Android now supporting Kotlin means more people playing around with it. Ben Trengrove is one of them - he has made a quite neat way of representing units in a type-safe wrapper. This disallows doing operations on two units of different measurements - for example speed cannot be added to a distance. Adding helper extensions to numeric types allows you to use it like this:

```
val distance = 21.kilometers
// This is OK because they are both distances
println(distance + 5.miles)
// This fails because you can't add distance to time
println(distance + 9.minutes)
```

You can have a look at Ben’s code here. Currently Ben’s code allows you to multiply one quantity by another. The result is a quantity with the same unit of the operands passed to the multiplication. This doesn’t follow the rules of dimensional analysis - if a distance is multiplied by another, the result not a distance, it’s a 2D area.

What this means is that you can do code like this:

```
val width = 10.meters
val height = 5.meters
// Area has unit Distance.Meter, not meters squared
val area = width * height
```

This piqued my interest - how could you implement units like speed and area, that are composed of multiple units? Of course you could just remove the `.div`

and `.times`

methods and replace them with extension functions that return a `Quantity<Speed>`

or `Quantity<Area>`

for each combination of units that you’re interested in.

But surely we can do better? This is what I set out to do, I wanted to be able to define the base units and derive every other unit from them. If you want to skip the rambling, you can check out the end result here.

The premise of this approach is to make two new subclasses of `Unit`

^{1} that each have two generic constraints - each of which must also be a type of `Unit`

. These represent a division type and a multiplication type, `QuotientUnit`

and `ProductUnit`

. All units have a suffix attribute that stores the standard identifier for that type (like “m” for meters, “s” for seconds, etc). `QuotientUnit`

and `ProductUnit`

create their suffix from the suffixes of their parts with either “/” or “.” inbetween.

The basic units are still defined in a similar way: ^{2}

```
abstract class Unit(val suffix: String, val ratio: Double) {
internal fun convertToBaseUnit(amount: Double) = amount * ratio
internal fun convertFromBaseUnit(amount: Double) = amount / ratio
override fun toString() = suffix
}
open class Distance(suffix: String, ratio: Double): Unit(suffix, ratio) {
companion object {
val Mile = Distance("mi", 1.60934 * 1000.0)
val Kilometer = Distance("km", 1000.0)
val Meter = Distance("m", 1.0)
val Centimeter = Distance("cm", 0.1)
val Millimeter = Distance("mm", 0.01)
}
}
```

The implementation of the composite units looks like this: ^{3}

```
class QuotientUnit<A: Unit, B: Unit>(a: A, b: B):
Unit("$a/$b", a.ratio / b.ratio)
class ProductUnit<A: Unit, B: Unit>(a: A, b: B):
Unit("$a.$b", a.ratio * b.ratio)
```

They are really just a placeholder to keep the type system in check. We can then use these to extend our `.div`

and `.times`

methods to return quantities with composite types. So inside the Quantity class we add:

```
operator fun <R: Unit> div(quantity: Quantity<R>): Quantity<QuotientUnit<T, R>> {
return Quantity(amount / quantity.amount, QuotientUnit(unit, quantity.unit))
}
operator fun <R: Unit> times(quantity: Quantity<R>): Quantity<ProductUnit<T, R>> {
return Quantity(amount * quantity.amount, ProductUnit(unit, quantity.unit))
}
```

So now when we divide a distance in kilometers by a time in hours, we get a `QuotientUnit<Distance, Time>`

with a suffix of “km/h”:

```
val distance = 21.kilometers
val time = 1.5.hours
println("Speed is: ${distance / time}") // Speed is: 14 km/h
```

And we should be able to do conversions between composite units as well, because the ratio of a composite unit is calculated based on the original units.

```
val speed = 21.kilometers / 1.5.hours
val milesPerHour = speed.to(QuotientUnit(Mile, Hour))
println("Speed is $milesPerHour") // Speed is 8.7 mi/h
```

Now that’s quite useful. However typing `QuotientUnit(Mile, Hour)`

is not very elegant. Perhaps we can use some helper function to make this a bit more readable?

