# Getting started with Tempo

```elixir
Mix.install([
  {:ex_tempo, "~> 1.6"},
  {:tz, "~> 0.28"}
])

Calendar.put_time_zone_database(Tz.TimeZoneDatabase)
import Tempo.Sigils
```

## Time as an interval, not an instant

Every mainstream library treats a date as a scalar — an instant, usually midnight, that everyone then *uses* as if it were a span. Tempo makes the span the value itself: `~o"2026-06-15"` **is** the half-open interval `[2026-06-15T00:00, 2026-06-16T00:00)`, a year is a year-long interval, and one `%Tempo{}` type carries any resolution.

The `~o` sigil parses the full ISO 8601 Part 1 and Part 2 grammar (plus IXDTF zone suffixes):

```elixir
~o"2026-06-15"
```

The value knows its own resolution — and its bounds are real. Materialising gives a half-open interval whose endpoints stay at the value's resolution, with the walk granularity carried separately on `:unit`:

```elixir
{:ok, day} = Tempo.to_interval(~o"2026-06-15")
{from, to} = Tempo.Interval.endpoints(day)
{Tempo.day(from), Tempo.day(to), day.unit}
```

One type covers every resolution — a year, a month, a minute, a zoned datetime:

```elixir
[~o"2026", ~o"2026-06", ~o"2026-06-15T14:30", ~o"2026-06-15T14:30[Australia/Sydney]"]
```

## Constructing values at runtime

The sigil is for literals. For runtime data use `Tempo.new/1`, which accepts components in any order and validates them against the calendar, or `Tempo.from_elixir/1` to bridge from stdlib types:

```elixir
Tempo.new!(day: 15, year: 2026, month: 6, hour: 14, minute: 30)
```

```elixir
Tempo.from_elixir(~U[2026-06-15 14:30:00Z])
```

## Iteration walks the span

Because a value is a span, `Enum` walks *into* it at the next finer resolution: a month yields its days, a year its months. Even a partially-specified value like `~o"156X"` — "sometime in the 1560s" — is a span you can walk:

```elixir
Enum.count(~o"2026-06")
```

```elixir
Enum.take(~o"156X", 5)
```

## Comparison speaks Allen's algebra

Two intervals stand in exactly one of thirteen relations. `Tempo.relation/2` names it; the predicates answer the everyday questions:

```elixir
Tempo.relation(~o"2026-01", ~o"2026-02")
```

> January doesn't come *before* February — they **meet**, with no gap. `before?/2` is strict about that:

```elixir
{Tempo.before?(~o"2026-01", ~o"2026-02"), Tempo.before?(~o"2026-01", ~o"2026-03")}
```

```elixir
Tempo.within?(~o"2026-06-01/2026-06-15", ~o"2026-06")
```

## Set algebra

Union, intersection, difference, and complement work on any combination of values, across resolutions. The workday minus lunch is the working time:

```elixir
workday = ~o"2026-06-15T09/2026-06-15T17"
lunch = ~o"2026-06-15T12/2026-06-15T13"

{:ok, working} = Tempo.difference(workday, lunch)
working
```

> *"The working time is the workday **minus** lunch — two spans, morning and afternoon."*

Cut a free region into bookable slots:

```elixir
working
|> Tempo.IntervalSet.slots(~o"PT2H")
|> Tempo.IntervalSet.to_list()
```

## Locale-aware formatting

Rendering reflects the span: a year formats as its first-through-last month, in any CLDR locale, and durations follow ECMA-402 conventions:

```elixir
{Tempo.to_string(~o"2026"), Tempo.to_string(~o"2026-06")}
```

```elixir
{Tempo.to_string(~o"P3DT2H"), Tempo.to_string(~o"P3DT2H", format: :short)}
```

```elixir
Tempo.to_string(~o"P1Y6M", locale: :de)
```

And when a value puzzles you, ask it to explain itself:

```elixir
Tempo.explain(~o"156X") |> IO.puts()
```

## Where next

* The [scheduling livebook](scheduling-workbook.livemd) — free-busy, bookable slots, arrival times, and recurrence.
* The [uncertain dates livebook](uncertain-dates-workbook.livemd) — masks, one-of sets, margins, and three-valued certainty.
* The [cookbook](https://hexdocs.pm/ex_tempo/cookbook.html) and [guides](https://hexdocs.pm/ex_tempo/readme.html) on hexdocs.