Analyzing recursive programs using a fixed-point calculus

Salvatore La Torre, Madhusudan Parthasarathy, Gennaro Parlato
2009 Proceedings of the 2009 ACM SIGPLAN conference on Programming language design and implementation - PLDI '09  
We show that recursive programs where variables range over finite domains can be effectively and efficiently analyzed by describing the analysis algorithm using a formula in a fixed-point calculus. In contrast with programming in traditional languages, a fixedpoint calculus serves as a high-level programming language to easily, correctly, and succinctly describe model-checking algorithms. While there have been declarative high-level formalisms that have been proposed earlier for analysis
more » ... for analysis problems (e.g., Datalog), the fixed-point calculus we propose has the salient feature that it also allows algorithmic aspects to be specified. We exhibit two classes of algorithms of symbolic (BDD-based) algorithms written using this framework-one for checking for errors in sequential recursive Boolean programs, and the other to check for errors reachable within a bounded number of contextswitches in a concurrent recursive Boolean program. Our formalization of these otherwise complex algorithms is extremely simple, and spans just a page of fixed-point formulae. Moreover, we implement these algorithms in a tool called GETAFIX which expresses algorithms as fixed-point formulae and evaluates them efficiently using a symbolic fixed-point solver called MUCKE. The resulting model-checking tools are surprisingly efficient and are competitive in performance with mature existing tools that have been fine-tuned for these problems.
doi:10.1145/1542476.1542500 dblp:conf/pldi/TorreMP09 fatcat:b7a2tnqcdrdltloiaqzwaebiei