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A.18.9 The Package Containers.Ordered_Sets

Static Semantics

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The generic library package Containers.Ordered_Sets has the following declaration:

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     generic
        type Element_Type is private;
        with function "<" (Left, Right Element_Type) return Boolean is <>;
        with function "=" (Left, Right Element_Type) return Boolean is <>;
     package Ada.Containers.Ordered_Sets is   pragma Preelaborate(Ordered_Sets);

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        function Equivalent_Elements (Left, Right Element_Type) return Boolean;

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        type Set is tagged private;
        pragma Preelaborable_Initialization(Set);

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        type Cursor is private;
        pragma Preelaborable_Initialization(Cursor);

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        Empty_Set constant Set;

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        No_Element constant Cursor;

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        function "=" (Left, Right Set) return Boolean;

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        function Equivalent_Sets (Left, Right Set) return Boolean;

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        function To_Set (New_Item Element_Type) return Set;

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        function Length (Container Set) return Count_Type;

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        function Is_Empty (Container Set) return Boolean;

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        procedure Clear (Container in out Set);

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        function Element (Position Cursor) return Element_Type;

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        procedure Replace_Element (Container in out Set;
                                   Position  in     Cursor;
                                   New_Item  in     Element_Type);

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        procedure Query_Element
          (Position in Cursor;
           Process  not null access procedure (Element in Element_Type));

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        procedure Move (Target in out Set;
                        Source in out Set);

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        procedure Insert (Container in out Set;
                          New_Item  in     Element_Type;
                          Position     out Cursor;
                          Inserted     out Boolean);

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        procedure Insert (Container in out Set;
                          New_Item  in     Element_Type);

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        procedure Include (Container in out Set;
                           New_Item  in     Element_Type);

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        procedure Replace (Container in out Set;
                           New_Item  in     Element_Type);

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        procedure Exclude (Container in out Set;
                           Item      in     Element_Type);

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        procedure Delete (Container in out Set;
                          Item      in     Element_Type);

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        procedure Delete (Container in out Set;
                          Position  in out Cursor);

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        procedure Delete_First (Container in out Set);

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        procedure Delete_Last (Container in out Set);

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        procedure Union (Target in out Set;
                         Source in     Set);

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        function Union (Left, Right Set) return Set;

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        function "or" (Left, Right Set) return Set renames Union;

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        procedure Intersection (Target in out Set;
                                Source in     Set);

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        function Intersection (Left, Right Set) return Set;

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        function "and" (Left, Right Set) return Set renames Intersection;

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        procedure Difference (Target in out Set;
                              Source in     Set);

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        function Difference (Left, Right Set) return Set;

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        function "−" (Left, Right Set) return Set renames Difference;

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        procedure Symmetric_Difference (Target in out Set;
                                        Source in     Set);

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        function Symmetric_Difference (Left, Right Set) return Set;

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        function "xor" (Left, Right Set) return Set renames
           Symmetric_Difference;

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        function Overlap (Left, Right Set) return Boolean;

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        function Is_Subset (Subset Set;
                            Of_Set Set) return Boolean;

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        function First (Container Set) return Cursor;

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        function First_Element (Container Set) return Element_Type;

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        function Last (Container Set) return Cursor;

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        function Last_Element (Container Set) return Element_Type;

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        function Next (Position Cursor) return Cursor;

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        procedure Next (Position in out Cursor);

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        function Previous (Position Cursor) return Cursor;

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        procedure Previous (Position in out Cursor);

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        function Find (Container Set;
                       Item      Element_Type)
           return Cursor;

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        function Floor (Container Set;
                        Item      Element_Type)
           return Cursor;

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        function Ceiling (Container Set;
                          Item      Element_Type)
           return Cursor;

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        function Contains (Container Set;
                           Item      Element_Type) return Boolean;

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        function Has_Element (Position Cursor) return Boolean;

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        function "<" (Left, Right Cursor) return Boolean;

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        function ">" (Left, Right Cursor) return Boolean;

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        function "<" (Left Cursor; Right Element_Type)
           return Boolean;

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        function ">" (Left Cursor; Right Element_Type)
           return Boolean;

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        function "<" (Left Element_Type; Right Cursor)
           return Boolean;

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        function ">" (Left Element_Type; Right Cursor)
           return Boolean;

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        procedure Iterate
          (Container in Set;
           Process   not null access procedure (Position in Cursor));

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        procedure Reverse_Iterate
          (Container in Set;
           Process   not null access procedure (Position in Cursor));

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        generic
           type Key_Type (<>) is private;
           with function Key (Element Element_Type) return Key_Type;
           with function "<" (Left, Right Key_Type)
              return Boolean is <>;
        package Generic_Keys is

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            function Equivalent_Keys (Left, Right Key_Type)
               return Boolean;

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            function Key (Position Cursor) return Key_Type;

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            function Element (Container Set;
                              Key       Key_Type)
               return Element_Type;

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            procedure Replace (Container in out Set;
                               Key       in     Key_Type;
                               New_Item  in     Element_Type);

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            procedure Exclude (Container in out Set;
                               Key       in     Key_Type);

