gcc/ada/a-cforse.ads

   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 _ S E T S    --
   6 --                                                                          --
   7 --                                 S p e c                                  --
   8 --                                                                          --
   9 --          Copyright (C) 2004-2015, 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_Sets 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
  44 --    a 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 three new functions:
  50
  51 --      function Strict_Equal (Left, Right : Set) return Boolean;
  52 --      function First_To_Previous (Container : Set; Current : Cursor)
  53 --         return Set;
  54 --      function Current_To_Last (Container : Set; Current : Cursor)
  55 --         return Set;
  56
  57 --    See detailed specifications for these subprograms
  58
  59 private with Ada.Containers.Red_Black_Trees;
  60
  61 generic
  62    type Element_Type is private;
  63
  64    with function "<" (Left, Right : Element_Type) return Boolean is <>;
  65    with function "=" (Left, Right : Element_Type) return Boolean is <>;
  66
  67 package Ada.Containers.Formal_Ordered_Sets with
  68   Pure,
  69   SPARK_Mode
  70 is
  71    pragma Annotate (GNATprove, External_Axiomatization);
  72    pragma Annotate (CodePeer, Skip_Analysis);
  73
  74    function Equivalent_Elements (Left, Right : Element_Type) return Boolean
  75    with
  76      Global => null;
  77
  78    type Set (Capacity : Count_Type) is private with
  79      Iterable => (First       => First,
  80                   Next        => Next,
  81                   Has_Element => Has_Element,
  82                   Element     => Element),
  83      Default_Initial_Condition => Is_Empty (Set);
  84    pragma Preelaborable_Initialization (Set);
  85
  86    type Cursor is private;
  87    pragma Preelaborable_Initialization (Cursor);
  88
  89    Empty_Set : constant Set;
  90
  91    No_Element : constant Cursor;
  92
  93    function "=" (Left, Right : Set) return Boolean with
  94      Global => null;
  95
  96    function Equivalent_Sets (Left, Right : Set) return Boolean with
  97      Global => null;
  98
  99    function To_Set (New_Item : Element_Type) return Set with
 100      Global => null;
 101
 102    function Length (Container : Set) return Count_Type with
 103      Global => null;
 104
 105    function Is_Empty (Container : Set) return Boolean with
 106      Global => null;
 107
 108    procedure Clear (Container : in out Set) with
 109      Global => null;
 110
 111    procedure Assign (Target : in out Set; Source : Set) with
 112      Pre => Target.Capacity >= Length (Source);
 113
 114    function Copy (Source : Set; Capacity : Count_Type := 0) return Set with
 115      Global => null,
 116      Pre    => Capacity = 0 or else Capacity >= Source.Capacity;
 117
 118    function Element
 119      (Container : Set;
 120       Position  : Cursor) return Element_Type
 121    with
 122      Global => null,
 123      Pre    => Has_Element (Container, Position);
 124
 125    procedure Replace_Element
 126      (Container : in out Set;
 127       Position  : Cursor;
 128       New_Item  : Element_Type)
 129    with
 130      Global => null,
 131      Pre    => Has_Element (Container, Position);
 132
 133    procedure Move (Target : in out Set; Source : in out Set) with
 134      Global => null,
 135      Pre    => Target.Capacity >= Length (Source);
 136
 137    procedure Insert
 138      (Container : in out Set;
 139       New_Item  : Element_Type;
 140       Position  : out Cursor;
 141       Inserted  : out Boolean)
 142    with
 143      Global => null,
 144      Pre    => Length (Container) < Container.Capacity;
 145
 146    procedure Insert
 147      (Container : in out Set;
 148       New_Item  : Element_Type)
 149    with
 150      Global => null,
 151      Pre    => Length (Container) < Container.Capacity
 152                  and then (not Contains (Container, New_Item));
 153
 154    procedure Include
 155      (Container : in out Set;
 156       New_Item  : Element_Type)
 157    with
