Use more concepts and seperate iterator implementations

11 files changed, 327 insertions, 295 deletions

diff --git a/arch/x86_64/include/arch/memory/allocator/physical_frame.hpp b/arch/x86_64/include/arch/memory/allocator/physical_frame.hpp
index 43a22a2..a39517a 100644
--- a/arch/x86_64/include/arch/memory/allocator/physical_frame.hpp
+++ b/arch/x86_64/include/arch/memory/allocator/physical_frame.hpp
@@ -2,7 +2,7 @@
 #define TEACHOS_ARCH_X86_64_MEMORY_ALLOCATOR_PHYSICAL_FRAME_HPP
 
 #include "arch/shared/container.hpp"
-#include "arch/shared/random_access_iterator.hpp"
+#include "arch/shared/forward_value_iterator.hpp"
 
 #include <compare>
 #include <cstdint>
@@ -66,44 +66,6 @@ namespace teachos::arch::memory::allocator
     auto operator++() -> physical_frame &;
 
     /**
-     * @brief Addition assignment operator. Returns a reference to the changed value.
-     *
-     * @param operand Value we want to add to the underlying address.
-     * @return Reference to the changed underlying address.
-     */
-    auto operator+=(std::size_t operand) -> physical_frame &;
-
-    /**
-     * @brief Subtraction assignment operator. Returns a reference to the changed value.
-     *
-     * @param operand Value we want to subtract from the underlying address.
-     * @return Reference to the changed underlying address.
-     */
-    auto operator-=(std::size_t operand) -> physical_frame &;
-
-    /**
-     * @brief Post increment operator. Returns a copy of the value.
-     *
-     * @return Copy of the incremented underlying address.
-     */
-    auto operator+(std::size_t operand) const -> physical_frame;
-
-    /**
-     * @brief Pre increment operator. Returns a reference to the changed value.
-     *
-     * @return Reference to the incremented underlying address.
-     */
-    auto operator-(std::size_t operand) const -> physical_frame;
-
-    /**
-     * @brief Subtraction operator. Returns the size difference between two iterators.
-     *
-     * @param other Other iterator we want to substract the underlying address with ours.
-     * @return Size difference between the underlying address of this instance and the given iterator.
-     */
-    auto operator-(physical_frame const & other) const -> std::size_t;
-
-    /**
      * @brief Defaulted equals operator.
      */
     auto operator==(physical_frame const & other) const -> bool = default;
@@ -117,7 +79,7 @@ namespace teachos::arch::memory::allocator
         {};  ///< Index number of the current physical frame, used to distinguish it from other frames.
   };
 
-  typedef shared::container<shared::random_access_iterator<physical_frame>> frame_container;
+  typedef shared::container<shared::forward_value_iterator<physical_frame>> frame_container;
 }  // namespace teachos::arch::memory::allocator
 
 #endif  // TEACHOS_ARCH_X86_64_MEMORY_ALLOCATOR_PHYSICAL_FRAME_HPP
diff --git a/arch/x86_64/include/arch/memory/multiboot/elf_symbols_section.hpp b/arch/x86_64/include/arch/memory/multiboot/elf_symbols_section.hpp
index 6227fc9..549839a 100644
--- a/arch/x86_64/include/arch/memory/multiboot/elf_symbols_section.hpp
+++ b/arch/x86_64/include/arch/memory/multiboot/elf_symbols_section.hpp
@@ -3,7 +3,7 @@
 
 #include "arch/memory/multiboot/info.hpp"
 #include "arch/shared/container.hpp"
-#include "arch/shared/random_access_iterator.hpp"
+#include "arch/shared/contiguous_pointer_iterator.hpp"
 
 #include <bitset>
 #include <cstdint>
@@ -162,7 +162,7 @@ namespace teachos::arch::memory::multiboot
                                   ///< contained in the section, to ensure byte alignment is actually 4 byte.
   };
 
