Source file disjointDomain.ml
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(** Abstract domains for collections of elements from disjoint unions of domains.
Formally, the elements form a cofibered domain from a discrete category.
Elements are grouped into disjoint buckets by a congruence or/and a projection.
All operations on elements are performed bucket-wise and must be bucket-closed.
Examples of such domains are path-sensitivity and address sets. *)
(** {1 Sets} *)
(** {2 By projection} *)
(** Buckets defined by projection.
The module is the image (representative) of the projection function {!of_elt}. *)
module type Representative =
sig
include Printable.S (** @closed *)
type elt (** Type of elements, i.e. the domain of the projection function {!of_elt}. *)
val of_elt: elt -> t (** Projection function. *)
end
(** Set of elements [E.t] grouped into buckets by [R],
where each bucket is described by the set [B].
Common choices for [B] are {!SetDomain.Joined} and {!HoareDomain.SetEM}.
Handles {!Lattice.BotValue} from [B]. *)
module ProjectiveSet (E: Printable.S) (B: SetDomain.S with type elt = E.t) (R: Representative with type elt = E.t):
sig
include SetDomain.S with type elt = E.t
val fold_buckets: (R.t -> B.t -> 'a -> 'a) -> t -> 'a -> 'a
end
=
struct
type elt = E.t
module M = MapDomain.MapBot (R) (B)
(** Invariant: no explicit bot buckets.
Required for efficient [is_empty], [cardinal] and [choose]. *)
let name () = "ProjectiveSet (" ^ B.name () ^ ")"
type t = M.t
let equal = M.equal
let compare = M.compare
let hash = M.hash
let tag = M.tag
let relift = M.relift
let is_bot = M.is_bot
let bot = M.bot
let is_top = M.is_top
let top = M.top
let is_empty = M.is_empty
let empty = M.empty
let cardinal = M.cardinal
let leq = M.leq
let join = M.join
let pretty_diff = M.pretty_diff
let fold f m a = M.fold (fun _ e a -> B.fold f e a) m a
let iter f m = M.iter (fun _ e -> B.iter f e) m
let exists p m = M.exists (fun _ e -> B.exists p e) m
let for_all p m = M.for_all (fun _ e -> B.for_all p e) m
let singleton e = M.singleton (R.of_elt e) (B.singleton e)
let choose m = B.choose (snd (M.choose m))
let mem e m =
match M.find_opt (R.of_elt e) m with
| Some b -> B.mem e b
| None -> false
let add e m =
let r = R.of_elt e in
let b' = match M.find_opt r m with
| Some b -> B.add e b
| None -> B.singleton e
in
M.add r b' m
let remove e m =
let r = R.of_elt e in
match M.find_opt r m with
| Some b ->
begin match B.remove e b with
| b' when B.is_bot b' ->
M.remove r m
| exception Lattice.BotValue ->
M.remove r m
| b' ->
M.add r b' m
end
| None -> m
let diff m1 m2 =
M.merge (fun _ b1 b2 ->
match b1, b2 with
| Some b1, Some b2 ->
begin match B.diff b1 b2 with
| b' when B.is_bot b' ->
None
| exception Lattice.BotValue ->
None
| b' ->
Some b'
end
| Some _, None -> b1
| None, _ -> None
) m1 m2
let of_list es = List.fold_left (fun acc e ->
add e acc
) (empty ()) es
let elements m = fold List.cons m []
let map f m = fold (fun e acc ->
add (f e) acc
) m (empty ())
let widen m1 m2 =
Lattice.assert_valid_widen ~leq ~pretty_diff m1 m2;
M.widen m1 m2
let meet m1 m2 =
M.merge (fun _ b1 b2 ->
match b1, b2 with
| Some b1, Some b2 ->
begin match B.meet b1 b2 with
| b' when B.is_bot b' ->
None
| exception Lattice.BotValue ->
None
| b' ->
Some b'
end
| _, _ -> None
) m1 m2
let narrow m1 m2 =
M.merge (fun _ b1 b2 ->
match b1, b2 with
| Some b1, Some b2 ->
begin match B.narrow b1 b2 with
| b' when B.is_bot b' ->
None
| exception Lattice.BotValue ->
None
| b' ->
Some b'
end
| _, _ -> None
) m1 m2
let union = join
let inter = meet
let subset = leq
include SetDomain.Print (E) (
struct
