UnitTypes.jl

This package provides physical units as Julia types.

julia> using UnitTypes

julia> x = Meter(3)
3m

julia> typeof(x)
Meter

julia> typeof(x) <: AbstractLength
true

julia> typeof(x) <: AbstractCapacitance
false

This allows you to easily write functions with arguments restricted to variables having certain types.

julia> function goFaster(a::T) where T<:AbstractAcceleration end

This leads to correctness and very clear error messages.

julia> v = MeterPerSecond(3)
3m/s

julia> goFaster(v)
ERROR: MethodError: no method matching goFaster(::MeterPerSecond)

Closest candidates are:
  goFaster(::T) where T<:AbstractAcceleration

Docs

Macros are used to introduce and create relationships around new types:

• @makeBaseMeasure Torque NewtonMeter "N*m" - introduces a new basic Measure like Meter for Length or Meter3 Volume,
• @deriveMeasure NewtonMeter(1) = MilliNewtonMeter(1000) "mN*m - introduces a new name for a Measure, often a prefix like Millimeter or an alternate name like Inch,
• @makeDimension Diameter Meter - creates a Dimension, which is a Measure in some particular context, as diameter, radius, and circumference all refer to lengths of a circle.

UnitTypes introduces an abstract type hierarchy of:

• AbstractMeasure Meter, Millimeter, ..., MeterPerSecond, MeterPerSecond2, ... See src/SIDerived.jl Inch, Foot, Mile, ..., See src/Imperial.jl

• AbstractDimension - src/Dimension.jl AbstractDiameter, AbstractRadius, ... AbstractDuration, ...

See src/typeTree.txt for a full list of the pre-defined types.

Please open an issue or PR to add more units.

As said, the idea is that a Measure is some quantity bearing units, while a Dimension is some context-specific application of a Measure. Within a Dimension multiple Measures may logically be used as long as they are dimensionally consistent. For instance, a circle may be described by its radius, diameter, or circumference, concepts that can be interchangeably converted, using any Measure of extent (<:AbstractLength). A function creating a circle can then internally store radii while accepting Radius, Diameter, or Circumference arguments, as the type system provides conversion between the argument and the function's internal convention.

Concrete Dimensions look like

struct Diameter{T <: AbstractLength } <: AbstractDimension
  value::T
end

and a concrete Measure is represented by

struct Meter <: AbstractLength
  value::Number
  toBase::Number
  unit::String
end

Measures.jl and the macros define the necessary convert()s and other operators. Please open an issue with a minimal working example if you run into conversion errors.

Using units correctly requires distinguishing between valid and invalid operations, which in some cases means not allowing convenient operations. Inches can be added, as can inch and millimeter, but only when computing area does inch*inch make sense. Inch * 3 is convenient while 3 / Inch is unlikely to be desirable.

With use and issues, these coherence rules will become more clear and explained by example.

Unitful leverages parametric types to store units, giving flexibility at the cost of compile-time type uncertainty. It's two major limitations are the avoidance of angular measures, as they are not first-class but rather ratios, and rather lengthy type unions that clutter outputs, especially on error:

julia> function goSlower(x::T) where T<:Unitful.Acceleration end
goSlower (generic function with 1 method)

julia> a = 1u"mm"

julia> goSlower(a)
ERROR: MethodError: no method matching goSlower(::Quantity{Int64, 𝐋 , Unitful.FreeUnits{(mm,), 𝐋 , nothing}})

Closest candidates are:
  goSlower(::T) where T<:(Union{Quantity{T, 𝐋 𝐓^-2, U}, Level{L, S, Quantity{T, 𝐋 𝐓^-2, U}} where {L, S}} where {T, U}) 

As Unitful is the dominant unit package and has wide use and support, we provide a separate package ExchangeUnitful to enable interoperation with Unitful.

DynamicQuantities is newer and faster than Unitful because it "defines a simple statically-typed Quantity type for storing physical units." It does this by storing the exponents on the basic units, allowing any unit traceable to SI to be used. But this performant representation hurts readability, and while the unit representation may be able to be hidden behind overrides of show(), Julia is designed for types to be read and manipulated directly by users.

In the presence of Julia's type-heavy UI, these two, good attempts feel misdirected and motivate this package's literal typing of units. The limitation is that UnitTypes does not have a catch-all unit representation. Only units that have been defined by one of the macros may be represented, and complex units may need to have additional methods written to correctly convert between units, ie Celsius to Fahrenheit. See SIDerived.jl and Imperial.jl for examples.

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Released under MIT.