-  typedef shared::container<shared::random_access_iterator<elf_section_header *>> elf_section_header_container;
+  typedef shared::container<shared::contiguous_pointer_iterator<elf_section_header>> elf_section_header_container;
 }  // namespace teachos::arch::memory::multiboot
 
 #endif  // TEACHOS_ARCH_X86_64_MEMORY_MULTIBOOT_ELF_SYBOLS_SECTION_HPP
diff --git a/arch/x86_64/include/arch/memory/multiboot/memory_map.hpp b/arch/x86_64/include/arch/memory/multiboot/memory_map.hpp
index ccd5cf0..413f5a1 100644
--- a/arch/x86_64/include/arch/memory/multiboot/memory_map.hpp
+++ b/arch/x86_64/include/arch/memory/multiboot/memory_map.hpp
@@ -3,7 +3,7 @@
 
 #include "arch/memory/multiboot/info.hpp"
 #include "arch/shared/container.hpp"
-#include "arch/shared/random_access_iterator.hpp"
+#include "arch/shared/contiguous_pointer_iterator.hpp"
 
 #include <cstdint>
 
@@ -46,7 +46,7 @@ namespace teachos::arch::memory::multiboot
     struct memory_area entries;  ///< Specific memory regions.
   };
 
-  typedef shared::container<shared::random_access_iterator<memory_area *>> memory_area_container;
+  typedef shared::container<shared::contiguous_pointer_iterator<memory_area>> memory_area_container;
 }  // namespace teachos::arch::memory::multiboot
 
 #endif  // TEACHOS_ARCH_X86_64_MEMORY_MULTIBOOT_MEMORY_MAP_HPP
diff --git a/arch/x86_64/include/arch/memory/paging/kernel_mapper.hpp b/arch/x86_64/include/arch/memory/paging/kernel_mapper.hpp
index d301c91..2eb3c4a 100644
--- a/arch/x86_64/include/arch/memory/paging/kernel_mapper.hpp
+++ b/arch/x86_64/include/arch/memory/paging/kernel_mapper.hpp
@@ -101,23 +101,23 @@ namespace teachos::arch::memory::paging
       exception_handling::assert(!mem_info.sections.empty(), "[Kernel Mapper] Kernel elf sections empty");
       for (auto const & section : mem_info.sections)
       {
-        if (!section->flags.contains_flags(multiboot::elf_section_flags::OCCUPIES_MEMORY))
+        if (!section.flags.contains_flags(multiboot::elf_section_flags::OCCUPIES_MEMORY))
         {
           continue;
         }
-        exception_handling::assert(section->physical_address % allocator::PAGE_FRAME_SIZE == 0U,
+        exception_handling::assert(section.physical_address % allocator::PAGE_FRAME_SIZE == 0U,
                                    "[Kernel Mapper] Section must be page aligned");
-        auto const start_frame = allocator::physical_frame::containing_address(section->physical_address);
+        auto const start_frame = allocator::physical_frame::containing_address(section.physical_address);
         // End address is exclusive, so that it is not part of the section anymore (one past the last frame of this
         // section). But end frame would now point to the actual last frame and not one past the last frame, therefore
         // we increment by one to get one past the last frame of this section.
         auto end_frame =
-            ++(allocator::physical_frame::containing_address(section->physical_address + section->section_size - 1));
+            ++(allocator::physical_frame::containing_address(section.physical_address + section.section_size - 1));
 
         allocator::frame_container::iterator const begin{start_frame};
         allocator::frame_container::iterator const end{end_frame};
         allocator::frame_container frames{begin, end};
-        entry entry{section->flags};
+        entry entry{section.flags};
 
         for (auto const & frame : frames)
         {
diff --git a/arch/x86_64/include/arch/shared/container.hpp b/arch/x86_64/include/arch/shared/container.hpp
index 9b4192e..b335e72 100644
--- a/arch/x86_64/include/arch/shared/container.hpp
+++ b/arch/x86_64/include/arch/shared/container.hpp
@@ -5,16 +5,20 @@
 
 namespace teachos::arch::shared
 {
+  /**
+   * @brief Minimal iterator concept required for usage in container
+   */
   template<typename T>
-  concept Iterator = std::contiguous_iterator<T>;
+  concept Iterator = std::forward_iterator<T>;
 
