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 A.18.6 The Package Containers.Ordered_Maps

Static Semantics

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{AI95-00302-03} The generic library package Containers.Ordered_Maps has the following declaration: 
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generic
   type Key_Type is private;
   type Element_Type is private;
   with function "<" (Left, Right : Key_Type) return Boolean is <>;
   with function "=" (Left, Right : Element_Type) return Boolean is <>;
package Ada.Containers.Ordered_Maps is
   pragma Preelaborate(Ordered_Maps);
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   function Equivalent_Keys (Left, Right : Key_Type) return Boolean;
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   type Map is tagged private;
   pragma Preelaborable_Initialization(Map);
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   type Cursor is private;
   pragma Preelaborable_Initialization(Cursor);
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   Empty_Map : constant Map;
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   No_Element : constant Cursor;
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   function "=" (Left, Right : Map) return Boolean;
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   function Length (Container : Map) return Count_Type;
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   function Is_Empty (Container : Map) return Boolean;
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   procedure Clear (Container : in out Map);
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   function Key (Position : Cursor) return Key_Type;
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   function Element (Position : Cursor) return Element_Type;
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   procedure Replace_Element (Container : in out Map;
                              Position  : in     Cursor;
                              New_Item  : in     Element_Type);
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   procedure Query_Element
     (Position : in Cursor;
      Process  : not null access procedure (Key     : in Key_Type;
                                            Element : in Element_Type));
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   procedure Update_Element
     (Container : in out Map;
      Position  : in     Cursor;
      Process   : not null access procedure
                      (Key     : in     Key_Type;
                       Element : in out Element_Type));
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   procedure Move (Target : in out Map;
                   Source : in out Map);
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   procedure Insert (Container : in out Map;
                     Key       : in     Key_Type;
                     New_Item  : in     Element_Type;
                     Position  :    out Cursor;
                     Inserted  :    out Boolean);
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   procedure Insert (Container : in out Map;
                     Key       : in     Key_Type;
                     Position  :    out Cursor;
                     Inserted  :    out Boolean);
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   procedure Insert (Container : in out Map;
                     Key       : in     Key_Type;
                     New_Item  : in     Element_Type);
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   procedure Include (Container : in out Map;
                      Key       : in     Key_Type;
                      New_Item  : in     Element_Type);
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   procedure Replace (Container : in out Map;
                      Key       : in     Key_Type;
                      New_Item  : in     Element_Type);
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   procedure Exclude (Container : in out Map;
                      Key       : in     Key_Type);
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   procedure Delete (Container : in out Map;
                     Key       : in     Key_Type);
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   procedure Delete (Container : in out Map;
                     Position  : in out Cursor);
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   procedure Delete_First (Container : in out Map);
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   procedure Delete_Last (Container : in out Map);
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   function First (Container : Map) return Cursor;
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   function First_Element (Container : Map) return Element_Type;
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   function First_Key (Container : Map) return Key_Type;
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   function Last (Container : Map) return Cursor;
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   function Last_Element (Container : Map) return Element_Type;
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   function Last_Key (Container : Map) return Key_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 : Map;
                  Key       : Key_Type) return Cursor;
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   function Element (Container : Map;
                     Key       : Key_Type) return Element_Type;
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   function Floor (Container : Map;
                   Key       : Key_Type) return Cursor;
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   function Ceiling (Container : Map;
                     Key       : Key_Type) return Cursor;
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   function Contains (Container : Map;
                      Key       : Key_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 : Key_Type) return Boolean;
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   function ">" (Left : Cursor; Right : Key_Type) return Boolean;
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   function "<" (Left : Key_Type; Right : Cursor) return Boolean;
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   function ">" (Left : Key_Type; Right : Cursor) return Boolean;
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   procedure Iterate
     (Container : in Map;
      Process   : not null access procedure (Position : in Cursor));
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   procedure Reverse_Iterate
     (Container : in Map;
      Process   : not null access procedure (Position : in Cursor));
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private
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   ... -- not specified by the language
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end Ada.Containers.Ordered_Maps;
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 {AI95-00302-03} {equivalent key (of an ordered map)} Two keys K1 and K2 are equivalent if both K1 < K2 and K2 < K1 return False, using the generic formal "<" operator for keys. Function Equivalent_Keys returns True if Left and Right are equivalent, and False otherwise.
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 {AI95-00302-03} The actual function for the generic formal function "<" on Key_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.{unspecified [partial]}
56.a/2
Implementation Note: The implementation is not required to protect against "<" raising an exception, or returning random results, or any other “bad” behavior. It's not practical to do so, and a broken "<" function makes the container unusable.
56.b/2
