension base_dim_time{"time"};
+  inline constexpr base_dimension base_dim_current{"current"};
+  inline constexpr base_dimension base_dim_temperature{"temperature"};
+  inline constexpr base_dimension base_dim_substance{"substance"};
+  inline constexpr base_dimension base_dim_luminous_intensity{"luminous intensity"};
 
 }  // namespace std::experimental::units
diff --git a/src/include/units/dimensions/capacitance.h b/src/include/units/dimensions/capacitance.h
index 51b7a457..cf77b7ac 100644
--- a/src/include/units/dimensions/capacitance.h
+++ b/src/include/units/dimensions/capacitance.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/dimensions/electric_charge.h>
 #include <units/dimensions/voltage.h>
 
diff --git a/src/include/units/dimensions/current.h b/src/include/units/dimensions/current.h
index 101e678a..db9b02d9 100644
--- a/src/include/units/dimensions/current.h
+++ b/src/include/units/dimensions/current.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/quantity.h>
 
 namespace std::experimental::units {
diff --git a/src/include/units/dimensions/electric_charge.h b/src/include/units/dimensions/electric_charge.h
index eb0ac89a..fdcfb626 100644
--- a/src/include/units/dimensions/electric_charge.h
+++ b/src/include/units/dimensions/electric_charge.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/dimensions/time.h>
 #include <units/dimensions/current.h>
 
diff --git a/src/include/units/dimensions/energy.h b/src/include/units/dimensions/energy.h
index be491c5c..bf381f39 100644
--- a/src/include/units/dimensions/energy.h
+++ b/src/include/units/dimensions/energy.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/dimensions/force.h>
 #include <units/dimensions/pressure.h>
 
diff --git a/src/include/units/dimensions/force.h b/src/include/units/dimensions/force.h
index e431ef94..153fcdec 100644
--- a/src/include/units/dimensions/force.h
+++ b/src/include/units/dimensions/force.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/dimensions/mass.h>
 #include <units/dimensions/length.h>
 #include <units/dimensions/time.h>
diff --git a/src/include/units/dimensions/frequency.h b/src/include/units/dimensions/frequency.h
index bca18c2a..b8853672 100644
--- a/src/include/units/dimensions/frequency.h
+++ b/src/include/units/dimensions/frequency.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/dimensions/time.h>
 
 namespace std::experimental::units {
diff --git a/src/include/units/dimensions/length.h b/src/include/units/dimensions/length.h
index d9d8dff8..6cf457fd 100644
--- a/src/include/units/dimensions/length.h
+++ b/src/include/units/dimensions/length.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/quantity.h>
 
 namespace std::experimental::units {
diff --git a/src/include/units/dimensions/luminous_intensity.h b/src/include/units/dimensions/luminous_intensity.h
index 2cf74bfb..47717ebb 100644
--- a/src/include/units/dimensions/luminous_intensity.h
+++ b/src/include/units/dimensions/luminous_intensity.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/quantity.h>
 
 namespace std::experimental::units {
diff --git a/src/include/units/dimensions/mass.h b/src/include/units/dimensions/mass.h
index bd9e8690..c3bb12cd 100644
--- a/src/include/units/dimensions/mass.h
+++ b/src/include/units/dimensions/mass.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/quantity.h>
 
 namespace std::experimental::units {
diff --git a/src/include/units/dimensions/power.h b/src/include/units/dimensions/power.h
index 0423e17d..a461c3b2 100644
--- a/src/include/units/dimensions/power.h
+++ b/src/include/units/dimensions/power.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/dimensions/energy.h>
 
 namespace std::experimental::units {
diff --git a/src/include/units/dimensions/pressure.h b/src/include/units/dimensions/pressure.h
index 70dcb0e6..e2f7ffff 100644
--- a/src/include/units/dimensions/pressure.h
+++ b/src/include/units/dimensions/pressure.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/dimensions/force.h>
 
