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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 _ S E T S    --
--                                                                          --
--                                 S p e c                                  --
--                                                                          --
--          Copyright (C) 2004-2011, Free Software Foundation, Inc.         --
--                                                                          --
-- This specification is derived from the Ada Reference Manual for use with --
-- GNAT. The copyright notice above, and the license provisions that follow --
-- apply solely to the  contents of the part following the private keyword. --
--                                                                          --
-- GNAT is free software;  you can  redistribute it  and/or modify it under --
-- terms of the  GNU General Public License as published  by the Free Soft- --
-- ware  Foundation;  either version 3,  or (at your option) any later ver- --
-- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
-- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --
-- or FITNESS FOR A PARTICULAR PURPOSE.                                     --
--                                                                          --
-- As a special exception under Section 7 of GPL version 3, you are granted --
-- additional permissions described in the GCC Runtime Library Exception,   --
-- version 3.1, as published by the Free Software Foundation.               --
--                                                                          --
-- You should have received a copy of the GNU General Public License and    --
-- a copy of the GCC Runtime Library Exception along with this program;     --
-- see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see    --
-- <http://www.gnu.org/licenses/>.                                          --
------------------------------------------------------------------------------
 
--  This spec is derived from package Ada.Containers.Bounded_Ordered_Sets in
--  the Ada 2012 RM. The modifications are to facilitate formal proofs by
--  making it easier to express properties.
 
--  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 three new functions:
 
--      function Strict_Equal (Left, Right : Set) return Boolean;
--      function Left  (Container : Set; Position : Cursor) return Set;
--      function Right (Container : Set; Position : Cursor) return Set;
 
--    See detailed specifications for these subprograms
 
private with Ada.Containers.Red_Black_Trees;
private with Ada.Streams;
 
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.Formal_Ordered_Sets is
   pragma Pure;
 
   function Equivalent_Elements (Left, Right : Element_Type) return Boolean;
 
   type Set (Capacity : Count_Type) is tagged private;
   --  why is this commented out ???
   --  pragma Preelaborable_Initialization (Set);
 
   type Cursor is private;
   pragma Preelaborable_Initialization (Cursor);
 
   Empty_Set : constant Set;
 
   No_Element : constant Cursor;
 
   function "=" (Left, Right : Set) return Boolean;
 
   function Equivalent_Sets (Left, Right : Set) return Boolean;
 
   function To_Set (New_Item : Element_Type) return Set;
 
   function Length (Container : Set) return Count_Type;
 
   function Is_Empty (Container : Set) return Boolean;
 
   procedure Clear (Container : in out Set);
 
   procedure Assign (Target : in out Set; Source : Set);
 
   function Copy (Source : Set; Capacity : Count_Type := 0) return Set;
 
   function Element (Container : Set; Position : Cursor) return Element_Type;
 
   procedure Replace_Element
     (Container : in out Set;
      Position  : Cursor;
      New_Item  : Element_Type);
 
   procedure Query_Element
     (Container : in out Set;
      Position  : Cursor;
      Process   : not null access procedure (Element : Element_Type));
 
   procedure Move (Target : in out Set; Source : in out Set);
 
   procedure Insert
     (Container : in out Set;
      New_Item  : Element_Type;
      Position  : out Cursor;
      Inserted  : out Boolean);
 
   procedure Insert
     (Container : in out Set;
      New_Item  : Element_Type);
 
   procedure Include
     (Container : in out Set;
      New_Item  : Element_Type);
 
   procedure Replace
     (Container : in out Set;
      New_Item  : Element_Type);
 
   procedure Exclude
     (Container : in out Set;
      Item      : Element_Type);
 
   procedure Delete
     (Container : in out Set;
      Item      : Element_Type);
 
   procedure Delete
     (Container : in out Set;
      Position  : in out Cursor);
 
   procedure Delete_First (Container : in out Set);
 
   procedure Delete_Last (Container : in out Set);
 
   procedure Union (Target : in out Set; Source : Set);
 
   function Union (Left, Right : Set) return Set;
 
   function "or" (Left, Right : Set) return Set renames Union;
 
   procedure Intersection (Target : in out Set; Source : Set);
 
   function Intersection (Left, Right : Set) return Set;
 
   function "and" (Left, Right : Set) return Set renames Intersection;
 
   procedure Difference (Target : in out Set; Source : Set);
 
   function Difference (Left, Right : Set) return Set;
 
   function "-" (Left, Right : Set) return Set renames Difference;
 
   procedure Symmetric_Difference (Target : in out Set; Source : Set);
 
