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A.18.3 The Generic Package Containers.Doubly_Linked_Lists

1/2
{AI95-00302-03} The language-defined generic package Containers.Doubly_Linked_Lists provides private types List and Cursor, and a set of operations for each type. A list container is optimized for insertion and deletion at any position.
2/2
{AI95-00302-03} A doubly-linked list container object manages a linked list of internal nodes, each of which contains an element and pointers to the next (successor) and previous (predecessor) internal nodes. A cursor designates a particular node within a list (and by extension the element contained in that node). A cursor keeps designating the same node (and element) as long as the node is part of the container, even if the node is moved in the container.
3/2
{AI95-00302-03} The length of a list is the number of elements it contains.

Static Semantics

4/2
{AI95-00302-03} The generic library package Containers.Doubly_Linked_Lists has the following declaration: 
5/3
{AI05-0084-1} {AI05-0212-1} with Ada.Iterator_Interfaces;
generic
   type Element_Type is private;
   with function "=" (Left, Right : Element_Type)
      return Boolean is <>;
package Ada.Containers.Doubly_Linked_Lists is
   pragma Preelaborate(Doubly_Linked_Lists);
   pragma Remote_Types(Doubly_Linked_Lists);
6/3
{AI05-0212-1}    type List is tagged private
      with Constant_Indexing => Constant_Reference,
           Variable_Indexing => Reference,
           Default_Iterator  => Iterate,
           Iterator_Element  => Element_Type;
   pragma Preelaborable_Initialization(List);
7/2
   type Cursor is private;
   pragma Preelaborable_Initialization(Cursor);
8/2
   Empty_List : constant List;
9/2
   No_Element : constant Cursor;
9.1/3
{AI05-0212-1}    function Has_Element (Position : Cursor) return Boolean;
9.2/3
{AI05-0212-1}    package List_Iterator_Interfaces is new
       Ada.Iterator_Interfaces (Cursor, Has_Element);
10/2
   function "=" (Left, Right : List) return Boolean;
11/2
   function Length (Container : List) return Count_Type;
12/2
   function Is_Empty (Container : List) return Boolean;
13/2
   procedure Clear (Container : in out List);
14/2
   function Element (Position : Cursor)
      return Element_Type;
15/2
   procedure Replace_Element (Container : in out List;
                              Position  : in     Cursor;
                              New_Item  : in     Element_Type);
16/2
   procedure Query_Element
     (Position : in Cursor;
      Process  : not null access procedure (Element : in Element_Type));
17/2
   procedure Update_Element
     (Container : in out List;
      Position  : in     Cursor;
      Process   : not null access procedure
                      (Element : in out Element_Type));
17.1/3
{AI05-0212-1}    type Constant_Reference_Type
         (Element : not null access constant Element_Type) is private
      with Implicit_Dereference => Element;
17.2/3
{AI05-0212-1}    type Reference_Type (Element : not null access Element_Type) is private
      with Implicit_Dereference => Element;
17.3/3
{AI05-0212-1}    function Constant_Reference (Container : aliased in List;
                                Position  : in Cursor)
      return Constant_Reference_Type;
17.4/3
{AI05-0212-1}    function Reference (Container : aliased in out List;
                       Position  : in Cursor)
      return Reference_Type;
17.5/3
{AI05-0001-1}    procedure Assign (Target : in out List; Source : in List);
17.6/3
{AI05-0001-1}    function Copy (Source : List) return List;
18/2
   procedure Move (Target : in out List;
                   Source : in out List);
19/2
   procedure Insert (Container : in out List;
                     Before    : in     Cursor;
                     New_Item  : in     Element_Type;
                     Count     : in     Count_Type := 1);
20/2
   procedure Insert (Container : in out List;
                     Before    : in     Cursor;
                     New_Item  : in     Element_Type;
                     Position  :    out Cursor;
                     Count     : in     Count_Type := 1);
21/2
   procedure Insert (Container : in out List;
                     Before    : in     Cursor;
                     Position  :    out Cursor;
                     Count     : in     Count_Type := 1);
22/2
   procedure Prepend (Container : in out List;
                      New_Item  : in     Element_Type;
                      Count     : in     Count_Type := 1);
23/2
   procedure Append (Container : in out List;
                     New_Item  : in     Element_Type;
                     Count     : in     Count_Type := 1);
24/2
   procedure Delete (Container : in out List;
                     Position  : in out Cursor;
                     Count     : in     Count_Type := 1);
25/2
   procedure Delete_First (Container : in out List;
                           Count     : in     Count_Type := 1);
26/2
   procedure Delete_Last (Container : in out List;
                          Count     : in     Count_Type := 1);
27/2
   procedure Reverse_Elements (Container : in out List);
28/2
   procedure Swap (Container : in out List;
                   I, J      : in     Cursor);
29/2
   procedure Swap_Links (Container : in out List;
                         I, J      : in     Cursor);
30/2
   procedure Splice (Target   : in out List;
                     Before   : in     Cursor;
                     Source   : in out List);
31/2
   procedure Splice (Target   : in out List;
                     Before   : in     Cursor;
                     Source   : in out List;
                     Position : in out Cursor);
32/2
   procedure Splice (Container: in out List;
                     Before   : in     Cursor;
                     Position : in     Cursor);
33/2
   function First (Container : List) return Cursor;
34/2
   function First_Element (Container : List)
      return Element_Type;
35/2
   function Last (Container : List) return Cursor;
36/2
   function Last_Element (Container : List)
      return Element_Type;
37/2
   function Next (Position : Cursor) return Cursor;
38/2
   function Previous (Position : Cursor) return Cursor;
39/2
   procedure Next (Position : in out Cursor);
40/2
   procedure Previous (Position : in out Cursor);
41/2
   function Find (Container : List;
