In this paper we define a type inference semi-algorithm for singly sor
ted pure type systems. For that, we define the notion of pure type sys
tems without the Pi-condition and a mapping from pure type systems wit
hout the Pi-condition to pure type systems. This allows us to prove th
e two main results: first that weak normalisation is preserved by the
extension and second the correctness of the type inference semi-algori
thm. (C) 1998 Academic Press.