 158      Global => null,
 159      Pre    => Length (Container) < Container.Capacity;
 160
 161    procedure Replace
 162      (Container : in out Set;
 163       New_Item  : Element_Type)
 164    with
 165      Global => null,
 166      Pre    => Contains (Container, New_Item);
 167
 168    procedure Exclude
 169      (Container : in out Set;
 170       Item      : Element_Type)
 171    with
 172      Global => null;
 173
 174    procedure Delete
 175      (Container : in out Set;
 176       Item      : Element_Type)
 177    with
 178      Global => null,
 179      Pre    => Contains (Container, Item);
 180
 181    procedure Delete
 182      (Container : in out Set;
 183       Position  : in out Cursor)
 184    with
 185      Global => null,
 186      Pre    => Has_Element (Container, Position);
 187
 188    procedure Delete_First (Container : in out Set) with
 189      Global => null;
 190
 191    procedure Delete_Last (Container : in out Set) with
 192      Global => null;
 193
 194    procedure Union (Target : in out Set; Source : Set) with
 195      Global => null,
 196      Pre    => Length (Target) + Length (Source) -
 197                  Length (Intersection (Target, Source)) <= Target.Capacity;
 198
 199    function Union (Left, Right : Set) return Set with
 200      Global => null,
 201      Pre    => Length (Left) + Length (Right) -
 202                  Length (Intersection (Left, Right)) <= Count_Type'Last;
 203
 204    function "or" (Left, Right : Set) return Set renames Union;
 205
 206    procedure Intersection (Target : in out Set; Source : Set) with
 207      Global => null;
 208
 209    function Intersection (Left, Right : Set) return Set with
 210      Global => null;
 211
 212    function "and" (Left, Right : Set) return Set renames Intersection;
 213
 214    procedure Difference (Target : in out Set; Source : Set) with
 215      Global => null;
 216
 217    function Difference (Left, Right : Set) return Set with
 218      Global => null;
 219
 220    function "-" (Left, Right : Set) return Set renames Difference;
 221
 222    procedure Symmetric_Difference (Target : in out Set; Source : Set) with
 223      Global => null,
 224      Pre    => Length (Target) + Length (Source) -
 225                  2 * Length (Intersection (Target, Source)) <= Target.Capacity;
 226
 227    function Symmetric_Difference (Left, Right : Set) return Set with
 228      Global => null,
 229      Pre    => Length (Left) + Length (Right) -
 230                  2 * Length (Intersection (Left, Right)) <= Count_Type'Last;
 231
 232    function "xor" (Left, Right : Set) return Set renames Symmetric_Difference;
 233
 234    function Overlap (Left, Right : Set) return Boolean with
 235      Global => null;
 236
 237    function Is_Subset (Subset : Set; Of_Set : Set) return Boolean with
 238      Global => null;
 239
 240    function First (Container : Set) return Cursor with
 241      Global => null;
 242
 243    function First_Element (Container : Set) return Element_Type with
 244      Global => null,
 245      Pre    => not Is_Empty (Container);
 246
 247    function Last (Container : Set) return Cursor;
 248
 249    function Last_Element (Container : Set) return Element_Type with
 250      Global => null,
 251      Pre    => not Is_Empty (Container);
 252
 253    function Next (Container : Set; Position : Cursor) return Cursor with
 254      Global => null,
 255      Pre    => Has_Element (Container, Position) or else Position = No_Element;
 256
 257    procedure Next (Container : Set; Position : in out Cursor) with
 258      Global => null,
 259      Pre    => Has_Element (Container, Position) or else Position = No_Element;
 260
 261    function Previous (Container : Set; Position : Cursor) return Cursor with
 262      Global => null,
 263      Pre    => Has_Element (Container, Position) or else Position = No_Element;
 264
 265    procedure Previous (Container : Set; Position : in out Cursor) with
 266      Global => null,
 267      Pre    => Has_Element (Container, Position) or else Position = No_Element;
 268
 269    function Find (Container : Set; Item : Element_Type) return Cursor with
 270      Global => null;
 271
