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The SBML editors had an off-line discussion which we
realized needs to be put on sbml-discuss. It concerns an
issue that Sarah Keating ran into while implementing unit
validation in libSBML.

The issue is how the units of pure numbers in MathML should
be treated. Here's an example, in the case of the 'delay'
field on Events:

<delay>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<cn> 1 </cn>
</math>
</delay>

Note the literal "1". What units, if any, should be
assumed for the number?

One option is to treat literal numbers as always being
without units. This is a valid viewpoint, but it leads to
more model validation failures. Although modelers should
define parameters (which can have defined units) for a lot
of the cases where they often write numbers directly, the
practical reality is that many people won't think of doing
that.

A second option is to take the units to be whatever units
are defined as the default for the field in question, or if
there is an associated field definining the units, then
whatever that field says the units are. (For instance,
there is a 'timeUnits' field on Events that could apply in
this example.) The logic behind this idea is that even
though the user didn't specify the units explicitly, a
reasonable interpretation of their intention is that the
units are meant to be whatever the defaults are. In other
words, the modeler didn't mean "1" without units, they meant
"1 in the units of time" for this example.

Sounds reasonable? But it gets more complicated. Imagine
now something like

<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<plus/>
<ci> S </ci>
<cn> 2 </cn>
</apply>
</math>

For the purpose of this second example, the "S" can be
anything (e.g., a species identifier) and the context can be
anything, not just the Events example above.

The question is, what should be assumed for the units of "2"?

If we follow the same guideline, i.e., that the literal
number has whatever units are appropriate for the situation,
then it creates validation problems. First, it implies a
unit validator must deduce the expected units somehow, and
this may sometimes be impossible due to ambiguities in a
given situation. Second, Stefan Hoops pointed out it opens
a hole in validation: it effectively means that numbers in
MathML are assumed to always have the appropriate units, so
unit checking becomes worthless.

To cope with this, we are tentatively thinking of using the
following set of guidelines:

1) If the number is the only thing contained inside a <math>
(such as the original example involving a delay on
Events), assume that the units of the number are the
units defined for that field (so, timeUnits for delays).

2) In all other cases, assume pure numbers have no units.

This handles the first case, and also addresses the second
case. (In the second case, there would be a unit validation
failure because the "2" would not have units and therefore
the overall expression could not have consistent units.)

The downside is that this "rule" is defined with an
exception.

What do the rest of you SBMLers think?

Whatever is decided, the next SBML specification will have
to spell out the guidelines precisely.

MH

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