# Narrowing a date and time

[Narrowing](../narrowing.md) › date and time. The names in the examples are those of [section 2](../narrowing.md#2-the-names-in-the-examples).

A `date and time` alternative is the bare kind or `{:date_and_time, set}`: a set of the **second** a value falls in, on the lines of `Feel.Type.Moment` (D-109, D-118). The page for [time](time.md) explains the lines: the clock of the values with no zone, and the instant and the zoned clock of those with one, which is needed because the order of two of them depends on their zones. `any zone` means the set has the clock and the instants of every zone. A date and time is not a date: they are of different kinds, so each is left only by its own.

## Comparisons

With a value that has **no zone** the comparison is on the clock, and the set is a plain interval (`any zone`). With one that **has** a zone the values with no zone are compared by their clock, and the values with a zone by their instant, so the set has the lines:

| Condition | `dt` when true | `dt` when not true |
| --- | --- | --- |
| `dt < @"2024-01-01T00:00:00"` | `date and time in [-999999999-01-01T00:00:00..2024-01-01T00:00:00) any zone` | `date and time in [2024-01-01T00:00:00..999999999-12-31T23:59:59] any zone \| Null` |
| `dt >= @"2024-01-01T00:00:00Z"` | `date and time in [2024-01-01T00:00:00..999999999-12-31T23:59:59], instants [2024-01-01T00:00:00Z..1000000000-01-01T17:59:59Z]` | `date and time in [-999999999-01-01T00:00:00..2024-01-01T00:00:00), instants [-1000000000-12-31T06:00:00Z..2024-01-01T00:00:00Z) \| Null` |
| `dt < d` | — | `date and time \| Null` |
| `dt instance of date and time` | `date and time` | `Null` |

The instants reach past the end of the calendar (`1000000000-01-01T17:59:59Z`) because the last clock in an offset of −18 hours is that many hours later in UTC.

| Condition | `dtr` when true | `dtr` when not true |
| --- | --- | --- |
| `dtr < @"2024-01-15T12:00:00"` | `date and time in [2024-01-01T00:00:00..2024-01-15T12:00:00) any zone` | `date and time in [2024-01-15T12:00:00..2024-01-31T23:59:59] any zone \| Null` |
| `dtr = @"2024-01-15T12:00:00"` | `date and time = 2024-01-15T12:00:00 any zone` | `date and time in [2024-01-01T00:00:00..2024-01-15T12:00:00), (2024-01-15T12:00:00..2024-01-31T23:59:59] any zone \| Null` |
| `dtr >= @"2024-01-15T12:00:00Z"` | `date and time in [2024-01-15T12:00:00..2024-01-31T23:59:59], zoned clock [2024-01-14T18:00:00..2024-01-31T23:59:59], instants [2024-01-15T12:00:00Z..2024-02-01T17:59:59Z]` | `date and time in [2024-01-01T00:00:00..2024-01-15T12:00:00), zoned clock [2024-01-01T00:00:00..2024-01-16T06:00:00], instants [2023-12-31T06:00:00Z..2024-01-15T12:00:00Z) \| Null` |

(`dtr` is a date and time in `[2024-01-01T00:00:00..2024-01-31T23:59:59]`; `dt` is any.) The last row has all three lines: a value with no zone is on the clock line; one with a zone has both its zoned clock and its instant in the set. The zoned clock of a value whose instant is at noon UTC is between 18:00 the day before (an offset of −18 hours) and 06:00 the day after.

## Properties

A fact about `year`, `month`, `day`, `weekday`, `hour`, `minute` or `second` is a fact about the value: the seconds of the set that have it, on each line of clocks, the instants cut to match (D-109). It narrows only as far as the set is bounded, as for a [date](date.md#properties-of-a-date): the days are exact, the hours, minutes and seconds are counted from one end to the other of each interval **up to a number of pieces**, and beyond that number the set is left as it was.

| Condition | `dt` when true | `dt` when not true |
| --- | --- | --- |
| `dt.year = 2024` | `date and time in [2024-01-01T00:00:00..2024-12-31T23:59:59] any zone` | `date and time in [-999999999-01-01T00:00:00..2023-12-31T23:59:59], [2025-01-01T00:00:00..999999999-12-31T23:59:59] any zone \| Null` |
| `dt.hour >= 18` | `date and time` | `date and time \| Null` |

| Condition | `dtr` when true | `dtr` when not true |
| --- | --- | --- |
| `dtr.day = 15` | `date and time in [2024-01-15T00:00:00..2024-01-15T23:59:59] any zone` | `date and time in [2024-01-01T00:00:00..2024-01-14T23:59:59], [2024-01-16T00:00:00..2024-01-31T23:59:59] any zone \| Null` |
| `dtr.hour >= 18` | `date and time in [2024-01-01T18:00:00..2024-01-31T23:59:59] any zone` | `date and time in [2024-01-01T00:00:00..2024-01-31T23:59:59] any zone \| Null` |
| `dtr.day = 15 and dtr.hour >= 18` | `date and time in [2024-01-15T00:00:00..2024-01-15T23:59:59] any zone` | `date and time in [2024-01-01T00:00:00..2024-01-31T23:59:59] any zone \| Null` |
| `dtr.weekday = 1` | `date and time in [2024-01-01T00:00:00..2024-01-29T23:59:59] any zone` | `date and time in [2024-01-02T00:00:00..2024-01-31T23:59:59] any zone \| Null` |
| `dtr.year = 2024` | `date and time in [2024-01-01T00:00:00..2024-01-31T23:59:59] any zone` | `Null` |
| `dtr.month = 2` | — | `date and time in [2024-01-01T00:00:00..2024-01-31T23:59:59] any zone \| Null` |

- `dt.hour >= 18` on an unbounded value narrows nothing: the hours come back every day.
- `dtr.hour >= 18` is the **hull**, from six in the evening of the first day to the end of the last: a superset, and the best that one interval can say. `dtr.day = 15 and dtr.hour >= 18` is no narrower than the day, because the hour would make a piece for each day.
- `dtr.year = 2024` is true for every value of the set, so only `null` is left when it is not.
- `dtr.month = 2` cannot be true for a value in January.

### The properties of the zone

`time offset`, `timezone` and `value` exist only for a value that has a zone. A true fact about one therefore leaves the **instants** only:

| Condition | `dt` when true | `dt` when not true |
| --- | --- | --- |
| `dt.timezone = "Z"` | `date and time in instants [-1000000000-12-31T06:00:00Z..1000000000-01-01T17:59:59Z]` | `date and time \| Null` |
| `dt.time offset = @"PT0S"` | `date and time in instants [-999999999-01-01T00:00:00Z..999999999-12-31T23:59:59Z]` | `date and time \| Null` |

`dt.value > 0` (the seconds since 1970 of the instant) leaves the instants from `1969-12-31T23:59:59Z` on. They are worked out by `Feel.Analysis.MomentZones` (D-109).

## Limits

- The lines of the instants and the zoned clock are each within **18 hours** of the other, and are cut to that.
- A set of more than the pieces a property can keep is left as it was.
- The fraction of the second is a line of its own, `[0..1)` when nothing is known. A condition on `second` (`dtr.second < 30`) narrows nothing: a second comes back in every minute.

See also: [time](time.md), [date](date.md), [days and time duration](days-and-time-duration.md).