A Discipline of Programming with Quantities

In scientific and engineering applications, physical quantities embodied as units of measurement (UoM) are frequently used. The loss of the Mars climate orbiter, attributed to a confusion between the metric and imperial unit systems, popularised the disastrous consequences of incorrectly handling measurement values. Dimensional analysis can be used to ensure expressions containing annotated values are evaluated correctly. This has led to the development of a large number of libraries, languages and validators to ensure developers can specify and verify UoM information in their designs and codes. Many tools can also automatically convert values between commensurable UoM, such as yards and metres. However these systems do not differentiate between quantities and dimensions. For instance torque and work, which share the same UoM, can not be interchanged because they do not represent the same entity. We present a named quantity layer that complements dimensional analysis by ensuring that values of different quantities are safely managed. Our technique is a mixture of analysis and discipline, where expressions involving multiplications are relegated to functions, in order to ensure that named quantities are handled soundly.