How to define a class instance of type_synonym?

type is an instance of semilattice_sup class:

datatype type = BType | IType | AType

instantiation type :: semilattice_sup
begin
end

I'm trying to declare type × bool type as an instance of this class too:

type_synonym stype = "type × bool"

instantiation stype :: semilattice_sup
begin
end

But I get the following error:

Bad type name: "stype"

How to define a class instance of type_synonym?