# ASound Type System for Physical Quantities, Units, and Measurements

 Title: A Sound Type System for Physical Quantities, Units, and Measurements Authors: Simon Foster and Burkhart Wolff Submission date: 2020-10-20 Abstract: The present Isabelle theory builds a formal model for both the International System of Quantities (ISQ) and the International System of Units (SI), which are both fundamental for physics and engineering. Both the ISQ and the SI are deeply integrated into Isabelle's type system. Quantities are parameterised by dimension types, which correspond to base vectors, and thus only quantities of the same dimension can be equated. Since the underlying "algebra of quantities" induces congruences on quantity and SI types, specific tactic support is developed to capture these. 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). BibTeX: @article{Physical_Quantities-AFP, author = {Simon Foster and Burkhart Wolff}, title = {A Sound Type System for Physical Quantities, Units, and Measurements}, journal = {Archive of Formal Proofs}, month = oct, year = 2020, note = {\url{https://isa-afp.org/entries/Physical_Quantities.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Status: [skipped] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.