# `Feel.Analysis.Images.Conversion`
[🔗](https://github.com/FeeJai/BDM/blob/feel-v0.1.0/apps/feel/lib/feel/analysis/images/conversion.ex#L1)

The rules for the conversion functions (`Feel.Analysis.Images`, D-170; `Feel.Builtin.Conversion`): `date`, `date and time`,
`duration`, `number`, `range`, `string`, `time` and `years and months duration`.

A rule gives the whole type of the result, `Null` included, from the types of the arguments. Each argument is read for the
kinds the parameter takes, and whether the call is `null` for it: `null`, a value of another kind, a list of any other
length than one (a list of one is its item, section 10.3.2.9.4; `string` takes the list as it is), and a value of a type
that is not known. Then the result is found in one of two ways, from the exact to the kind:

  * **The function is run on the values of a finite set.** The strings of a list (`{"1", "x"}`), the numbers that are
    single, and the booleans give the values of an argument, and the function itself (`Feel.Builtin.call/3`) is called on
    every combination of them, up to 64: `number(s)` for `{"1", "2.5"}` is `{1, 2.5}`, `number(s)` for `{"1", "x"}` is the
    number `1` or `Null`, `date(s)` for `{"2021-01-31"}` is a date, and `string(n)` for `{1, 2}` is `{"1", "2"}`. A call
    that passes a limit of the run ends it and has no value, and then the kind answers.
  * **The kind, and what the types say of the rest.** A number is itself for `number`, a date for `date`, a time for `time`;
    the date of a date and time is a date, and its time a time; a string is a value of the kind or `Null`, since a string
    that is none exists; and a number outside what a date or a time takes (a month 13, a second 60) is `Null`.

## What is `null`

`Null` is in the type only if some arguments make the run give it. That is a `null` argument and an argument of another kind,
and a string that is none of the kind (`date(s)` for any string), and what the function turns down of the right kinds:

| Function | `null` for |
| -------- | ---------- |
| `date(year, month, day)` | a year past ±999,999,999, a month not in `1..12`, a day not in the month (the fraction of each is cut off) |
| `time(hour, minute, second[, offset])` | an hour not in `0..23`, a minute not in `0..59`, a second not in `[0..60)`, an offset that is not whole seconds within 14 hours |
| `date and time(date, time, timezone)` | a time that has a zone, a zone that is none |
| `string(from)` | `null`, a function, and a list or a context that has one |
| `date and time(date, time)`, `years and months duration` | nothing |

Where the days of a month are in question, a day past the 28th is taken to be `null` for some month, which is so when the set
of months and years has a month that does not have it; the type is then a superset.

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*Consult [api-reference.md](api-reference.md) for complete listing*