   /**
    * @brief Read-only container for given template type, that allow to easily use this container instance in C++20
    * ranges calls.
    *
-   * @tparam T Iterator the container uses to signal the start and end of it's data.
+   * @tparam T Iterator the container uses to signal the start and end of it's data, has to atleast be a simple forward
+   * iterator.
    */
-  template<typename T>
+  template<Iterator T>
   struct container
   {
     using iterator = T;             ///< Iterators used by this container.
diff --git a/arch/x86_64/include/arch/shared/contiguous_pointer_iterator.hpp b/arch/x86_64/include/arch/shared/contiguous_pointer_iterator.hpp
new file mode 100644
index 0000000..7d5019a
--- /dev/null
+++ b/arch/x86_64/include/arch/shared/contiguous_pointer_iterator.hpp
@@ -0,0 +1,189 @@
+#ifndef TEACHOS_ARCH_X86_64_SHARED_CONTIGUOUS_POINTER_ITERATOR_HPP
+#define TEACHOS_ARCH_X86_64_SHARED_CONTIGUOUS_POINTER_ITERATOR_HPP
+
+#include <iterator>
+
+namespace teachos::arch::shared
+{
+  /**
+   * @brief Generic contiguous iterator for given template type. Allows to easily use this iterator instance in
+   * algorithm calls.
+   *
+   * @note Allows any value that is contained in an array in memory, which is a block of contiguous memory. This is the
+   * case because we assume we can simply increment or decrement the pointer address to get the next valid instance of
+   * the given value type.
+   *
+   * @tparam T Value the iterator points too.
+   */
+  template<typename T>
+  struct contiguous_pointer_iterator
+  {
+    using iterator_category = std::contiguous_iterator_tag;  ///< Iterator category of this type.
+    using difference_type = std::ptrdiff_t;  ///< Type when diving one instance of this iterator by another.
+    using value_type = T;                    ///< Underlying value pointed to by this iterator.
+    using reference_type = value_type &;     ///< Reference to value returned by dereference * operation.
+    using pointer_type = value_type *;       ///< Pointer to value returned by arrow -> operation.
+
+    /**
+     * @brief Defaulted constructor.
+     */
+    contiguous_pointer_iterator() = default;
+
+    /**
+     * @brief Constructor.
+     *
+     * @param p Underlying address the iterator should point too.
+     */
+    explicit contiguous_pointer_iterator(value_type * p)
+        : ptr(p)
+    {
+      // Nothing to do
+    }
+
+    /**
+     * @brief Dereferences the initally given pointer to its value.
+     *
+     * @return Reference to the value.
+     */
+    auto operator*() const -> reference_type { return *ptr; }
+
+    /**
+     * @brief Get underlying value, which is the intially passed pointer.
+     *
+     * @return Pointer to the underlying value passed intially.
+     */
+    auto operator->() const -> pointer_type { return ptr; }
+
+    /**
+     * @brief Pre decrement operator. Returns a reference to the changed address.
+     *
+     * @return Reference to the decremented underlying address.
+     */
+    auto operator--() -> contiguous_pointer_iterator &
+    {
+      contiguous_pointer_iterator const old_value = *this;
+      ++ptr;
+      return old_value;
+    }
+
+    /**
+     * @brief Pre increment operator. Returns a reference to the changed address.
+     *
+     * @return Reference to the incremented underlying address.
+     */
+    auto operator++() -> contiguous_pointer_iterator &
+    {
+      ++ptr;
+      return *this;
+    }
+
+    /**
+     * @brief Post decrement operator. Returns a copy of the address.
+     *
+     * @return Copy of the decremented underlying address.
+     */
+    auto operator--(int) -> contiguous_pointer_iterator
+    {
+      auto const old_value = *this;
+      --ptr;
+      return old_value;
+    }
+
+    /**
+     * @brief Post increment operator. Returns a copy of the address.
+     *
+     * @return Copy of the incremented underlying address.
+     */
+    auto operator++(int) -> contiguous_pointer_iterator
+    {
+      auto const old_value = *this;
+      ++ptr;
+      return old_value;
+    }
+
+    /**
+     * @brief Addition assignment operator. Returns a reference to the changed address.
+     *
+     * @param value Value we want to add to the underlying address.
+     * @return Reference to the changed underlying address.
+     */
+    auto operator+=(difference_type value) -> contiguous_pointer_iterator &
+    {
+      ptr += value;
+      return *this;
+    }
+
+    /**
+     * @brief Subtraction assignment operator. Returns a reference to the changed address.
+     *
+     * @param value Value we want to subtract from the underlying address.
+     * @return Reference to the changed underlying address.
+     */
+    auto operator-=(difference_type value) -> contiguous_pointer_iterator &
+    {
+      ptr -= value;
+      return *this;
+    }
+
+    /**
+     * @brief Addition operator. Returns the changed address.
+     *
