Abstract
Formal verification of cyber-physical systems requires that we can accurately model physical quantities. SI units allow a higher degree of rigour, since we can ensure compatibility of quantities in calculations. In this paper, we contribute a mechanisation of the International System of Quantities (ISQ) and the SI unit system in Isabelle/HOL. We show how Isabelle can be used to provide a type system for physical quantities, and automated proof support. Quantities are parameterised by dimension types and so only quantities of the same dimension can be equated. Our construction is validated by a test-set of known equivalences between both quantities and SI units. Moreover, the presented theory can be used for type-safe conversions between the SI system and others, like the British Imperial System (BIS).