A notation query

When a type T is expressed in the form

                 T = T1 -> (T2 -> (... (Tn -> e)..))

where e is an atom, what is the most common name for the
components T1,...,Tn? Hypotheses of T? Antecedents of T?
Some other name?

 And, if T is itself a component of a larger type S, is there
any standard name for the relation of T1,...,Tn to S? I thought
of calling T1,...,Tn INTERIOR ANTECEDENTS of S (because they
are antecedents of something inside S).  Or perhaps SUB-ANTECEDENTS
or SUBHYPOTHESES. But all these seem big mouthfuls.

 ANTEPARTS or HYPOPARTS would be slicker, but rather uninformative.

 Is there an already established notation?

                   Roger Hindley, j.r.hindley@swansea.ac.uk

[Please e-mail answers to Roger.  Roger, please summarise answers
for this list!  -- Philip Wadler, moderator, Types Forum]