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 _ H A S H 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_Hashed_Sets in the 33-- 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: Element, Next, Query_Element, Has_Element, Key, 42-- Iterate, Equivalent_Elements. This change is motivated by the need to 43-- 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. 47 48-- There are three new functions: 49 50-- function Strict_Equal (Left, Right : Set) return Boolean; 51-- function First_To_Previous (Container : Set; Current : Cursor) 52-- return Set; 53-- function Current_To_Last (Container : Set; Current : Cursor) 54-- return Set; 55 56-- See detailed specifications for these subprograms 57 58private with Ada.Containers.Hash_Tables; 59 60generic 61 type Element_Type is private; 62 63 with function Hash (Element : Element_Type) return Hash_Type; 64 65 with function Equivalent_Elements (Left, Right : Element_Type) 66 return Boolean; 67 68 with function "=" (Left, Right : Element_Type) return Boolean is <>; 69 70package Ada.Containers.Formal_Hashed_Sets with 71 Pure, 72 SPARK_Mode 73is 74 pragma Annotate (GNATprove, External_Axiomatization); 75 76 type Set (Capacity : Count_Type; Modulus : Hash_Type) is private with 77 Iterable => (First => First, 78 Next => Next, 79 Has_Element => Has_Element, 80 Element => Element), 81 Default_Initial_Condition => Is_Empty (Set); 82 pragma Preelaborable_Initialization (Set); 83 84 type Cursor is private; 85 pragma Preelaborable_Initialization (Cursor); 86 87 Empty_Set : constant Set; 88 89 No_Element : constant Cursor; 90 91 function "=" (Left, Right : Set) return Boolean with 92 Global => null; 93 94 function Equivalent_Sets (Left, Right : Set) return Boolean with 95 Global => null; 96 97 function To_Set (New_Item : Element_Type) return Set with 98 Global => null; 99 100 function Capacity (Container : Set) return Count_Type with 101 Global => null; 102 103 procedure Reserve_Capacity 104 (Container : in out Set; 105 Capacity : Count_Type) 106 with 107 Global => null, 108 Pre => Capacity <= Container.Capacity; 109 110 function Length (Container : Set) return Count_Type with 111 Global => null; 112 113 function Is_Empty (Container : Set) return Boolean with 114 Global => null; 115 116 procedure Clear (Container : in out Set) with 117 Global => null; 118 119 procedure Assign (Target : in out Set; Source : Set) with 120 Global => null, 121 Pre => Target.Capacity >= Length (Source); 122 123 function Copy 124 (Source : Set; 125 Capacity : Count_Type := 0) return Set 126 with 127 Global => null, 128 Pre => Capacity = 0 or else Capacity >= Source.Capacity; 129 130 function Element 131 (Container : Set; 132 Position : Cursor) return Element_Type 133 with 134 Global => null, 135 Pre => Has_Element (Container, Position); 136 137 procedure Replace_Element 138 (Container : in out Set; 139 Position : Cursor; 140 New_Item : Element_Type) 141 with 142 Global => null, 143 Pre => Has_Element (Container, Position); 144 145 procedure Move (Target : in out Set; Source : in out Set) with 146 Global => null, 147 Pre => Target.Capacity >= Length (Source); 148 149 procedure Insert 150 (Container : in out Set; 151 New_Item : Element_Type; 152 Position : out Cursor; 153 Inserted : out Boolean) 154 with 155 Global => null, 156 Pre => Length (Container) < Container.Capacity; 157 158 procedure Insert (Container : in out Set; New_Item : Element_Type) with 159 Global => null, 160 Pre => Length (Container) < Container.Capacity 161 and then (not Contains (Container, New_Item)); 162 163 procedure Include (Container : in out Set; New_Item : Element_Type) with 164 Global => null, 165 Pre => Length (Container) < Container.Capacity; 166 167 procedure Replace (Container : in out Set; New_Item : Element_Type) with 168 Global => null, 169 Pre => Contains (Container, New_Item); 170 171 procedure Exclude (Container : in out Set; Item : Element_Type) with 172 Global => null; 173 174 procedure Delete (Container : in out Set; Item : Element_Type) with 175 Global => null, 176 Pre => Contains (Container, Item); 177 178 procedure Delete (Container : in out Set; Position : in out Cursor) with 179 Global => null, 180 Pre => Has_Element (Container, Position); 181 182 procedure Union (Target : in out Set; Source : Set) with 183 Global => null, 184 Pre => Length (Target) + Length (Source) - 185 Length (Intersection (Target, Source)) <= Target.Capacity; 186 187 function Union (Left, Right : Set) return Set with 188 Global => null, 189 Pre => Length (Left) + Length (Right) - 190 Length (Intersection (Left, Right)) <= Count_Type'Last; 191 192 function "or" (Left, Right : Set) return Set renames Union; 193 194 procedure Intersection (Target : in out Set; Source : Set) with 195 Global => null; 196 197 function Intersection (Left, Right : Set) return Set with 198 Global => null; 199 200 function "and" (Left, Right : Set) return Set renames Intersection; 201 202 procedure Difference (Target : in out Set; Source : Set) with 203 Global => null; 204 205 