Formalizing and Verifying a Modern Build Language

CLOUDMAKE is a software utility that automatically builds executable programs and libraries from source code—a modern MAKE utility. Its design gives rise to a number of possible optimizations, like cached builds, and the exe-cutables to be built are described using a functional programming language. This paper formally and mechanically verifies the correctness of central CLOUDMAKE algorithms. The paper defines the CLOUDMAKE language using an operational semantics, but with a twist: the central operation exec is defined axiomatically, making it pluggable so that it can be replaced by calls to compilers, linkers, and other tools. The formalization and proofs of the central CLOUDMAKE algorithms are done entirely in DAFNY, the proof engine of which is an SMT-based program verifier

Towards defining semantic foundations for purpose-based privacy policies

We define a semantic model for purpose, based on which purpose-based privacy policies can be meaningfully expressed and enforced in a business system. The model is based on the intuition that the purpose of an action is determined by its situation among other inter-related actions. Actions and their relationships can be modeled in the form of an action graph which is based on the business processes in a system. Accordingly, a modal logic and the corresponding model checking algorithm are developed for formal expression of purpose-based policies and verifying whether a particular system complies with them. It is also shown through various examples, how various typical purpose-based policies as well as some new policy types can be expressed and checked using our model

Proof-checking Euclid

We used computer proof-checking methods to verify the correctness of our proofs of the propositions in Euclid Book I. We used axioms as close as possible to those of Euclid, in a language closely related to that used in Tarski's formal geometry. We used proofs as close as possible to those given by Euclid, but filling Euclid's gaps and correcting errors. Euclid Book I has 48 propositions, we proved 235 theorems. The extras were partly "Book Zero", preliminaries of a very fundamental nature, partly propositions that Euclid omitted but were used implicitly, partly advanced theorems that we found necessary to fill Euclid's gaps, and partly just variants of Euclid's propositions. We wrote these proofs in a simple fragment of first-order logic corresponding to Euclid's logic, debugged them using a custom software tool, and then checked them in the well-known and trusted proof checkers HOL Light and Coq.Comment: 53 page

CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates

Termination is an important property of programs; notably required for programs formulated in proof assistants. It is a very active subject of research in the Turing-complete formalism of term rewriting systems, where many methods and tools have been developed over the years to address this problem. Ensuring reliability of those tools is therefore an important issue. In this paper we present a library formalizing important results of the theory of well-founded (rewrite) relations in the proof assistant Coq. We also present its application to the automated verification of termination certificates, as produced by termination tools

Total Haskell is Reasonable Coq

We would like to use the Coq proof assistant to mechanically verify properties of Haskell programs. To that end, we present a tool, named hs-to-coq, that translates total Haskell programs into Coq programs via a shallow embedding. We apply our tool in three case studies -- a lawful Monad instance, "Hutton's razor", and an existing data structure library -- and prove their correctness. These examples show that this approach is viable: both that hs-to-coq applies to existing Haskell code, and that the output it produces is amenable to verification.Comment: 13 pages plus references. Published at CPP'18, In Proceedings of 7th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP'18). ACM, New York, NY, USA, 201