type nonrec t = t
type nonrec elt = elt
let elements = elements
let iter = iter
end
)
let arbitrary () = failwith "Projective.arbitrary"
let filter p m = SetDomain.unsupported "Projective.filter"
let partition p m = SetDomain.unsupported "Projective.partition"
let min_elt m = SetDomain.unsupported "Projective.min_elt"
let max_elt m = SetDomain.unsupported "Projective.max_elt"
let disjoint m1 m2 = is_empty (inter m1 m2)
let fold_buckets = M.fold
end
module type MayEqualSetDomain =
sig
include SetDomain.S
val may_be_equal: elt -> elt -> bool
end
module ProjectiveSetPairwiseMeet (E: Printable.S) (B: MayEqualSetDomain with type elt = E.t) (R: Representative with type elt = E.t): SetDomain.S with type elt = E.t = struct
include ProjectiveSet (E) (B) (R)
let meet m1 m2 =
let meet_buckets b1 b2 acc =
B.fold (fun e1 acc ->
B.fold (fun e2 acc ->
if B.may_be_equal e1 e2 then
add e1 (add e2 acc)
else
acc
) b2 acc
) b1 acc
in
fold_buckets (fun _ b1 acc ->
fold_buckets (fun _ b2 acc ->
meet_buckets b1 b2 acc
) m2 acc
) m1 (empty ())
end
(** {2 By congruence} *)
(** Buckets defined by congruence. *)
module type Congruence =
sig
type elt (** Type of elements. *)
val cong: elt -> elt -> bool (** Congruence relation on elements. *)
end
(** Set of elements [E.t] grouped into buckets by [C],
where each bucket is described by the set [B].
Common choices for [B] are {!SetDomain.Joined} and {!HoareDomain.SetEM}.
Handles {!Lattice.BotValue} from [B]. *)
module PairwiseSet (E: Printable.S) (B: SetDomain.S with type elt = E.t) (C: Congruence with type elt = E.t): SetDomain.S with type elt = E.t =
struct
type elt = E.t
module S = SetDomain.Make (B)
(** Invariant: no explicit bot buckets.
Required for efficient [is_empty], [cardinal] and [choose]. *)
let name () = "Pairwise (" ^ B.name () ^ ")"
type t = S.t
let equal = S.equal
let compare = S.compare
let hash = S.hash
let tag = S.tag
let relift = S.relift
let is_bot = S.is_bot
let bot = S.bot
let is_top = S.is_top
let top = S.top
let is_empty = S.is_empty
let empty = S.empty
let cardinal = S.cardinal
let fold f s a = S.fold (fun b a -> B.fold f b a) s a
let iter f s = S.iter (fun b -> B.iter f b) s
let exists p s = S.exists (fun b -> B.exists p b) s
let for_all p s = S.for_all (fun b -> B.for_all p b) s
let singleton e = S.singleton (B.singleton e)
let choose s = B.choose (S.choose s)
let mem e s =
S.exists (fun b -> C.cong (B.choose b) e && B.mem e b) s
let add e s =
let (s_match, s_rest) = S.partition (fun b -> C.cong (B.choose b) e) s in
let b' = match S.choose s_match with
| b ->
assert (S.cardinal s_match = 1);
B.add e b
| exception Not_found -> B.singleton e
in
S.add b' s_rest
let remove e s =
let (s_match, s_rest) = S.partition (fun b -> C.cong (B.choose b) e) s in
match S.choose s_match with
| b ->
assert (S.cardinal s_match = 1);
begin match B.remove e b with
| b' when B.is_bot b' ->
s_rest
| exception Lattice.BotValue ->
s_rest
| b' ->
S.add b' s
end
| exception Not_found -> s
let diff s1 s2 =
let f b2 (s1, acc) =
let e2 = B.choose b2 in
let (s1_match, s1_rest) = S.partition (fun b1 -> C.cong (B.choose b1) e2) s1 in
let acc' = match S.choose s1_match with
| b1 ->
assert (S.cardinal s1_match = 1);
begin match B.diff b1 b2 with
| b' when B.is_bot b' ->
acc
| exception Lattice.BotValue ->
acc
| b' ->
S.add b' acc
end
| exception Not_found -> acc
in
(s1_rest, acc')
in
let (s1', acc) = S.fold f s2 (s1, empty ()) in
S.union s1' acc
let of_list es = List.fold_left (fun acc e ->
add e acc
) (empty ()) es
let elements m = fold List.cons m []
let map f s = fold (fun e acc ->
add (f e) acc
) s (empty ())
let leq s1 s2 =
S.for_all (fun b1 ->
