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section\<open>Object\<close>
text\<open>In this theory, we introduce the typed pointer for the class Object. This class is the
common superclass of our class model.\<close>
theory ObjectPointer
  imports
    Ref
begin

datatype 'object_ptr object_ptr = Ext 'object_ptr
register_default_tvars "'object_ptr object_ptr"

instantiation object_ptr :: (linorder) linorder
begin
definition less_eq_object_ptr :: "'object_ptr::linorder object_ptr \<Rightarrow> 'object_ptr object_ptr \<Rightarrow> bool"
  where "less_eq_object_ptr x y \<equiv> (case x of Ext i \<Rightarrow> (case y of Ext j \<Rightarrow> i \<le> j))"
definition less_object_ptr :: "'object_ptr::linorder object_ptr \<Rightarrow> 'object_ptr object_ptr \<Rightarrow> bool"
  where "less_object_ptr x y \<equiv> x \<le> y \<and> \<not> y \<le> x"
instance by(standard, auto simp add: less_eq_object_ptr_def less_object_ptr_def
      split: object_ptr.splits)
end

end
