Effective Interactive Proofs for Higher-Order Imperative Programs

We present a new approach for constructing and verifying higher-order, 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.Engineering and Applied Science

Automatically proving equivalence by type-safe reflection

We are also grateful for the support of the Scottish Informatics and Computer Science Alliance (SICSA) and EPSRC grant EP/N024222/1.One difficulty with reasoning and programming with dependent types is that proof obligations arise naturally once programs become even moderately sized. For example, implementing an adder for binary numbers indexed over their natural number equivalents naturally leads to proof obligations for equalities of expressions over natural numbers. The need for these equality proofs comes, in intensional type theories, from the fact that the propositional equality enables us to prove as equal terms that are not judgementally equal, which means that the typechecker can’t always obtain equalities by reduction. As far as possible, we would like to solve such proof obligations automatically. In this paper, we show one way to automate these proofs by reflection in the dependently typed programming language Idris. We show how defining reflected terms indexed by the original Idris expression allows us to construct and manipulate proofs. We build a hierarchy of tactics for proving equivalences in semi-groups, monoids, commutative monoids, groups, commutative groups, semi-rings and rings. We also show how each tactic reuses those from simpler structures, thus avoiding duplication of code and proofs.Postprin

C4: Verified Transactional Objects

A framework for Verified Transactional Objects in Coq. - Formalization of concurrent objects, linearizability, strict serializability, and associated proof techniques. - Verified linearizable concurrent hash map - Verified strictly serializable TML - Verified strictly serializable transaction-predicated ma

Age Drives Distortion of Brain Metabolic, Vascular and Cognitive Functions, and the Gut Microbiome

Advancing age is the top risk factor for the development of neurodegenerative disorders, including Alzheimer’s disease (AD). However, the contribution of aging processes to AD etiology remains unclear. Emerging evidence shows that reduced brain metabolic and vascular functions occur decades before the onset of cognitive impairments, and these reductions are highly associated with low-grade, chronic inflammation developed in the brain over time. Interestingly, recent findings suggest that the gut microbiota may also play a critical role in modulating immune responses in the brain via the brain-gut axis. In this study, our goal was to identify associations between deleterious changes in brain metabolism, cerebral blood flow (CBF), gut microbiome and cognition in aging, and potential implications for AD development. We conducted our study with a group of young mice (5–6 months of age) and compared those to old mice (18–20 months of age) by utilizing metabolic profiling, neuroimaging, gut microbiome analysis, behavioral assessments and biochemical assays. We found that compared to young mice, old mice had significantly increased levels of numerous amino acids and fatty acids that are highly associated with inflammation and AD biomarkers. In the gut microbiome analyses, we found that old mice had increased Firmicutes/Bacteroidetes ratio and alpha diversity. We also found impaired blood-brain barrier (BBB) function and reduced CBF as well as compromised learning and memory and increased anxiety, clinical symptoms often seen in AD patients, in old mice. Our study suggests that the aging process involves deleterious changes in brain metabolic, vascular and cognitive functions, and gut microbiome structure and diversity, all which may lead to inflammation and thus increase the risk for AD. Future studies conducting comprehensive and integrative characterization of brain aging, including crosstalk with peripheral systems and factors, will be necessary to define the mechanisms underlying the shift from normal aging to pathological processes in the etiology of AD

Gut Dysbiosis in Cutaneous T-Cell Lymphoma Is Characterized by Shifts in Relative Abundances of Specific Bacterial Taxa and Decreased Diversity in More Advanced Disease