 272    function Floor (Container : Set; Item : Element_Type) return Cursor with
 273      Global => null;
 274
 275    function Ceiling (Container : Set; Item : Element_Type) return Cursor with
 276      Global => null;
 277
 278    function Contains (Container : Set; Item : Element_Type) return Boolean with
 279      Global => null;
 280
 281    function Has_Element (Container : Set; Position : Cursor) return Boolean
 282    with
 283      Global => null;
 284
 285    generic
 286       type Key_Type (<>) is private;
 287
 288       with function Key (Element : Element_Type) return Key_Type;
 289
 290       with function "<" (Left, Right : Key_Type) return Boolean is <>;
 291
 292    package Generic_Keys with SPARK_Mode is
 293
 294       function Equivalent_Keys (Left, Right : Key_Type) return Boolean with
 295         Global => null;
 296
 297       function Key (Container : Set; Position : Cursor) return Key_Type with
 298         Global => null;
 299
 300       function Element (Container : Set; Key : Key_Type) return Element_Type
 301       with
 302         Global => null;
 303
 304       procedure Replace
 305         (Container : in out Set;
 306          Key       : Key_Type;
 307          New_Item  : Element_Type)
 308       with
 309         Global => null;
 310
 311       procedure Exclude (Container : in out Set; Key : Key_Type) with
 312         Global => null;
 313
 314       procedure Delete (Container : in out Set; Key : Key_Type) with
 315         Global => null;
 316
 317       function Find (Container : Set; Key : Key_Type) return Cursor with
 318         Global => null;
 319
 320       function Floor (Container : Set; Key : Key_Type) return Cursor with
 321         Global => null;
 322
 323       function Ceiling (Container : Set; Key : Key_Type) return Cursor with
 324         Global => null;
 325
 326       function Contains (Container : Set; Key : Key_Type) return Boolean with
 327         Global => null;
 328
 329    end Generic_Keys;
 330
 331    function Strict_Equal (Left, Right : Set) return Boolean with
 332      Ghost,
 333      Global => null;
 334    --  Strict_Equal returns True if the containers are physically equal, i.e.
 335    --  they are structurally equal (function "=" returns True) and that they
 336    --  have the same set of cursors.
 337
 338    function First_To_Previous (Container : Set; Current : Cursor) return Set
 339    with
 340      Ghost,
 341      Global => null,
 342      Pre    => Has_Element (Container, Current) or else Current = No_Element;
 343
 344    function Current_To_Last (Container : Set; Current : Cursor) return Set
 345    with
 346      Ghost,
 347      Global => null,
 348      Pre    => Has_Element (Container, Current) or else Current = No_Element;
 349    --  First_To_Previous returns a container containing all elements preceding
 350    --  Current (excluded) in Container. Current_To_Last returns a container
 351    --  containing all elements following Current (included) in Container.
 352    --  These two new functions can be used to express invariant properties in
 353    --  loops which iterate over containers. First_To_Previous returns the part
 354    --  of the container already scanned and Current_To_Last the part not
 355    --  scanned yet.
 356
 357 private
 358    pragma SPARK_Mode (Off);
 359
 360    pragma Inline (Next);
 361    pragma Inline (Previous);
 362
 363    type Node_Type is record
 364       Has_Element : Boolean := False;
 365       Parent  : Count_Type := 0;
 366       Left    : Count_Type := 0;
 367       Right   : Count_Type := 0;
 368       Color   : Red_Black_Trees.Color_Type;
 369       Element : Element_Type;
 370    end record;
 371
 372    package Tree_Types is
 373      new Red_Black_Trees.Generic_Bounded_Tree_Types (Node_Type);
 374
 375    type Set (Capacity : Count_Type) is
 376      new Tree_Types.Tree_Type (Capacity) with null record;
 377
 378    use Red_Black_Trees;
 379
 380    type Cursor is record
 381       Node : Count_Type;
 382    end record;
 383
 384    No_Element : constant Cursor := (Node => 0);
 385
 386    Empty_Set : constant Set := (Capacity => 0, others => <>);
 387
 388 end Ada.Containers.Formal_Ordered_Sets;