+     * @param value Value we want to add to a copy of the underlying address.
+     * @return Copy of underlying address incremented by the given value.
+     */
+    auto operator+(difference_type value) const -> contiguous_pointer_iterator
+    {
+      return contiguous_pointer_iterator{ptr + value};
+    }
+
+    /**
+     * @brief Subtraction operator. Returns the changed address.
+     *
+     * @param value Value we want to subtrcat from a copy of the underlying address.
+     * @return Copy of underlying address decremented by the given value.
+     */
+    auto operator-(difference_type value) const -> contiguous_pointer_iterator
+    {
+      return contiguous_pointer_iterator{ptr - value};
+    }
+
+    /**
+     * @brief Subtraction operator. Returns the size difference between two iterators.
+     *
+     * @param other Other iterator we want to substract the underlying address with ours.
+     * @return Size difference between the underlying address of this instance and the given iterator.
+     */
+    auto operator-(const contiguous_pointer_iterator & other) const -> difference_type { return ptr - other.ptr; }
+
+    /**
+     * @brief Index operator overload. Returns a reference to the value at the given index. Simply returns the
+     * dereferenced underlying pointer incremented by the given index.
+     *
+     * @param index Index we want to access and get the value from.
+     * @return Reference to the value at the given index.
+     */
+    auto operator[](difference_type index) const -> value_type & { return *(ptr + index); }
+
+    /**
+     * @brief Defaulted comparsion operator. Simply compares the memory address of both iterators.
+     *
+     * @param other Other iterator to compare to.
+     * @return Whether both iterators point to the same underlying address in memory.
+     */
+    auto operator==(contiguous_pointer_iterator const & other) const -> bool = default;
+
+    /**
+     * @brief Defaulted threeway comparsion operator. Simply compares the memory address of both iterators.
+     *
+     * @param other Other iterator to compare to.
+     * @return Whether the given iterator is smaller or larger than this iterator.
+     */
+    auto operator<=>(contiguous_pointer_iterator const & other) const -> std::strong_ordering = default;
+
+  private:
+    pointer_type ptr =
+        {};  ///< Underlying value the iterator is currently pointing too and should increment or decrement.
+  };
+}  // namespace teachos::arch::shared
+
+#endif  // TEACHOS_ARCH_X86_64_SHARED_CONTIGUOUS_POINTER_ITERATOR_HPP
diff --git a/arch/x86_64/include/arch/shared/forward_value_iterator.hpp b/arch/x86_64/include/arch/shared/forward_value_iterator.hpp
new file mode 100644
index 0000000..a84d291
--- /dev/null
+++ b/arch/x86_64/include/arch/shared/forward_value_iterator.hpp
@@ -0,0 +1,109 @@
+#ifndef TEACHOS_ARCH_X86_64_SHARED_FORWARD_VALUE_ITERATOR_HPP
+#define TEACHOS_ARCH_X86_64_SHARED_FORWARD_VALUE_ITERATOR_HPP
+
+#include <iterator>
+
+namespace teachos::arch::shared
+{
+  /**
+   * @brief Concept for a type to have a post and prefix increment operator, that returns the correct type.
+   */
+  template<typename T>
+  concept Incrementable = requires(T t) {
+    { ++t } -> std::same_as<T &>;
+    { t++ } -> std::same_as<T>;
+  };
+
+  /**
+   * @brief Iterable concept for the forward value iterator, meaning the type itself is incrementable and comparable.
+   */
+  template<typename T>
+  concept Iterable = std::regular<T> && Incrementable<T>;
+
+  /**
+   * @brief Generic forward iterator for given template type. Allows to easily use this iterator
+   * instance in algorithm calls.
+   *
+   * @note Allows any value that itself can be incremented until we have reached the end, does not interact with the
+   * address of the value in any way.
+   *
+   * @tparam T Value the iterator contains.
+   */
+  template<Iterable T>
+  struct forward_value_iterator
+  {
+    using iterator_category = std::forward_iterator_tag;  ///< Iterator category of this type.
+    using difference_type = std::ptrdiff_t;  ///< Type when diving one instance of this iterator by another.
+    using value_type = T;                    ///< Underlying value contained by this iterator.
+    using const_reference_type =
+        value_type const &;  ///< Constant reference to value returned by dereference * operation.
+    using const_pointer_type = value_type const *;  ///< Constant pointer to value returned by arrow -> operation.
+
+    /**
+     * @brief Defaulted constructor.
+     */
+    forward_value_iterator() = default;
+
+    /**
+     * @brief Constructor.
+     *
+     * @param value Underlying value the iterator contains.
+     */
+    explicit forward_value_iterator(value_type value)
+        : value(value)
+    {
+      // Nothing to do
+    }
+
+    /**
+     * @brief Returns the initally given value.
+     *
+     * @return Reference to the value.
