We report on our experience implementing a lightweight, fully verified relational database management system (RDBMS). The functional specification of RDBMS behavior, RDBMS implementation, and proof that the implementation meets the specification are all written and verified in Coq. Our contributions include: (1) a complete specification of the relational algebra in Coq; (2) an efficient realization of that model (B+ trees) implemented with the Ynot extension to Coq; and (3) a set of simple query optimizations proven to respect both semantics and run-time cost. In addition to describing the design and implementation of these artifacts, we highlight the challenges we encountered formalizing them, including the choice of representation for finite relations of typed tuples and the challenges of reasoning about data structures with complex sharing. Our experience shows that though many challenges remain, building fully-verified systems software in Coq is within reach.

We present a new approach for constructing and verifying higherorder, imperative programs using the Coq proof assistant. We build on the past work on the Ynot system, which is based on Hoare Type Theory. That original system was a proof of concept, where every program verification was accomplished via laborious manual proofs, with much code devoted to uninteresting low-level details. In this paper, we present a re-implementation of Ynot which makes it possible to implement fully-verified, higher-order imperative programs with reasonable proof burden. At the same time, our new system is implemented entirely in Coq source files, showcasing the versatility of that proof assistant as a platform for research on language design and verification.Both versions of the system have been evaluated with case studies in the verification of imperative data structures, such as hash tables with higher-order iterators. The verification burden in our new system is reduced by at least an order of magnitude compared to the old system, by replacing manual proof with automation. The core of the automation is a simplification procedure for implications in higher-order separation logic, with hooks that allow programmers to add domain-specific simplification rules.We argue for the effectiveness of our infrastructure by verifying a number of data structures and a packrat parser, and we compare to similar efforts within other projects. Compared to competing approaches to data structure verification, our system includes much less code that must be trusted; namely, about a hundred lines of Coq code defining a program logic. All of our theorems and decision procedures have or build machine-checkable correctness proofs from first principles, removing opportunities for tool bugs to create faulty verifications.

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We present interaction trees (ITrees), a general-purpose data structure in Coq for formalizing the behaviors of recursive programs that interact with their environment. ITrees are built of uninterpreted events and their continuations-a coinductive variant of a "free monad. " We study the compositional properties of interpreters built from event handlers and show how to use them to implement a general mutual recursion operator. The resulting theory enables equational reasoning about ITrees up to weak bisimulation. Using this theory, we prove the termination-sensitive correctness of a compiler from a simple imperative source language to an assembly-like target whose meanings are given as an ITree-based denotational semantics. Crucially, the correctness proof follows entirely by structural induction and the equational theory of combinators for control-flow graphs, which are built on top of the mutual recursion operator. ITrees are also executable, e.g. through extraction, making them suitable for debugging, testing, and implementing executable artifacts.

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