# Narrowing a time

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

A `time` alternative is the bare kind, every time of day, or `{:time, set}`: a set of the **second of the day** a value falls in (`Feel.Type.Moment`, D-109, D-118). A time is not ordered as a number is, because the order of two times depends on their zones (`Feel.Runtime.Temporal.compare/3`):

- when either has **no zone**, their local clocks are compared;
- when **both** have a zone, their instants are compared, at the second.

So a set has several *lines* of numbers, far apart on the number line, and a value is in it when its numbers are on the right lines:

| Line | Of | Written |
| --- | --- | --- |
| the clock | the values with no zone | `[08:00:00..18:00:00]` |
| the zoned clock | the values with a zone: their local clock | `zoned clock [08:00:00..18:00:00]` |
| the instants | the values with a zone: the instant, as the seconds of the day less the offset (not wrapped, so it can be negative or past 24:00) | `instants [-10:00:00Z..12:00:00Z)` |

A set that has the clock and the instants of every zone is written **`any zone`**: `time in [08:00:00..18:00:00] any zone` is a time between eight and six, whatever its zone. A fourth line, the fraction of the second, is the same for every zone (D-118): comparisons look at the second, and only sums, differences and the `second` property look at the fraction.

## Comparing with a time without a zone

The other side has a clock and no zone, so the comparison is on the clock whatever the subject's zone is: the subject's own clock for a value with a zone as well.

| Condition | `tm` when true | `tm` when not true |
| --- | --- | --- |
| `tm < @"12:00:00"` | `time in [00:00:00..12:00:00) any zone` | `time in [12:00:00..23:59:59] any zone \| Null` |
| `tm = @"12:00:00"` | `time = 12:00:00 any zone` | `time in [00:00:00..12:00:00), (12:00:00..23:59:59] any zone \| Null` |
| `tm instance of time` | `time` | `Null` |

| Condition | `tmr` when true | `tmr` when not true |
| --- | --- | --- |
| `tmr < @"12:00:00"` | `time in [08:00:00..12:00:00) any zone` | `time in [12:00:00..18:00:00] any zone \| Null` |
| `tmr between @"09:00:00" and @"10:00:00"` | `time in [09:00:00..10:00:00] any zone` | `time in [08:00:00..09:00:00), (10:00:00..18:00:00] any zone \| Null` |

(`tmr` is a time in `[08:00:00..18:00:00]`; `tm` is any time.)

## Comparing with a time that has a zone

Now the values with no zone are compared by their clock with the other side's, and the values with a zone by their instant. The sets for which a comparison *can be true* and for which it *can be false* are no longer each other's complement: two times ten hours apart can be either, since the other side may or may not have a zone. So the lines overlap, within the largest offset, which is **18 hours** (a fixed offset is within 14, and the zones of the time zone database had a local mean time of up to 15 hours 56 minutes).

| Condition | `tm` when true | `tm` when not true |
| --- | --- | --- |
| `tm < @"12:00:00Z"` | `time in [00:00:00..12:00:00), instants [-18:00:00Z..12:00:00Z)` | `time in [12:00:00..23:59:59], instants [12:00:00Z..41:59:59Z] \| Null` |
| `tm < @"12:00:00+01:00"` | `time in [00:00:00..12:00:00), instants [-18:00:00Z..11:00:00Z)` | `time in [12:00:00..23:59:59], instants [11:00:00Z..41:59:59Z] \| Null` |

| Condition | `tmr` when true | `tmr` when not true |
| --- | --- | --- |
| `tmr >= @"12:00:00Z"` | `time in [12:00:00..18:00:00], zoned clock [08:00:00..18:00:00], instants [12:00:00Z..36:00:00Z]` | `time in [08:00:00..12:00:00), zoned clock [08:00:00..18:00:00], instants [-10:00:00Z..12:00:00Z) \| Null` |

Read the first row as: a time below noon UTC is either one without a zone whose clock is before twelve, or one with a zone whose instant is before `12:00:00Z`. The instants can reach `-18:00:00Z` (a clock at midnight in an offset of +18 hours) and past `24:00` (`41:59:59Z` is `23:59:59` in an offset of −18 hours).

## Properties of a time

A fact about `tm.hour`, `tm.minute` or `tm.second` is a fact about `tm` too: the seconds of the set that have it, on each line of clocks, and the instants cut to match (`Feel.Analysis.MomentProperties`). The seconds of the days are exact. Those of an hour, a minute or a second are the seconds of each hour, minute or day of the interval **up to a number of pieces**, and beyond that number the set is left as it was.

| Condition | `tmr` when true | `tmr` when not true |
| --- | --- | --- |
| `tmr.hour >= 12` | `time in [12:00:00..18:00:00] any zone` | `time in [08:00:00..11:59:59] any zone \| Null` |
| `tmr.hour = 9 and tmr.minute < 30` | `time in [09:00:00..09:29:59] any zone` | `time in [08:00:00..18:00:00] any zone \| Null` |

| Condition | `tm` when true | `tm` when not true |
| --- | --- | --- |
| `tm.hour >= 12` | `time in [12:00:00..23:59:59] any zone` | `time in [00:00:00..11:59:59] any zone \| Null` |

A time has no `year`, `month`, `day` or `weekday` (`tm.year` is `null`, with an `invalid_property` warning).

`time offset`, `timezone` and `value` depend on the zone, so a time **without** one has none of them, and a true fact about one leaves only the line of the instants: the values that have a zone (`Feel.Analysis.MomentZones` works out their sets).

| Condition | `tm` when true | `tm` when not true |
| --- | --- | --- |
| `tm.time offset = @"PT0S"` | `time in instants [00:00:00Z..23:59:59Z]` | `time \| Null` |

## Limits

- The line of the instants and the line of the zoned clock are each within 18 hours of the other, and `normalize/2` cuts both to that.
- A set of seconds that is too fragmented (`tm.second = 0` is a second in every minute of the day) is left as it was, with the lines of the clock and the instants whole.
- The fraction line has every fraction when nothing is known.

See also: [date and time](date-and-time.md), [date](date.md); `Feel.Type.Moment` and `Feel.Analysis.MomentTests` have the algebra.