                  Item      : Element_Type;
                  Position  : Cursor := No_Element)
      return Cursor;
42/2
   function Reverse_Find (Container : List;
                          Item      : Element_Type;
                          Position  : Cursor := No_Element)
      return Cursor;
43/2
   function Contains (Container : List;
                      Item      : Element_Type) return Boolean;
44/3
This paragraph was deleted.{AI05-0212-1}
45/2
   procedure Iterate
     (Container : in List;
      Process   : not null access procedure (Position : in Cursor));
46/2
   procedure Reverse_Iterate
     (Container : in List;
      Process   : not null access procedure (Position : in Cursor));
46.1/3
{AI05-0212-1}    function Iterate (Container : in List)
      return List_Iterator_Interfaces.Reversible_Iterator'Class;
46.2/3
{AI05-0212-1}    function Iterate (Container : in List; Start : in Cursor)
      return List_Iterator_Interfaces.Reversible_Iterator'Class;
47/2
   generic
      with function "<" (Left, Right : Element_Type)
         return Boolean is <>;
   package Generic_Sorting is
48/2
      function Is_Sorted (Container : List) return Boolean;
49/2
      procedure Sort (Container : in out List);
50/2
      procedure Merge (Target  : in out List;
                       Source  : in out List);
51/2
   end Generic_Sorting;
52/2
private
53/2
   ... -- not specified by the language
54/2
end Ada.Containers.Doubly_Linked_Lists;
55/2
 {AI95-00302-03} The actual function for the generic formal function "=" on Element_Type values is expected to define a reflexive and symmetric relationship and return the same result value each time it is called with a particular pair of values. If it behaves in some other manner, the functions Find, Reverse_Find, and "=" on list values return an unspecified value. The exact arguments and number of calls of this generic formal function by the functions Find, Reverse_Find, and "=" on list values are unspecified.
55.a/2
Ramification: If the actual function for "=" is not symmetric and consistent, the result returned by the listed functions cannot be predicted. The implementation is not required to protect against "=" raising an exception, or returning random results, or any other “bad” behavior. And it can call "=" in whatever manner makes sense. But note that only the results of Find, Reverse_Find, and List "=" are unspecified; other subprograms are not allowed to break if "=" is bad (they aren't expected to use "="). 
56/2
 {AI95-00302-03} The type List is used to represent lists. The type List needs finalization (see 7.6).
57/2
 {AI95-00302-03} Empty_List represents the empty List object. It has a length of 0. If an object of type List is not otherwise initialized, it is initialized to the same value as Empty_List.
58/2
 {AI95-00302-03} No_Element represents a cursor that designates no element. If an object of type Cursor is not otherwise initialized, it is initialized to the same value as No_Element.
59/2
 {AI95-00302-03} The predefined "=" operator for type Cursor returns True if both cursors are No_Element, or designate the same element in the same container.
60/2
 {AI95-00302-03} Execution of the default implementation of the Input, Output, Read, or Write attribute of type Cursor raises Program_Error.
60.a/2
Reason: A cursor will probably be implemented in terms of one or more access values, and the effects of streaming access values is unspecified. Rather than letting the user stream junk by accident, we mandate that streaming of cursors raise Program_Error by default. The attributes can always be specified if there is a need to support streaming. 
60.1/3
   {AI05-0001-1} {AI05-0262-1} List'Write for a List object L writes Length(L) elements of the list to the stream. It also may write additional information about the list.
60.2/3
   {AI05-0001-1} {AI05-0262-1} List'Read reads the representation of a list from the stream, and assigns to Item a list with the same length and elements as was written by List'Write.
60.b/3
Ramification: Streaming more elements than the container length is wrong. For implementation implications of this rule, see the Implementation Note in A.18.2.
61/2
 {AI95-00302-03} [Some operations of this generic package have access-to-subprogram parameters. To ensure such operations are well-defined, they guard against certain actions by the designated subprogram. In particular, some operations check for “tampering with cursors” of a container because they depend on the set of elements of the container remaining constant, and others check for “tampering with elements” of a container because they depend on elements of the container not being replaced.]
62/2
 {AI95-00302-03} A subprogram is said to tamper with cursors of a list object L if:
63/2
it inserts or deletes elements of L, that is, it calls the Insert, Clear, Delete, or Delete_Last procedures with L as a parameter; or
63.a/2
To be honest: Operations which are defined to be equivalent to a call on one of these operations also are included. Similarly, operations which call one of these as part of their definition are included. 
64/2
it reorders the elements of L, that is, it calls the Splice, Swap_Links, or Reverse_Elements procedures or the Sort or Merge procedures of an instance of Generic_Sorting with L as a parameter; or
65/2
it finalizes L; or
65.1/3
{AI05-0001-1} it calls the Assign procedure with L as the Target parameter; or
65.a.1/3
Ramification: We don't need to explicitly mention assignment_statement, because that finalizes the target object as part of the operation, and finalization of an object is already defined as tampering with cursors.
66/2
it calls the Move procedure with L as a parameter. 
66.a/2
Reason: Swap copies elements rather than reordering them, so it doesn't tamper with cursors. 
67/2
 {AI95-00302-03} A subprogram is said to tamper with elements of a list object L if:
68/2
it tampers with cursors of L; or
69/2
it replaces one or more elements of L, that is, it calls the Replace_Element or Swap procedures with L as a parameter.
69.a/2
Reason: Complete replacement of an element can cause its memory to be deallocated while another operation is holding onto a reference to it. That can't be allowed. However, a simple modification of (part of) an element is not a problem, so Update_Element does not cause a problem. 