let e1 = B.choose b1 in
S.exists (fun b2 -> C.cong (B.choose b2) e1 && B.leq b1 b2) s2
) s1
let pretty_diff () (s1, s2) =
let s1_not_leq = S.filter (fun b1 ->
let e1 = B.choose b1 in
not (S.exists (fun b2 -> C.cong (B.choose b2) e1 && B.leq b1 b2) s2)
) s1
in
let b1_not_leq = S.choose s1_not_leq in
let e1_not_leq = B.choose b1_not_leq in
GoblintCil.Pretty.(
dprintf "%a:\n" B.pretty b1_not_leq
++
S.fold (fun b2 acc ->
if C.cong (B.choose b2) e1_not_leq then
dprintf "not leq %a because %a\n" B.pretty b2 B.pretty_diff (b1_not_leq, b2) ++ acc
else
dprintf "not cong %a\n" B.pretty b2 ++ acc
) s2 nil
)
let join s1 s2 =
let f b2 (s1, acc) =
let e2 = B.choose b2 in
let (s1_match, s1_rest) = S.partition (fun b1 -> C.cong (B.choose b1) e2) s1 in
let b' = match S.choose s1_match with
| b1 ->
assert (S.cardinal s1_match = 1);
B.join b1 b2
| exception Not_found -> b2
in
(s1_rest, S.add b' acc)
in
let (s1', acc) = S.fold f s2 (s1, empty ()) in
S.union s1' acc
let widen s1 s2 =
Lattice.assert_valid_widen ~leq ~pretty_diff s1 s2;
let f b2 (s1, acc) =
let e2 = B.choose b2 in
let (s1_match, s1_rest) = S.partition (fun e1 -> C.cong (B.choose e1) e2) s1 in
let b' = match S.choose s1_match with
| b1 ->
assert (S.cardinal s1_match = 1);
B.widen b1 b2
| exception Not_found -> b2
in
(s1_rest, S.add b' acc)
in
let (s1', acc) = S.fold f s2 (s1, empty ()) in
assert (is_empty s1');
acc
let meet s1 s2 =
let f b2 (s1, acc) =
let e2 = B.choose b2 in
let (s1_match, s1_rest) = S.partition (fun b1 -> C.cong (B.choose b1) e2) s1 in
let acc' = match S.choose s1_match with
| b1 ->
assert (S.cardinal s1_match = 1);
begin match B.meet b1 b2 with
| b' when B.is_bot b' ->
acc
| exception Lattice.BotValue ->
acc
| b' ->
S.add b' acc
end
| exception Not_found -> acc
in
(s1_rest, acc')
in
snd (S.fold f s2 (s1, S.empty ()))
let narrow s1 s2 =
let f b2 (s1, acc) =
let e2 = B.choose b2 in
let (s1_match, s1_rest) = S.partition (fun b1 -> C.cong (B.choose b1) e2) s1 in
let acc' = match S.choose s1_match with
| b1 ->
assert (S.cardinal s1_match = 1);
begin match B.narrow b1 b2 with
| b' when B.is_bot b' ->
acc
| exception Lattice.BotValue ->
acc
| b' ->
S.add b' acc
end
| exception Not_found -> acc
in
(s1_rest, acc')
in
snd (S.fold f s2 (s1, S.empty ()))
let union = join
let inter = meet
let subset = leq
include SetDomain.Print (E) (
struct
type nonrec t = t
type nonrec elt = elt
let elements = elements
let iter = iter
end
)
let arbitrary () = failwith "Pairwise.arbitrary"
let filter p s = SetDomain.unsupported "Pairwise.filter"
let partition p s = SetDomain.unsupported "Pairwise.partition"
let min_elt s = SetDomain.unsupported "Pairwise.min_elt"
let max_elt s = SetDomain.unsupported "Pairwise.max_elt"
let disjoint s1 s2 = is_empty (inter s1 s2)
end
(** Buckets defined by a coarse projection and a fine congruence.
Congruent elements must have the same representative, but not vice versa ({!Representative} would then suffice). *)
module type RepresentativeCongruence =
sig
include Representative
include Congruence with type elt := elt
end
(** Set of elements [E.t] grouped into buckets by [RC],
where each bucket is described by the set [B]. *)
module CombinedSet (E: Printable.S) (B: SetDomain.S with type elt = E.t) (RC: RepresentativeCongruence with type elt = E.t) =
ProjectiveSet (E) (PairwiseSet (E) (B) (RC)) (RC)
(** {1 Maps}
Generalization of above sets into maps, whose key set behaves like above sets,
but each element can also be associated with a value. *)
(** {2 By projection} *)
(** Map of keys [E.t] grouped into buckets by [R],
where each bucket is described by the map [B] with values [V.t].
