Analyzing recursive programs using a fixed-point calculus

  • Authors:

  • Salvatore La Torre;Madhusudan Parthasarathy;Gennaro Parlato

  • Affiliations:

  • Università degli Studi di Salerno, Salerno, Italy;University of Illinois at Urbana-Champaign, Urbana, IL, USA;University of Illinois at Urbana-Champaign, Urbana, IL, USA

  • Venue:
  • Proceedings of the 2009 ACM SIGPLAN conference on Programming language design and implementation
  • Year:
  • 2009

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Abstract

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 fixed-point 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 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 context-switches 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.