package goblint
Static analysis framework for C
Install
Dune Dependency
Authors
Maintainers
Sources
goblint-2.5.0.tbz
sha256=452d8491527aea21f2cbb11defcc14ba0daf9fdb6bdb9fc0af73e56eac57b916
sha512=1993cd45c4c7fe124ca6e157f07d17ec50fab5611b270a434ed1b7fb2910aa85a8e6eaaa77dad770430710aafb2f6d676c774dd33942d921f23e2f9854486551
doc/src/goblint.domain/setDomain.ml.html
Source file setDomain.ml
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499
(** Set domains. *) module Pretty = GoblintCil.Pretty open Pretty (* Exception raised when the set domain can not support the requested operation. * This will be raised, when trying to iterate a set that has been set to Top *) exception Unsupported of string let unsupported s = raise (Unsupported s) (** A set domain must support all the standard library set operations. They have been copied instead of included since our [empty] has a different signature. *) module type S = sig include Lattice.S type elt val empty: unit -> t val is_empty: t -> bool val mem: elt -> t -> bool val add: elt -> t -> t val singleton: elt -> t val remove: elt -> t -> t (** See {!Set.S.remove}. {b NB!} On set abstractions this is a {e strong} removal, i.e. all subsumed elements are also removed. @see <https://github.com/goblint/analyzer/pull/809#discussion_r936336198> *) val union: t -> t -> t val inter: t -> t -> t val diff: t -> t -> t (** See {!Set.S.diff}. {b NB!} On set abstractions this is a {e strong} removal, i.e. all subsumed elements are also removed. @see <https://github.com/goblint/analyzer/pull/809#discussion_r936336198> *) val subset: t -> t -> bool val disjoint: t -> t -> bool val iter: (elt -> unit) -> t -> unit (** See {!Set.S.iter}. On set abstractions this iterates only over canonical elements, not all subsumed elements. *) val map: (elt -> elt) -> t -> t (** See {!Set.S.map}. On set abstractions this maps only canonical elements, not all subsumed elements. *) val fold: (elt -> 'a -> 'a) -> t -> 'a -> 'a (** See {!Set.S.fold}. On set abstractions this folds only over canonical elements, not all subsumed elements. *) val for_all: (elt -> bool) -> t -> bool (** See {!Set.S.for_all}. On set abstractions this checks only canonical elements, not all subsumed elements. *) val exists: (elt -> bool) -> t -> bool (** See {!Set.S.exists}. On set abstractions this checks only canonical elements, not all subsumed elements. *) val filter: (elt -> bool) -> t -> t (** See {!Set.S.filter}. On set abstractions this filters only canonical elements, not all subsumed elements. *) val partition: (elt -> bool) -> t -> t * t (** See {!Set.S.partition}. On set abstractions this partitions only canonical elements, not all subsumed elements. *) val cardinal: t -> int (** See {!Set.S.cardinal}. On set abstractions this counts only canonical elements, not all subsumed elements. *) val elements: t -> elt list (** See {!Set.S.elements}. On set abstractions this lists only canonical elements, not all subsumed elements. *) val of_list: elt list -> t val min_elt: t -> elt (** See {!Set.S.min_elt}. On set abstractions this chooses only a canonical element, not any subsumed element. *) val max_elt: t -> elt (** See {!Set.S.max_elt}. On set abstractions this chooses only a canonical element, not any subsumed element. *) val choose: t -> elt (** See {!Set.S.choose}. On set abstractions this chooses only a canonical element, not any subsumed element. *) end (** Subsignature of {!S}, which is sufficient for {!Print}. *) module type Elements = sig type t type elt val elements: t -> elt list val iter: (elt -> unit) -> t -> unit end (** Reusable output definitions for sets. *) module Print (E: Printable.S) (S: Elements with type elt = E.t) = struct let pretty () x = let elts = S.elements x in let content = List.map (E.pretty ()) elts in let rec separate x = match x with | [] -> [] | [x] -> [x] | (x::xs) -> x ++ (text "," ++ break) :: separate xs in let separated = separate content in let content = List.fold_left (++) nil separated in (text "{" ++ align) ++ content ++ (unalign ++ text "}") (** Short summary for sets. *) let show x : string = let all_elems : string list = List.map E.show (S.elements x) in Printable.get_short_list "{" "}" all_elems let to_yojson x = [%to_yojson: E.t list] (S.elements x) let printXml f xs = BatPrintf.fprintf f "<value>\n<set>\n"; S.iter (E.printXml f) xs; BatPrintf.fprintf f "</set>\n</value>\n" end (** A functor for creating a simple set domain, there is no top element, and * calling [top ()] will raise an exception *) module Make (Base: Printable.S): S with type elt = Base.t and type t = BatSet.Make (Base).t = (* TODO: remove, only needed in VarEq for some reason... *) struct include Printable.Std include BatSet.Make(Base) let name () = "Set (" ^ Base.name () ^ ")" let empty _ = empty let leq = subset let join = union let widen = join let meet = inter let narrow = meet let bot = empty let is_bot = is_empty let top () = unsupported "Make.top" let is_top _ = false include Print (Base) ( struct type nonrec t = t type nonrec elt = elt let elements = elements let iter = iter end ) let hash x = fold (fun x y -> 13 * y + Base.hash x) x 0 let relift x = map Base.relift x let pretty_diff () ((x:t),(y:t)): Pretty.doc = if leq x y then dprintf "%s: These are fine!" (name ()) else if is_bot y then dprintf "%s: %a instead of bot" (name ()) pretty x else begin let evil = choose (diff x y) in Pretty.dprintf "%s: %a not leq %a\n @[because %a@]" (name ()) pretty x pretty y Base.pretty evil end let arbitrary () = QCheck.map ~rev:elements of_list @@ QCheck.small_list (Base.arbitrary ()) end (** A functor for creating a path sensitive set domain, that joins the base * analysis whenever the user elements coincide. Just as above there is no top * element, and calling [top ()] will raise an exception *) (* TODO: unused *) module SensitiveConf (C: Printable.ProdConfiguration) (Base: Lattice.S) (User: Printable.S) = struct module Elt = Printable.ProdConf (C) (Base) (User) include Make(Elt) let name () = "Sensitive " ^ name () let leq s1 s2 = (* I want to check that forall e in x, the same key is in y with it's base * domain element being leq of this one *) let p (b1,u1) = exists (fun (b2,u2) -> User.equal u1 u2 && Base.leq b1 b2) s2 in for_all p s1 let pretty_diff () ((x:t),(y:t)): Pretty.doc = Pretty.dprintf "%s: %a not leq %a" (name ()) pretty x pretty y let join s1 s2 = (* Ok, so for each element (b2,u2) in s2, we check in s1 for elements that have * equal user values (there should be at most 1) and we either join with it, or * just add the element to our accumulator res and remove it from s1 *) let f (b2,u2) (s1,res) = let (s1_match, s1_rest) = partition (fun (b1,u1) -> User.equal u1 u2) s1 in let el = try let (b1,u1) = choose s1_match in (Base.join b1 b2, u2) with Not_found -> (b2,u2) in (s1_rest, add el res) in let (s1', res) = fold f s2 (s1, empty ()) in union s1' res let add e s = join (singleton e) s (* The meet operation is slightly different from the above, I think this is * the right thing, the intuition is from thinking of this as a MapBot *) let meet s1 s2 = let f (b2,u2) (s1,res) = let (s1_match, s1_rest) = partition (fun (b1,u1) -> User.equal u1 u2) s1 in let res = try let (b1,u1) = choose s1_match in add (Base.meet b1 b2, u2) res with Not_found -> res in (s1_rest, res) in snd (fold f s2 (s1, empty ())) end [@@deprecated] (** Auxiliary signature for naming the top element *) module type ToppedSetNames = sig val topname: string end module LiftTop (S: S) (N: ToppedSetNames): S with type elt = S.elt and type t = [`Top | `Lifted of S.t] = (* Expose t for HoareDomain.Set_LiftTop *) struct include Printable.Std include Lattice.LiftTop (S) type elt = S.elt let empty () = `Lifted (S.empty ()) let is_empty x = match x with | `Top -> false | `Lifted x -> S.is_empty x let mem x s = match s with | `Top -> true | `Lifted s -> S.mem x s let add x s = match s with | `Top -> `Top | `Lifted s -> `Lifted (S.add x s) let singleton x = `Lifted (S.singleton x) let remove x s = match s with | `Top -> `Top (* NB! NB! NB! *) | `Lifted s -> `Lifted (S.remove x s) let union x y = match x, y with | `Top, _ -> `Top | _, `Top -> `Top | `Lifted x, `Lifted y -> `Lifted (S.union x y) let inter x y = match x, y with | `Top, y -> y | x, `Top -> x | `Lifted x, `Lifted y -> `Lifted (S.inter x y) let diff x y = match x, y with | x, `Top -> empty () | `Top, y -> `Top (* NB! NB! NB! *) | `Lifted x, `Lifted y -> `Lifted (S.diff x y) let subset x y = match x, y with | _, `Top -> true | `Top, _ -> false | `Lifted x, `Lifted y -> S.subset x y let disjoint x y = match x, y with | `Top, `Top -> false | `Lifted x, `Top | `Top, `Lifted x -> S.is_empty x | `Lifted x, `Lifted y -> S.disjoint x y let schema normal abnormal x = match x with | `Top -> unsupported abnormal | `Lifted t -> normal t let schema_default v f = function | `Top -> v | `Lifted x -> f x (* HACK! Map is an exception in that it doesn't throw an exception! *) let map f x = match x with | `Top -> `Top | `Lifted t -> `Lifted (S.map f t) let