We can actually do better than a helper function, instead we can make an extension operator that defines `/`

and `*`

on pairs of units. This lets us spell a composite unit like this: `Mile / Hour`

, which is the same as `QuotientUnit(Mile, Hour)`

. You can do this like so:

```
operator fun <A: Unit, B: Unit> A.div(other: B) = QuotientUnit(this, other)
operator fun <A: Unit, B: Unit> A.times(other: B) = ProductUnit(this, other)
```

With all this, we can now do the unit conversion problems you get in physics class with almost no effort:

```
// James Bond is running along the roof of a train
// It takes him 1 minute to run the length of a 20-metre carriage
// The train is moving at 60 miles per hour
// How fast is James moving relative to the ground, in km/h?
val jamesSpeed = 20.meters / 1.minute
val trainSpeed = 60.miles / 1.hour
val totalSpeed = jamesSpeed + trainSpeed
val metricSpeed = totalSpeed.to(Kilometer / Hour)
println("Speed relative to ground is: $metricSpeed")
// Speed relative to ground is: 97.76 km/h
```

Easy!

The last thing I wanted to clear up was the need to repeat code for all the helper properties (`6.minutes`

, `9.kilometers`

etc). These have to be repeated for every type of unit, and I wanted a way of creating units without this repitition. In reality you’d probably keep these to make it easier on yourself, but it’s nice to have an alternative.

How about just a simple infix function that operates on a number and a unit? Or how about if you multiply a number by a unit, it creates a quantity with that unit? What about invoking the unit with brackets - like a function call - to create a quantity in that unit? These are all quite straightforward: ^{4}

```
// 5 into Minute makes a Quantity(5, Minute)
infix fun <T: Unit> Number.into(unit: T) = Quantity(this.toDouble(), unit)
// 79 * Kilometer makes a Quantity(79, Kilometer)
operator fun <T: Unit> Number.times(unit: T) = this into unit
// Second * 3 makes a Quantity(3, Second)
operator fun <T: Unit> T.times(value: Number) = value into this
// Hour(12) makes a Quantity(12, Hour)
operator fun <T: Unit> T.invoke(value: Number) = value into this
```

All of these make it super easy to create quantities. And of course, you can use them with composite units: `5 * (Kilometer / Hour)`

, `Second(8)`

, `9.into(Metre * Metre)`

each create speed, duration, and area quantities.

Using these we could solve our physics problem from above like so:

```
// James' target is running twice as fast as him along the train
// How fast is the target moving relative to the ground, in m/s?
val jamesSpeed = 20 * (Meter / Minute)
val targetSpeed = 2 * jamesSpeed
val trainSpeed = 60 * (Mile / Hour)
val totalSpeed = targetSpeed + trainSpeed
val metricSpeed = totalSpeed.into(Meter / Second)
println("Speed relative to ground is: $metricSpeed")
// Speed relative to ground is: 27.5 m/s
```

Another helper that we can add is a division operator that operates on two quantities of the same type, producing a ratio of the two values rather than another quantity. You can use this to see “how many items of length X fit in space Y?”. This is done like so, inside the `Quantity`

class:

```
operator fun div(other: Quantity<T>) = unit.convertToBaseUnit(amount) / other.unit.convertToBaseUnit(other.amount)
// To work out the ratio between two speeds:
println("Speed ratio: ${jamesSpeed / targetSpeed}")
// Speed ratio: 0.5
```

For completeness I also added operators for multiplying values by numbers with no units - letting you do things like “double this distance” with `2 * distance`

. Quantities are also comparable, so less than and greater than also work.

Hopefully this explanation illuminates some of the magic generics in the code - which you can view here. I’m sure there are operations and helpers that I’m missing, or ways that this code can be cleaned up and simplified. This would make for a kick-ass back-end for a unit conversion app!