These semantics make the type incompatible with the Num class and attempting to plug your type into, say, a run of the mill ode solver likely won't do what you

These semantics make the type incompatible with the Num class and attempting to plug your type into, say, a run of the mill ode solver likely won't do what you want. So you have two options. 1) Rewrite all code to become "quantity aware". Multiplying two Matrix[Inch] results in a Matrix[Inch2] and so on. 2) Litter your code with floatToInch and inchToFloat conversions. I think you can see why both options suck? If you really can't, then perhaps try finding some safety-critical software that relies on "physical quantity types" in some form or another?