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KAT-ML: an interactive theorem prover for Kleene algebra with tests

Kamal Aboul-Hosn, Dexter Kozen
2006 Journal of Applied Non-Classical Logics  
We describe KAT-ML, an implementation of an interactive theorem prover for Kleene algebra with tests (KAT).  ...  We explain how the system works and illustrate its use with some examples, including an extensive scheme equivalence proof.  ...  Acknowledgements We are indebted to Nikita Kuznetsov for his work on the heuristics and reduction system. This work was supported in part by NSF grant CCR-0105586 and ONR Grant N00014-01-1-0968.  ... 
doi:10.3166/jancl.16.9-33 fatcat:2n3ic72ewjglfju7htr6twxmgy

Using probabilistic Kleene algebra pKA for protocol verification

A.K. McIver, C. Gonzalia, E. Cohen, C.C. Morgan
2008 The Journal of Logic and Algebraic Programming  
We propose a method for verification of probabilistic distributed systems in which a variation of Kozen's Kleene Algebra with Tests [Dexter Kozen, Kleene algebra with tests, ACM Trans.  ...  Programming 28 (1997) 171-192; Roberto Segala, Modeling and verification of randomized distributed real-time systems, Separation theorems simplify reasoning about distributed systems, where with purely  ...  This tool is designed to help a user to perform interactive equational (and quasi-equational) proofs in the formal system of Kleene algebras with tests (KAT ), an extension of Kleene algebras with an embedded  ... 
doi:10.1016/j.jlap.2007.10.005 fatcat:nuuhuzvb3bgrlcqykiw7opbw7a

Using Probabilistic Kleene Algebra for Protocol Verification [chapter]

A. K. McIver, E. Cohen, C. C. Morgan
2006 Lecture Notes in Computer Science  
We propose a method for verification of probabilistic distributed systems in which a variation of Kozen's Kleene Algebra with Tests [11] is used to take account of the well-known interaction of probability  ...  Finally we show how the algebraic proofs for these theorems can be automated using a modification of Kozen and Aboul-Hosn's KAT-ML [3].  ...  Such is the case for KAT-ML, a tool originally designed by Aboul-Hosn and Kozen [3] for reasoning within standard Kleene algebra with tests.  ... 
doi:10.1007/11828563_20 fatcat:nlh7zni2bzgtnaws4uuoze6nve

An Axiomatization of Arrays for Kleene Algebra with Tests [chapter]

Kamal Aboul-Hosn
2006 Lecture Notes in Computer Science  
In this paper we augment the rules of Kleene algebra with tests (KAT) with rules for the equational manipulation of arrays in the style of schematic KAT.  ...  The formal analysis of programs with arrays is a notoriously difficult problem due largely to aliasing considerations.  ...  A Kleene algebra with tests (KAT) [10] is just a Kleene algebra with an embedded Boolean subalgebra.  ... 
doi:10.1007/11828563_4 fatcat:bilvxvhv5rdu7gv2n6syj2bbnq

A formal semantics for Gaia liveness rules and expressions

Tim Miller, Peter McBurney
2007 International Journal of Agent-Oriented Software Engineering  
The Gaia methodology is a development methodology for multi-agent systems that uses the concept of roles to define behaviour.  ...  In this paper, we present a formal semantics for liveness rules and expressions, and discuss our work in developing axioms about them.  ...  Acknowledgements The authors are grateful for financial support from the European Commission's Information Society Technologies Programme through the Project Personalized Information Platform for Life  ... 
doi:10.1504/ijaose.2007.016268 fatcat:ztxlxdcumbdvpndjmt6bsubniq

Automated soundness proofs for dataflow analyses and transformations via local rules

Sorin Lerner, Todd Millstein, Erika Rice, Craig Chambers
2005 SIGPLAN notices  
We present Rhodium, a new language for writing compiler optimizations that can be automatically proved sound.  ...  We have implemented a soundness checker for Rhodium and have specified and automatically proven the soundness of all of Cobalt's optimizations plus a variety of optimizations not expressible in Cobalt,  ...  We would also like to thank Dan Grossman, Alexandru Sȃlcianu, and the anonymous re-viewers for their useful suggestions on how to improve the paper.  ... 
doi:10.1145/1047659.1040335 fatcat:s2yvodhlnjg3nb3wzygqkqqckm

Automated soundness proofs for dataflow analyses and transformations via local rules

Sorin Lerner, Todd Millstein, Erika Rice, Craig Chambers
2005 Proceedings of the 32nd ACM SIGPLAN-SIGACT sysposium on Principles of programming languages - POPL '05  
We present Rhodium, a new language for writing compiler optimizations that can be automatically proved sound.  ...  We have implemented a soundness checker for Rhodium and have specified and automatically proven the soundness of all of Cobalt's optimizations plus a variety of optimizations not expressible in Cobalt,  ...  We would also like to thank Dan Grossman, Alexandru Sȃlcianu, and the anonymous re-viewers for their useful suggestions on how to improve the paper.  ... 
doi:10.1145/1040305.1040335 dblp:conf/popl/LernerMRC05 fatcat:kbghd4yafzctpog6zp6qnq5xgq

Organizing committee Sponsor

Tarmo Uustalu, Jüri Vain, Juhan Ernits, Wang Yi, Tarmo Uustalu, Monika Perkmann
2008 Nordic Workshop on Programming Theory NWPT   unpublished
specification of programs, program verification, program construction, program transformation and refinement, real-time and hybrid systems, models of concurrent, distributed and mobile computing, tools for  ...  Acknowledgements We thank Simon Peyton Jones for suggesting several of the examples and explaining how to achieve whole program compilation with GHC.  ...  Whether this also holds for weighted timed automata is an open question, as is computability of the other bisimulation distances, both for (weighted) timed automata and for other interesting formalisms  ... 
fatcat:hoaq5jc5xzfrdmsnrvhbl7be34