69.1/4
   {AI05-0265-1} {AI12-0110-1} When tampering with cursors is prohibited for a particular list object L, Program_Error is propagated by a call of any language-defined subprogram that is defined to tamper with the cursors of L, leaving L unmodified. Similarly, when tampering with elements is prohibited for a particular list object L, Program_Error is propagated by a call of any language-defined subprogram that is defined to tamper with the elements of L [(or tamper with the cursors of L)], leaving L unmodified. These checks are made before any other defined behavior of the body of the language-defined subprogram. 
69.b/3
Proof: Tampering with elements includes tampering with cursors, so we mention it only from completeness in the second sentence. 
69.2/3
function Has_Element (Position : Cursor) return Boolean;
69.3/3
{AI05-0212-1} Returns True if Position designates an element, and returns False otherwise.
69.c/3
To be honest: {AI05-0005-1} {AI05-0212-1} This function might not detect cursors that designate deleted elements; such cursors are invalid (see below) and the result of calling Has_Element with an invalid cursor is unspecified (but not erroneous). 
70/2
function "=" (Left, Right : List) return Boolean;
71/3
{AI95-00302-03} {AI05-0264-1} If Left and Right denote the same list object, then the function returns True. If Left and Right have different lengths, then the function returns False. Otherwise, it compares each element in Left to the corresponding element in Right using the generic formal equality operator. If any such comparison returns False, the function returns False; otherwise, it returns True. Any exception raised during evaluation of element equality is propagated.
71.a/2
Implementation Note: This wording describes the canonical semantics. However, the order and number of calls on the formal equality function is unspecified for all of the operations that use it in this package, so an implementation can call it as many or as few times as it needs to get the correct answer. Specifically, there is no requirement to call the formal equality additional times once the answer has been determined. 
72/2
function Length (Container : List) return Count_Type;
73/2
{AI95-00302-03} Returns the number of elements in Container.
74/2
function Is_Empty (Container : List) return Boolean;
75/2
{AI95-00302-03} Equivalent to Length (Container) = 0.
76/2
procedure Clear (Container : in out List);
77/2
{AI95-00302-03} Removes all the elements from Container.
78/2
function Element (Position : Cursor) return Element_Type;
79/2
{AI95-00302-03} If Position equals No_Element, then Constraint_Error is propagated. Otherwise, Element returns the element designated by Position.
80/2
procedure Replace_Element (Container : in out List;
                           Position  : in     Cursor;
                           New_Item  : in     Element_Type);
81/3
{AI95-00302-03} {AI05-0264-1} If Position equals No_Element, then Constraint_Error is propagated; if Position does not designate an element in Container, then Program_Error is propagated. Otherwise, Replace_Element assigns the value New_Item to the element designated by Position.
82/2
procedure Query_Element
  (Position : in Cursor;
   Process  : not null access procedure (Element : in Element_Type));
83/3
{AI95-00302-03} {AI05-0021-1} {AI05-0265-1} If Position equals No_Element, then Constraint_Error is propagated. Otherwise, Query_Element calls Process.all with the element designated by Position as the argument. Tampering with the elements of the list that contains the element designated by Position is prohibited during the execution of the call on Process.all. Any exception raised by Process.all is propagated.
84/2
procedure Update_Element
  (Container : in out List;
   Position  : in     Cursor;
   Process   : not null access procedure (Element : in out Element_Type));
85/3
{AI95-00302-03} {AI05-0264-1} {AI05-0265-1} If Position equals No_Element, then Constraint_Error is propagated; if Position does not designate an element in Container, then Program_Error is propagated. Otherwise, Update_Element calls Process.all with the element designated by Position as the argument. Tampering with the elements of Container is prohibited during the execution of the call on Process.all. Any exception raised by Process.all is propagated.
86/2
If Element_Type is unconstrained and definite, then the actual Element parameter of Process.all shall be unconstrained.
86.a/2
Ramification: This means that the elements cannot be directly allocated from the heap; it must be possible to change the discriminants of the element in place. 
86.1/3
type Constant_Reference_Type
      (Element : not null access constant Element_Type) is private
   with Implicit_Dereference => Element;
86.2/3
type Reference_Type (Element : not null access Element_Type) is private
   with Implicit_Dereference => Element;
86.3/3
{AI05-0212-1} The types Constant_Reference_Type and Reference_Type need finalization.
86.4/3
The default initialization of an object of type Constant_Reference_Type or Reference_Type propagates Program_Error.
86.b/3
Reason: It is expected that Reference_Type (and Constant_Reference_Type) will be a controlled type, for which finalization will have some action to terminate the tampering check for the associated container. If the object is created by default, however, there is no associated container. Since this is useless, and supporting this case would take extra work, we define it to raise an exception. 
86.5/3
function Constant_Reference (Container : aliased in List;
                             Position  : in Cursor)
   return Constant_Reference_Type;
86.6/3
{AI05-0212-1} {AI05-0269-1} This function (combined with the Constant_Indexing and Implicit_Dereference aspects) provides a convenient way to gain read access to an individual element of a list given a cursor.
86.7/3
{AI05-0212-1} {AI05-0265-1} If Position equals No_Element, then Constraint_Error is propagated; if Position does not designate an element in Container, then Program_Error is propagated. Otherwise, Constant_Reference returns an object whose discriminant is an access value that designates the element designated by Position. Tampering with the elements of Container is prohibited while the object returned by Constant_Reference exists and has not been finalized.
