Properties of Terms with Types
In this chapter we establish some basic properties of terms which have types in the systems introduced in earlier ones. We only consider type inference systems à la Curry. Some of the results shown in this chapter are meaningless for typed systems a la Church, while some others can be easily adapted to them (like, for instance, the Subject Reduction Theorem). In Section 9.1 we study the subject reduction property for recursive type systems, in Section 9.2 the problem of finding types for untyped terms, and in Section 9.3 we study restrictions on recursive types such that strong normalization holds for terms that inhabit these.
9.1 First properties of
We will show that for invertible A the recursive type systems ...