Common choice for [B] is {!MapDomain.Joined}.
Handles {!Lattice.BotValue} from [B]. *)
module ProjectiveMap (E: Printable.S) (V: Printable.S) (B: MapDomain.S with type key = E.t and type value = V.t) (R: Representative with type elt = E.t): MapDomain.S with type key = E.t and type value = B.value =
struct
type key = E.t
type value = B.value
module M = MapDomain.MapBot (R) (B)
(** Invariant: no explicit bot buckets.
Required for efficient [is_empty], [cardinal] and [choose]. *)
let name () = "ProjectiveMap (" ^ B.name () ^ ")"
type t = M.t
let equal = M.equal
let compare = M.compare
let hash = M.hash
let tag = M.tag
let relift = M.relift
let is_bot = M.is_bot
let bot = M.bot
let is_top = M.is_top
let top = M.top
let is_empty = M.is_empty
let empty = M.empty
let cardinal = M.cardinal
let leq = M.leq
let join = M.join
let pretty_diff = M.pretty_diff
let fold f m a = M.fold (fun _ e a -> B.fold f e a) m a
let iter f m = M.iter (fun _ e -> B.iter f e) m
let exists p m = M.exists (fun _ e -> B.exists p e) m
let for_all p m = M.for_all (fun _ e -> B.for_all p e) m
let singleton e v = M.singleton (R.of_elt e) (B.singleton e v)
let choose m = B.choose (snd (M.choose m))
let mem e m =
match M.find_opt (R.of_elt e) m with
| Some b -> B.mem e b
| None -> false
let find e m =
let r = R.of_elt e in
let b = M.find r m in
B.find e b
let find_opt e m =
let r = R.of_elt e in
match M.find_opt r m with
| Some b ->
B.find_opt e b
| None -> None
let add e v m =
let r = R.of_elt e in
let b' = match M.find_opt r m with
| Some b -> B.add e v b
| None -> B.singleton e v
in
M.add r b' m
let remove e m =
let r = R.of_elt e in
match M.find_opt r m with
| Some b ->
begin match B.remove e b with
| b' when B.is_bot b' ->
M.remove r m
| exception Lattice.BotValue ->
M.remove r m
| b' ->
M.add r b' m
end
| None -> m
let add_list evs m = List.fold_left (fun acc (e, v) ->
add e v acc
) m evs
let add_list_set es v m = List.fold_left (fun acc e ->
add e v acc
) m es
let add_list_fun es f m = List.fold_left (fun acc e ->
add e (f e) acc
) m es
let bindings m = fold (fun e v acc -> (e, v) :: acc) m []
let map f m = M.map (fun b ->
B.map f b
) m
let mapi f m = M.map (fun b ->
B.mapi f b
) m
let long_map2 f m1 m2 = M.long_map2 (fun b1 b2 ->
B.long_map2 f b1 b2
) m1 m2
let map2 f m1 m2 = M.map2 (fun b1 b2 ->
B.map2 f b1 b2
) m1 m2
let merge f m1 m2 = failwith "ProjectiveMap.merge"
let widen m1 m2 =
Lattice.assert_valid_widen ~leq ~pretty_diff m1 m2;
M.widen m1 m2
let meet m1 m2 =
M.merge (fun _ b1 b2 ->
match b1, b2 with
| Some b1, Some b2 ->
begin match B.meet b1 b2 with
| b' when B.is_bot b' ->
None
| exception Lattice.BotValue ->
None
| b' ->
Some b'
end
| _, _ -> None
) m1 m2
let narrow m1 m2 =
M.merge (fun _ b1 b2 ->
match b1, b2 with
| Some b1, Some b2 ->
begin match B.narrow b1 b2 with
| b' when B.is_bot b' ->
None
| exception Lattice.BotValue ->
None
| b' ->
Some b'
end
| _, _ -> None
) m1 m2
include MapDomain.Print (E) (V) (
struct
type nonrec t = t
type nonrec key = key
type nonrec value = value
let fold = fold
let iter = iter
end
)
let arbitrary () = failwith "ProjectiveMap.arbitrary"
let filter p m = failwith "ProjectiveMap.filter"
let leq_with_fct _ _ _ = failwith "ProjectiveMap.leq_with_fct"
let join_with_fct _ _ _ = failwith "ProjectiveMap.join_with_fct"
let widen_with_fct _ _ _ = failwith "ProjectiveMap.widen_with_fct"
end
(** {2 By congruence} *)
(** Map of keys [E.t] grouped into buckets by [C],
where each bucket is described by the map [B] with values [R.t].
