Rarotonga greet canoe crew with old ties, young eagerness

Logical frameworks supporting higher-order abstract syntax (HOAS) allow a direct and concise specification of a wide variety of languages and deductive systems. Reasoning about such systems within the same framework is well-known to be problematic. We describe the new version of the Hybrid system, implemented on top of Isabelle/HOL (as well as Coq), in which a de Bruijn representation of \u3bb-terms provides a definitional layer that allows the user to represent object languages in HOAS style, while offering tools for reasoning about them at the higher level. We briefly describe how to carry out two-level reasoning in the style of frameworks such as Linc, and briefly discuss our system's capabilities for reasoning using tactical theorem proving and principles of induction and coinduction

The next 700 challenge problems for reasoning with higher-order abstract syntax representations : part 2: a survey

Over the past three decades, a variety of meta-reasoning systems which support reasoning about higher-order abstract specifications have been designed and developed. In this paper, we survey and compare four meta-reasoning systems, Twelf, Beluga, Abella and Hybrid, using several benchmarks from the open repository ORBI that describes challenge problems for reasoning with higher-order abstract syntax representations. In particular, we investigate how these systems mechanize and support reasoning using a context of assumptions. This highlights commonalities and differences in these systems and is a first step towards translating between them

Declarative Network Verification

In this paper, we present our initial design and implementation of a declarative network verifier (DNV). DNV utilizes theorem proving, a well established verification technique where logic-based axioms that automatically capture network semantics are generated, and a userdriven proof process is used to establish network correctness properties. DNV takes as input declarative networking specifications written in the Network Datalog (NDlog) query language, and maps that automatically into logical axioms that can be directly used in existing theorem provers to validate protocol correctness. DNV is a significant improvement compared to existing use case of theorem proving which typically require several man-months to construct the system specifications. Moreover, NDlog, a high-level specification, whose semantics are precisely compiled into DNV without loss, can be directly executed as implementations, hence bridging specifications, verification, and implementation. To validate the use of DNV, we present case studies using DNV in conjunction with the PVS theorem prover to verify routing protocols, including eventual properties of protocols in dynamic settings

Fully Abstract Operation Contracts

Proof reuse in formal software verification is crucial in presence of constant evolutionary changes to the verification target. Contract-based verification makes it possible to verify large programs, because each method in a program can be verified against its contract separately. A small change to some contract, however, invalidates all proofs that rely on it, which makes reuse difficult. We introduce fully abstract contracts and class invariants which permit to completely decouple reasoning about programs from the applicability check of contracts. We implemented tool support for abstract contracts as part of the KeY verification system and empirically show the considerable reuse potential of our approach