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   1 ------------------------------------------------------------------------------
   2 --                                                                          --
   3 --                         GNAT LIBRARY COMPONENTS                          --
   4 --                                                                          --
   5 --   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    --
   6 --                                                                          --
   7 --                                 S p e c                                  --
   8 --                                                                          --
   9 --          Copyright (C) 2004-2013, Free Software Foundation, Inc.         --
  10 --                                                                          --
  11 -- This specification is derived from the Ada Reference Manual for use with --
  12 -- GNAT. The copyright notice above, and the license provisions that follow --
  13 -- apply solely to the  contents of the part following the private keyword. --
  14 --                                                                          --
  15 -- GNAT is free software;  you can  redistribute it  and/or modify it under --
  16 -- terms of the  GNU General Public License as published  by the Free Soft- --
  17 -- ware  Foundation;  either version 3,  or (at your option) any later ver- --
  18 -- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
  19 -- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --
  20 -- or FITNESS FOR A PARTICULAR PURPOSE.                                     --
  21 --                                                                          --
  22 -- As a special exception under Section 7 of GPL version 3, you are granted --
  23 -- additional permissions described in the GCC Runtime Library Exception,   --
  24 -- version 3.1, as published by the Free Software Foundation.               --
  25 --                                                                          --
  26 -- You should have received a copy of the GNU General Public License and    --
  27 -- a copy of the GCC Runtime Library Exception along with this program;     --
  28 -- see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see    --
  29 -- <http://www.gnu.org/licenses/>.                                          --
  30 ------------------------------------------------------------------------------
  31
  32 --  This spec is derived from package Ada.Containers.Bounded_Ordered_Maps in
  33 --  the Ada 2012 RM. The modifications are meant to facilitate formal proofs by
  34 --  making it easier to express properties, and by making the specification of
  35 --  this unit compatible with SPARK 2014. Note that the API of this unit may be
  36 --  subject to incompatible changes as SPARK 2014 evolves.
  37
  38 --  The modifications are:
  39
  40 --    A parameter for the container is added to every function reading the
  41 --    content of a container: Key, Element, Next, Query_Element, Previous,
  42 --    Has_Element, Iterate, Reverse_Iterate. This change is motivated by the
  43 --    need to have cursors which are valid on different containers (typically a
  44 --    container C and its previous version C'Old) for expressing properties,
  45 --    which is not possible if cursors encapsulate an access to the underlying
  46 --    container. The operators "<" and ">" that could not be modified that way
  47 --    have been removed.
  48
  49 --    There are four new functions:
  50
  51 --      function Strict_Equal (Left, Right : Map) return Boolean;
  52 --      function Overlap (Left, Right : Map) return Boolean;
  53 --      function First_To_Previous  (Container : Map; Current : Cursor)
  54 --         return Map;
  55 --      function Current_To_Last (Container : Map; Current : Cursor)
  56 --         return Map;
  57
  58 --    See detailed specifications for these subprograms
  59
  60 private with Ada.Containers.Red_Black_Trees;
  61
  62 generic
  63    type Key_Type is private;
  64    type Element_Type is private;
  65
  66    with function "<" (Left, Right : Key_Type) return Boolean is <>;
  67    with function "=" (Left, Right : Element_Type) return Boolean is <>;
  68
  69 package Ada.Containers.Formal_Ordered_Maps is
  70    pragma Annotate (GNATprove, External_Axiomatization);
  71    pragma Pure;
  72
  73    function Equivalent_Keys (Left, Right : Key_Type) return Boolean with
  74      Global => null;
  75
  76    type Map (Capacity : Count_Type) is private with
  77      Iterable => (First       => First,
  78                   Next        => Next,
  79                   Has_Element => Has_Element,
  80                   Element     => Element);
  81    pragma Preelaborable_Initialization (Map);
  82
  83    type Cursor is private;
  84    pragma Preelaborable_Initialization (Cursor);
  85
  86    Empty_Map : constant Map;
  87
  88    No_Element : constant Cursor;
  89
  90    function "=" (Left, Right : Map) return Boolean with
  91      Global => null;
  92
  93    function Length (Container : Map) return Count_Type with
  94      Global => null;
  95
  96    function Is_Empty (Container : Map) return Boolean with
  97      Global => null;
  98
  99    procedure Clear (Container : in out Map) with
 100      Global => null;
 101
 102    procedure Assign (Target : in out Map; Source : Map) with
 103      Global => null,
 104      Pre    => Target.Capacity >= Length (Source);
 105
 106    function Copy (Source : Map; Capacity : Count_Type := 0) return Map with
 107      Global => null,
 108      Pre    => Capacity = 0 or else Capacity >= Source.Capacity;
 109
 110    function Key (Container : Map; Position : Cursor) return Key_Type with
 111      Global => null,
 112      Pre    => Has_Element (Container, Position);
 113
 114    function Element
 115      (Container : Map;
 116       Position  : Cursor) return Element_Type
 117    with
 118      Global => null,
 119      Pre    => Has_Element (Container, Position);
 120
 121    procedure Replace_Element
 122      (Container : in out Map;
 123       Position  : Cursor;
 124       New_Item  : Element_Type)
 125    with
 126      Global => null,
 127      Pre    => Has_Element (Container, Position);
 128
 129    procedure Move (Target : in out Map; Source : in out Map) with
