Module HoareDomain.Set

Set of Lattice.S elements with Hoare ordering. This abstracts a set by its maximal elements.

Element-wise SetDomain.S operations only observe the maximal elements.

This has extrapolation heuristics instead of a true widen, i.e. convergence is only guaranteed if the number of maximal elements converges. Otherwise use SetEM.

Parameters

module B : Lattice.S

Signature

include SetDomain.S with type elt = B.t
include Lattice.S
include Lattice.PO
include Printable.S
type t
val equal : t -> t -> bool
val hash : t -> int
val compare : t -> t -> int
val show : t -> string
val pretty : unit -> t -> Printable.Pretty.doc
val printXml : 'a BatInnerIO.output -> t -> unit
val name : unit -> string
val to_yojson : t -> Yojson.Safe.t
val tag : t -> int

Unique ID, given by HConsed, for context identification in witness

val arbitrary : unit -> t QCheck.arbitrary
val relift : t -> t
val leq : t -> t -> bool
val join : t -> t -> t
val meet : t -> t -> t
val widen : t -> t -> t

widen x y assumes leq x y. Solvers guarantee this by calling widen old (join old new).

val narrow : t -> t -> t
val pretty_diff : unit -> (t * t) -> Lattice.Pretty.doc

If leq x y = false, then pretty_diff () (x, y) should explain why.

include Lattice.Bot with type t := t
val bot : unit -> t
val is_bot : t -> bool
include Lattice.Top with type t := t
val top : unit -> t
val is_top : t -> bool
type elt = B.t
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.

NB! On set abstractions this is a strong removal, i.e. all subsumed elements are also removed.

val union : t -> t -> t
val inter : t -> t -> t
val diff : t -> t -> t

See Set.S.diff.

NB! On set abstractions this is a strong removal, i.e. all subsumed elements are also removed.

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 to_seq : t -> elt Stdlib.Seq.t

See Set.S.to_seq.

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.

val apply_list : (elt list -> elt list) -> t -> t