How does TableView work?

15.02.2023: Created and published for community
16.02.2023: Minor change of Excel notation
TableView is supposed to work like a spreadsheet, but I can’t see how to evaluate formulas within such a “spreadsheet”. As an example I use a cell A1 (in Excel notation) with a value a and a cell B1 which should be evaluated to a^2.

Example 1

In[]:=
a=2;​​TableView[{{a,a^2}}]
Out[]=
... doesn’t change B1 after modification of A1 to 3.

Example 2

In[]:=
a=2;​​TableView[Dynamic[{{a,a^2}}]]
Out[]=
... correctly changes B1 after modification of A1 but gives an error message (within the Messages window) Set::write: Tag Power in 3^2 is Protected.

Example 3

In[]:=
a=2;​​TableView[Dynamic[{{a,b=a^2}}]]
Out[]=
... correctly changes B1 after modification of A1 but gives an error message (within the Messages window) Set::write: Tag Set in b=9 is Protected.

Example 4

In[]:=
a=2;​​TableView[{{a,Dynamic[a^2]}}]
Out[]=
TableView[{{2,
2
a
}}]
... is syntactically incorrect.

Example 5

Enclosing TableView into

Dynam
icModule doesn’t change anything on this behavior. E.g.:
In[]:=
DynamicModule[{a=2},​​TableView[Dynamic[{{a,a^2}}]]​​]
Out[]=