open Ast
open Formula

module type NUMERICAL_ENVIRONMENT_DOMAIN = sig
    type t
    type itv

    (* construction *)
    val init        : t
    val bottom      : t
    val vbottom     : t -> t       (* bottom value with same environment *)
    val is_bot      : t -> bool

    (* variable management *)
    val addvar      : t -> id -> bool -> t     (* integer or real variable ? *)
    val rmvar       : t -> id -> t
    val vars        : t -> (id * bool) list

    val forgetvar   : t -> id -> t             (* remove var from constraints *)
    val var_itv     : t -> id -> itv

    (* set-theoretic operations *)
    val join        : t -> t -> t       (* union *)
    val meet        : t -> t -> t       (* intersection *)
    val widen       : t -> t -> t

    (* order *)
    val subset      : t -> t -> bool
    val eq          : t -> t -> bool

    (* abstract operation *)
    val apply_ncl   : t -> num_cons list -> t
    val assign      : t -> (id * num_expr) list -> t

    (* pretty-printing *)
    val print_vars  : Format.formatter -> t -> id list -> unit
    val print_all   : Format.formatter -> t -> unit
    val print_itv   : Format.formatter -> itv -> unit
end