86.8/3
function Reference (Container : aliased in out List;
                    Position  : in Cursor)
   return Reference_Type;
86.9/3
{AI05-0212-1} {AI05-0269-1} This function (combined with the Variable_Indexing and Implicit_Dereference aspects) provides a convenient way to gain read and write access to an individual element of a list given a cursor.
86.10/3
{AI05-0212-1} {AI05-0265-1} If Position equals No_Element, then Constraint_Error is propagated; if Position does not designate an element in Container, then Program_Error is propagated. Otherwise, Reference returns an object whose discriminant is an access value that designates the element designated by Position. Tampering with the elements of Container is prohibited while the object returned by Reference exists and has not been finalized.
86.11/3
procedure Assign (Target : in out List; Source : in List);
86.12/3
{AI05-0001-1} {AI05-0248-1} If Target denotes the same object as Source, the operation has no effect. Otherwise, the elements of Source are copied to Target as for an assignment_statement assigning Source to Target. 
86.c/3
Discussion: {AI05-0005-1} This routine exists for compatibility with the bounded list container. For an unbounded list, Assign(A, B) and A := B behave identically. For a bounded list, := will raise an exception if the container capacities are different, while Assign will not raise an exception if there is enough room in the target. 
86.13/3
function Copy (Source : List) return List;
86.14/3
{AI05-0001-1} Returns a list whose elements match the elements of Source.
87/2
procedure Move (Target : in out List;
                Source : in out List);
88/3
{AI95-00302-03} {AI05-0001-1} {AI05-0248-1} {AI05-0262-1} If Target denotes the same object as Source, then the operation has no effect. Otherwise, the operation is equivalent to Assign (Target, Source) followed by Clear (Source).
89/2
procedure Insert (Container : in out List;
                  Before    : in     Cursor;
                  New_Item  : in     Element_Type;
                  Count     : in     Count_Type := 1);
90/2
{AI95-00302-03} If Before is not No_Element, and does not designate an element in Container, then Program_Error is propagated. Otherwise, Insert inserts Count copies of New_Item prior to the element designated by Before. If Before equals No_Element, the new elements are inserted after the last node (if any). Any exception raised during allocation of internal storage is propagated, and Container is not modified.
90.a/2
Ramification: The check on Before checks that the cursor does not belong to some other Container. This check implies that a reference to the container is included in the cursor value. This wording is not meant to require detection of dangling cursors; such cursors are defined to be invalid, which means that execution is erroneous, and any result is allowed (including not raising an exception). 
91/2
procedure Insert (Container : in out List;
                  Before    : in     Cursor;
                  New_Item  : in     Element_Type;
                  Position  :    out Cursor;
                  Count     : in     Count_Type := 1);
92/3
{AI95-00302-03} {AI05-0257-1} If Before is not No_Element, and does not designate an element in Container, then Program_Error is propagated. Otherwise, Insert allocates Count copies of New_Item, and inserts them prior to the element designated by Before. If Before equals No_Element, the new elements are inserted after the last element (if any). Position designates the first newly-inserted element, or if Count equals 0, then Position is assigned the value of Before. Any exception raised during allocation of internal storage is propagated, and Container is not modified.
93/2
procedure Insert (Container : in out List;
                  Before    : in     Cursor;
                  Position  :    out Cursor;
                  Count     : in     Count_Type := 1);
94/3
{AI95-00302-03} {AI05-0257-1} If Before is not No_Element, and does not designate an element in Container, then Program_Error is propagated. Otherwise, Insert inserts Count new elements prior to the element designated by Before. If Before equals No_Element, the new elements are inserted after the last node (if any). The new elements are initialized by default (see 3.3.1). Position designates the first newly-inserted element, or if Count equals 0, then Position is assigned the value of Before. Any exception raised during allocation of internal storage is propagated, and Container is not modified.
95/2
procedure Prepend (Container : in out List;
                   New_Item  : in     Element_Type;
                   Count     : in     Count_Type := 1);
96/2
{AI95-00302-03} Equivalent to Insert (Container, First (Container), New_Item, Count).
97/2
procedure Append (Container : in out List;
                  New_Item  : in     Element_Type;
                  Count     : in     Count_Type := 1);
98/2
{AI95-00302-03} Equivalent to Insert (Container, No_Element, New_Item, Count).
99/2
procedure Delete (Container : in out List;
                  Position  : in out Cursor;
                  Count     : in     Count_Type := 1);
100/3
{AI95-00302-03} {AI05-0264-1} If Position equals No_Element, then Constraint_Error is propagated. If Position does not designate an element in Container, then Program_Error is propagated. Otherwise, Delete removes (from Container) Count elements starting at the element designated by Position (or all of the elements starting at Position if there are fewer than Count elements starting at Position). Finally, Position is set to No_Element.
101/2
procedure Delete_First (Container : in out List;
                        Count     : in     Count_Type := 1);
102/3
{AI95-00302-03} {AI05-0021-1} If Length (Container) <= Count, then Delete_First is equivalent to Clear (Container). Otherwise, it removes the first Count nodes from Container.
103/2
procedure Delete_Last (Container : in out List;
                       Count     : in     Count_Type := 1);
104/3
{AI95-00302-03} {AI05-0264-1} If Length (Container) <= Count, then Delete_Last is equivalent to Clear (Container). Otherwise, it removes the last Count nodes from Container.
105/2
