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+Declaring subtypes of private types
+===================================
+
+:date: 2017-09-02 16:44
+:tags: contracts, private types, predicates
+:author: Jacob Sparre Andersen
+
+Sometimes, you want to declare a subtype for a subset of the possible values of a private type.
+
+You might for example want a subtype of `Ada.Calendar.Time`, which only can include times in the past.  If `Ada.Calendar.Time` was a numeric type, we could declare a subset using `range`, but as it is a private type, we have to do it differently:
+
+.. code-block:: ada
+
+   subtype Past_Time is Ada.Calendar.Time
+     with Dynamic_Predicate => Past_Time < Ada.Calendar.Time.Clock;
+
+You could even expand this to a subtype representing values in the last hour:
+
+.. code-block:: ada
+
+   subtype Last_Hour is Past_Time
+     with Dynamic_Predicate => Ada.Calendar.Time.Clock - 3600.0 <= Last_Hour;
+
+Notice that while `Past_Time` is an ever expanding subtype, `Last_Hour` is an ever changing subtype, such that values which were valid earlier, not necessarily are valid now.
+