  We study the notion of subtyping for session types in a logical setting,
where session types are propositions of multiplicative/additive linear logic
extended with least and greatest fixed points. The resulting subtyping relation
admits a simple characterization that can be roughly spelled out as the
following lapalissade: every session type is larger than the smallest session
type and smaller than the largest session type. At the same time, we observe
that this subtyping, unlike traditional ones, preserves termination in addition
to the usual safety properties of sessions. We present a calculus of sessions
that adopts this subtyping relation and we show that subtyping, while useful in
practice, is superfluous in the theory: every use of subtyping can be "compiled
away" via a coercion semantics.
