What is dimensionality? You can think of any unit of measure as distanced x massm x timet for some positive or negative integers d, m and t. For example speed = distance × time-1. The dimensionality of a unit of measure is that tuple: d, m and t.
The same notion can apply to units of measure in business programming, e.g. does variable size measure rows or columns? It is dangerous to get it backwards. If the units of measure were formally declared, the compiler could catch you if you used the variable in the wrong context.
Some people have suggested piggybacking a scheme for checking units of measure atop Java. Others want to go further and have automatic conversions applied.
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