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) 2004-2013, 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_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 59private with Ada.Containers.Red_Black_Trees; 60 61generic 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 67package Ada.Containers.Formal_Ordered_Sets is 68 pragma Annotate (GNATprove, External_Axiomatization); 69 pragma Pure; 70 71 function Equivalent_Elements (Left, Right : Element_Type) return Boolean 72 with 73 Global => null; 74 75 type Set (Capacity : Count_Type) is private with 76 Iterable => (First => First, 77 Next => Next, 78 Has_Element => Has_Element, 79 Element => Element); 80 pragma Preelaborable_Initialization (Set); 81 82 type Cursor is private; 83 pragma Preelaborable_Initialization (Cursor); 84 85 Empty_Set : constant Set; 86 87 No_Element : constant Cursor; 88 89 function "=" (Left, Right : Set) return Boolean with 90 Global => null; 91 92 function Equivalent_Sets (Left, Right : Set) return Boolean with 93 Global => null; 94 95 function To_Set (New_Item : Element_Type) return Set with 96 Global => null; 97 98 function Length (Container : Set) return Count_Type with 99 Global => null; 100 101 function Is_Empty (Container : Set) return Boolean with 102 Global => null; 103 104 procedure Clear (Container : in out Set) with 105 Global => null; 106 107 procedure Assign (Target : in out Set; Source : Set) with 108 Pre => Target.Capacity >= Length (Source); 109 110 function Copy (Source : Set; Capacity : Count_Type := 0) return Set with 111 Global => null, 112 Pre => Capacity = 0 or else Capacity >= Source.Capacity; 113 114 function Element 115 (Container : Set; 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 Set; 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 Set; Source : in out Set) with 130 Global => null, 131 Pre => Target.Capacity >= Length (Source); 132 133 procedure Insert 134 (Container : in out Set; 135 New_Item : Element_Type; 136 Position : out Cursor; 137 Inserted : out Boolean) 138 with 139 Global => null, 140 Pre => Length (Container) < Container.Capacity; 141 142 procedure Insert 143 (Container : in out Set; 144 New_Item : Element_Type) 145 with 146 Global => null, 147 Pre => Length (Container) < Container.Capacity 148 and then (not Contains (Container, New_Item)); 149 150 procedure Include 151 (Container : in out Set; 152 New_Item : Element_Type) 153 with 154 Global => null, 155 Pre => Length (Container) < Container.Capacity; 156 157 procedure Replace 158 (Container : in out Set; 159 New_Item : Element_Type) 160 with 161 Global => null, 162 Pre => Contains (Container, New_Item); 163 164 procedure Exclude 165 (Container : in out Set; 166 Item : Element_Type) 167 with 168 Global => null; 169 170 procedure Delete 171 (Container : in out Set; 172 Item : Element_Type) 173 with 174 Global => null, 175 Pre => Contains (Container, Item); 176 177 procedure Delete 178 (Container : in out Set; 179 Position : in out Cursor) 180 with 181 Global => null, 182 Pre => Has_Element (Container, Position); 183 184 procedure Delete_First (Container : in out Set) with 185 Global => null; 186 187 procedure Delete_Last (Container : in out Set) with 188 Global => null; 189 190 procedure Union (Target : in out Set; Source : Set) with 191 Global => null, 192 Pre => Length (Target) + Length (Source) - 193 Length (Intersection (Target, Source)) <= Target.Capacity; 194 195 function Union (Left, Right : Set) return Set with 196 Global => null, 197 Pre => Length (Left) + Length (Right) - 198 Length (Intersection (Left, Right)) <= Count_Type'Last; 199 200 function "or" (Left, Right : Set) return Set renames Union; 201 202 procedure Intersection (Target : in out Set; Source : Set) with 203 Global => null; 204 205 function Intersection (Left, Right : Set) return Set with 206 Global => null; 207 208 function "and" (Left, Right : Set) return Set renames Intersection; 209 210 procedure Difference (Target : in out Set; Source : Set) with 211 Global => null; 212 213 function Difference (Left, Right : Set) return Set with 214 Global => null; 215 216 function "-" (Left, Right : Set) return Set renames Difference; 217 218 procedure Symmetric_Difference (Target : in out Set; Source : Set) with 219 Global => null, 220 Pre => Length (Target) + Length (Source) - 221 2 * Length (Intersection (Target, Source)) <= Target.Capacity; 222 223 function Symmetric_Difference (Left, Right : Set) return Set with 224 Global => null, 225 Pre => Length (Left) + Length (Right) - 226 2 * Length (Intersection (Left, Right)) <= Count_Type'Last; 227 228 function "xor" (Left, Right : Set) return Set renames Symmetric_Difference; 229 230 function Overlap (Left, Right : Set) return Boolean with 231 Global => null; 232 233 function Is_Subset (Subset : Set; Of_Set : Set) return