Proving Concurrent Constraint Programming Correct, Revisited

Abstract

Concurrent Constraint Programming (CCP) is a simple and powerful model of concurrency where processes interact by telling and asking constraints into a global store of partial information. Since its inception, CCP has been endowed with declarative semantics where processes are interpreted as formulas in a given logic. This allows for the use of logical machinery to reason about the behavior of programs and to prove properties in a declarative way. Nevertheless, the logical characterization of CCP programs exhibits normally a weak level of adequacy since proofs in the logical system may not correspond directly to traces of the program. In this paper, relying on a focusing discipline, we show that it is possible to give a logical characterization to different CCP-based languages with the highest level of adequacy. We shall also provide a neater way of interpreting procedure calls by adding fixed points to the logical structure.

A proof theoretic view of spatial and temporal dependencies in biochemical systems

“…In [32,33] we have shown that CCP can indeed be used as a declarative language to implement simulation tools for biochemical systems. Such tools can be improved by the recent findings in [34], where optimizations for CCP were derived from the proof theory of linear logic. Similarly, we hope that the results in this paper and the body of knowledge in proof theory will allow us to build more automatic (and efficient) theorem provers to verify biochemical systems.…”