Common choice for [B] is {!MapDomain.Joined}.
Handles {!Lattice.BotValue} from [B]. *)
module PairwiseMap (E: Printable.S) (R: Printable.S) (B: MapDomain.S with type key = E.t and type value = R.t) (C: Congruence with type elt = E.t): MapDomain.S with type key = E.t and type value = B.value =
struct
type key = E.t
type value = B.value
module S = SetDomain.Make (B)
(** Invariant: no explicit bot buckets.
Required for efficient [is_empty], [cardinal] and [choose]. *)
let name () = "PairwiseMap (" ^ B.name () ^ ")"
type t = S.t
let equal = S.equal
let compare = S.compare
let hash = S.hash
let tag = S.tag
let relift = S.relift
let is_bot = S.is_bot
let bot = S.bot
let is_top = S.is_top
let top = S.top
let is_empty = S.is_empty
let empty = S.empty
let cardinal = S.cardinal
let fold f s a = S.fold (fun b a -> B.fold f b a) s a
let iter f s = S.iter (fun b -> B.iter f b) s
let exists p s = S.exists (fun b -> B.exists p b) s
let for_all p s = S.for_all (fun b -> B.for_all p b) s
let singleton e r = S.singleton (B.singleton e r)
let choose s = B.choose (S.choose s)
let mem e s =
S.exists (fun b -> C.cong (fst (B.choose b)) e && B.mem e b) s
let find e s =
let (s_match, s_rest) = S.partition (fun b -> C.cong (fst (B.choose b)) e) s in
let b = S.choose s_match in
assert (S.cardinal s_match = 1);
B.find e b
let find_opt e s =
let (s_match, s_rest) = S.partition (fun b -> C.cong (fst (B.choose b)) e) s in
match S.choose s_match with
| b ->
assert (S.cardinal s_match = 1);
B.find_opt e b
| exception Not_found -> None
let add e r s =
let (s_match, s_rest) = S.partition (fun b -> C.cong (fst (B.choose b)) e) s in
let b' = match S.choose s_match with
| b ->
assert (S.cardinal s_match = 1);
B.add e r b
| exception Not_found -> B.singleton e r
in
S.add b' s_rest
let remove e s =
let (s_match, s_rest) = S.partition (fun b -> C.cong (fst (B.choose b)) e) s in
match S.choose s_match with
| b ->
assert (S.cardinal s_match = 1);
begin match B.remove e b with
| b' when B.is_bot b' ->
s_rest
| exception Lattice.BotValue ->
s_rest
| b' ->
S.add b' s
end
| exception Not_found -> s
let add_list ers m = List.fold_left (fun acc (e, r) ->
add e r acc
) m ers
let add_list_set es r m = List.fold_left (fun acc e ->
add e r acc
) m es
let add_list_fun es f m = List.fold_left (fun acc e ->
add e (f e) acc
) m es
let bindings m = fold (fun e r acc -> (e, r) :: acc) m []
let map f m = S.map (fun b ->
B.map f b
) m
let mapi f m = S.map (fun b ->
B.mapi f b
) m
let long_map2 f s1 s2 =
let f b2 (s1, acc) =
let e2 = fst (B.choose b2) in
let (s1_match, s1_rest) = S.partition (fun b1 -> C.cong (fst (B.choose b1)) e2) s1 in
let b' = match S.choose s1_match with
| b1 ->
assert (S.cardinal s1_match = 1);
B.long_map2 f b1 b2
| exception Not_found -> b2
in
(s1_rest, S.add b' acc)
in
let (s1', acc) = S.fold f s2 (s1, empty ()) in
S.union s1' acc
let map2 f s1 s2 =
let f b2 (s1, acc) =
let e2 = fst (B.choose b2) in
let (s1_match, s1_rest) = S.partition (fun b1 -> C.cong (fst (B.choose b1)) e2) s1 in
let acc' = match S.choose s1_match with
| b1 ->
assert (S.cardinal s1_match = 1);