   function Symmetric_Difference (Left, Right : Set) return Set;
 
   function "xor" (Left, Right : Set) return Set renames Symmetric_Difference;
 
   function Overlap (Left, Right : Set) return Boolean;
 
   function Is_Subset (Subset : Set; Of_Set : Set) return Boolean;
 
   function First (Container : Set) return Cursor;
 
   function First_Element (Container : Set) return Element_Type;
 
   function Last (Container : Set) return Cursor;
 
   function Last_Element (Container : Set) return Element_Type;
 
   function Next (Container : Set; Position : Cursor) return Cursor;
 
   procedure Next (Container : Set; Position : in out Cursor);
 
   function Previous (Container : Set; Position : Cursor) return Cursor;
 
   procedure Previous (Container : Set; Position : in out Cursor);
 
   function Find (Container : Set; Item : Element_Type) return Cursor;
 
   function Floor (Container : Set; Item : Element_Type) return Cursor;
 
   function Ceiling (Container : Set; Item : Element_Type) return Cursor;
 
   function Contains (Container : Set; Item : Element_Type) return Boolean;
 
   function Has_Element (Container : Set; Position : Cursor) return Boolean;
 
   procedure Iterate
     (Container : Set;
      Process   :
        not null access procedure (Container : Set; Position : Cursor));
 
   procedure Reverse_Iterate
     (Container : Set;
      Process   : not null access
                    procedure (Container : Set; Position : Cursor));
 
   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
 
      function Equivalent_Keys (Left, Right : Key_Type) return Boolean;
 
      function Key (Container : Set; Position : Cursor) return Key_Type;
 
      function Element (Container : Set; Key : Key_Type) return Element_Type;
 
      procedure Replace
        (Container : in out Set;
         Key       : Key_Type;
         New_Item  : Element_Type);
 
      procedure Exclude (Container : in out Set; Key : Key_Type);
 
      procedure Delete (Container : in out Set; Key : Key_Type);
 
      function Find (Container : Set; Key : Key_Type) return Cursor;
 
      function Floor (Container : Set; Key : Key_Type) return Cursor;
 
      function Ceiling (Container : Set; Key : Key_Type) return Cursor;
 
      function Contains (Container : Set; Key : Key_Type) return Boolean;
 
      procedure Update_Element_Preserving_Key
        (Container : in out Set;
         Position  : Cursor;
         Process   : not null access
                       procedure (Element : in out Element_Type));
 
   end Generic_Keys;
 
   function Strict_Equal (Left, Right : Set) return Boolean;
   --  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 Left  (Container : Set; Position : Cursor) return Set;
   function Right (Container : Set; Position : Cursor) return Set;
   --  Left returns a container containing all elements preceding Position
   --  (excluded) in Container. Right returns a container containing all
   --  elements following Position (included) in Container. These two new
   --  functions can be used to express invariant properties in loops which
   --  iterate over containers. Left returns the part of the container already
   --  scanned and Right the part not scanned yet.
 
private
 
   pragma Inline (Next);
   pragma Inline (Previous);
 
   type Node_Type is record
      Has_Element : Boolean := False;
      Parent  : Count_Type := 0;
      Left    : Count_Type := 0;
      Right   : Count_Type := 0;
      Color   : Red_Black_Trees.Color_Type;
      Element : Element_Type;
   end record;
 
   package Tree_Types is
     new Red_Black_Trees.Generic_Bounded_Tree_Types (Node_Type);
 
   type Set (Capacity : Count_Type) is
     new Tree_Types.Tree_Type (Capacity) with null record;
 
   use Red_Black_Trees;
   use Ada.Streams;
 
   type Set_Access is access all Set;
   for Set_Access'Storage_Size use 0;
 
   type Cursor is record
      Node : Count_Type;
   end record;
 
   procedure Write
     (Stream : not null access Root_Stream_Type'Class;
      Item   : Cursor);
 
   for Cursor'Write use Write;
 
   procedure Read
     (Stream : not null access Root_Stream_Type'Class;
      Item   : out Cursor);
 
   for Cursor'Read use Read;
 
   No_Element : constant Cursor := (Node => 0);
 
   procedure Write
     (Stream    : not null access Root_Stream_Type'Class;
      Container : Set);
 
   for Set'Write use Write;
 
   procedure Read
     (Stream    : not null access Root_Stream_Type'Class;
      Container : out Set);
 
   for Set'Read use Read;
 
   Empty_Set : constant Set := (Capacity => 0, others => <>);
 
end Ada.Containers.Formal_Ordered_Sets;