There exist, however, typed lambda calculi that are not strongly normalizing.

Given the standard semantics, the simply typed lambda calculus is strongly normalizing: that is, well-typed terms always reduce to a value, i.e., a abstraction.

Since it is strongly normalizing, it is decidable whether or not a simply typed lambda calculus program halts: it does!

Tait showed in 1967 that -reduction is strongly normalizing.

A system of type theory is said to be strongly normalizing if all terms have a "normal form" and any order of reductions reaches it.

All the systems mentioned so far, with the exception of the untyped lambda calculus, are strongly normalizing: all computations terminate.

The systems from the lambda cube are all known to be strongly normalizing.

A rewrite system that is strongly normalizing and confluent.

As a term rewriting system, System F is strongly normalizing.

All eight calculi are strongly normalizing.