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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;