procedure Reverse_Elements (Container : in out List);
106/2
{AI95-00302-03} Reorders the elements of Container in reverse order.
106.a/2
Discussion: Unlike the similar routine for a vector, elements should not be copied; rather, the nodes should be exchanged. Cursors are expected to reference the same elements afterwards.
107/2
procedure Swap (Container : in out List;
                I, J      : in     Cursor);
108/2
{AI95-00302-03} If either I or J is No_Element, then Constraint_Error is propagated. If either I or J do not designate an element in Container, then Program_Error is propagated. Otherwise, Swap exchanges the values of the elements designated by I and J.
108.a/2
Ramification: After a call to Swap, I designates the element value previously designated by J, and J designates the element value previously designated by I. The cursors do not become ambiguous from this operation. 
108.b/2
To be honest: The implementation is not required to actually copy the elements if it can do the swap some other way. But it is allowed to copy the elements if needed. 
109/2
procedure Swap_Links (Container : in out List;
                      I, J      : in     Cursor);
110/2
{AI95-00302-03} If either I or J is No_Element, then Constraint_Error is propagated. If either I or J do not designate an element in Container, then Program_Error is propagated. Otherwise, Swap_Links exchanges the nodes designated by I and J.
110.a/2
Ramification: Unlike Swap, this exchanges the nodes, not the elements. No copying is performed. I and J designate the same elements after this call as they did before it. This operation can provide better performance than Swap if the element size is large.
111/2
procedure Splice (Target   : in out List;
                  Before   : in     Cursor;
                  Source   : in out List);
112/2
{AI95-00302-03} If Before is not No_Element, and does not designate an element in Target, then Program_Error is propagated. Otherwise, if Source denotes the same object as Target, the operation has no effect. Otherwise, Splice reorders elements such that they are removed from Source and moved to Target, immediately prior to Before. If Before equals No_Element, the nodes of Source are spliced after the last node of Target. The length of Target is incremented by the number of nodes in Source, and the length of Source is set to 0.
113/2
procedure Splice (Target   : in out List;
                  Before   : in     Cursor;
                  Source   : in out List;
                  Position : in out Cursor);
114/3
{AI95-00302-03} {AI05-0264-1} If Position is No_Element, then Constraint_Error is propagated. If Before does not equal No_Element, and does not designate an element in Target, then Program_Error is propagated. If Position does not equal No_Element, and does not designate a node in Source, then Program_Error is propagated. If Source denotes the same object as Target, then there is no effect if Position equals Before, else the element designated by Position is moved immediately prior to Before, or, if Before equals No_Element, after the last element. In both cases, Position and the length of Target are unchanged. Otherwise, the element designated by Position is removed from Source and moved to Target, immediately prior to Before, or, if Before equals No_Element, after the last element of Target. The length of Target is incremented, the length of Source is decremented, and Position is updated to represent an element in Target. 
114.a/2
Ramification: If Source is the same as Target, and Position = Before, or Next(Position) = Before, Splice has no effect, as the element does not have to move to meet the postcondition.
115/2
procedure Splice (Container: in out List;
                  Before   : in     Cursor;
                  Position : in     Cursor);
116/3
{AI95-00302-03} {AI05-0264-1} If Position is No_Element, then Constraint_Error is propagated. If Before does not equal No_Element, and does not designate an element in Container, then Program_Error is propagated. If Position does not equal No_Element, and does not designate a node in Container, then Program_Error is propagated. If Position equals Before there is no effect. Otherwise, the element designated by Position is moved immediately prior to Before, or, if Before equals No_Element, after the last element. The length of Container is unchanged.
117/2
function First (Container : List) return Cursor;
118/3
{AI95-00302-03} {AI05-0264-1} If Container is empty, First returns the value No_Element. Otherwise, it returns a cursor that designates the first node in Container.
119/2
function First_Element (Container : List) return Element_Type;
120/2
{AI95-00302-03} Equivalent to Element (First (Container)).
121/2
function Last (Container : List) return Cursor;
122/3
{AI95-00302-03} {AI05-0264-1} If Container is empty, Last returns the value No_Element. Otherwise, it returns a cursor that designates the last node in Container.
123/2
function Last_Element (Container : List) return Element_Type;
124/2
{AI95-00302-03} Equivalent to Element (Last (Container)).
125/2
function Next (Position : Cursor) return Cursor;
126/2
{AI95-00302-03} If Position equals No_Element or designates the last element of the container, then Next returns the value No_Element. Otherwise, it returns a cursor that designates the successor of the element designated by Position.
127/2
function Previous (Position : Cursor) return Cursor;
128/2
{AI95-00302-03} If Position equals No_Element or designates the first element of the container, then Previous returns the value No_Element. Otherwise, it returns a cursor that designates the predecessor of the element designated by Position.
129/2
procedure Next (Position : in out Cursor);
130/2
{AI95-00302-03} Equivalent to Position := Next (Position).
131/2
procedure Previous (Position : in out Cursor);
132/2
{AI95-00302-03} Equivalent to Position := Previous (Position).
133/2
function Find (Container : List;
               Item      : Element_Type;
               Position  : Cursor := No_Element)
  return Cursor;
134/2
{AI95-00302-03} If Position is not No_Element, and does not designate an element in Container, then Program_Error is propagated. Find searches the elements of Container for an element equal to Item (using the generic formal equality operator). The search starts at the element designated by Position, or at the first element if Position equals No_Element. It proceeds towards Last (Container). If no equal element is found, then Find returns No_Element. Otherwise, it returns a cursor designating the first equal element encountered.
