Observational equivalences for linear logic concurrent constraint languages

Abstract

Linear logic Concurrent Constraint programming (LCC) is an extension of concurrent constraint programming (CC), where the constraint system is based on Girard's linear logic instead of the classical logic. In this paper, we address the problem of program equivalence for this programming framework. For this purpose, we present a structural operational semantics for LCC based on a label transition system and investigate different notions of observational equivalences inspired by the state of art of process algebras. Then, we demonstrate that the asynchronous π-calculus can be viewed as simple syntactical restrictions of LCC. Finally, we show that LCC observational equivalences can be transposed straightforwardly to classical Concurrent Constraint languages and Constraint Handling Rules, and investigate the resulting equivalences.

Models and emerging trends of concurrent constraint programming

“…Furthermore, in [12] the authors provided an algorithm for the automatic verification of bisimilarity. In the same lines, [105] studies a labeled bisimulation for Linear CCP processes. The latter equivalence is shown to coincide with a may-testing equivalence and the barbed congruence.…”

“…The semantics of the local operator can also be given by using fresh variables, i.e., variables that do not appear elsewhere in the processes as in [138,77,105]. In this case, configurations are augmented with a set of eigenvariables.…”

“…Linear CCP (lcc) [179,77,22,23,105] is a variant of CCP where constraints are built from a linear constraint system based on Girard's intuitionistic linear logic (ILL) [97].…”

“…Due to the removal of information, lcc is intrinsically non-deterministic and the constraint d above has to be carefully chosen to avoid the unwanted weakening of the store as in !c c [106,137,105]. Nevertheless, since lcc is not monotonic (in the sense that the information in the store can be dropped), this model introduces some forms of imperative programming particularly useful for reactive systems.…”

“…We note also that CCP has been shown to be expressive enough to encode other models of computation, different from its predecessors Concurrent Logic Programming and Constraint Logic Programming. For instance, different (fragments of) asynchronous concurrent formalisms such as the asynchronous π-calculus, Actor models, Linda, Petri nets have been encoded as (linear and higher order) CCP processes [121,181,179,127,105]. Furthermore, sequential models of computations such as the the untyped λ-calculus and Minsky machines have been encoded into CCP [179,157].…”