semantic equation matching during manual entry of equations in new derivations

[bhpayne]

Imaging working on a derivation. Each equation involves typing Latex symbols as input for equations. I've previously thought that re-using the same symbol definitions (x=pdg1392) within a derivation was a reasonable feature that decreases the manual cleanup that happens after a derivation. (Since x gets used over and over in expressions throughout a single derivation, then I should only need to associate x with the PDG ID once.

Building on that feature-to-be, if the current step being entered is part way through the derivation, then the meaning of the symbols (what is $x$, what is $t$) is typically already known. With that knowledge, as new equations are entered, the PDG backend could be comparing what's being typed in against expressions that are already in the PDG database. Not just symbolic comparison ("does v = d / t appear in the database?") but a semantic comparison of what is being entered against what exists elsewhere in the PDG.

Currently the identification of overlap/intersection is manual reuse of expression IDs. This is extremely tedious.

The association of x=pdg1392='represents distance'='has units of length' means the expression is able to be matched to semantically equivalent expressions.

The expression v = d / t and the expression d / t = v are semantically equivalent even though they are not symbolically equivalent -- they have different unique IDs in the PDG database. If I'm typing v = then the PDG can identify that 1) d / t = v is already in the database and 2) suggest v = d / t as an auto-complete suggestion.

[bhpayne]

This would be computationally expensive in terms of queries, since every keystroke triggers a search of the PDG database to compare the symbols entered so far against existing expressions in all existing derivations.

Initially there'd be a bunch of candidate matches, but as the user enters additional Latex symbols the search space gets smaller

[bhpayne]

The same functionality is needed for user search - #238