A protocol for a value of the caller's that stands for the time it covers, so that it can be related to, compared with and combined with Tempo's expressions as it is, without first being copied into a Tempo.t/0.

A value that implements it is accepted wherever two expressions are compared or combined: Tempo.relation/2, the predicates such as Tempo.overlaps?/3 and Tempo.within?/3, Tempo.compare/3 (so that Enum.sort(bookings, Tempo) sorts by time), the set operations such as Tempo.union/3 and Tempo.difference/3, the filters such as Tempo.members_overlapping/3, Tempo.Allen, and the members given to Tempo.IntervalSet.new/2. Each such function reads the value with to_tempo/1 once, as it is given. Other functions take a Tempo.t/0, which to_tempo/1 gives.

The answers are Tempo's expressions. A value that wants to be found again in an answer, a booking among the members that overlap a slot, puts itself in the metadata of the expression it gives: set operations keep a member's metadata, so the booking is in the members they answer with.

defmodule Booking do
  defstruct [:guest, :check_in, :check_out]
end

defimpl Tempo.Intervallic, for: Booking do
  def to_tempo(%Booking{check_in: from, check_out: to} = booking) do
    Tempo.Interval.new(from: from, to: to, metadata: %{booking: booking})
  end
end

Elixir's Date, Time, NaiveDateTime, DateTime and Date.Range implement it, each read as Tempo.from_elixir/2 reads it: a Date is the day, a DateTime the second in its zone. An Elixir Duration does not, a length being no span of time. Any other value stands for no expression, and to_tempo/1 returns a Tempo.ConversionError for it.