The Generic Package Containers.Ordered_Sets
Author: JTC1/SC22/WG9/ARG, by Randall Brukardt, ARG Editor

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# A.18.9 The Generic 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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with Ada.Iterator_Interfaces;
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);
pragma Remote_Types(Ordered_Sets);
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function Equivalent_Elements (Left, Right : Element_Type) return Boolean;
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type Set is tagged private
with Constant_Indexing => Constant_Reference,
Default_Iterator => Iterate,
Iterator_Element => Element_Type;
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;
7.1/3
function Has_Element (Position : Cursor) return Boolean;
7.2/3
package Set_Iterator_Interfaces is new
Ada.Iterator_Interfaces (Cursor, Has_Element);
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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));
16.1/3
type Constant_Reference_Type
(Element : not null access constant Element_Type) is private
with Implicit_Dereference => Element;
16.2/3
function Constant_Reference (Container : aliased in Set;
Position : in Cursor)
return Constant_Reference_Type;
16.3/3
procedure Assign (Target : in out Set; Source : in Set);
16.4/3
function Copy (Source : Set) return Set;
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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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This paragraph was deleted.
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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));
61.1/3
function Iterate (Container : in Set)
return Set_Iterator_Interfaces.Reversible_Iterator'Class;
61.2/3
function Iterate (Container : in Set; Start : in Cursor)
return Set_Iterator_Interfaces.Reversible_Iterator'Class;
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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));
73.1/3
type Reference_Type
(Element : not null access Element_Type) is private
with Implicit_Dereference => Element;
73.2/3
function Reference_Preserving_Key (Container : aliased in out Set;
Position : in Cursor)
return Reference_Type;
73.3/3
function Constant_Reference (Container : aliased in Set;
Key : in Key_Type)
return Constant_Reference_Type;
73.4/3
function Reference_Preserving_Key (Container : aliased in out Set;
Key : in Key_Type)
return Reference_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 weak ordering relationship (see A.18). 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.
79.1/3
If the actual function for the generic formal function "=" returns True for any pair of nonequivalent elements, then the behavior of the container function "=" is unspecified.
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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.
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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.
81.1/3
function Copy (Source : Set) return Set;
81.2/3
Returns a set whose elements are initialized from the corresponding elements of Source.
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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 predecessor element of 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;
99/3
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;
101/2
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;
105/2
Equivalent to Element (Left) < Right.
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function ">" (Left : Cursor; Right : Element_Type) return Boolean;
107/2
Equivalent to Right < Element (Left).
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function "<" (Left : Element_Type; Right : Cursor) return Boolean;
109/2
Equivalent to Left < Element (Right).
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function ">" (Left : Element_Type; Right : Cursor) return Boolean;
111/2
Equivalent to Element (Right) < Left.
112/2
procedure Reverse_Iterate
(Container : in Set;
Process : not null access procedure (Position : in Cursor));
113/3
Iterates over the elements in Container as per procedure Iterate, with the difference that the elements are traversed in predecessor order, starting with the last element.
113.1/3
function Iterate (Container : in Set)
return Set_Iterator_Interfaces.Reversible_Iterator'Class;
113.2/3
Iterate returns a reversible iterator object (see 5.5.1) that will generate a value for a loop parameter (see 5.5.2) designating each element in Container, starting with the first element and moving the cursor according to the successor relation when used as a forward iterator, and starting with the last element and moving the cursor according to the predecessor relation when used as a reverse iterator. Tampering with the cursors of Container is prohibited while the iterator object exists (in particular, in the sequence_of_statements of the loop_statement whose iterator_specification denotes this object). The iterator object needs finalization.
113.3/3
function Iterate (Container : in Set; Start : in Cursor)
return Set_Iterator_Interfaces.Reversible_Iterator'Class;
113.4/3
If Start is not No_Element and does not designate an item in Container, then Program_Error is propagated. If Start is No_Element, then Constraint_Error is propagated. Otherwise, Iterate returns a reversible iterator object (see 5.5.1) that will generate a value for a loop parameter (see 5.5.2) designating each element in Container, starting with the element designated by Start and moving the cursor according to the successor relation when used as a forward iterator, or moving the cursor according to the predecessor relation when used as a reverse iterator. Tampering with the cursors of Container is prohibited while the iterator object exists (in particular, in the sequence_of_statements of the loop_statement whose iterator_specification denotes this object). The iterator object needs finalization.
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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.
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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).

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