Physical Quantities

A physical quantity combines a numeric representation with a dimension. Dimensions participate in static type checking and need not survive as runtime objects.

Type Products

Applying arithmetic to type values describes the type produced by that operation. A duration may therefore be described as a real-valued representation multiplied by the Time dimension:

const Duration:type = <T of real>(T * Time)

Duration<int64> preserves int64 as its numeric representation while requiring a time dimension.

Unit Values

Juxtaposing a number with a unit multiplies them. The second and its scales are the prelude's; every other unit is imported from the library module units:

from units import m

let timeout = 300ms
let distance = 10m

A unit carries an exact scale and dimension. Constant expressions fold that scale completely; a quantity that reaches runtime carries only its number in the canonical scale and no unit tag.

Dimensions and Canonical Scales

The base dimensions are Time, Length, Mass, Current, Temperature, Amount, Luminosity, and Angle. Their canonical units are the second, metre, kilogram, ampere, kelvin, mole, candela, and the whole turn. Every other unit is a rational scale of a canonical unit, so prefixes and derived units are exact: ms is 1/1000 s, N is kg * m / s^2 with scale one, ° is 1/360 turn. The radian's scale is irrational and is represented in fixed point.

Addition, subtraction, and comparison require identical dimensions and are otherwise compile errors. Multiplication and division combine dimensions; ^ with a constant integer exponent raises them. Dividing a quantity by a unit of the same dimension yields the dimensionless count in that unit. A quantity's number is an integer, rational, or fixed-point value, promoted by the same rules as dimensionless arithmetic.

Trigonometry

cos, sin, and tan accept a rational or fixed-point angle quantity and return fixed. Range reduction happens exactly on the turn count before evaluation.

Time and Sleeping

s, ms, us, and ns, together with their written names and minute/hour, denote exact time scales. sleep accepts a rational time quantity and converts it to whole nanoseconds at the system boundary; a dimensionless number is rejected.

Provisional Scope

The type-product model, representation parameterization, the base-dimension algebra with canonical scales, and erasure are settled. Provisional: a quantity's display unit (printing 4500 J rather than the canonical number) and x as km to select one, declaring base dimensions in library code, offset scales such as Celsius and their point/delta semantics, calendar-relative durations, and catalog organization.