begin match B.map2 f b1 b2 with
| b' when B.is_bot b' ->
acc
| exception Lattice.BotValue ->
acc
| b' ->
S.add b' acc
end
| exception Not_found -> acc
in
(s1_rest, acc')
in
snd (S.fold f s2 (s1, S.empty ()))
let merge f m1 m2 = failwith "PairwiseMap.merge"
let leq s1 s2 =
S.for_all (fun b1 ->
let e1 = fst (B.choose b1) in
S.exists (fun b2 -> C.cong (fst (B.choose b2)) e1 && B.leq b1 b2) s2
) s1
let pretty_diff () (s1, s2) =
let s1_not_leq = S.filter (fun b1 ->
let e1 = fst (B.choose b1) in
not (S.exists (fun b2 -> C.cong (fst (B.choose b2)) e1 && B.leq b1 b2) s2)
) s1
in
let b1_not_leq = S.choose s1_not_leq in
let e1_not_leq = fst (B.choose b1_not_leq) in
GoblintCil.Pretty.(
dprintf "%a:\n" B.pretty b1_not_leq
++
S.fold (fun b2 acc ->
if C.cong (fst (B.choose b2)) e1_not_leq then
dprintf "not leq %a because %a\n" B.pretty b2 B.pretty_diff (b1_not_leq, b2) ++ acc
else
dprintf "not cong %a\n" B.pretty b2 ++ acc
) s2 nil
)
let join s1 s2 =
let f b2 (s1, acc) =
let e2 = fst (B.choose b2) in
let (s1_match, s1_rest) = S.partition (fun b1 -> C.cong (fst (B.choose b1)) e2) s1 in
let b' = match S.choose s1_match with
| b1 ->
assert (S.cardinal s1_match = 1);
B.join b1 b2
| exception Not_found -> b2
in
(s1_rest, S.add b' acc)
in
let (s1', acc) = S.fold f s2 (s1, empty ()) in
S.union s1' acc
let widen s1 s2 =
Lattice.assert_valid_widen ~leq ~pretty_diff s1 s2;
let f b2 (s1, acc) =
let e2 = fst (B.choose b2) in
let (s1_match, s1_rest) = S.partition (fun e1 -> C.cong (fst (B.choose e1)) e2) s1 in
let b' = match S.choose s1_match with
| b1 ->
assert (S.cardinal s1_match = 1);
B.widen b1 b2
| exception Not_found -> b2
in
(s1_rest, S.add b' acc)
in
let (s1', acc) = S.fold f s2 (s1, empty ()) in
assert (is_empty s1');
acc
let meet s1 s2 =
let f b2 (s1, acc) =
let e2 = fst (B.choose b2) in
let (s1_match, s1_rest) = S.partition (fun b1 -> C.cong (fst (B.choose b1)) e2) s1 in
let acc' = match S.choose s1_match with
| b1 ->
assert (S.cardinal s1_match = 1);
begin match B.meet b1 b2 with
| b' when B.is_bot b' ->
acc
| exception Lattice.BotValue ->
acc
| b' ->
S.add b' acc
end
| exception Not_found -> acc
in
(s1_rest, acc')
in
snd (S.fold f s2 (s1, S.empty ()))
let narrow s1 s2 =
let f b2 (s1, acc) =
let e2 = fst (B.choose b2) in
let (s1_match, s1_rest) = S.partition (fun b1 -> C.cong (fst (B.choose b1)) e2) s1 in
let acc' = match S.choose s1_match with
| b1 ->
assert (S.cardinal s1_match = 1);
begin match B.narrow b1 b2 with
| b' when B.is_bot b' ->
acc
| exception Lattice.BotValue ->
acc
| b' ->
S.add b' acc
end
| exception Not_found -> acc
in
(s1_rest, acc')
in
snd (S.fold f s2 (s1, S.empty ()))
include MapDomain.Print (E) (R) (
struct
type nonrec t = t
type nonrec key = key
type nonrec value = value
let fold = fold
let iter = iter
end
)
let arbitrary () = failwith "PairwiseMap.arbitrary"
let filter p s = failwith "PairwiseMap.filter"
let leq_with_fct _ _ _ = failwith "PairwiseMap.leq_with_fct"
let join_with_fct _ _ _ = failwith "PairwiseMap.join_with_fct"
let widen_with_fct _ _ _ = failwith "PairwiseMap.widen_with_fct"
end