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--                                                                          --
--                         GNAT LIBRARY COMPONENTS                          --
--                                                                          --
--   A D A . C O N T A I N E R S . F O R M A L _ O R D E R E D _ M A P S    --
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--                                 S p e c                                  --
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-- This specification is derived from the Ada Reference Manual for use with --
-- GNAT. The copyright notice above, and the license provisions that follow --
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------------------------------------------------------------------------------

--  This spec is derived from package Ada.Containers.Bounded_Ordered_Maps in
--  the Ada 2012 RM. The modifications are meant to facilitate formal proofs by
--  making it easier to express properties, and by making the specification of
--  this unit compatible with SPARK 2014. Note that the API of this unit may be
--  subject to incompatible changes as SPARK 2014 evolves.

--  The modifications are:

--    A parameter for the container is added to every function reading the
--    content of a container: Key, Element, Next, Query_Element, Previous,
--    Has_Element, Iterate, Reverse_Iterate. This change is motivated by the
--    need to have cursors which are valid on different containers (typically a
--    container C and its previous version C'Old) for expressing properties,
--    which is not possible if cursors encapsulate an access to the underlying
--    container. The operators "<" and ">" that could not be modified that way
--    have been removed.

--    There are four new functions:

--      function Strict_Equal (Left, Right : Map) return Boolean;
--      function Overlap (Left, Right : Map) return Boolean;
--      function First_To_Previous  (Container : Map; Current : Cursor)
--         return Map;
--      function Current_To_Last (Container : Map; Current : Cursor)
--         return Map;

--    See detailed specifications for these subprograms

private with Ada.Containers.Red_Black_Trees;

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.Formal_Ordered_Maps with
  Pure,
  SPARK_Mode
is
   pragma Annotate (GNATprove, External_Axiomatization);
   pragma Annotate (CodePeer, Skip_Analysis);

   function Equivalent_Keys (Left, Right : Key_Type) return Boolean with
     Global => null;

   type Map (Capacity : Count_Type) is private with
     Iterable => (First       => First,
                  Next        => Next,
                  Has_Element => Has_Element,
                  Element     => Element),
     Default_Initial_Condition => Is_Empty (Map);
   pragma Preelaborable_Initialization (Map);

   type Cursor is private;
   pragma Preelaborable_Initialization (Cursor);

   Empty_Map : constant Map;

   No_Element : constant Cursor;

   function "=" (Left, Right : Map) return Boolean with
     Global => null;

   function Length (Container : Map) return Count_Type with
     Global => null;

   function Is_Empty (Container : Map) return Boolean with
     Global => null;

   procedure Clear (Container : in out Map) with
     Global => null;

   procedure Assign (Target : in out Map; Source : Map) with
     Global => null,
     Pre    => Target.Capacity >= Length (Source);

   function Copy (Source : Map; Capacity : Count_Type := 0) return Map with
     Global => null,
     Pre    => Capacity = 0 or else Capacity >= Source.Capacity;

   function Key (Container : Map; Position : Cursor) return Key_Type with
     Global => null,
     Pre    => Has_Element (Container, Position);

   function Element
     (Container : Map;
      Position  : Cursor) return Element_Type
   with
     Global => null,
     Pre    => Has_Element (Container, Position);

   procedure Replace_Element
     (Container : in out Map;
      Position  : Cursor;
      New_Item  : Element_Type)
   with
     Global => null,
     Pre    => Has_Element (Container, Position);

   procedure Move (Target : in out Map; Source : in out Map) with
     Global => null,
     Pre    => Target.Capacity >= Length (Source);

   procedure Insert
     (Container : in out Map;
      Key       : Key_Type;
      New_Item  : Element_Type;
      Position  : out Cursor;
      Inserted  : out Boolean)
   with
     Global => null,
     Pre    => Length (Container) < Container.Capacity;

   procedure Insert
     (Container : in out Map;
      Key       : Key_Type;
      New_Item  : Element_Type)
   with
     Global => null,
     Pre    => Length (Container) < Container.Capacity
                 and then (not Contains (Container, Key));

   procedure Include
     (Container : in out Map;
      Key       : Key_Type;
      New_Item  : Element_Type)
   with
     Global => null,
     Pre    => Length (Container) < Container.Capacity;

   procedure Replace
     (Container : in out Map;
      Key       : Key_Type;
      New_Item  : Element_Type)
   with
     Global => null,
     Pre    => Contains (Container, Key);