 namespace std::experimental::units {
diff --git a/src/include/units/dimensions/substance.h b/src/include/units/dimensions/substance.h
index 203885cd..eca2fa1e 100644
--- a/src/include/units/dimensions/substance.h
+++ b/src/include/units/dimensions/substance.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/quantity.h>
 
 namespace std::experimental::units {
diff --git a/src/include/units/dimensions/temperature.h b/src/include/units/dimensions/temperature.h
index 544eba4c..a41f7e88 100644
--- a/src/include/units/dimensions/temperature.h
+++ b/src/include/units/dimensions/temperature.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/quantity.h>
 
 namespace std::experimental::units {
diff --git a/src/include/units/dimensions/time.h b/src/include/units/dimensions/time.h
index d2ace8c4..d1f53f1c 100644
--- a/src/include/units/dimensions/time.h
+++ b/src/include/units/dimensions/time.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/quantity.h>
 
 namespace std::experimental::units {
diff --git a/src/include/units/dimensions/voltage.h b/src/include/units/dimensions/voltage.h
index ffb4bf08..3dd92d71 100644
--- a/src/include/units/dimensions/voltage.h
+++ b/src/include/units/dimensions/voltage.h
@@ -22,7 +22,7 @@
 
 #pragma once
 
-#include <units/base_dimensions.h>
+#include <units/dimensions/base_dimensions.h>
 #include <units/dimensions/power.h>
 #include <units/dimensions/current.h>
 #include <units/dimensions/energy.h>
diff --git a/src/include/units/unit.h b/src/include/units/unit.h
index 30561d61..755ddab3 100644
--- a/src/include/units/unit.h
+++ b/src/include/units/unit.h
@@ -63,18 +63,18 @@ namespace std::experimental::units {
     template<typename E, typename... Rest>
     struct get_unit_base_dim<dimension<E, Rest...>> {
       static_assert(sizeof...(Rest) == 0, "Base unit expected");
-      using dimension = E::dimension;
+      static constexpr const base_dimension& dimension = E::dimension;
     };
 
-    template<typename BaseDimension, typename... Us>
+    template<const base_dimension& BaseDimension, typename... Us>
     struct get_ratio {
       using ratio = ::std::experimental::units::ratio<1>;
     };
 
-    template<typename BaseDimension, typename U, typename... Rest>
+    template<const base_dimension& BaseDimension, typename U, typename... Rest>
     struct get_ratio<BaseDimension, U, Rest...> {
-      using unit_base_dim = get_unit_base_dim<typename U::dimension::base_type>::dimension;
-      using ratio = conditional<unit_base_dim::value == BaseDimension::value, typename U::ratio,
+      static constexpr const base_dimension& unit_base_dim = get_unit_base_dim<typename U::dimension::base_type>::dimension;
+      using ratio = conditional<&unit_base_dim == &BaseDimension, typename U::ratio,
                                 typename get_ratio<BaseDimension, Rest...>::ratio>;
     };
 
@@ -105,7 +105,7 @@ namespace std::experimental::units {
     template<typename E, typename... Rest, typename... Us>
     struct derived_ratio<dimension<E, Rest...>, Us...> {
       using rest_ratio = derived_ratio<dimension<Rest...>, Us...>::ratio;
-      using e_ratio = get_ratio<typename E::dimension, Us...>::ratio;
+      using e_ratio = get_ratio<E::dimension, Us...>::ratio;
       using ratio = ratio_op<rest_ratio, E::value, e_ratio>::ratio;
     };
 
diff --git a/test/unit_test/test_dimension.cpp b/test/unit_test/test_dimension.cpp
index 8b637224..8f4bb9bb 100644
--- a/test/unit_test/test_dimension.cpp
+++ b/test/unit_test/test_dimension.cpp
@@ -27,46 +27,48 @@ using namespace std::experimental::units;
 
 namespace {
 
-  template<int Id, int Value>
-  using e = exp<dim_id<Id>, Value>;
+  inline constexpr base_dimension d0{"d0"};
+  inline constexpr base_dimension d1{"d1"};
+  inline constexpr base_dimension d2{"d2"};
+  inline constexpr base_dimension d3{"d3"};
 
