@callback discrete?() :: boolean()

Is this implementation of an interval considered discrete?

The interval is implicitly continuous if not discrete.

@callback new(new_opts()) :: Interval.t()

Create a new Interval.t/0

@callback new(left :: Interval.point(), right :: Interval.point(), bounds :: String.t()) ::
  Interval.t()

Create a new interval with the specified left and right endpoints, and bounds.

This is a specialization of the more general new/1

@callback point_compare(a :: Interval.point(), b :: Interval.point()) :: :eq | :gt | :lt

Compare two points, returning if a == b, a > b or a < b.

@callback point_format(point :: Interval.point()) :: String.t()

Return a string representation of a point for use in formatting intervals.

@callback point_normalize(point :: Interval.point()) :: :error | {:ok, Interval.point()}

Normalize a point to a canonical form. Returns :error if the point is invalid.

@callback point_parse(string :: String.t()) :: {:ok, Interval.point()} | :error

Parse a string representation of a point into a point, for use in parsing intervals.

@callback point_step(point :: Interval.point(), n :: integer()) :: Interval.point()

Step a discrete point n steps.

If n is negative, the point is stepped backwards. For integers this is simply addition (point + n)