Boolean with 234 Global => null; 235 236 function First (Container : Set) return Cursor with 237 Global => null; 238 239 function First_Element (Container : Set) return Element_Type with 240 Global => null, 241 Pre => not Is_Empty (Container); 242 243 function Last (Container : Set) return Cursor; 244 245 function Last_Element (Container : Set) return Element_Type with 246 Global => null, 247 Pre => not Is_Empty (Container); 248 249 function Next (Container : Set; Position : Cursor) return Cursor with 250 Global => null, 251 Pre => Has_Element (Container, Position) or else Position = No_Element; 252 253 procedure Next (Container : Set; Position : in out Cursor) with 254 Global => null, 255 Pre => Has_Element (Container, Position) or else Position = No_Element; 256 257 function Previous (Container : Set; Position : Cursor) return Cursor with 258 Global => null, 259 Pre => Has_Element (Container, Position) or else Position = No_Element; 260 261 procedure Previous (Container : Set; Position : in out Cursor) with 262 Global => null, 263 Pre => Has_Element (Container, Position) or else Position = No_Element; 264 265 function Find (Container : Set; Item : Element_Type) return Cursor with 266 Global => null; 267 268 function Floor (Container : Set; Item : Element_Type) return Cursor with 269 Global => null; 270 271 function Ceiling (Container : Set; Item : Element_Type) return Cursor with 272 Global => null; 273 274 function Contains (Container : Set; Item : Element_Type) return Boolean with 275 Global => null; 276 277 function Has_Element (Container : Set; Position : Cursor) return Boolean 278 with 279 Global => null; 280 281 generic 282 type Key_Type (<>) is private; 283 284 with function Key (Element : Element_Type) return Key_Type; 285 286 with function "<" (Left, Right : Key_Type) return Boolean is <>; 287 288 package Generic_Keys is 289 290 function Equivalent_Keys (Left, Right : Key_Type) return Boolean with 291 Global => null; 292 293 function Key (Container : Set; Position : Cursor) return Key_Type with 294 Global => null; 295 296 function Element (Container : Set; Key : Key_Type) return Element_Type 297 with 298 Global => null; 299 300 procedure Replace 301 (Container : in out Set; 302 Key : Key_Type; 303 New_Item : Element_Type) 304 with 305 Global => null; 306 307 procedure Exclude (Container : in out Set; Key : Key_Type) with 308 Global => null; 309 310 procedure Delete (Container : in out Set; Key : Key_Type) with 311 Global => null; 312 313 function Find (Container : Set; Key : Key_Type) return Cursor with 314 Global => null; 315 316 function Floor (Container : Set; Key : Key_Type) return Cursor with 317 Global => null; 318 319 function Ceiling (Container : Set; Key : Key_Type) return Cursor with 320 Global => null; 321 322 function Contains (Container : Set; Key : Key_Type) return Boolean with 323 Global => null; 324 325 end Generic_Keys; 326 327 function Strict_Equal (Left, Right : Set) return Boolean with 328 Global => null; 329 -- Strict_Equal returns True if the containers are physically equal, i.e. 330 -- they are structurally equal (function "=" returns True) and that they 331 -- have the same set of cursors. 332 333 function First_To_Previous (Container : Set; Current : Cursor) return Set 334 with 335 Global => null, 336 Pre => Has_Element (Container, Current) or else Current = No_Element; 337 function Current_To_Last (Container : Set; Current : Cursor) return Set 338 with 339 Global => null, 340 Pre => Has_Element (Container, Current) or else Current = No_Element; 341 -- First_To_Previous returns a container containing all elements preceding 342 -- Current (excluded) in Container. Current_To_Last returns a container 343 -- containing all elements following Current (included) in Container. 344 -- These two new functions can be used to express invariant properties in 345 -- loops which iterate over containers. First_To_Previous returns the part 346 -- of the container already scanned and Current_To_Last the part not 347 -- scanned yet. 348 349private 350 351 pragma Inline (Next); 352 pragma Inline (Previous); 353 354 type Node_Type is record 355 Has_Element : Boolean := False; 356 Parent : Count_Type := 0; 357 Left : Count_Type := 0; 358 Right : Count_Type := 0; 359 Color : Red_Black_Trees.Color_Type; 360 Element : Element_Type; 361 end record; 362 363 package Tree_Types is 364 new Red_Black_Trees.Generic_Bounded_Tree_Types (Node_Type); 365 366 type Set (Capacity : Count_Type) is 367 new Tree_Types.Tree_Type (Capacity) with null record; 368 369 use Red_Black_Trees; 370 371 type Cursor is record 372 Node : Count_Type; 373 end record; 374 375 No_Element : constant Cursor := (Node => 0); 376 377 Empty_Set : constant Set := (Capacity => 0, others => <>); 378 379end Ada.Containers.Formal_Ordered_Sets; 380