Experimental support for conversions between units with the same dimension, for example feet and metres. This interface is not necessarily stable!

Rather than defining dimensions explicitly, we pick a "canonical" base unit for each dimension, and record the conversion ratio between each base unit and the canonical base unit for its dimension. This means we can automatically calculate the conversion ratio between a unit and its canonical representation, and hence between any two units that share a dimension (i.e. have the same canonical representation).

For example, to declare m as a canonical base unit, write:

instance HasCanonicalBaseUnit "m"

To declare ft as a derived unit, write:

instance HasCanonicalBaseUnit "ft" where
  type CanonicalBaseUnit "ft" = "m"
  conversionBase _ = [u| 3.28 ft/m |]

The above declarations can be written using the u declaration quasiquoter as [u| m, ft = 1 % 3.28 ft/m |], or generated automatically using declareConvertibleUnit.

Now it is possible to convert between quantities whose units involve feet or metres. For example:

>>> convert [u| 10m |] :: Quantity Double [u| ft |]
[u| 32.8 ft |]
>>> convert [u| 3ft^2 |] :: Quantity Double [u| m^2 |]
[u| 0.27885187388459254 m^2 |]

You are likely to get unpleasant compiler error messages if you attempt to convert without the units being fully determined by type inference, or if the units do not have the same dimension.

If you wish to define a dimensionless unit that requires explicit conversion to 1, such as radians, write [u| rad = 1 1 |]. The syntax [u| dimensionless = 1 |] defines dimensionless as a unit synonym for 1 that does not require conversion.