  We study Milner's lambda-calculus with partial substitutions. Particularly,
we show confluence on terms and metaterms, preservation of \b{eta}-strong
normalisation and characterisation of strongly normalisable terms via an
intersection typing discipline. The results on terms transfer to Milner's
bigraphical model of the calculus. We relate Milner's calculus to calculi with
definitions, to calculi with explicit substitutions, and to MELL Proof-Nets.
