  The logical technique of focusing can be applied to the $\lambda$-calculus;
in a simple type system with atomic types and negative type formers (functions,
products, the unit type), its normal forms coincide with $\beta\eta$-normal
forms. Introducing a saturation phase gives a notion of quasi-normal forms in
presence of positive types (sum types and the empty type). This rich structure
let us prove the decidability of $\beta\eta$-equivalence in presence of the
empty type, the fact that it coincides with contextual equivalence, and a
finite model property.
