Formal system development needs expressive specification languages, but also calls for highly automated tools. These two goals are not easy to reconcile, especially if one also aims at high assurances for correctness. In this paper, we describe a combination of Isabelle/HOL with a proof-producing SMT (Satisfiability Modulo Theories) solver that contains a SAT engine and a decision procedure for quantifier-free first-order logic with equality. As a result, a user benefits from the expressiveness of Isabelle/HOL when modeling a system, but obtains much better automation for those fragments of the proofs that fall within the scope of the (automatic) SMT solver. Soundness is not compromised because all proofs are submitted to the trusted kernel of Isabelle for certification. This architecture is straightforward to extend for other interactive proof assistants and proof-producing reasoners.

Abstract. We present the formalization of the rely-guarantee method in the theorem prover Isabelle/HOL. This method consists of a Hoarelike system of rules to verify concurrent imperative programs with shared variables in a compositional way. Syntax, semantics and proof rules are defined in higher-order logic. Soundness of the proof rules w.r.t. the semantics is proven mechanically. Also parameterized programs, where the number of parallel components is a parameter, are included in the programming language and thus can be verified directly in the system. We prove that the system is complete for parameterized programs. Finally, we show by an example how the formalization can be used for verifying concrete programs.

Abstract. We present a formalization of the Gries/Owicki method for correctness proofs of concurrent imperative programs with shared variables in the theorem prover Isabelle/HOL. Syntax, semantics and proof rules are defined in higher-order logic. The correctness of the proof rules w.r.t. the semantics is proved. The verification of some typical example programs like producer/consumer is presented.

Information flow type systems provide an elegant means to enforce confidentiality of programs. Using the proof assistant Isabelle/HOL, we have machine-checked a recent work of Boudol and Castellani [4], which defines an information flow type system for a concurrent language with scheduling, and shows that typable programs are non-interferent. As a benefit of using a proof assistant, we are able to deal with a more general language than the one studied by Boudol and Castellani. The development constitutes to our best knowledge the first machine-checked account of non-interference for a concurrent language.