We consider superfluous elements in a bounded lattice with 0 and 1, introduce various types of graphs associated these elements. The notions such as element graph (S(L)), join intersection (JI(L)) lattice, distributive (SI(L)) are defined. Dual atoms play an important role to find connections between the lattice-theoretic properties those corresponding graph-theoretic properties. Consequently, ...

It is shown that the inhabitation problem for intersection types without the intersection introduction rule is Expspace-complete and that the further restriction without subtyping is Pspace-complete.

Let (A,

Problem and motivation. A static type system can be an extremely powerful tool for a programmer, providing early error detection, and offering strong compile-time guarantees on the behavior of a program. However, compared to dynamic typing, static typing often comes at the expense of development speed and flexibility, as statically-typed code might be more difficult to adapt to changing require...