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            procedure Delete (Container in out Set;
                              Key       in     Key_Type);

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            function Find (Container Set;
                           Key       Key_Type)
               return Cursor;

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            function Floor (Container Set;
                            Key       Key_Type)
               return Cursor;

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            function Ceiling (Container Set;
                              Key       Key_Type)
               return Cursor;

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            function Contains (Container Set;
                               Key       Key_Type) return Boolean;

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            procedure Update_Element_Preserving_Key
              (Container in out Set;
               Position  in     Cursor;
               Process   not null access procedure
                               (Element in out Element_Type));

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        end Generic_Keys;

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     private

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        ... −− not specified by the language

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     end Ada.Containers.Ordered_Sets;

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Two elements E1 and E2 are equivalent if both E1 < E2 and E2 < E1 return False, using the generic formal "<" operator for elements.Function Equivalent_Elements returns True if Left and Right are equivalent, and False otherwise.

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The actual function for the generic formal function "<" on Element_Type values is expected to return the same value each time it is called with a particular pair of key values. It should define a strict ordering relationship, that is, be irreflexive, asymmetric, and transitive. If the actual for "<" behaves in some other manner, the behavior of this package is unspecified. Which subprograms of this package call "<" and how many times they call it, is unspecified.80/2
If the value of an element stored in a set is changed other than by an operation in this package such that at least one of "<" or "=" give different results, the behavior of this package is unspecified.81/2
The first element of a nonempty set is the one which is less than all the other elements in the set. The last element of a nonempty set is the one which is greater than all the other elements in the set. The successor of an element is the smallest element that is larger than the given element. The predecessor of an element is the largest element that is smaller than the given element. All comparisons are done using the generic formal "<" operator for elements.

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     procedure Delete_First (Container in out Set);

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If Container is empty, Delete_First has no effect. Otherwise the element designated by First (Container) is removed from Container. Delete_First tampers with the cursors of Container.

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     procedure Delete_Last (Container in out Set);

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If Container is empty, Delete_Last has no effect. Otherwise the element designated by Last (Container) is removed from Container. Delete_Last tampers with the cursors of Container.

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     function First_Element (Container Set) return Element_Type;

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Equivalent to Element (First (Container)).

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     function Last (Container Set) return Cursor;

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Returns a cursor that designates the last element in Container. If Container is empty, returns No_Element.

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     function Last_Element (Container Set) return Element_Type;

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Equivalent to Element (Last (Container)).

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     function Previous (Position Cursor) return Cursor;

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If Position equals No_Element, then Previous returns No_Element. Otherwise Previous returns a cursor designating the element that precedes the one designated by Position. If Position designates the first element, then Previous returns No_Element.

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     procedure Previous (Position in out Cursor);

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Equivalent to Position := Previous (Position).

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     function Floor (Container Set;
                     Item      Element_Type) return Cursor;

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Floor searches for the last element which is not greater than Item. If such an element is found, a cursor that designates it is returned. Otherwise No_Element is returned.

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     function Ceiling (Container Set;
                       Item      Element_Type) return Cursor;

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Ceiling searches for the first element which is not less than Item. If such an element is found, a cursor that designates it is returned. Otherwise No_Element is returned.

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     function "<" (Left, Right Cursor) return Boolean;

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Equivalent to Element (Left) < Element (Right).

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     function ">" (Left, Right Cursor) return Boolean;

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Equivalent to Element (Right) < Element (Left).

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     function "<" (Left Cursor; Right Element_Type) return Boolean;

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Equivalent to Element (Left) < Right.

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     function ">" (Left Cursor; Right Element_Type) return Boolean;

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Equivalent to Right < Element (Left).

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     function "<" (Left Element_Type; Right Cursor) return Boolean;

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Equivalent to Left < Element (Right).

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     function ">" (Left Element_Type; Right Cursor) return Boolean;

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Equivalent to Element (Right) < Left.

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     procedure Reverse_Iterate
        (Container in Set;
         Process   not null access procedure (Position in Cursor));

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Iterates over the elements in Container as per Iterate, with the difference that the elements are traversed in predecessor order, starting with the last element.

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For any two elements E1 and E2, the boolean values (E1 < E2) and (Key(E1) < Key(E2)) are expected to be equal. If the actuals for Key or Generic_Keys."<" behave in some other manner, the behavior of this package is unspecified. Which subprograms of this package call Key and Generic_Keys."<", and how many times the functions are called, is unspecified.115/2
In addition to the semantics described in A.18.7, the subprograms in package Generic_Keys named Floor and Ceiling, are equivalent to the corresponding subprograms in the parent package, with the difference that the Key subprogram parameter is compared to elements in the container using the Key and "<" generic formal functions. The function named Equivalent_Keys in package Generic_Keys returns True if both Left < Right and Right < Left return False using the generic formal "<" operator, and returns True otherwise.

Implementation Advice

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If N is the length of a set, then the worst−case time complexity of the Insert, Include, Replace, Delete, Exclude and Find operations that take an element parameter should be O((log N)**2) or better. The worst−case time complexity of the subprograms that take a cursor parameter should be O(1).