+     */
+    auto operator*() const -> const_reference_type { return value; }
+
+    /**
+     * @brief Gets pointer to the underlying value passed intially.
+     *
+     * @return Pointer to the underlying value passed intially.
+     */
+    auto operator->() const -> const_pointer_type { return &value; }
+
+    /**
+     * @brief Pre increment operator. Returns a reference to the changed value.
+     *
+     * @return Reference to the incremented underlying value.
+     */
+    auto operator++() -> forward_value_iterator &
+    {
+      ++value;
+      return *this;
+    }
+
+    /**
+     * @brief Post increment operator. Returns a copy of the value.
+     *
+     * @return Copy of the incremented underlying value.
+     */
+    auto operator++(int) -> forward_value_iterator
+    {
+      auto const old_value = *this;
+      ++value;
+      return old_value;
+    }
+
+    /**
+     * @brief Defaulted comparsion operator. Simply compares the memory address of both iterators.
+     *
+     * @param other Other iterator to compare to.
+     * @return Whether both iterators point to the same underlying address in memory.
+     */
+    auto operator==(forward_value_iterator const & other) const -> bool = default;
+
+  private:
+    value_type value =
+        {};  ///< Underlying value the iterator is currently pointing too and should increment or decrement.
+  };
+}  // namespace teachos::arch::shared
+
+#endif  // TEACHOS_ARCH_X86_64_SHARED_FORWARD_VALUE_ITERATOR_HPP
diff --git a/arch/x86_64/include/arch/shared/random_access_iterator.hpp b/arch/x86_64/include/arch/shared/random_access_iterator.hpp
deleted file mode 100644
index 69617f3..0000000
--- a/arch/x86_64/include/arch/shared/random_access_iterator.hpp
+++ /dev/null
@@ -1,204 +0,0 @@
-#ifndef TEACHOS_ARCH_X86_64_SHARED_RANDOM_ACCESS_ITERATOR_HPP
-#define TEACHOS_ARCH_X86_64_SHARED_RANDOM_ACCESS_ITERATOR_HPP
-
-#include <iterator>
-
-namespace teachos::arch::shared
-{
-  template<typename T>
-  concept Iterable = std::incrementable<T> && std::three_way_comparable<T> && std::indirectly_readable<T>;
-
-  /**
-   * @brief Generic random access iterator for given template type. Allows any value that  Allows to easily use this
-   * iterator instance in algorithm calls.
-   *
-   * @tparam T Value the iterator points too.
-   */
-  template<Iterable T>
-  struct random_access_iterator
-  {
-    using iterator_category = std::contiguous_iterator_tag;  ///< Iterator category of this type.
-    using difference_type = std::ptrdiff_t;           ///< Type when diving one instance of this iterator by another.
-    using value_type = T;                             ///< Underlying value pointed to by this iterator.
-    using reference_type = value_type &;              ///< Reference to value returned by dereference * operation.
-    using pointer_type = value_type *;                ///< Pointer to value returned by arrow -> operation.
-    using const_reference_type = value_type const &;  ///< Reference to value returned by const dereference * operation.
-    using const_pointer_type = value_type const *;    ///< Pointer to value returned by const arrow -> operation.
-
-    /**
-     * @brief Defaulted constructor.
-     */
-    random_access_iterator() = default;
-
-    /**
-     * @brief Constructor.
-     *
-     * @param value Underlying value the iterator should point too and increment or decrement.
-     */
-    explicit random_access_iterator(value_type value)
-        : value(value)
-    {
-      // Nothing to do
-    }
-
-    /**
-     * @brief Gets a reference to the underlying value.
-     *
-     * @return Reference to the value.
-     */
-    auto operator*() -> reference_type { return value; }
-
-    /**
-     * @brief Gets a pointer to the underlying value.
-     *
-     * @return Underlying value passed intially.
-     */
-    auto operator->() -> pointer_type { return &value; }
-
-    /**
-     * @brief Gets a const reference to the underlying value.
-     *
-     * @return Reference to the value.
-     */
-    auto operator*() const -> const_reference_type { return value; }
-
-    /**
-     * @brief Gets a const pointer to the underlying value.
-     *
-     * @return Underlying value passed intially.
-     */
-    auto operator->() const -> const_pointer_type { return &value; }
-
-    /**
-     * @brief Pre decrement operator. Returns a reference to the changed value.
-     *
-     * @return Reference to the decrement underlying value.
-     */
-    auto operator--() -> random_access_iterator &
-    {
-      --value;
-      return *this;
-    }
-
-    /**
-     * @brief Pre increment operator. Returns a reference to the changed value.
-     *
-     * @return Reference to the incremented underlying value.
-     */
-    auto operator++() -> random_access_iterator &
-    {
-      ++value;
-      return *this;
-    }
-
-    /**
-     * @brief Post decrement operator. Returns a copy of the value.