135/2
function Reverse_Find (Container : List;
                       Item      : Element_Type;
                       Position  : Cursor := No_Element)
   return Cursor;
136/2
{AI95-00302-03} If Position is not No_Element, and does not designate an element in Container, then Program_Error is propagated. Find searches the elements of Container for an element equal to Item (using the generic formal equality operator). The search starts at the element designated by Position, or at the last element if Position equals No_Element. It proceeds towards First (Container). If no equal element is found, then Reverse_Find returns No_Element. Otherwise, it returns a cursor designating the first equal element encountered.
137/2
function Contains (Container : List;
                   Item      : Element_Type) return Boolean;
138/2
{AI95-00302-03} Equivalent to Find (Container, Item) /= No_Element.
139/3
140/3
{AI95-00302-03} {AI05-0212-1}
140.a/3
{AI05-0212-1}
Paragraphs 139 and 140 were moved above. 
141/2
procedure Iterate
  (Container : in List;
   Process   : not null access procedure (Position : in Cursor));
142/3
{AI95-00302-03} {AI05-0265-1} Iterate calls Process.all with a cursor that designates each node in Container, starting with the first node and moving the cursor as per the Next function. Tampering with the cursors of Container is prohibited during the execution of a call on Process.all. Any exception raised by Process.all is propagated.
142.a/2
Implementation Note: The purpose of the tamper with cursors check is to prevent erroneous execution from the Position parameter of Process.all becoming invalid. This check takes place when the operations that tamper with the cursors of the container are called. The check cannot be made later (say in the body of Iterate), because that could cause the Position cursor to be invalid and potentially cause execution to become erroneous -- defeating the purpose of the check.
142.b/2
See Iterate for vectors (A.18.2) for a suggested implementation of the check. 
143/2
procedure Reverse_Iterate
  (Container : in List;
   Process   : not null access procedure (Position : in Cursor));
144/3
{AI95-00302-03} {AI05-0212-1} Iterates over the nodes in Container as per procedure Iterate, except that elements are traversed in reverse order, starting with the last node and moving the cursor as per the Previous function.
144.1/3
function Iterate (Container : in List)
   return List_Iterator_Interfaces.Reversible_Iterator'Class;
144.2/3
{AI05-0212-1} {AI05-0265-1} {AI05-0269-1} 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 node in Container, starting with the first node and moving the cursor as per the Next function when used as a forward iterator, and starting with the last node and moving the cursor as per the Previous function 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.
144.3/3
function Iterate (Container : in List; Start : in Cursor)
   return List_Iterator_Interfaces.Reversible_Iterator'Class;
144.4/3
{AI05-0212-1} {AI05-0262-1} {AI05-0265-1} {AI05-0269-1} 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 node in Container, starting with the node designated by Start and moving the cursor as per the Next function when used as a forward iterator, or moving the cursor as per the Previous function 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.
144.a/3
Discussion: Exits are allowed from the loops created using the iterator objects. In particular, to stop the iteration at a particular cursor, just add
144.b/3
exit when Cur = Stop;
144.c/3
in the body of the loop (assuming that Cur is the loop parameter and Stop is the cursor that you want to stop at). 
145/3
  {AI05-0044-1} {AI05-0262-1} The actual function for the generic formal function "<" of Generic_Sorting is expected to return the same value each time it is called with a particular pair of element values. It should define a strict weak ordering relationship (see A.18); it should not modify Container. If the actual for "<" behaves in some other manner, the behavior of the subprograms of Generic_Sorting are unspecified. The number of times the subprograms of Generic_Sorting call "<" is unspecified.
146/2
function Is_Sorted (Container : List) return Boolean;
147/2
{AI95-00302-03} Returns True if the elements are sorted smallest first as determined by the generic formal "<" operator; otherwise, Is_Sorted returns False. Any exception raised during evaluation of "<" is propagated.
148/2
procedure Sort (Container : in out List);
149/2
{AI95-00302-03} Reorders the nodes of Container such that the elements are sorted smallest first as determined by the generic formal "<" operator provided. The sort is stable. Any exception raised during evaluation of "<" is propagated.
149.a/2
Ramification: Unlike array sorts, we do require stable sorts here. That's because algorithms in the merge sort family (as described by Knuth) can be both fast and stable. Such sorts use the extra memory as offered by the links to provide better performance.
149.b/2
Note that list sorts never copy elements; it is the nodes, not the elements, that are reordered. 
150/2
procedure Merge (Target  : in out List;
                 Source  : in out List);
151/3
{AI95-00302-03} {AI05-0021-1} If Source is empty, then Merge does nothing. If Source and Target are the same nonempty container object, then Program_Error is propagated. Otherwise, Merge removes elements from Source and inserts them into Target; afterwards, Target contains the union of the elements that were initially in Source and Target; Source is left empty. If Target and Source are initially sorted smallest first, then Target is ordered smallest first as determined by the generic formal "<" operator; otherwise, the order of elements in Target is unspecified. Any exception raised during evaluation of "<" is propagated.
151.a/2
Ramification: It is a bounded error if either of the lists is unsorted, see below. The bounded error can be recovered by sorting Target after the merge call, or the lists can be pretested with Is_Sorted. 