The implementation can call "<" whenever it is needed; we don't want to specify how often that happens. The result must remain the same (this is a logically pure function), or the behavior is unspecified. 
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 {AI95-00302-03} If the value of a key stored in a map 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.{unspecified [partial]}
57.a/2
Implementation Note: The implementation is not required to protect against changes to key values other than via the operations declared in the Ordered_Maps package.
57.b/2
To see how this could happen, imagine an instance of Ordered_Maps package where the key type is an access-to-variable type and "<" returns a value derived from comparing the components of the designated objects. Then, any operation that has a key value (even if the key value is constant) could modify those components and change the result of "<":
57.c/2
Key (Map).Some_Component := New_Value;
57.d/2
This is really a design error on the part of the user of the map; it shouldn't be possible to modify keys stored in a map such that "<" changes. But we can't prevent this error anymore than we can prevent someone passing as "<" a routine that produces random answers. 
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 {AI95-00302-03} {first node (of an ordered map)} {last node (of an ordered map)} {successor node (of an ordered map)} The first node of a nonempty map is the one whose key is less than the key of all the other nodes in the map. The last node of a nonempty map is the one whose key is greater than the key of all the other elements in the map. The successor of a node is the node with the smallest key that is larger than the key of the given node. The predecessor of a node is the node with the largest key that is smaller than the key of the given node. All comparisons are done using the generic formal "<" operator for keys.
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procedure Delete_First (Container : in out Map);
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{AI95-00302-03} If Container is empty, Delete_First has no effect. Otherwise the node 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 Map);
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{AI95-00302-03} If Container is empty, Delete_Last has no effect. Otherwise the node designated by Last (Container) is removed from Container. Delete_Last tampers with the cursors of Container.
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function First_Element (Container : Map) return Element_Type;
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{AI95-00302-03} Equivalent to Element (First (Container)).
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function First_Key (Container : Map) return Key_Type;
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{AI95-00302-03} Equivalent to Key (First (Container)).
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function Last (Container : Map) return Cursor;
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{AI95-00302-03} Returns a cursor that designates the last node in Container. If Container is empty, returns No_Element.
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function Last_Element (Container : Map) return Element_Type;
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{AI95-00302-03} Equivalent to Element (Last (Container)).
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function Last_Key (Container : Map) return Key_Type;
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{AI95-00302-03} Equivalent to Key (Last (Container)).
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function Previous (Position : Cursor) return Cursor;
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{AI95-00302-03} If Position equals No_Element, then Previous returns No_Element. Otherwise Previous returns a cursor designating the node 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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{AI95-00302-03} Equivalent to Position := Previous (Position).
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function Floor (Container : Map;
                Key       : Key_Type) return Cursor;
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{AI95-00302-03} Floor searches for the last node whose key is not greater than Key, using the generic formal "<" operator for keys. If such a node is found, a cursor that designates it is returned. Otherwise No_Element is returned.
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function Ceiling (Container : Map;
                  Key       : Key_Type) return Cursor;
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{AI95-00302-03} Ceiling searches for the first node whose key is not less than Key, using the generic formal "<" operator for keys. If such a node 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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{AI95-00302-03} Equivalent to Key (Left) < Key (Right).
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function ">" (Left, Right : Cursor) return Boolean;
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{AI95-00302-03} Equivalent to Key (Right) < Key (Left).
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function "<" (Left : Cursor; Right : Key_Type) return Boolean;
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{AI95-00302-03} Equivalent to Key (Left) < Right.
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function ">" (Left : Cursor; Right : Key_Type) return Boolean;
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{AI95-00302-03} Equivalent to Right < Key (Left).
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function "<" (Left : Key_Type; Right : Cursor) return Boolean;
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{AI95-00302-03} Equivalent to Left < Key (Right).
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function ">" (Left : Key_Type; Right : Cursor) return Boolean;
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{AI95-00302-03} Equivalent to Key (Right) < Left.
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procedure Reverse_Iterate
  (Container : in Map;
   Process   : not null access procedure (Position : in Cursor));
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{AI95-00302-03} Iterates over the nodes in Container as per Iterate, with the difference that the nodes are traversed in predecessor order, starting with the last node.

Implementation Advice

95/2
 {AI95-00302-03} If N is the length of a map, then the worst-case time complexity of the Element, Insert, Include, Replace, Delete, Exclude and Find operations that take a key 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). 
95.a/2
Implementation Advice: The worst-case time complexity of Element, Insert, Include, Replace, Delete, Exclude and Find operations that take a key parameter for Containers.Ordered_Maps should be O((log N)**2) or better. The worst-case time complexity of the subprograms of Containers.Ordered_Maps that take a cursor parameter should be O(1).
95.b/2
Implementation Note: A balanced (red-black) tree for keys has O(log N) worst-case performance. Note that a O(N) worst-case implementation (like a list) would be wrong. 
95.c/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) to find elements, that program could be unusable when the maps are large. We allow the extra log N factors 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. 

Extensions to Ada 95

95.d/2
{AI95-00302-03} {extensions to Ada 95} The generic package Containers.Ordered_Maps is new. 

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