Add support for TableDum and TableDee (Tutorial D)

[rlaiola]

Reference issue

#15

What does this implement/fix?

This PR provides a way to define two special relations proposed in Tutorial D. TableDum denotes a relation of degree zero (no attributes) and cardinality zero (no tuples). On the other hand, TableDee represents a relation of degree zero and cardinality one (it has one single tuple of degree zero). In other words, TableDee represents a true proposition (identity relation under join operators) whereas TableDum is a false one.

Dum and Dee relations can be represented as follows in both Relational and Multiset Algebra:

Dum = {}   -- inline relation with empty heading and no tuples
Dee = {()} -- inline relation with empty heading but one tuple of degree zero

Given a relation R with n (n > 0) attributes and t (t > 0) tuples

R x Dum -- returns a relation with the same schema of R but no tuples
R x Dee -- returns the very same relation R

How to test this PR?

Test it live at https://rlaiola.github.io/relax/calc/local/uibk/local/0. For automated tests visit https://rlaiola.github.io/relax/test.html

References

• https://wiki.c2.com/?TheThirdManifesto
• https://dn-uni.com/wp-content/uploads/2018/12/An-Introduction-to-Relational-Database-Theory.pdf