   procedure Exclude (Container : in out Map; Key : Key_Type) with
     Global => null;

   procedure Delete (Container : in out Map; Key : Key_Type) with
     Global => null,
     Pre    => Contains (Container, Key);

   procedure Delete (Container : in out Map; Position : in out Cursor) with
     Global => null,
     Pre    => Has_Element (Container, Position);

   procedure Delete_First (Container : in out Map) with
     Global => null;

   procedure Delete_Last (Container : in out Map) with
     Global => null;

   function First (Container : Map) return Cursor with
     Global => null;

   function First_Element (Container : Map) return Element_Type with
     Global => null,
     Pre    => not Is_Empty (Container);

   function First_Key (Container : Map) return Key_Type with
     Global => null,
     Pre    => not Is_Empty (Container);

   function Last (Container : Map) return Cursor with
     Global => null;

   function Last_Element (Container : Map) return Element_Type with
     Global => null,
     Pre    => not Is_Empty (Container);

   function Last_Key (Container : Map) return Key_Type with
     Global => null,
     Pre    => not Is_Empty (Container);

   function Next (Container : Map; Position : Cursor) return Cursor with
     Global => null,
     Pre    => Has_Element (Container, Position) or else Position = No_Element;

   procedure Next (Container : Map; Position : in out Cursor) with
     Global => null,
     Pre    => Has_Element (Container, Position) or else Position = No_Element;

   function Previous (Container : Map; Position : Cursor) return Cursor with
     Global => null,
     Pre    => Has_Element (Container, Position) or else Position = No_Element;

   procedure Previous (Container : Map; Position : in out Cursor) with
     Global => null,
     Pre    => Has_Element (Container, Position) or else Position = No_Element;

   function Find (Container : Map; Key : Key_Type) return Cursor with
     Global => null;

   function Element (Container : Map; Key : Key_Type) return Element_Type with
     Global => null,
     Pre    => Contains (Container, Key);

   function Floor (Container : Map; Key : Key_Type) return Cursor with
     Global => null;

   function Ceiling (Container : Map; Key : Key_Type) return Cursor with
     Global => null;

   function Contains (Container : Map; Key : Key_Type) return Boolean with
     Global => null;

   function Has_Element (Container : Map; Position : Cursor) return Boolean
   with
     Global => null;

   function Strict_Equal (Left, Right : Map) return Boolean with
     Ghost,
     Global => null;
   --  Strict_Equal returns True if the containers are physically equal, i.e.
   --  they are structurally equal (function "=" returns True) and that they
   --  have the same set of cursors.

   function First_To_Previous (Container : Map; Current : Cursor) return Map
   with
     Ghost,
     Global => null,
     Pre    => Has_Element (Container, Current) or else Current = No_Element;

   function Current_To_Last (Container : Map; Current : Cursor) return Map
   with
     Ghost,
     Global => null,
     Pre    => Has_Element (Container, Current) or else Current = No_Element;
   --  First_To_Previous returns a container containing all elements preceding
   --  Current (excluded) in Container. Current_To_Last returns a container
   --  containing all elements following Current (included) in Container.
   --  These two new functions can be used to express invariant properties in
   --  loops which iterate over containers. First_To_Previous returns the part
   --  of the container already scanned and Current_To_Last the part not
   --  scanned yet.

   function Overlap (Left, Right : Map) return Boolean with
     Global => null;
   --  Overlap returns True if the containers have common keys

private
   pragma SPARK_Mode (Off);

   pragma Inline (Next);
   pragma Inline (Previous);

   subtype Node_Access is Count_Type;

   use Red_Black_Trees;

   type Node_Type is record
      Has_Element : Boolean := False;
      Parent  : Node_Access := 0;
      Left    : Node_Access := 0;
      Right   : Node_Access := 0;
      Color   : Red_Black_Trees.Color_Type := Red;
      Key     : Key_Type;
      Element : Element_Type;
   end record;

   package Tree_Types is
     new Ada.Containers.Red_Black_Trees.Generic_Bounded_Tree_Types (Node_Type);

   type Map (Capacity : Count_Type) is
     new Tree_Types.Tree_Type (Capacity) with null record;

   type Cursor is record
      Node : Node_Access;
   end record;

   Empty_Map : constant Map := (Capacity => 0, others => <>);

   No_Element : constant Cursor := (Node => 0);

end Ada.Containers.Formal_Ordered_Maps;