function Difference (Left, Right : Set) return Set with 206 Global => null; 207 208 function "-" (Left, Right : Set) return Set renames Difference; 209 210 procedure Symmetric_Difference (Target : in out Set; Source : Set) with 211 Global => null, 212 Pre => Length (Target) + Length (Source) - 213 2 * Length (Intersection (Target, Source)) <= Target.Capacity; 214 215 function Symmetric_Difference (Left, Right : Set) return Set with 216 Global => null, 217 Pre => Length (Left) + Length (Right) - 218 2 * Length (Intersection (Left, Right)) <= Count_Type'Last; 219 220 function "xor" (Left, Right : Set) return Set 221 renames Symmetric_Difference; 222 223 function Overlap (Left, Right : Set) return Boolean with 224 Global => null; 225 226 function Is_Subset (Subset : Set; Of_Set : Set) return Boolean with 227 Global => null; 228 229 function First (Container : Set) return Cursor with 230 Global => null; 231 232 function Next (Container : Set; Position : Cursor) return Cursor with 233 Global => null, 234 Pre => Has_Element (Container, Position) or else Position = No_Element; 235 236 procedure Next (Container : Set; Position : in out Cursor) with 237 Global => null, 238 Pre => Has_Element (Container, Position) or else Position = No_Element; 239 240 function Find 241 (Container : Set; 242 Item : Element_Type) return Cursor 243 with 244 Global => null; 245 246 function Contains (Container : Set; Item : Element_Type) return Boolean with 247 Global => null; 248 249 function Has_Element (Container : Set; Position : Cursor) return Boolean 250 with 251 Global => null; 252 253 function Equivalent_Elements (Left : Set; CLeft : Cursor; 254 Right : Set; CRight : Cursor) return Boolean 255 with 256 Global => null; 257 258 function Equivalent_Elements 259 (Left : Set; CLeft : Cursor; 260 Right : Element_Type) return Boolean 261 with 262 Global => null; 263 264 function Equivalent_Elements 265 (Left : Element_Type; 266 Right : Set; CRight : Cursor) return Boolean 267 with 268 Global => null; 269 270 function Default_Modulus (Capacity : Count_Type) return Hash_Type with 271 Global => null; 272 273 generic 274 type Key_Type (<>) is private; 275 276 with function Key (Element : Element_Type) return Key_Type; 277 278 with function Hash (Key : Key_Type) return Hash_Type; 279 280 with function Equivalent_Keys (Left, Right : Key_Type) return Boolean; 281 282 package Generic_Keys is 283 284 function Key (Container : Set; Position : Cursor) return Key_Type with 285 Global => null; 286 287 function Element (Container : Set; Key : Key_Type) return Element_Type 288 with 289 Global => null; 290 291 procedure Replace 292 (Container : in out Set; 293 Key : Key_Type; 294 New_Item : Element_Type) 295 with 296 Global => null; 297 298 procedure Exclude (Container : in out Set; Key : Key_Type) with 299 Global => null; 300 301 procedure Delete (Container : in out Set; Key : Key_Type) with 302 Global => null; 303 304 function Find (Container : Set; Key : Key_Type) return Cursor with 305 Global => null; 306 307 function Contains (Container : Set; Key : Key_Type) return Boolean with 308 Global => null; 309 310 end Generic_Keys; 311 312 function Strict_Equal (Left, Right : Set) return Boolean with 313 Ghost, 314 Global => null; 315 -- Strict_Equal returns True if the containers are physically equal, i.e. 316 -- they are structurally equal (function "=" returns True) and that they 317 -- have the same set of cursors. 318 319 function First_To_Previous (Container : Set; Current : Cursor) return Set 320 with 321 Ghost, 322 Global => null, 323 Pre => Has_Element (Container, Current) or else Current = No_Element; 324 325 function Current_To_Last (Container : Set; Current : Cursor) return Set 326 with 327 Ghost, 328 Global => null, 329 Pre => Has_Element (Container, Current) or else Current = No_Element; 330 -- First_To_Previous returns a container containing all elements preceding 331 -- Current (excluded) in Container. Current_To_Last returns a container 332 -- containing all elements following Current (included) in Container. 333 -- These two new functions can be used to express invariant properties in 334 -- loops which iterate over containers. First_To_Previous returns the part 335 -- of the container already scanned and Current_To_Last the part not 336 -- scanned yet. 337 338private 339 pragma SPARK_Mode (Off); 340 341 pragma Inline (Next); 342 343 type Node_Type is 344 record 345 Element : Element_Type; 346 Next : Count_Type; 347 Has_Element : Boolean := False; 348 end record; 349 350 package HT_Types is new 351 Ada.Containers.Hash_Tables.Generic_Bounded_Hash_Table_Types (Node_Type); 352 353 type Set (Capacity : Count_Type; Modulus : Hash_Type) is 354 new HT_Types.Hash_Table_Type (Capacity, Modulus) with null record; 355 356 use HT_Types; 357 358 type Cursor is record 359 Node : Count_Type; 360 end record; 361 362 No_Element : constant Cursor := (Node => 0); 363 364 Empty_Set : constant Set := (Capacity => 0, Modulus => 0, others => <>); 365 366end Ada.Containers.Formal_Hashed_Sets; 367