-     *
-     * @return Copy of the decremented underlying value.
-     */
-    auto operator--(int) -> random_access_iterator
-    {
-      auto const old_value = *this;
-      --value;
-      return old_value;
-    }
-
-    /**
-     * @brief Post increment operator. Returns a copy of the value.
-     *
-     * @return Copy of the incremented underlying value.
-     */
-    auto operator++(int) -> random_access_iterator
-    {
-      auto const old_value = *this;
-      ++value;
-      return old_value;
-    }
-
-    /**
-     * @brief Addition assignment operator. Returns a reference to the changed value.
-     *
-     * @param operand Value we want to add to the underlying value the iterator is pointing too.
-     * @return Reference to the changed underlying value.
-     */
-    auto operator+=(difference_type operand) -> random_access_iterator &
-    {
-      value += operand;
-      return *this;
-    }
-
-    /**
-     * @brief Subtraction assignment operator. Returns a reference to the changed value.
-     *
-     * @param operand Value we want to subtract from the underlying value the iterator is pointing too.
-     * @return Reference to the changed underlying value.
-     */
-    auto operator-=(difference_type operand) -> random_access_iterator &
-    {
-      value -= operand;
-      return *this;
-    }
-
-    /**
-     * @brief Addition operator. Returns the changed value.
-     *
-     * @param operand Value we want to add to a copy of the underlying value the iterator is pointing too.
-     * @return Copy of underlying value incremented by the given value.
-     */
-    auto operator+(difference_type operand) const -> random_access_iterator
-    {
-      return random_access_iterator{value + operand};
-    }
-
-    /**
-     * @brief Subtraction operator. Returns the changed value.
-     *
-     * @param operand Value we want to subtract from a copy of the underlying value the iterator is pointing too.
-     * @return Copy of underlying value decremented by the given value.
-     */
-    auto operator-(difference_type operand) const -> random_access_iterator
-    {
-      return random_access_iterator{value - operand};
-    }
-
-    /**
-     * @brief Subtraction operator. Returns the size difference between two iterators.
-     *
-     * @param other Other iterator we want to substract the underlying value with ours.
-     * @return Size difference between the underlying value of this instance and the given iterator.
-     */
-    auto operator-(random_access_iterator const & other) const -> difference_type { return value - other.value; }
-
-    /**
-     * @brief Index operator overload. Returns a reference to the value at the given index. Simply returns the
-     * underlying value  the iterator is pointing too incremented by the given index.
-     *
-     * @param index Index we want to access and get the value from.
-     * @return Reference to the value at the given index.
-     */
-    auto operator[](difference_type index) const -> value_type const & { return value + index; }
-
-    /**
-     * @brief Defaulted comparsion operator. Forwards to the comparsion operator of the given template type.
-     *
-     * @param other Other iterator to compare to.
-     * @return Whether both iterators point to the same underlying value in memory.
-     */
-    auto operator==(random_access_iterator const & other) const -> bool = default;
-
-    /**
-     * @brief Defaulted threeway comparsion operator. Forwards to the threeway comparsion operator of the given
-     * template type.
-     *
-     * @param other Other iterator to compare to.
-     * @return Whether the given iterator is smaller or larger than this iterator.
-     */
-    auto operator<=>(random_access_iterator const & other) const -> std::strong_ordering = default;
-
-  private:
-    value_type value =
-        {};  ///< Underlying value the iterator is currently pointing too and should increment or decrement.
-  };
-}  // namespace teachos::arch::shared
-
-#endif  // TEACHOS_ARCH_X86_64_SHARED_RANDOM_ACCESS_ITERATOR_HPP
diff --git a/arch/x86_64/src/memory/allocator/area_frame_allocator.cpp b/arch/x86_64/src/memory/allocator/area_frame_allocator.cpp
index 42aff68..3bc9676 100644
--- a/arch/x86_64/src/memory/allocator/area_frame_allocator.cpp
+++ b/arch/x86_64/src/memory/allocator/area_frame_allocator.cpp
@@ -24,16 +24,16 @@ namespace teachos::arch::memory::allocator
   {
     current_area = std::nullopt;
     auto next_area_with_free_frames = memory_areas | std::views::filter([this](auto const & area) {
-                                        auto address = area->base_address + area->area_length - 1;
+                                        auto address = area.base_address + area.area_length - 1;
                                         return physical_frame::containing_address(address) >= next_free_frame;
                                       });
 