 130      Global => null,
 131      Pre    => Target.Capacity >= Length (Source);
 132
 133    procedure Insert
 134      (Container : in out Map;
 135       Key       : Key_Type;
 136       New_Item  : Element_Type;
 137       Position  : out Cursor;
 138       Inserted  : out Boolean)
 139    with
 140      Global => null,
 141      Pre    => Length (Container) < Container.Capacity;
 142
 143    procedure Insert
 144      (Container : in out Map;
 145       Key       : Key_Type;
 146       New_Item  : Element_Type)
 147    with
 148      Global => null,
 149      Pre    => Length (Container) < Container.Capacity
 150                  and then (not Contains (Container, Key));
 151
 152    procedure Include
 153      (Container : in out Map;
 154       Key       : Key_Type;
 155       New_Item  : Element_Type)
 156    with
 157      Global => null,
 158      Pre    => Length (Container) < Container.Capacity;
 159
 160    procedure Replace
 161      (Container : in out Map;
 162       Key       : Key_Type;
 163       New_Item  : Element_Type)
 164    with
 165      Global => null,
 166      Pre    => Contains (Container, Key);
 167
 168    procedure Exclude (Container : in out Map; Key : Key_Type) with
 169      Global => null;
 170
 171    procedure Delete (Container : in out Map; Key : Key_Type) with
 172      Global => null,
 173      Pre    => Contains (Container, Key);
 174
 175    procedure Delete (Container : in out Map; Position : in out Cursor) with
 176      Global => null,
 177      Pre    => Has_Element (Container, Position);
 178
 179    procedure Delete_First (Container : in out Map) with
 180      Global => null;
 181
 182    procedure Delete_Last (Container : in out Map) with
 183      Global => null;
 184
 185    function First (Container : Map) return Cursor with
 186      Global => null;
 187
 188    function First_Element (Container : Map) return Element_Type with
 189      Global => null,
 190      Pre    => not Is_Empty (Container);
 191
 192    function First_Key (Container : Map) return Key_Type with
 193      Global => null,
 194      Pre    => not Is_Empty (Container);
 195
 196    function Last (Container : Map) return Cursor with
 197      Global => null;
 198
 199    function Last_Element (Container : Map) return Element_Type with
 200      Global => null,
 201      Pre    => not Is_Empty (Container);
 202
 203    function Last_Key (Container : Map) return Key_Type with
 204      Global => null,
 205      Pre    => not Is_Empty (Container);
 206
 207    function Next (Container : Map; Position : Cursor) return Cursor with
 208      Global => null,
 209      Pre    => Has_Element (Container, Position) or else Position = No_Element;
 210
 211    procedure Next (Container : Map; Position : in out Cursor) with
 212      Global => null,
 213      Pre    => Has_Element (Container, Position) or else Position = No_Element;
 214
 215    function Previous (Container : Map; Position : Cursor) return Cursor with
 216      Global => null,
 217      Pre    => Has_Element (Container, Position) or else Position = No_Element;
 218
 219    procedure Previous (Container : Map; Position : in out Cursor) with
 220      Global => null,
 221      Pre    => Has_Element (Container, Position) or else Position = No_Element;
 222
 223    function Find (Container : Map; Key : Key_Type) return Cursor with
 224      Global => null;
 225
 226    function Element (Container : Map; Key : Key_Type) return Element_Type with
 227      Global => null,
 228      Pre    => Contains (Container, Key);
 229
 230    function Floor (Container : Map; Key : Key_Type) return Cursor with
 231      Global => null;
 232
 233    function Ceiling (Container : Map; Key : Key_Type) return Cursor with
 234      Global => null;
 235
 236    function Contains (Container : Map; Key : Key_Type) return Boolean with
 237      Global => null;
 238
 239    function Has_Element (Container : Map; Position : Cursor) return Boolean
 240    with
 241      Global => null;
 242
 243    function Strict_Equal (Left, Right : Map) return Boolean with
 244      Global => null;
 245    --  Strict_Equal returns True if the containers are physically equal, i.e.
 246    --  they are structurally equal (function "=" returns True) and that they
 247    --  have the same set of cursors.
 248
 249    function First_To_Previous (Container : Map; Current : Cursor) return Map
 250    with
 251      Global => null,
 252      Pre    => Has_Element (Container, Current) or else Current = No_Element;
 253    function Current_To_Last (Container : Map; Current : Cursor) return Map
 254    with
 255      Global => null,
 256      Pre    => Has_Element (Container, Current) or else Current = No_Element;
 257    --  First_To_Previous returns a container containing all elements preceding
 258    --  Current (excluded) in Container. Current_To_Last returns a container
 259    --  containing all elements following Current (included) in Container.
 260    --  These two new functions can be used to express invariant properties in
 261    --  loops which iterate over containers. First_To_Previous returns the part
 262    --  of the container already scanned and Current_To_Last the part not
 263    --  scanned yet.
 264
 265    function Overlap (Left, Right : Map) return Boolean with
 266      Global => null;
 267    --  Overlap returns True if the containers have common keys
 268 private
 269
 270    pragma Inline (Next);
 271    pragma Inline (Previous);
 272
 273    subtype Node_Access is Count_Type;
 274
 275    use Red_Black_Trees;
 276
 277    type Node_Type is record
 278       Has_Element : Boolean := False;
 279       Parent  : Node_Access := 0;
 280       Left    : Node_Access := 0;
 281       Right   : Node_Access := 0;
 282       Color   : Red_Black_Trees.Color_Type := Red;
 283       Key     : Key_Type;
 284       Element : Element_Type;
 285    end record;
 286
 287    package Tree_Types is
 288      new Ada.Containers.Red_Black_Trees.Generic_Bounded_Tree_Types (Node_Type);
 289
 290    type Map (Capacity : Count_Type) is
 291       new Tree_Types.Tree_Type (Capacity) with null record;
 292
 293    type Cursor is record
 294       Node : Node_Access;
 295    end record;
 296
 297    Empty_Map : constant Map := (Capacity => 0, others => <>);
 298
 299    No_Element : constant Cursor := (Node => 0);
 300
 301 end Ada.Containers.Formal_Ordered_Maps;