Thus we ask: can't we abstract computation as interaction
rather than
functions at a fundamental level? In other words, can't
we have a
foundational theory of computation in which computation is uniformly
represented as interaction rather than functions from the ground-up?
This
bold question was posed by theorists such as Girard, Hoare and
Milner,
with different motivations and orientations. After the study
by many people
following them, we are now witnessing the convergence of the
ideas of these
original thinkers, centring on the idea of name passing
interaction. The
accurate precision with which the new theory captures diverse
computational
phenomena is being demonstrated by recent results --- some of
them you
can see in the main page.
This, then, is the main focus of my present study, the study
which centres on
a small calculus based on asynchronous name passing interaction,
the
asynchronous core of the pi-calculus (see [1] and [5] in the
main page),
which relates not only to other variants of the pi-calculus
but also to
so-called game semantics, Linear Logic and Hewitt's actors.
Another nice
thing about this formalism is that it leads to rich applications
in analysis of
programming languages and computation, both in the world of
sequential and
concurrent/distributed computing. This calculus seems a nice
starting point
for our investigation.
But it is just a starting point: a long intellectual journey
by researchers will
be required to reach a general science of computation and information
based on the idea of interaction.