You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
146 lines
4.8 KiB
146 lines
4.8 KiB
(*
|
|
* Copyright (c) Facebook, Inc. and its affiliates.
|
|
*
|
|
* This source code is licensed under the MIT license found in the
|
|
* LICENSE file in the root directory of this source tree.
|
|
*)
|
|
|
|
(** Symbolic Heap Formulas *)
|
|
|
|
(** Segment of memory starting at [loc] containing a byte-array [arr] of
|
|
size [siz], contained in an enclosing allocation-block starting at [bas]
|
|
of length [len]. Byte-array expressions are either [Var]iables or
|
|
[Splat] vectors. *)
|
|
type seg = {loc: Term.t; bas: Term.t; len: Term.t; siz: Term.t; arr: Term.t}
|
|
|
|
type starjunction = private
|
|
{ us: Var.Set.t (** vocabulary / variable context of formula *)
|
|
; xs: Var.Set.t (** existentially-bound variables *)
|
|
; cong: Equality.t (** congruence induced by rest of formula *)
|
|
; pure: Term.t list (** conjunction of pure boolean constraints *)
|
|
; heap: seg list (** star-conjunction of segment atomic formulas *)
|
|
; djns: disjunction list (** star-conjunction of disjunctions *) }
|
|
|
|
and disjunction = starjunction list
|
|
|
|
type t = starjunction [@@deriving compare, equal, sexp]
|
|
|
|
val pp_seg_norm : Equality.t -> seg pp
|
|
val pp_us : ?pre:('a, 'a) fmt -> ?vs:Var.Set.t -> unit -> Var.Set.t pp
|
|
val pp : t pp
|
|
val pp_raw : t pp
|
|
val pp_diff_eq : ?us:Var.Set.t -> ?xs:Var.Set.t -> Equality.t -> t pp
|
|
val pp_djn : disjunction pp
|
|
val simplify : t -> t
|
|
|
|
include Invariant.S with type t := t
|
|
|
|
(** Construct *)
|
|
|
|
val emp : t
|
|
(** Empty heap formula. *)
|
|
|
|
val false_ : Var.Set.t -> t
|
|
(** Inconsistent formula with given vocabulary. *)
|
|
|
|
val seg : seg -> t
|
|
(** Atomic segment formula. *)
|
|
|
|
val star : t -> t -> t
|
|
(** Star-conjoin formulas, extending to a common vocabulary, and avoiding
|
|
capturing existentials. *)
|
|
|
|
val or_ : t -> t -> t
|
|
(** Disjoin formulas, extending to a common vocabulary, and avoiding
|
|
capturing existentials. *)
|
|
|
|
val pure : Term.t -> t
|
|
(** Atomic pure boolean constraint formula. *)
|
|
|
|
val and_ : Term.t -> t -> t
|
|
(** Conjoin a boolean constraint to a formula. *)
|
|
|
|
val and_cong : Equality.t -> t -> t
|
|
(** Conjoin constraints of a congruence to a formula, extending to a common
|
|
vocabulary, and avoiding capturing existentials. *)
|
|
|
|
val and_subst : Equality.Subst.t -> t -> t
|
|
(** Conjoin constraints of a solution substitution to a formula, extending
|
|
to a common vocabulary, and avoiding capturing existentials. *)
|
|
|
|
(** Update *)
|
|
|
|
val with_pure : Term.t list -> t -> t
|
|
(** [with_pure pure q] is [{q with pure}], which assumes that [q.pure] and
|
|
[pure] are defined in the same vocabulary. Note that [cong] is not
|
|
weakened, so if [pure] and [q.pure] do not induce the same congruence,
|
|
then the result will have a stronger [cong] than induced by its [pure]. *)
|
|
|
|
val rem_seg : seg -> t -> t
|
|
(** [star (seg s) (rem_seg s q)] is equivalent to [q], assuming that [s] is
|
|
(physically equal to) one of the elements of [q.heap]. Raises if [s] is
|
|
not an element of [q.heap]. *)
|
|
|
|
val filter_heap : f:(seg -> bool) -> t -> t
|
|
(** [filter_heap q f] Remove all segments in [q] for which [f] returns false *)
|
|
|
|
val norm : Equality.Subst.t -> t -> t
|
|
(** [norm s q] is [q] where subterms have been normalized with a
|
|
substitution. *)
|
|
|
|
(** Quantification and Vocabulary *)
|
|
|
|
val exists : Var.Set.t -> t -> t
|
|
(** Existential quantification, binding variables thereby removing them from
|
|
vocabulary. *)
|
|
|
|
val bind_exists : t -> wrt:Var.Set.t -> Var.Set.t * t
|
|
(** Bind existentials, freshened with respect to [wrt], extends vocabulary. *)
|
|
|
|
val rename : Var.Subst.t -> t -> t
|
|
(** Apply a substitution, remove its domain from vocabulary and add its
|
|
range. *)
|
|
|
|
val subst : Var.Subst.t -> t -> t
|
|
(** Apply a substitution, remove its domain from vocabulary and add its
|
|
range. *)
|
|
|
|
val freshen : wrt:Var.Set.t -> t -> t * Var.Subst.t
|
|
(** Freshen free variables with respect to [wrt], and extend vocabulary with
|
|
[wrt], renaming bound variables as needed. *)
|
|
|
|
val extend_us : Var.Set.t -> t -> t
|
|
(** Extend vocabulary, renaming existentials as needed. *)
|
|
|
|
(** Query *)
|
|
|
|
val is_emp : t -> bool
|
|
(** Holds of [emp], with any vocabulary, existentials, and congruence. *)
|
|
|
|
val is_false : t -> bool
|
|
(** Holds only of inconsistent formulas, does not hold of all inconsistent
|
|
formulas. *)
|
|
|
|
val fv : ?ignore_cong:unit -> t -> Var.Set.t
|
|
(** Free variables, a subset of vocabulary. *)
|
|
|
|
val var_strength : t -> [`Anonymous | `Existential | `Universal] Var.Map.t
|
|
(** Classify each variable in a formula as either [Universal],
|
|
[Existential], or [Anonymous], meaning existential but with only one
|
|
occurrence. *)
|
|
|
|
val pure_approx : t -> t
|
|
(** [pure_approx q] is inconsistent only if [q] is inconsistent. *)
|
|
|
|
val fold_dnf :
|
|
conj:(starjunction -> 'conjuncts -> 'conjuncts)
|
|
-> disj:(Var.Set.t * 'conjuncts -> 'disjuncts -> 'disjuncts)
|
|
-> t
|
|
-> Var.Set.t * 'conjuncts
|
|
-> 'disjuncts
|
|
-> 'disjuncts
|
|
(** Enumerate the cubes and clauses of a disjunctive-normal form expansion. *)
|
|
|
|
val dnf : t -> disjunction
|
|
(** Convert to disjunctive-normal form. *)
|