Bounded (Run-Time) Errors

152/2
  {AI95-00302-03} Calling Merge in an instance of Generic_Sorting with either Source or Target not ordered smallest first using the provided generic formal "<" operator is a bounded error. Either Program_Error is raised after Target is updated as described for Merge, or the operation works as defined.
152.1/3
    {AI05-0022-1} {AI05-0248-1} It is a bounded error for the actual function associated with a generic formal subprogram, when called as part of an operation of this package, to tamper with elements of any List parameter of the operation. Either Program_Error is raised, or the operation works as defined on the value of the List either prior to, or subsequent to, some or all of the modifications to the List.
152.2/3
    {AI05-0027-1} It is a bounded error to call any subprogram declared in the visible part of Containers.Doubly_Linked_Lists when the associated container has been finalized. If the operation takes Container as an in out parameter, then it raises Constraint_Error or Program_Error. Otherwise, the operation either proceeds as it would for an empty container, or it raises Constraint_Error or Program_Error. 

Erroneous Execution

153/2
  {AI95-00302-03} A Cursor value is invalid if any of the following have occurred since it was created:
154/2
The list that contains the element it designates has been finalized;
154.1/3
{AI05-0160-1} The list that contains the element it designates has been used as the Target of a call to Assign, or as the target of an assignment_statement;
155/2
[The list that contains the element it designates has been used as the Source or Target of a call to Move;] or 
155.a/3
Proof: {AI05-0001-1} Move has been reworded in terms of Assign and Clear, which are covered by other bullets, so this text is redundant. 
156/3
{AI05-0160-1} {AI05-0262-1} The element it designates has been removed from the list that previously contained the element. 
156.a/3
To be honest: {AI05-0160-1} The cursor modified by the four parameter Splice is not invalid, even though the element it designates has been removed from the source list, because that cursor has been modified to designate that element in the target list – the cursor no longer designates an element in the source list. 
156.b/3
Ramification: {AI05-0160-1} This can happen directly via calls to Delete, Delete_Last, Clear, Splice with a Source parameter, and Merge; and indirectly via calls to Delete_First, Assign, and Move. 
157/2
  {AI95-00302-03} The result of "=" or Has_Element is unspecified if it is called with an invalid cursor parameter. Execution is erroneous if any other subprogram declared in Containers.Doubly_Linked_Lists is called with an invalid cursor parameter.
157.a/2
Discussion: The list above is intended to be exhaustive. In other cases, a cursor value continues to designate its original element. For instance, cursor values survive the insertion and deletion of other nodes.
157.b/2
While it is possible to check for these cases, in many cases the overhead necessary to make the check is substantial in time or space. Implementations are encouraged to check for as many of these cases as possible and raise Program_Error if detected. 
157.1/3
    {AI05-0212-1} Execution is erroneous if the list associated with the result of a call to Reference or Constant_Reference is finalized before the result object returned by the call to Reference or Constant_Reference is finalized.
157.c/3
Reason: Each object of Reference_Type and Constant_Reference_Type probably contains some reference to the originating container. If that container is prematurely finalized (which is only possible via Unchecked_Deallocation, as accessibility checks prevent passing a container to Reference that will not live as long as the result), the finalization of the object of Reference_Type will try to access a nonexistent object. This is a normal case of a dangling pointer created by Unchecked_Deallocation; we have to explicitly mention it here as the pointer in question is not visible in the specification of the type. (This is the same reason we have to say this for invalid cursors.) 

