Source file setDomain.ml

(** 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