We need a lattice of values that embodies type information, NULLness, Noneness, constant values, version numbers, at the least.

The lattice should look something like this:

graph BT;
    t("True");
    f("False");
    bl("bool");
    nnull(not NULL);
    nnone(not None);
    ot(other types);
    oc(other constants);
    b("bottom(unknown)");
    b-->NULL;
    b-->nnull;
    nnull-->nnone;
    nnull-->None;
    nnone-->ot;
    nnone-->bl;
    ot-->oc;
    oc-->top;
    None-->top;
    NULL-->top;
    bl-->t;
    bl-->f;
    t-->top;
    f-->top;

There should be edges from all the nodes (except bottom) to top, but I've omitted those to avoid the diagram becoming a mess

There should be edges from all the nodes (except bottom) to top, but I've omitted those to avoid the diagram becoming a mess

Maybe top needn't be part of the diagram at all? It ought to be unreachable (IIUC it represents an impossible condition). Might as well simplify the diagram a bit further.

According to Wikipedia, in type theory, Bottom (⊥) is the type that has no values, whereas Top (⊤) is the type that encompasses all values. Maybe we should switch to this terminology, and swap top and bottom in the diagram above, so that "unknown" is named "top" and there is an arrow from every other nod to "bottom"? (Possibly also just flipping the diagram upside down so that "top" is drawn at the top and "bottom" at the bottom?)

Offline we agreed that Top is the universal type and Bottom is the empty type, like in my latest diagram. I will update diagrams and text where these terms are used.

See faster-cpython/ideas#658