Physical units and quantities

Units are ordinary values

RiX loads its standard units into the .Units map. A unit can be retrieved, assigned, passed around, multiplied, or divided like another value:

Runnable RiXRun cell

m := .Units[:m]; s := .Units[:s]; distance := 120 * m; elapsed := 10 * s; distance / elapsed

The result is 12~[m/s]. Internally RiX keeps an exact magnitude, a physical dimension vector, and a display unit.

Concise scientific notation

The bracket form is lookup-and-multiply sugar over the same .Units values:

Runnable RiXRun cell

explicit := 9 * .Units[:m] / .Units[:s]^2; concise := 9~[m/s^2]; explicit == concise

Unknown names inside ~[...] are errors rather than silently becoming labels.

Compatible addition

Compatible quantities are normalized before arithmetic. Addition preserves the left operand's display unit:

Runnable RiXRun cell

inSeconds := 30~[s] + 2~[min]; inMinutes := 2~[min] + 30~[s]; {: inSeconds, inMinutes }

The values describe the same duration but display as 150~[s] and 2..1/2~[min]. Trying 1~[m] + 1~[s] raises a dimensional error.

Explicit conversion

The quantity already knows its source unit, so conversion only needs a target:

Runnable RiXRun cell

speed := 36~[km/h]; .ConvertUnit(speed, .Units[:m] / .Units[:s])

Target strings are also accepted: .ConvertUnit(speed, "m/s").

Affine temperature coordinates

Units double as one-argument constructors. This matters for Celsius and Fahrenheit because their zero points differ:

Runnable RiXRun cell

roomC := .Units[:degC](20); .ConvertUnit(roomC, .Units[:degF])

Subtracting two temperature points produces a linear difference:

Runnable RiXRun cell

.Units[:degC](20) - .Units[:degC](12)

Adding two temperature points or compounding an affine coordinate is rejected.

Extend the active collection

.DefineUnit returns a unit value. Put it in an ordinary map overlay named Units; the sugar checks that lexical map before the system default:

Runnable RiXRun cell

fortnight := .DefineUnit(:fortnight, 14 * .Units[:day]); Units := .Units.Merge({= fortnight=fortnight }); .ConvertUnit(1~[fortnight], .Units[:day])

Next

The next lesson uses the parallel .Exact collection for π, i, and algebraic generators. Physical units and exact symbolic magnitudes can be composed.