   // exp_invert
 
-  static_assert(std::is_same_v<exp_invert_t<e<0, 1>>, e<0, -1>>);
-  static_assert(std::is_same_v<exp_invert_t<e<1, -1>>, e<1, 1>>);
+  static_assert(std::is_same_v<exp_invert_t<exp<d0, 1>>, exp<d0, -1>>);
+  static_assert(std::is_same_v<exp_invert_t<exp<d1, -1>>, exp<d1, 1>>);
 
   // make_dimension
 
-  static_assert(std::is_same_v<make_dimension_t<e<0, 1>>, dimension<e<0, 1>>>);
-  static_assert(std::is_same_v<make_dimension_t<e<0, 1>, e<1, 1>>, dimension<e<0, 1>, e<1, 1>>>);
-  static_assert(std::is_same_v<make_dimension_t<e<1, 1>, e<0, 1>>, dimension<e<0, 1>, e<1, 1>>>);
-  static_assert(std::is_same_v<make_dimension_t<e<1, 1>, e<1, 1>>, dimension<e<1, 2>>>);
-  static_assert(std::is_same_v<make_dimension_t<e<1, 1>, e<1, -1>>, dimension<>>);
+  static_assert(std::is_same_v<make_dimension_t<exp<d0, 1>>, dimension<exp<d0, 1>>>);
+  static_assert(std::is_same_v<make_dimension_t<exp<d0, 1>, exp<d1, 1>>, dimension<exp<d0, 1>, exp<d1, 1>>>);
+  static_assert(std::is_same_v<make_dimension_t<exp<d1, 1>, exp<d0, 1>>, dimension<exp<d0, 1>, exp<d1, 1>>>);
+  static_assert(std::is_same_v<make_dimension_t<exp<d1, 1>, exp<d1, 1>>, dimension<exp<d1, 2>>>);
+  static_assert(std::is_same_v<make_dimension_t<exp<d1, 1>, exp<d1, -1>>, dimension<>>);
 
-  static_assert(std::is_same_v<make_dimension_t<e<0, 1>, e<1, 1>, e<0, 1>, e<1, 1>>, dimension<e<0, 2>, e<1, 2>>>);
+  static_assert(std::is_same_v<make_dimension_t<exp<d0, 1>, exp<d1, 1>, exp<d0, 1>, exp<d1, 1>>, dimension<exp<d0, 2>, exp<d1, 2>>>);
   static_assert(
-      std::is_same_v<make_dimension_t<e<0, -1>, e<1, -1>, e<0, -1>, e<1, -1>>, dimension<e<0, -2>, e<1, -2>>>);
+      std::is_same_v<make_dimension_t<exp<d0, -1>, exp<d1, -1>, exp<d0, -1>, exp<d1, -1>>, dimension<exp<d0, -2>, exp<d1, -2>>>);
 
-  static_assert(std::is_same_v<make_dimension_t<e<0, 1>, e<1, 1>, e<1, -1>>, dimension<e<0, 1>>>);
-  static_assert(std::is_same_v<make_dimension_t<e<0, 1>, e<0, -1>, e<1, 1>>, dimension<e<1, 1>>>);
-  static_assert(std::is_same_v<make_dimension_t<e<0, 1>, e<1, 1>, e<0, -1>>, dimension<e<1, 1>>>);
-  static_assert(std::is_same_v<make_dimension_t<e<0, 1>, e<1, 1>, e<0, -1>, e<1, -1>>, dimension<>>);
+  static_assert(std::is_same_v<make_dimension_t<exp<d0, 1>, exp<d1, 1>, exp<d1, -1>>, dimension<exp<d0, 1>>>);
+  static_assert(std::is_same_v<make_dimension_t<exp<d0, 1>, exp<d0, -1>, exp<d1, 1>>, dimension<exp<d1, 1>>>);
+  static_assert(std::is_same_v<make_dimension_t<exp<d0, 1>, exp<d1, 1>, exp<d0, -1>>, dimension<exp<d1, 1>>>);
+  static_assert(std::is_same_v<make_dimension_t<exp<d0, 1>, exp<d1, 1>, exp<d0, -1>, exp<d1, -1>>, dimension<>>);
 
