Automating Algebraic Methods in Isabelle
We implement a large Isabelle/HOL repository of algebras for application in modelling computing systems. They subsume computational logics such as dynamic and Hoare logics and form a basis for various software development methods. Isabelle has recently been extended by automated theorem provers and SMT solvers. We use these integrated tools for automatically proving several rather intricate refinement and termination theorems. We also automate a modal correspondence result and soundness and relative completeness proofs of propositional Hoare logic. These results show, for the first time, that Isabelle’s tool integration makes automated algebraic reasoning particularly simple. This is a step towards increasing the automation of formal methods.
KeywordsBoolean Algebra Algebraic Method Relative Completeness Computational Logic Automate Theorem Prove
Unable to display preview. Download preview PDF.
- 17.Hoare, C.A.R., He, J.: Unifying theories of programming. Prentice Hall Europe (1998)Google Scholar
- 24.Krauss, A., Nipkow, T.: Proof pearl: Regular expression equivalence and relation algebra. Journal of Automated Reasoning (2011), http://dx.doi.org/10.1007/s10817-011-9223-4
- 28.Paulson, L.C., Blanchette, J.C.: Three years of experience with Sledgehammer, a practical link between automatic and interactive theorem provers. In: Sutcliffe, G., Ternovska, E., Schulz, S. (eds.) Proceedings of the 8th International Workshop on the Implementation of Logics, pp. 3–13 (2010)Google Scholar
- 29.Schirmer, N.: Verification of Sequential Imperative Programs in Isabelle/HOL. Ph.D. thesis, TU München (2006)Google Scholar