Managing Quantities and Units of Measurement in Code Bases

Early in the 20th century, expressions involving abstract physical quantities gained acceptance. For example, Newtons third law, F = ma, holds regardless of units, provided we understand and apply the rules of quantity calculus. Scientists, engineers and technicians are trained to use quantity equations. Perhaps unsurprisingly, this skill is difficult to express in computer software. This paper looks at a few ideas that could be useful, some more than a century old.

Nature

Modelling Foundations and Applications, 2018

Uncertainty is an inherent property of any measure or estimation performed in any physical setting, and therefore it needs to be considered when modeling systems that manage real data. Although several modeling languages permit the representation of measurement uncertainty for describing certain system attributes, these aspects are not normally incorporated into their type systems. Thus, operating with uncertain values and propagating uncertainty are normally cumbersome processes, difficult to achieve at the model level. This paper proposes an extension of OCL and UML datatypes to incorporate data uncertainty coming from physical measurements or user estimations into the models, along with the set of operations defined for the values of these types.

What can be done to guaranty correctness of a model? The paper discusses two approaches to automatic checking. First, Dymola's support of units, unit checking and unit deduction is described. It has already proven useful and has helped improving the quality of the Modelica Standard Library. The display unit concept allows users to enter parameters and plot variables in different units. The inputs, outputs and parameters of general blocks defining sources and mathematical operations have of course no units specified. Dymola infers their units in order to improve the variable browsers for entering parameter values and plotting variables during simulation. Second, the possibilities of checking quantity conservation automatically are discussed. It is in open area with a large potential to check that models fulfill the very basic laws of physics including energy conservation, Newton's third law "action equals reaction", etc. To really support automatic checking of quantity conservation it is necessary to include more information in the models. Fortunately, it seems as if most of this can be done in the basic components such as inertia, body, volume, capacitor etc which actually store some quantities and in dissipative elements as for example resistors or friction elements.

Several software quality metrics have been proposed during the last decades to reduce risks and faultiness during software development. Despite these many efforts, most defined measurements fail to reach a satisfactory level of performance due to the ambiguities detected in the way their definitions are expressed and later on interpreted. The paper introduces a formal extension of a well-known library of measures named FLAME. While this library is expressed using the semi-formal language OCL (Object Constraint Language) upon the UML meta-model, our extension make use of formal methods to provide a more precise and accurate measurements by proposing a formal definitions of software metrics upon a formal expression of the UML metamodel. Unlike the original definition of the library, this extension supports formal proofs and guarantees a unique interpretation which allows the built of tools support.

Journal of the Text Encoding Initiative, 2019

This paper presents a markup model for encoding non-SI units and measurements. Historical texts contain many examples of compound measurements, composed of sets of units and numerical components. Instead of using the <measure> element, which requires a single set of @unit and @quantity, we propose a newly dened set of tags for encoding idiosyncratic measurement semantics, namely <unitDecl> (model.encodingDescPart), <unitDef> (model.global and contained by <unitDecl>), <unit> (model.measureLike), and a relevant attribute @factor (which shows factors of numerical values given in a referenced <unit> element). All of these elements and attributes will be included in the TEI P5 Guidelines, and they are especially useful when encoding

2008

The Modelica language supports syntax for declaring physical units of variables, but it does not yet exist any defined semantics for how dimensional and unit consistency checking should be carried out. In this paper we explore different approaches and new constructs for improved dimensional inference and unit consistency checking in Modelica; both from an end-user, library, and tool perspective. A proposal for how dimensional inference and unit checking can be carried out is outlined and a prototype implementation is developed and verified using several examples from the Modelica standard library.

Companion to the 20th annual ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications - OOPSLA '05, 2005

In physics, like in other sciences, formulas are specified using explicit measurements, that is, a number with its unit. The first step to determine the validity of a physics formula's evaluation is to verify that the unit of the result corresponds with the prospective unit. In software development, physics, financial and other sciences formulas are programmed using mathematical expressions based only on numbers, being the units of these numbers implicitly given by the semantics of the program or assumed by the programmer's knowledge. Consequently, it is common that errors result from operating with values expressed in different units, e.g., dividing a quantity of years by a quantity of months, without obtaining any type of indication or objection to this error from the system. In this report, we discuss our experience designing and implementing a model that solves this problem reifying the concept of measurement, unit and their arithmetic. Our model relieves the programmer from the arduous task of verifying the validity of the arithmetic expressions regarding units, delegating that responsibility to the system, thereby, diminishing the errors introduced by the incorrect use of values expressed in different units. We also show that having implemented this model with a dynamically typed language simplified its programming and increased its reusability.

IEEE Engineering in Medicine and Biology Magazine, 2000

Computer models of physiology are based on physical laws governing chemical reaction kinetics, magnetic fields, hydrodynamics, ion fields, charge transfer, and other phenomena. Equations that instantiate these models represent the relationships among time, mass, distance, force, pressure, chemical concentration, and potential difference. In the Systeme Internationale (SI) system, the seven base units are ampere, candela, kelvin, kilogram, meter, mole, and second. The units may be fundamental, as in SI units, or derived, as with velocity (m/s) or pressure in its varied forms (e.g., 1 mmHg = 1.00000014 torr = 133.332Pa = 1333.22 g · cm −1 · s −2 ). Pressure may also be expressed as kilopascals, atmospheres, bars and microbars, pounds per square inch, etc. Models often refer to experimental values expressed in units that are convenient to use during the collection of data and vary in form or in the system of units that is used.

The most elementary check on equations used to model physics, chemistry or biology is to determine whether or not the units balance on each equation. When disparate models are combined into more comprehensive or multi-scale systems, conflicts in units commonly occur amongst the units used, such as kg versus g or kPa versus mmHg. Automated unit balance checking followed by unit conversions facilitates the effort of combining models. There are three unit balancing processes: (1) the identification and rejection of model equations containing invalid unit arithmetic; (2) the insertion of scalar multipliers into the equations to convert existing units into fundamental units; and (3) the assignment of units to variables and constants whose units are undeclared, based upon context. Used together these three methods automate the otherwise tedious and error-prone process of manual unit balance checking, thus producing more accurate and readable models. The approach is general and can be incorporated into modeling platforms as an essential first step in model verification. An example is the use in the JSim system for data analysis.