   // dimension_multiply
 
   static_assert(
-      std::is_same_v<dimension_multiply_t<dimension<e<0, 1>>, dimension<e<1, 1>>>, dimension<e<0, 1>, e<1, 1>>>);
-  static_assert(std::is_same_v<dimension_multiply_t<dimension<e<0, 1>, e<1, 1>, e<2, 1>>, dimension<e<3, 1>>>,
-                               dimension<e<0, 1>, e<1, 1>, e<2, 1>, e<3, 1>>>);
-  static_assert(std::is_same_v<dimension_multiply_t<dimension<e<0, 1>, e<1, 1>, e<2, 1>>, dimension<e<1, 1>>>,
-                               dimension<e<0, 1>, e<1, 2>, e<2, 1>>>);
-  static_assert(std::is_same_v<dimension_multiply_t<dimension<e<0, 1>, e<1, 1>, e<2, 1>>, dimension<e<1, -1>>>,
-                               dimension<e<0, 1>, e<2, 1>>>);
+      std::is_same_v<dimension_multiply_t<dimension<exp<d0, 1>>, dimension<exp<d1, 1>>>, dimension<exp<d0, 1>, exp<d1, 1>>>);
+  static_assert(std::is_same_v<dimension_multiply_t<dimension<exp<d0, 1>, exp<d1, 1>, exp<d2, 1>>, dimension<exp<d3, 1>>>,
+                               dimension<exp<d0, 1>, exp<d1, 1>, exp<d2, 1>, exp<d3, 1>>>);
+  static_assert(std::is_same_v<dimension_multiply_t<dimension<exp<d0, 1>, exp<d1, 1>, exp<d2, 1>>, dimension<exp<d1, 1>>>,
+                               dimension<exp<d0, 1>, exp<d1, 2>, exp<d2, 1>>>);
+  static_assert(std::is_same_v<dimension_multiply_t<dimension<exp<d0, 1>, exp<d1, 1>, exp<d2, 1>>, dimension<exp<d1, -1>>>,
+                               dimension<exp<d0, 1>, exp<d2, 1>>>);
 
   // dimension_divide
 
   static_assert(
-      std::is_same_v<dimension_divide_t<dimension<e<0, 1>>, dimension<e<1, 1>>>, dimension<e<0, 1>, e<1, -1>>>);
-  static_assert(std::is_same_v<dimension_divide_t<dimension<e<0, 1>>, dimension<e<0, 1>>>, dimension<>>);
+      std::is_same_v<dimension_divide_t<dimension<exp<d0, 1>>, dimension<exp<d1, 1>>>, dimension<exp<d0, 1>, exp<d1, -1>>>);
+  static_assert(std::is_same_v<dimension_divide_t<dimension<exp<d0, 1>>, dimension<exp<d0, 1>>>, dimension<>>);
 
 }  // namespace
diff --git a/test/unit_test/test_type_list.cpp b/test/unit_test/test_type_list.cpp
index 2c6cd240..ccf688a4 100644
--- a/test/unit_test/test_type_list.cpp
+++ b/test/unit_test/test_type_list.cpp
@@ -82,41 +82,21 @@ namespace {
       std::is_same_v<type_list_split_half<type_list<int, long, double, float>>::second_list, type_list<double, float>>);
 
   // type_list_merge_sorted
+  inline constexpr base_dimension d0{"d0"};
+  inline constexpr base_dimension d1{"d1"};
 
