 
Summary: Proofs as Processes
Samson Abramsky
April 14, 1994
The main purpose of this short paper is to serve as an introduction to the follow
ing paper, ``On the ßcalculus and Linear Logic'', by Gianluigi Bellin and Philip Scott.
The circumstances from which it arises are as follows. In June 1991 I gave a lecture on
``Proofs as Processes'' at the symposium held at TelAviv University to celebrate Boris
Trakhtenbrot's 70'th birthday [BT91]. Material from this lecture also appeared in lectures
subsequently given at the International Category Theory Meeting in Montreal (June 1991)
and the London Mathematical Society Symposium on Category Theory in Computer Sci
ence in Durham (July 1991). The material was also presented in my Tutorial Lectures on
Linear Logic given at the International Logic Programming Symposium in San Diego in
October 1991. The lecture notes for these talks, particularly the Tutorial Lecture, were
quite widely circulated; however, I did not write up a paper for publication, for reasons
shortly to be explained.
My point of departure in this work was the ``Propositions as Types'' paradigm (encom
passing such notions as ``CurryHoward Isomorphism'', Realizability, Functional Interpre
tation and BHK semantics) familiar from proof theory and typed functional programming
(see e.g. [GLT89]). In this paradigm, we have the correspondences
Formulas Types
