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Process Realizability Samson Abramsky
 

Summary: Process Realizability
Samson Abramsky
1 Introduction
Realizability has proved to be a fruitful approach to the semantics of computation, see
e.g. [AL91, Cro93, Lon95, AC98]. The scope of realizability methods has been limited
to Intuitionistic Logic (with some extensions to Classical Logic), on the logical side,
and to functional computation on the computational side. Our aim in the present work
is to explore the possibilities for broadening the scope of realizability:
ffl beyond Intuitionistic Logic, to Classical Linear Logic, and more;
ffl beyond functional computation, to encompass concurrent and non­deterministic
computation.
Why do this? We shall mention just one, fairly concrete motivation. Consider the well­
established paradigm of extracting functional programs from (Intuitionistic or Classical)
proofs, using the Curry­Howard isomorphism or realizability [GLT89, BS94]. Can we
analogously find a suitable combination of a logic and a realizability universe such that
we can extract interesting concurrent programs---communication protocols, distributed
algorithms, security protocols---from proofs of their specifications?
Two important caveats should be registered here. The first is that we don't envis­
age the extraction of programs from proofs as a practical programming methodology.
However, in the case of functional computation, the well­understood paradigm of pro­

  

Source: Abramsky, Samson - Computing Laboratory, University of Oxford

 

Collections: Computer Technologies and Information Sciences