It’s been a busy few weeks on Tempo with some interesting headline features. Turns out that when you model time as intervals — not instants — some more difficult problems in time become more straight forward.
Uncertainty is first-class (ISO 8601-2)
Mark a value uncertain (?), approximate (~), or both (%), per component and it round-trips: These annotations are particularly useful for historians and researchers.
iex> {:ok, t} = Tempo.from_iso8601("2004-06~-11")
iex> t.qualifications`
%{month: :approximate, year: :approximate}
Business days & working calendars
Territory-aware weekends (using Localize) and business-day arithmetic, computed in the value’s own calendar:
iex> Tempo.weekend?(~o"2026-06-12", :SA)
true # Friday is a weekend in Saudi Arabia
iex> Tempo.weekend?(~o"2026-06-12", :US)
false
iex> Tempo.add_working_days(~o"2026-06-12", 3, :US)
~o"2026Y6M17D"
Chronological networks — Tempo.Network
Tempo.Network is a chronological-network solver (the ChronoLog scheme from archaeology): describe periods by their start, end, and duration — each of which may be exact, bounded, ranged, or unknown — link them with sequences and relations, and it derives the tightest dates consistent with everything (or reports a contradiction).
Give it the Egyptian 26th dynasty as one anchor (Psammetichus I acceded 664 BCE) plus each reign’s length in succession, and it works out every accession date:
iex> dynasty =
...> Network.new()
...> |> Network.add_period(:psammetichus_i, start: ~o"-664Y", duration: ~o"P54Y")
...> |> Network.add_period(:necho_ii, duration: ~o"P15Y")
...> |> Network.add_period(:psammetichus_ii, duration: ~o"P6Y")
...> |> Network.add_period(:apries, duration: ~o"P19Y")
...> |> Network.add_period(:amasis_ii, duration: ~o"P44Y")
...> |> Network.add_period(:psammetichus_iii, duration: ~o"P1Y")
...> |> Network.add_sequence([`
...> :psammetichus_i, :necho_ii, :psammetichus_ii,
...> :apries, :amasis_ii, :psammetichus_iii
...> ])`
iex> {:ok, solved} = Network.Solver.tighten(dynasty)
iex> solved.periods[:amasis_ii].earliest_start
~o"-570Y" # Amasis II acceded 570 BCE`
iex> solved.periods[:psammetichus_iii].earliest_end
~o"-525Y" # dynasty ends 525 BCE
The dynasty’s dates are fully known here, so the solver just derives and confirms them — but the same model comes into its own when they aren’t: swap an exact duration for {:at_least, ~o"P20Y"}, add a relation like :starts_during or :overlaps, and tighten/1 still returns each period’s narrowest possible window (with trace/3 explaining why a bound holds), while consistent?/1 flags any contradiction. Negative years are BCE throughout.
Critical Path Scheduling — Tempo.Schedule
The interval model turned out to a very good fit for a constraint solver. Tempo.Schedule is critical-path project planning: declare tasks, durations and dependencies, then solve for each task’s window and slack. It uses Tempo.Network as the supporting platform.
iex> {:ok, plan} =
...> Tempo.Schedule.new()
...> |> Tempo.Schedule.task(:design, duration: ~o"P2D", start: ~o"2026-06-01")
...> |> Tempo.Schedule.task(:build, duration: ~o"P3D", after: :design)
...> |> Tempo.Schedule.task(:docs, duration: ~o"P1D", after: :design)
...> |> Tempo.Schedule.task(:ship, duration: ~o"P2D", after: [:build, :docs], deadline: ~o"2026-06-08")
...> |> Tempo.Schedule.solve()`
iex> plan[:ship].start
~o"2026Y6M6D"
iex> plan[:ship].critical?
true
iex> Tempo.Schedule.critical_path(plan)
[:design, :build, :ship]
Other recent enhancements
- Sub-second (microsecond) resolution, precision-preserving —
.120 ≠ .12
- Cron, extended — multi-year fields,
W nearest-weekday, POSIX dom/dow OR
- ISO 8601-2 expanded years (
+12022)
Enumerable for %Tempo{} — DST-aware count/slice- Free/busy → bookable
IntervalSet.slots/3, and IXDTF offset/zone validation (RFC 9557)
Updated Guides
As always, feedback and bug reports very welcome!
