Compute and check type of cells

[lars-reimann]

Is your feature request related to a problem?

Cells are our concept to lazily (i.e. the data must not be loaded immediately) execute vectorized operations on tables. The laziness is essential for efficiency, since it enables optimization of queries and more. However, the drawback of the laziness is that validation of operations on cells also happens very late.

Desired solution

Type computation:

• When creating a cell from a column/row store the type of the associated column in the cell.
• When calling a method of a cell, store the type of the operation's result in the returned cell.
• For now, it is not needed to compute the type of arbitrary Python expressions. If you don't know a type of an operator and the operation might return multiple incompatible types, set the type to None.

Type checking:

• At the start of the methods of a cell, check whether the operation can be applied to a cell based on the cell's type.

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[LIEeOoNn]

Question I am checking the types using

T_co = TypeVar("T_co", covariant=True)
P_contra = TypeVar("P_contra", contravariant=True)
R_co = TypeVar("R_co", covariant=True)
``` and for example doing 
```python 
 def add(self: Cell[T_co], other: Cell[T_co]) -> Cell[R_co]: ...

the user sees something like

(method) def add(other: Cell[int]) -> Cell[int]

but what do T_co R_co P_contra actually mean ?

[LIEeOoNn]

Add do we need to write new tests to see if the checking works ?

[lars-reimann]

That's Python's type system. T/R/P are the actual, arbitrary names of type variables. The _co/_contra suffix is a convention to indicate the variance of the type variable.

Python's type system is not capable of capturing the type of the cell at runtime, though. You need to add an actual field for that.