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

Examples:

>>> 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 * kilogram
>>> let mars_mass = 6.417e23 * kilogram
>>> let earth_radius = 6371e3 * meter
>>> let mars_radius = 3389.5e3 * 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 * kilogram)
785.5719790179963 kg*m/s^2
>>> weight_on_mars (80 * kilogram)
298.22370259533704 kg*m/s^2
>>> fromQuantity $ weight_on_mars 1 / (fromQuantity $ weight_on_earth 1)
0.3796261966575378

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:

>>> 2*meter .+ 3*meter
5 m
>>> 2*meter .+ 1*second

<interactive>:16:1-19: 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:

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

Multiplies two quantities correctly merging their units.

Examples:

>>> 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:

>>> 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 other adimensional quantities.

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

<interactive>:79:1-13: error:
    • Unit mismatch: <adimensional> and m
    • In the expression: adim .+ meter
      In an equation for ‘it’: it = adim .+ meter