We want to balance the ability to reference specific outputs from identified cells in a way that persists, leading to a deterministic trail of executions. This is facilitated by appending the cell id to the variable name. If we have cells 43de1f and f341d3 that both output a variable df, we can write the individual outputs as df$43de1f and df$f341d3. Because a cell's id is immutable, these references are persistent and stable. However, we may want different semantics when executing code.
We may want a variable to reference the latest version of df each time the cell is manually run. This may change the persistent identifer on each execution. We can allow a user to encode this by adding the caret symbol (^) to indicate the most recent version of the identifier. Each time the cell is run, the current identifier is ignored and updated to reference whatever the latest definition is. Thus, the code df$^43de1f shows that the last time the cell was run, it referenced the output from 43de1f, but if cell f341d3 was run most recently, the next run will update this reference to df$^f341d3 before executing the cell. (One thing that isn't clear yet is what should happen when this cell is a dependency of a downstream cell that is executing...)
We may also want to make sure that a reference persists at all times. We can add the = qualifier to the identifier to make sure that only that cell is referenced. Here, the code df$=43de1f will always reference cell 43de1f, and it will generate an error if that cell doesn't exist. (Currently, this doesn't substantially differ from the normal df$43de1f reference)
Often, we may wish to refer to a cell with a more meaningful tag rather than a persistent id. Here, we can refer to the tag first and (usually) auto-append the persistent id after it. Thus, a reference of df$main refers the df defined in the cell tagged as main. When that cell is executed, we append the persistent id to the tag as df$main:43de1f. By default, this is treated as df$~main:43de1f. This means that if main changes, we will update the persistent id accordingly. If we use the = qualifier, this references the persistent id. Thusdf$=main:43de1f will effectively only reference 43de1f (the tag is only for the user). If the tag is moved or deleted, this reference should change to df$=43de1f. If we use the ^ qualifier, we have similar behavior in that we only view this as df$^43de1f; the tag is effectively ignored but useful as a marker for readers.
We should probably allow cells to be tagged as %tag <name> as well as through the Jupyter interface. This also means that : needs to be an invalid character for a tag (along with spaces).