-  static_assert(std::is_same_v<type_list_merge_sorted<type_list<dim_id<0>>, type_list<dim_id<1>>, dim_id_less>,
-                               type_list<dim_id<0>, dim_id<1>>>);
-  static_assert(std::is_same_v<type_list_merge_sorted<type_list<dim_id<1>>, type_list<dim_id<0>>, dim_id_less>,
-                               type_list<dim_id<0>, dim_id<1>>>);
-
-  static_assert(std::is_same_v<type_list_merge_sorted<type_list<dim_id<27>, dim_id<38>>,
-                                                        type_list<dim_id<3>, dim_id<43>>, dim_id_less>,
-                               type_list<dim_id<3>, dim_id<27>, dim_id<38>, dim_id<43>>>);
-  static_assert(
-      std::is_same_v<type_list_merge_sorted<type_list<dim_id<9>, dim_id<82>>, type_list<dim_id<10>>, dim_id_less>,
-                     type_list<dim_id<9>, dim_id<10>, dim_id<82>>>);
+  static_assert(std::is_same_v<type_list_merge_sorted<type_list<exp<d0, 1>>, type_list<exp<d1, 1>>, exp_less>,
+                               type_list<exp<d0, 1>, exp<d1, 1>>>);
+  static_assert(std::is_same_v<type_list_merge_sorted<type_list<exp<d1, 1>>, type_list<exp<d0, 1>>, exp_less>,
+                               type_list<exp<d0, 1>, exp<d1, 1>>>);
 
   // type_list_sort
 
   template<TypeList List>
-  using dim_sort_t = type_list_sort<List, dim_id_less>;
+  using exp_sort_t = type_list_sort<List, exp_less>;
 
-  static_assert(std::is_same_v<dim_sort_t<type_list<dim_id<0>>>, type_list<dim_id<0>>>);
-  static_assert(std::is_same_v<dim_sort_t<type_list<dim_id<0>, dim_id<1>>>, type_list<dim_id<0>, dim_id<1>>>);
-  static_assert(std::is_same_v<dim_sort_t<type_list<dim_id<1>, dim_id<0>>>, type_list<dim_id<0>, dim_id<1>>>);
-  static_assert(std::is_same_v<
-                dim_sort_t<type_list<dim_id<38>, dim_id<27>, dim_id<43>, dim_id<3>, dim_id<9>, dim_id<82>, dim_id<10>>>,
-                type_list<dim_id<3>, dim_id<9>, dim_id<10>, dim_id<27>, dim_id<38>, dim_id<43>, dim_id<82>>>);
-
-  // exp_dim_id_less
-
-  template<int Id, int Value>
-  using e = exp<dim_id<Id>, Value>;
-
-  template<TypeList List>
-  using exp_sort_t = type_list_sort<List, exp_dim_id_less>;
-
-  static_assert(std::is_same_v<exp_sort_t<dimension<e<0, 1>>>, dimension<e<0, 1>>>);
-  static_assert(std::is_same_v<exp_sort_t<dimension<e<0, 1>, e<1, -1>>>, dimension<e<0, 1>, e<1, -1>>>);
-  static_assert(std::is_same_v<exp_sort_t<dimension<e<1, 1>, e<0, -1>>>, dimension<e<0, -1>, e<1, 1>>>);
+  static_assert(std::is_same_v<exp_sort_t<dimension<exp<d0, 1>>>, dimension<exp<d0, 1>>>);
+  static_assert(std::is_same_v<exp_sort_t<dimension<exp<d0, 1>, exp<d1, -1>>>, dimension<exp<d0, 1>, exp<d1, -1>>>);
+  static_assert(std::is_same_v<exp_sort_t<dimension<exp<d1, 1>, exp<d0, -1>>>, dimension<exp<d0, -1>, exp<d1, 1>>>);
 
 }  // namespace