R/Properties.R

In xoopR/set6: R6 Mathematical Sets Interface

#' @title Set Properties Class
#' @name Properties
#' @rdname Properties
#' @description Used to store the properties of a [Set]. Though this is not an abstract class,
#' it should never be constructed outside of the [Set] constructor.
Properties <- R6Class("Properties",
  public = list(
    #' @description Creates a new `Properties` object.
    #' @param closure One of "open", "half-open", or "closed."
    #' @param cardinality If non-`NULL` then either an integer, "Aleph0", or a Beth number.
    #' @return A new `Properties` object.
    initialize = function(closure = character(0), cardinality = NULL) {

      if (length(closure) != 0) {
        checkmate::assertChoice(closure, c("open", "half-open", "closed"))
        private$.closure <- closure
      }

      if (!is.null(cardinality)) {
        if (!(class(cardinality) %in% c("integer", "numeric"))) {
          if (grepl("^a(leph){0,1}0$", cardinality, ignore.case = TRUE)) {
            private$.cardinality <- "Aleph0"
            private$.countability <- "countably infinite"
          } else if (grepl("^b(eth){0,1}[0-9]+$", cardinality, ignore.case = TRUE)) {
            if (nchar(cardinality) < 5) {
              private$.cardinality <- paste0("Beth", substr(cardinality, 2, 100))
            } else {
              private$.cardinality <- paste0("Beth", substr(cardinality, 5, 100))
            }
            private$.countability <- "uncountable"
          } else {
            stop("Cardinality must either be a number or in {'Aleph0', 'A0', 'BethX', 'BX'} for some number X (case-insensitive)")
          }
        } else {
          private$.cardinality <- cardinality

          if (cardinality == Inf) {
            private$.countability <- "uncountable"
          } else {
            private$.countability <- "countably finite"
          }
        }

        private$.empty <- (cardinality == 0)
        private$.singleton <- (cardinality == 1)
      }

      invisible(self)
    },

    #' @description
    #' Prints the `Properties` list.
    #' @return Prints `Properties` list to console.
    print = function() {
      print(self$strprint())
    },

    #' @description
    #' Creates a printable representation of the `Properties`.
    #' @return A `list` of properties.
    strprint = function() {
      if (useUnicode() & length(self$cardinality) != 0) {
        if (self$cardinality == "Aleph0") {
          cardinality <- "\u2135\u2080"
        } else if (class(self$cardinality) != "character") {
          cardinality <- self$cardinality
        } else {
          .beths <- data.frame(X = 0:9, U = c(
            "\u2080", "\u2081", "\u2082", "\u2083", "\u2084", "\u2085",
            "\u2086", "\u2087", "\u2088", "\u2089"
          ))

          cardinality <- paste0("\u2136", paste0(.beths$U[match(
            unlist(strsplit(substr(
              self$cardinality,
              5, 100
            ), split = "")),
            .beths$X
          )], collapse = ""))
        }
      } else {
        cardinality <- self$cardinality
      }

      list(
        empty = self$empty,
        singleton = self$singleton,
        cardinality = cardinality,
        countability = self$countability,
        closure = self$closure
      )
    }
  ),

  active = list(
    #' @field closure
    #' Returns the closure of the `Set`. One of "open", "half-open", or "closed."
    closure = function() {
      return(private$.closure)
    },

    #' @field countability
    #' Returns the countability of the `Set`. One of "countably finite", "countably infinite", or "uncountable".
    countability = function() {
      return(private$.countability)
    },

    #' @field cardinality
    #' Returns the cardinality of the `Set`. Either an integer if the `Set` is countably finite, Aleph0 if countably infinite, or a Beth number.
    cardinality = function() {
      return(private$.cardinality)
    },

    #' @field empty
    #' Returns if the `Set` is empty or not. `TRUE` if the Set cardinality is `0`, `FALSE` otherwise.
    empty = function() {
      return(private$.empty)
    },

    #' @field singleton
    #' Returns if the `Set` is a singleton or not. `TRUE` if the Set cardinality is `1`, `FALSE` otherwise.
    singleton = function() {
      return(private$.singleton)
    }
  ),

  private = list(
    .closure = character(0),
    .countability = character(0),
    .cardinality = NULL,
    .empty = logical(0),
    .singleton = logical(0)
  )
)