     auto const lowest_area_with_free_frames = std::ranges::min_element(
-        next_area_with_free_frames, [](auto const & a, auto const & b) { return a->base_address < b->base_address; });
+        next_area_with_free_frames, [](auto const & a, auto const & b) { return a.base_address < b.base_address; });
 
     if (lowest_area_with_free_frames != next_area_with_free_frames.end())
     {
-      current_area = **lowest_area_with_free_frames;
+      current_area = *lowest_area_with_free_frames;
       // Update the `next_free_frame` according to the new memory area
       auto const start_frame = physical_frame::containing_address(current_area.value().base_address);
       if (next_free_frame < start_frame)
diff --git a/arch/x86_64/src/memory/allocator/physical_frame.cpp b/arch/x86_64/src/memory/allocator/physical_frame.cpp
index 63d84ec..ec387a1 100644
--- a/arch/x86_64/src/memory/allocator/physical_frame.cpp
+++ b/arch/x86_64/src/memory/allocator/physical_frame.cpp
@@ -21,31 +21,4 @@ namespace teachos::arch::memory::allocator
     ++frame_number;
     return *this;
   }
-
-  auto physical_frame::operator+=(std::size_t operand) -> physical_frame &
-  {
-    frame_number += operand;
-    return *this;
-  }
-
-  auto physical_frame::operator-=(std::size_t operand) -> physical_frame &
-  {
-    frame_number -= operand;
-    return *this;
-  }
-
-  auto physical_frame::operator+(std::size_t operand) const -> physical_frame
-  {
-    return physical_frame{frame_number + operand};
-  }
-
-  auto physical_frame::operator-(std::size_t operand) const -> physical_frame
-  {
-    return physical_frame{frame_number - operand};
-  }
-
-  auto physical_frame::operator-(const physical_frame & other) const -> std::size_t
-  {
-    return frame_number - other.frame_number;
-  }
 }  // namespace teachos::arch::memory::allocator
diff --git a/arch/x86_64/src/memory/multiboot/reader.cpp b/arch/x86_64/src/memory/multiboot/reader.cpp
index 178cc45..1dd18ff 100644
--- a/arch/x86_64/src/memory/multiboot/reader.cpp
+++ b/arch/x86_64/src/memory/multiboot/reader.cpp
@@ -51,27 +51,26 @@ namespace teachos::arch::memory::multiboot
 