Implementation Requirements

158/2
  {AI95-00302-03} No storage associated with a doubly-linked List object shall be lost upon assignment or scope exit.
159/3
  {AI95-00302-03} {AI05-0262-1} The execution of an assignment_statement for a list shall have the effect of copying the elements from the source list object to the target list object and changing the length of the target object to that of the source object.
159.a/3
Implementation Note: {AI05-0298-1} An assignment of a List is a “deep” copy; that is the elements are copied as well as the data structures. We say “effect of” in order to allow the implementation to avoid copying elements immediately if it wishes. For instance, an implementation that avoided copying until one of the containers is modified would be allowed. (Note that this implementation would require care, see A.18.2 for more.)

Implementation Advice

160/2
  {AI95-00302-03} Containers.Doubly_Linked_Lists should be implemented similarly to a linked list. In particular, if N is the length of a list, then the worst-case time complexity of Element, Insert with Count=1, and Delete with Count=1 should be O(log N). 
160.a/2
Implementation Advice: The worst-case time complexity of Element, Insert with Count=1, and Delete with Count=1 for Containers.Doubly_Linked_Lists should be O(log N).
160.b/2
Reason: We do not mean to overly constrain implementation strategies here. However, it is important for portability that the performance of large containers has roughly the same factors on different implementations. If a program is moved to an implementation that takes O(N) time to access elements, that program could be unusable when the lists are large. We allow O(log N) access because the proportionality constant and caching effects are likely to be larger than the log factor, and we don't want to discourage innovative implementations. 
161/2
  {AI95-00302-03} The worst-case time complexity of a call on procedure Sort of an instance of Containers.Doubly_Linked_Lists.Generic_Sorting should be O(N**2), and the average time complexity should be better than O(N**2).
161.a/2
Implementation Advice: A call on procedure Sort of an instance of Containers.Doubly_Linked_Lists.Generic_Sorting should have an average time complexity better than O(N**2) and worst case no worse than O(N**2).
161.b/2
Ramification: In other words, we're requiring the use of a better than O(N**2) sorting algorithm, such as Quicksort. No bubble sorts allowed! 
162/2
  {AI95-00302-03} Move should not copy elements, and should minimize copying of internal data structures. 
162.a/2
Implementation Advice: Containers.Doubly_Linked_Lists.Move should not copy elements, and should minimize copying of internal data structures.
162.b/2
Implementation Note: Usually that can be accomplished simply by moving the pointer(s) to the internal data structures from the Source container to the Target container. 
163/2
  {AI95-00302-03} If an exception is propagated from a list operation, no storage should be lost, nor any elements removed from a list unless specified by the operation. 
163.a/2
Implementation Advice: If an exception is propagated from a list operation, no storage should be lost, nor any elements removed from a list unless specified by the operation.
163.b/2
Reason: This is important so that programs can recover from errors. But we don't want to require heroic efforts, so we just require documentation of cases where this can't be accomplished.
NOTES
164/2
50  {AI95-00302-03} Sorting a list never copies elements, and is a stable sort (equal elements remain in the original order). This is different than sorting an array or vector, which may need to copy elements, and is probably not a stable sort. 

Extensions to Ada 95

164.a/2
{AI95-00302-03} The generic package Containers.Doubly_Linked_Lists is new. 

Inconsistencies With Ada 2005

164.b/3
{AI05-0248-1} {AI05-0257-1} Correction: The Insert versions that return a Position parameter are now defined to return Position = Before if Count = 0. This was unspecified for Ada 2005; so this will only be inconsistent if an implementation did something else and a program depended on that something else — this should be very rare. 

Incompatibilities With Ada 2005

164.c/3
{AI05-0001-1} Subprograms Assign and Copy are added to Containers.Doubly_Linked_Lists. If an instance of Containers.Doubly_Linked_Lists is referenced in a use_clause, and an entity E with the same defining_identifier as a new entity in Containers.Doubly_Linked_Lists is defined in a package that is also referenced in a use_clause, the entity E may no longer be use-visible, resulting in errors. This should be rare and is easily fixed if it does occur. 

Extensions to Ada 2005

164.d/3
{AI05-0212-1} Added iterator, reference, and indexing support to make list containers more convenient to use. 

Wording Changes from Ada 2005

164.e/3
{AI05-0001-1} Generalized the definition of Move. Specified which elements are read/written by stream attributes.
164.f/3
{AI05-0022-1} Correction: Added a Bounded (Run-Time) Error to cover tampering by generic actual subprograms.
164.g/3
{AI05-0027-1} Correction: Added a Bounded (Run-Time) Error to cover access to finalized list containers.
164.h/3
{AI05-0044-1} Correction: Redefined "<" actuals to require a strict weak ordering; the old definition allowed indeterminant comparisons that would not have worked in a container.
164.i/3
{AI05-0084-1} Correction: Added a pragma Remote_Types so that containers can be used in distributed programs.
164.j/3
{AI05-0160-1} Correction: Revised the definition of invalid cursors to cover missing (and new) cases.
164.k/3
{AI05-0257-1} Correction: Added missing wording to describe the Position after Inserting 0 elements.
164.l/3
{AI05-0265-1} Correction: Defined when a container prohibits tampering in order to more clearly define where the check is made and the exception raised.

Wording Changes from Ada 2012

164.m/4
{AI12-0110-1} Corrigendum: Clarified that tampering checks precede all other checks made by a subprogram (but come after those associated with the call). 

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