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Dimensional analysis of source code

The idea of restricting the operations that can be performed on a variable based on attributes appearing in its declaration is actually hundreds of years old and is more widely known as dimensional analysis. Readers are probably familiar with the concept of type checking where, for instance, a value having a floating-point type is not allowed to be added to a value having a pointer type. Unfortunately many of those computer languages that support the functionality I am talking about (e.g., Ada) also refer to it as type checking and differentiate it from the more common usage by calling it strong typing. The concept would be much easier for people to understand if a different term were used, e.g., unit checking or even dimension checking.

Dimensional analysis, as used in engineering and the physical sciences, relies on the fact that quantities are often expressed in terms of a small number of basic attributes, e.g., mass, length and time; velocity is calculated by dividing a length by a time, LT^{-1} and area is calculated by multiplying two lengths, L^{2}. Adding a length quantity to a velocity has no physical meaning and suggests that something is wrong with the calculation, while dividing velocity by time, LT^{-2}, can be interpreted as acceleration. Dividing two quantities that have the same units results in what is known as a dimensionless number.

Dimensional analysis can be used to check a calculation involving physical quantities for internal consistency and as a method for trying to deduce the combinations of quantities that an unknown equation might contain based on the physical units the result is known to be represented in.

The frink language has units of measure checking built into it.

How might dimensional analysis be used to check source code for internal consistency? Consider the following code:

x = a / b;
c = a;
y = c / b;
if (x + y ...
z = x + b;

c is assigned a‘s value and is therefore assumed to have the same units of measurement. The value assigned to y is calculated by dividing c by b and the train of reasoning leading to the assumption that it has the same units of measurement as x is easy to follow. Based on this analysis there is nothing suspicious about adding x and y, but adding x and b looks wrong (it would be perfectly ok if all of the variables in this code were dimensionless).

A number of tools have been written to check source code expressions for internal consistency e.g., Fortran (Automated computation and consistency checking of physical dimensions and units in scientific programs), C++ (Applied Template Metaprogramming in SI units) and C (Annotation-less Unit Type Inference for C), but so far only one PhD.

Providing a mechanism for developers to add unit information to variable declarations would enable compilers to perform consistency checks and reduce the likelihood of false positives being reported (because dimensionless values can generally be combined together in any way). It is too late in the day for such a major feature to be added to the next revision of the C++ standard; the C standard is also being revised but the committee is currently being very conservative and insists that any proposed new constructs already be implemented in at least one compiler.

A question to answer *