iter f = schema (S.iter f) "iter on `Top" (* let map f = schema (fun t -> `Lifted (S.map f t)) "map"*) let fold f x e = schema (fun t -> S.fold f t e) "fold on `Top" x let for_all f = schema_default false (S.for_all f) let exists f = schema_default true (S.exists f) let filter f = schema (fun t -> `Lifted (S.filter f t)) "filter on `Top" let elements = schema S.elements "elements on `Top" let of_list xs = `Lifted (S.of_list xs) let cardinal = schema S.cardinal "cardinal on `Top" let min_elt = schema S.min_elt "min_elt on `Top" let max_elt = schema S.max_elt "max_elt on `Top" let choose = schema S.choose "choose on `Top" let partition f = schema (fun t -> match S.partition f t with (a,b) -> (`Lifted a, `Lifted b)) "filter on `Top" (* The printable implementation *) (* Overrides `Top text *) let pretty () x = match x with | `Top -> text N.topname | `Lifted t -> S.pretty () t let show x : string = match x with | `Top -> N.topname | `Lifted t -> S.show t (* Lattice implementation *) (* Lift separately because lattice order might be different from subset order, e.g. after Reverse *) let bot () = `Lifted (S.bot ()) let is_bot x = match x with | `Top -> false | `Lifted x -> S.is_bot x let leq x y = match x, y with | _, `Top -> true | `Top, _ -> false | `Lifted x, `Lifted y -> S.leq x y let join x y = match x, y with | `Top, _ -> `Top | _, `Top -> `Top | `Lifted x, `Lifted y -> `Lifted (S.join x y) let widen x y = (* assumes y to be bigger than x *) match x, y with | `Top, _ | _, `Top -> `Top | `Lifted x, `Lifted y -> `Lifted (S.widen x y) let meet x y = match x, y with | `Top, y -> y | x, `Top -> x | `Lifted x, `Lifted y -> `Lifted (S.meet x y) let narrow x y = match x, y with | `Top, y -> y | x, `Top -> x | `Lifted x, `Lifted y -> `Lifted (S.narrow x y) let arbitrary () = QCheck.set_print show (arbitrary ()) end (** Functor for creating artificially topped set domains. *) module ToppedSet (Base: Printable.S) (N: ToppedSetNames): S with type elt = Base.t and type t = [`Top | `Lifted of Make (Base).t] = (* TODO: don't expose t *) struct module S = Make (Base) include LiftTop (S) (N) end (* This one just removes the extra "{" notation and also by always returning * false for the isSimple, the answer looks better, but this is essentially a * hack. All the pretty printing needs some rethinking. *) module HeadlessSet (Base: Printable.S) = struct include Make(Base) let name () = "Headless " ^ name () let pretty () x = let elts = elements x in let content = List.map (Base.pretty ()) elts in let rec separate x = match x with | [] -> [] | [x] -> [x] | (x::xs) -> x ++ (text ", ") ++ line :: separate xs in let separated = separate content in let content = List.fold_left (++) nil separated in content let pretty_diff () ((x:t),(y:t)): Pretty.doc = Pretty.dprintf "%s: %a not leq %a" (name ()) pretty x pretty y let printXml f xs = iter (Base.printXml f) xs end (** Reverses lattice order of a set domain while keeping the set operations same. *) module Reverse (Base: S) = struct include Base include Lattice.Reverse (Base) end module type FiniteSetElem = sig include Printable.S val elems: t list (** List of all possible elements. *) end module FiniteSet (E: FiniteSetElem) = struct module E = struct include E let arbitrary () = QCheck.oneofl E.elems end include Make (E) let top () = of_list E.elems let is_top x = equal x (top ()) end (** Set abstracted by a single (joined) element. Element-wise {!S} operations only observe the single element. *) module Joined (E: Lattice.S): S with type elt = E.t = struct type elt = E.t include E let singleton e = e let of_list es = List.fold_left E.join (E.bot ()) es let exists p e = p e let for_all p e = p e let mem e e' = E.leq e e' let choose e = e let elements e = [e] let remove e e' = if E.leq e' e then E.bot () (* NB! strong removal *) else e' let map f e = f e let fold f e a = f e a let empty () = E.bot () let add e e' = E.join e e' let is_empty e = E.is_bot e let union e e' = E.join e e' let diff e e' = remove e' e (* NB! strong removal *) let iter f e = f e let cardinal e = if is_empty e then 0 else 1 let inter e e' = E.meet e e' let subset e e' = E.leq e e' let filter p e = unsupported "Joined.filter" let partition p e = unsupported "Joined.partition" let min_elt e = unsupported "Joined.min_elt" let max_elt e = unsupported "Joined.max_elt" let disjoint e e' = is_empty (inter e e') end
sectionYPositions = computeSectionYPositions($el), 10)"
x-init="setTimeout(() => sectionYPositions = computeSectionYPositions($el), 10)"
>