A numerical quantity with some associated unit. Units are not created directly with this constructor, but through the individual unit functions.

Examples:

>>> import Units.Simple
>>> meter -- a unitary quantity associated to meters.
1 m
>>> 2.5*ampere -- constructing through literal arithmetic
2.5 A
>>> candela' 3.14 -- constructing through the unit constructors
3.14 cd
>>> :set -XDataKinds
>>> 2 :: Quantity (SingleUnit 'Second) Rational
2 % 1 s

Associated units are represented through a phantom parameter of the Units kind synonym. These are currently implemented as a type-level pair of lists representing the power to which each unit is raised. Units can be inspected through showUnits.

New constructors may be written by combining the provided ones, such as

>>> let newton = kilogram .* meter ./ (second .* second)
>>> 23*newton
23.0 kg*m/s^2

>>> let g = 6.67408e-11 * newton .* (meter .* meter) ./ (kilogram .* kilogram)
>>> g -- gravitational constant
6.67408e-11 m^3/kg*s^2
>>> let gravity m1 m2 r = g .* (m1 * kilogram) .* (m2 * kilogram) ./ (r*meter .* r*meter)
>>> let earth_mass = 5.972e24 * kilo gram
>>> let mars_mass = 6.417e23 * kilo gram
>>> let earth_radius = 6371 * kilo meter
>>> let mars_radius = 3389.5 * kilo meter
>>> let weight_on_earth mass = gravity mass earth_mass earth_radius
>>> let weight_on_mars mass = gravity mass mars_mass mars_radius
>>> weight_on_earth (80 * kilo gram)
785.5719790179963 kg*m/s^2
>>> weight_on_mars (80 * kilo gram)
298.22370259533704 kg*m/s^2
>>> weight_on_mars 1 / weight_on_earth 1
0.3796261966575378 <adimensional>

Unwraps a Quantity, losing all unit information

A string representation of Units. Useful for debugging.

Sums two quantities with the same units. Summing quantities with different units results in a type error.

Examples:

>>> import Units.Simple
>>> 2 * kilo meter .+ 3 * kilo meter
5000 m
>>> 2*meter .+ 1*second

<interactive>... error:
    • Unit mismatch: m and s
    • In the expression: 2 * meter .+ 1 * second
      In an equation for ‘it’: it = 2 * meter .+ 1 * second

Subtracts two quantities with the same units. Subtracting quantities with different units results in a type error.

Examples:

>>> import Units.Simple
>>> let newton = kilogram .* meter ./ (second .* second)
>>> 10*newton - 2*newton
8.0 kg*m/s^2

Multiplies two quantities correctly merging their units.

Examples:

>>> import Units.Simple
>>> meter .* meter
1 m^2
>>> let mps = meter ./ second
>>> 20*mps .* 60*second
1200.0 m

Important: Though Quantity a has a Num instance for convenience, it must not be used for anything other than interacting with literals, otherwise the units will not be correct:

>>> 2*meter * 3*meter -- note that (*) was used in place of (.*)
6 m
>>> 2*meter .* 3*meter -- this is the correct usage
6 m^2

Divides a quantity by another correctly merging their units.

Examples:

>>> import Units.Simple
>>> let coulomb = second .* ampere
>>> 20*coulomb ./ 2*second
10.0 A

A Quantity with no associated dimension. Can be multiplied or divided by any other Quantity, but can only be added to or subtracted from another adimensional Quantity.

>>> 2*adim + 4*adim
6 <adimensional>
>>> adim .+ meter

<interactive>... error:
    • Unit mismatch: <adimensional> and m
    • In the expression: adim .+ meter
      In an equation for ‘it’: it = adim .+ meter

A constructor for 1/1000th of a kilogram, to use with SI prefixes.

A constructor for 1/1000th of a kilogram, to use with SI prefixes.