Lambda-terms as total or partial functions on normal forms

In this paper the set of λ -terras is split into 2ω+1 disjoint classes Ph (−ω≤h≤ω). This classification takes into account the meaning of a λ-term F as function on normal forms, and more precisely: 1 iff when auccessively applied to any number of normal forms it gives a λ-term without normal form 2 (0<h<ω) iff when successively applied to h-1 arbitrary normal forms it gives a λ-term without normal form, but there exist h normal forms X1,...,Xh such that FX1...Xh possesses normal form 3 (0≤h>ω) iff when successively applied to h arbitrary normal forms it gives a λ-term which possesses normal form, but there exist h+1 normal forms X1,...,Xh+1 such that FX1...Xh+1 possesses no normal form 4 iff when successively applied to any number of normal forms it gives a λ-term which possesses normal form.