Typed variables

The variables we have right now can represent a number or a statement. However, they will undergo incorrect replacement if they get substituted with a matrix as we assume commutativity and unified cross and dot products (they are the same as scalar product for scalars). In mathematics we would write vector variables with an arrow on top and matrix variables with bolded uppercase letters, so that they are distinguished from normal variables, with cross product and dot product operations enabled, but with commutativity and implicit invertibility disabled.

How we want to represent this nuance (and where we write the shape of the variable e.g. RR^2), and whether function variables fall into this proposal, are pending analysis by the agent.

Will we have a proper design that lets quaternions and more be considered correctly?

Start by analyzing the current variable representation and substitution, commutativity, invertibility, cross-product, and dot-product behavior described in the issue. Done means the project has an agreed design covering vector and matrix shapes, function variables, quaternions, and the corresponding mathematical operations.

Written by the indexing model from the issue text.