# Unit definitions

New units of measurement can be introduced with the unit keyword. There are two types of units: base units and derived units.

A new base unit can be defined by specifying the physical dimension it represents. For example, in the International System of Units (SI), the second is the base unit for measuring times:

unit second: Time


Here, Time denotes the physical dimension. To learn more, you can read the corresponding chapter. But for now, we can just assume that they are already given.

Derived units are also introduced with the unit keyword. But unlike base units, they are defined through their relation to other units. For example, a minute can be defined as

unit minute: Time = 60 second


Here, the : Time annotation is optional. If a dimension is specified, it will be used to verify that the right hand side expression (60 second) is indeed of physical dimension Time. This is apparent in this simple example, but can be useful for more complicated unit definitions like

unit farad: Capacitance = ampere^2 second^4 / (kilogram meter^2)


## Prefixes

If a unit may be used with metric prefixes such as milli/m, kilo/k or mega/M, we can prepend the unit definition with the @metric_prefixes decorator:

@metric_prefixes
unit second: Time


This allows identifiers such as millisecond to be used in calculations. See the section below how prefixes interact with aliases.

Similarly, if a unit should be prependable with binary (IEC) prefixes such as kibi/Ki, mebi/Mi or gibi/Gi, you can add the @binary_prefixes decorator. A unit might also allow for both metric and binary prefixes, for example:

@binary_prefixes
@metric_prefixes
unit byte = 8 bit


This allows the usage of both mebibyte (1024² byte) as well as megabyte (1000² byte).

## Aliases

It is often useful to define alternative names for a unit. For example, we might want to use the plural form seconds or the commonly used short version s. We can use the @aliases decorator to specify them:

@metric_prefixes
@aliases(meters, metre, metres, m: short)
unit meter: Length


In addition to the name, we can also specify how aliases interact with prefixes using : long (the default), : short, : both or : none. The actual unit name (meter) and all long aliases will accept the long version of prefixes (…, milli, kilo, mega, giga, …). All short aliases (m in the example above) will only accept the respective short versions of the prefixes (…, m, k, M, G, …). Aliases annotated with : both or : none accept either both long and short prefixes, or none of them. The unit definition above allows all of following expressions:

millimeter
kilometer

millimeters
kilometers

millimetre
kilometre

millimetres
kilometres

mm
km
...


It is often useful to introduce ‘fictional’ physical units (and dimensions). This comes up frequently when you want to count things. For example:

unit book

@aliases(pages)
unit page

@aliases(words)
unit word

let words_per_book = 500 words/page × 300 pages/book


Note that those base unit definitions will implicitly create new dimensions which are capitalized versions of the unit names (Book, Page, Word). A definition like unit book is a shorthand for dimension Book; unit book: Book. Those units now allow us to count books, pages and words independently without any risk of mixing them. The words_per_book constant in this examples has a type of Word / Book.

Another example shows how we introduce a dot unit to do calculations with screen resolutions:

@aliases(dots)
unit dot

unit dpi = dots / inch

# Note: a Dot dimension was implicitly created for us
fn inter_dot_spacing(resolution: Dot / Length) -> Length = 1 dot / resolution

inter_dot_spacing(72 dpi) -> µm  # 353 µm