Embedding Static Analysis into Tableaux and Sequent Based Frameworks

In this paper we present a method for embedding static analysis into tableaux and sequent based frameworks. In these frameworks, the information flows from the root node to the leaf nodes. We show that the existence of free variables in such frameworks introduces a bi-directional flow, which can be used to collect and synthesize arbitrary information. We use free variables to embed a static program analysis in a sequent style theorem prover used for verification of Java programs. The analysis we embed is a reaching definitions analysis, which is a common and well-known analysis that shows the potential of our method. The achieved results are promising and open up for new areas of application of tableaux and sequent based theorem provers.