       auto const begin = elf_section_header_container::iterator{reinterpret_cast<elf_section_header *>(&symbol->end)};
       auto const end = begin + symbol->number_of_sections;
-      exception_handling::assert((*begin)->is_null(),
+      exception_handling::assert(begin->is_null(),
                                  "[Multiboot Reader] Elf symbols section not starting with SHT_NULL section");
 
       elf_section_header_container sections{begin, end};
 
       auto const elf_section_with_lowest_physical_address = std::ranges::min_element(
-          sections, [](auto const & a, auto const & b) { return a->physical_address < b->physical_address; });
+          sections, [](auto const & a, auto const & b) { return a.physical_address < b.physical_address; });
 
       auto const elf_section_with_highest_physical_address =
           std::ranges::max_element(sections, [](auto const & a, auto const & b) {
-            auto a_physical_address_end = a->physical_address + a->section_size;
-            auto b_physical_address_end = b->physical_address + b->section_size;
+            auto a_physical_address_end = a.physical_address + a.section_size;
+            auto b_physical_address_end = b.physical_address + b.section_size;
             return a_physical_address_end < b_physical_address_end;
           });
 
       auto const symbol_table_section_count = std::ranges::count_if(sections, [](auto const & section) {
-        return section->type == elf_section_type::DYNAMIC_SYMBOL_TABLE ||
-               section->type == elf_section_type::SYMBOL_TABLE;
+        return section.type == elf_section_type::DYNAMIC_SYMBOL_TABLE || section.type == elf_section_type::SYMBOL_TABLE;
       });
       auto const dynamic_section_count = std::ranges::count_if(
-          sections, [](auto const & section) { return section->type == elf_section_type::DYNAMIC; });
+          sections, [](auto const & section) { return section.type == elf_section_type::DYNAMIC; });
 
       exception_handling::assert(
           symbol_table_section_count == 1U,
@@ -81,10 +80,10 @@ namespace teachos::arch::memory::multiboot
           "[Multiboot Reader] ELF Specifications allows only (1) or less dynamic sections, but got more");
 
       auto const lowest_elf_section = *elf_section_with_lowest_physical_address;
-      kernel_start = lowest_elf_section->physical_address;
+      kernel_start = lowest_elf_section.physical_address;
 
       auto const highest_elf_section = *elf_section_with_highest_physical_address;
-      kernel_end = highest_elf_section->physical_address + highest_elf_section->section_size;
+      kernel_end = highest_elf_section.physical_address + highest_elf_section.section_size;
 
       return sections;
     }