On concurrent behaviors and focusing in linear logic

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 formula...

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Vydané v:Theoretical computer science Ročník 685; s. 46 - 64
Hlavní autori: Olarte, Carlos, Pimentel, Elaine
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 15.07.2017
Predmet:
Concurrent constraint programming
Fixed points
Focusing
Linear logic
Multi-focusing
Proof systems
Concurrent constraint programming
Linear logic
Fixed points
Proof systems
Multi-focusing
Focusing
ISSN:0304-3975, 1879-2294
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Popis
Shrnutí: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 of them. 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, we study different encodings from CCP into intuitionistic linear logic (ILL) and we compare the level of adequacy attained in each. By relying on a focusing discipline, we show that it is possible to give a logical characterization to CCP with the highest level of adequacy. Moreover, we show how to characterize maximal-parallelism semantics for CCP by relying on a multi-focusing discipline for ILL. These results, besides giving proof techniques for CCP, entail (safe) optimizations for the execution of CCP programs. Finally, we show how to interpret CCP procedure calls as fixed points in ILL, thus opening the possibility of reasoning by induction about properties of CCP programs.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2016.08.026