Rather than store each expression as an AST, I'm going to limit my effort to just storing expressions using Latex. As a consequence, the validity of inference rules applied to expressions not be able to be checked. If someone comes up with a representation more useful than Latex (ie ASTs, MathML, etc), then a conversion will need to be performed.
The second reason the choice of Latex is significant because it limits how far down in the hierarchy that can be enumerated. Specifically, in the context of these layers
Physics derivation graph
Expressions, inference rules
the Physics Derivation Graph with Latex will not be able to explore systematically the symbols and operators used.