(Kind) Units of measure

Dimensionless unit (identity element)

Base unit

Multiplication for units of measure

Division for units of measure

Exponentiation (to a positive power) for units of measure; negative exponents are not yet supported (they require an Integer kind)

A Quantity a u is represented identically to a value of underlying numeric type a, but with units u.

Extract the underlying value of a quantity

Zero is polymorphic in its units: this is required because the Num instance constrains the quantity to be dimensionless, so 0 :: Quantity a u is not well typed.

Construct a Quantity from a dimensionless value. Note that for numeric literals, the Num and Fractional instances allow them to be treated as quantities directly.

Addition (+) of quantities requires the units to match.

Multiplication (*) of quantities multiplies the units.

Subtraction (-) of quantities requires the units to match.

Negation (negate) of quantities is polymorphic in the units.

Absolute value (abs) of quantities is polymorphic in the units.

The sign (signum) of a quantity gives a dimensionless result.

Convert an Integer quantity into any Integral type (fromInteger).

Division (/) of quantities divides the units.

Reciprocal (recip) of quantities reciprocates the units.

Convert a Rational quantity into any Fractional type (fromRational).

Convert any Real quantity into a Rational type (toRational).

Taking the square root (sqrt) of a quantity requires its units to be a square. Fractional units are not currently supported.

Syntactic representation of a unit as a pair of lists of base units, for example One is represented as [] :/ [] and Base "m" /: Base "s" ^: 2 is represented as ["m"] :/ ["s","s"].

Unpack a unit as a syntactic representation, where the order of units is deterministic. For example:

 Unpack One = [] :/ []

 Unpack (Base "s" *: Base "m") = ["m","s"] :/ []

This does not break type soundness because Unpack will reduce only when the unit is entirely constant, and it does not allow the structure of the unit to be observed. The reduction behaviour is implemented by the plugin, because we cannot define it otherwise.

Pack up a syntactic representation of a unit as a unit. For example:

 Pack ([] :/ []) = One

 Pack (["m"] :/ ["s","s"]) = Base "m" /: Base "s" ^: 2

This is a perfectly ordinary closed type family. Pack is a left inverse of Unpack up to the equational theory of units, but it is not a right inverse (because there are multiple list representations of the same unit).

Take the product of a list of base units.

This is a bit of a hack, honestly, but a good hack. Constraints u ~~ v are just like equalities u ~ v, except solving them will be delayed until the plugin. This may lead to better inferred types.

This type family is used for translating unit names (as type-level strings) into units. It will be Base for base units or expand the definition for derived units.

The instances displayed by Haddock are available only if Data.UnitsOfMeasure.Defs is imported.