(*
  Cours "Sémantique et Application à la Vérification de programmes"

  Antoine Miné 2015
  Marc Chevalier 2018
  Josselin Giet 2021
  Ecole normale supérieure, Paris, France / CNRS / INRIA
*)

open! Cfg

(* Signature for the variables *)

module type VARS = sig
  val support: var list
end

(*
  Signature of abstract domains representing sets of envrionments
  (for instance: a map from variable to their bounds).
 *)

module type DOMAIN =
  sig

    (* type of abstract elements *)
    (* an element of type t abstracts a set of mappings from variables
       to integers
     *)
    type t

    (* initial environment, with all variables initialized to 0 *)
    val init: int -> t

    (* empty set of environments *)
    val bottom: t

    (* assign an integer expression to a variable *)
    val assign: t -> var -> int_expr -> t

    (* filter environments to keep only those satisfying the boolean expression *)
    val guard: t -> bool_expr -> t

    (* abstract join *)
    val join: t -> t -> t

    (* abstract meet *)
    val meet: t -> t -> t

    (* widening *)
    val widen: t -> t -> t

    (* narrowing *)
    val narrow: t -> t -> t

    (* whether an abstract element is included in another one *)
    val subset: t -> t -> bool

    (* whether the abstract element represents the empty set *)
    val is_bottom: t -> bool

    (* prints *)
    val print: Format.formatter -> t -> unit

  end