Experience report

Abstract

Many of the bugs in scientific programs have their roots in mistreatment of physical dimensions, via erroneous expressions in the quantity calculus. Now that the type system in the Glasgow Haskell Compiler is rich enough to support type-level integers and other promoted datatypes, we can type-check the quantity calculus in Haskell. In addition to basic dimension-aware arithmetic and unit conversions, our units library features an extensible system of dimensions and units, a notion of dimensions apart from that of units, and unit polymorphism designed to describe the laws of physics. We demonstrate the utility of units by writing an astrophysics research paper. This work is free of unit concerns because every quantity expression in the paper is rigorously type-checked.

Measuring with confidence: leveraging expressive type systems for correct-by-construction software

“…• Microsoft's F# [5] has units of measure built-in to static type checking; • C++'s Boost Units library [6] uses templates to check units statically; • Java has a proposed API adding classes for dimensioned quantities [7], but run-time casts are inevitable; • Haskell's type system can now encode basic units of measure as a library [8] or a typechecker plugin [9]; • Python libraries such as Pint [10] cannot do static checking of dimensional correctness, but implement runtime checks instead. Similarly, MATLAB has support for dynamic unit checking using the Symbolic Math Toolbox [11].…”

Expressive Type Systems for Metrology

“…• Haskell's type system can now encode basic units of measure as a library [ME14] or a typechecker plugin [Gun15];…”