Background Cutaneous T-cell lymphoma (CTCL) patients often suffer from recurrent skin infections and profound immune dysregulation in advanced disease. The gut microbiome has been recognized to influence cancers and cutaneous conditions; however, it has not yet been studied in CTCL.ObjectivesTo investigate the gut microbiome in patients with CTCL and in healthy controls.MethodsA case-control study was conducted between January 2019 and November 2020 at Northwestern’s busy multidisciplinary CTCL clinic (Chicago, Illinois, USA) utilizing 16S ribosomal RNA gene amplicon sequencing and bioinformatics analyses to characterize the microbiota present in fecal samples of CTCL patients (n = 38) and age-matched healthy controls (n = 13) from the same geographical region.ResultsGut microbial α-diversity trended lower in patients with CTCL and was significantly lower in patients with advanced CTCL relative to controls (P = 0.015). No differences in β-diversity were identified. Specific taxa were significantly reduced in patient samples; significance was determined using adjusted P-values (q-values) that accounted for a false discovery rate threshold of 0.05. Significantly reduced taxa in patient samples included the phylum Actinobacteria (q = 0.0002), classes Coriobacteriia (q = 0.002) and Actinobacteria (q = 0.03), order Coriobacteriales (q = 0.003), and genus Anaerotruncus (q = 0.01). The families Eggerthellaceae (q = 0.0007) and Lactobacillaceae (q = 0.02) were significantly reduced in patients with high skin disease burden.ConclusionsGut dysbiosis can be seen in patients with CTCL compared to healthy controls and is pronounced in more advanced CTCL. The taxonomic shifts associated with CTCL are similar to those previously reported in atopic dermatitis and opposite those of psoriasis, suggesting microbial parallels to the immune profile and skin barrier differences between these conditions. These findings may suggest new microbial disease biomarkers and reveal a new angle for intervention

Ketogenic Diet Enhances Neurovascular Function with Altered Gut Microbiome in Young Healthy Mice

Neurovascular integrity, including cerebral blood flow (CBF) and blood-brain barrier (BBB) function, plays a major role in determining cognitive capability. Recent studies suggest that neurovascular integrity could be regulated by the gut microbiome. The purpose of the study was to identify if ketogenic diet (KD) intervention would alter gut microbiome and enhance neurovascular functions, and thus reduce risk for neurodegeneration in young healthy mice (12–14 weeks old). Here we show that with 16 weeks of KD, mice had significant increases in CBF and P-glycoprotein transports on BBB to facilitate clearance of amyloid-beta, a hallmark of Alzheimer’s disease (AD). These neurovascular enhancements were associated with reduced mechanistic target of rapamycin (mTOR) and increased endothelial nitric oxide synthase (eNOS) protein expressions. KD also increased the relative abundance of putatively beneficial gut microbiota (Akkermansia muciniphila and Lactobacillus), and reduced that of putatively pro-inflammatory taxa (Desulfovibrio and Turicibacter). We also observed that KD reduced blood glucose levels and body weight, and increased blood ketone levels, which might be associated with gut microbiome alteration. Our findings suggest that KD intervention started in the early stage may enhance brain vascular function, increase beneficial gut microbiota, improve metabolic profile, and reduce risk for AD

A formally verified compiler back-end

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well

Apolipoprotein E Genotype-Dependent Nutrigenetic Effects to Prebiotic Inulin for Modulating Systemic Metabolism and Neuroprotection in Mice via Gut-Brain Axis

OBJECTIVE: The goal of the study was to identify the potential nutrigenetic effects to inulin, a prebiotic fiber, in mice with different human apolipoprotein E (APOE) genetic variants. Specifically, we compared responses to inulin for the potential modulation of the systemic metabolism and neuroprotection via gut-brain axis in mice with human APOE ϵ3 and ϵ4 alleles. METHOD: We performed experiments with young mice expressing the human APOE3 (E3FAD mice and APOE4 gene (E4FAD mice). We fed mice with either inulin or control diet for 16 weeks starting from 3 months of age. We determined gut microbiome diversity and composition using16s rRNA sequencing, systemic metabolism using in vivo MRI and metabolomics, and blood–brain barrier (BBB) tight junction expression using Western blot. RESULTS: In both E3FAD and E4FAD mice, inulin altered the alpha and beta diversity of the gut microbiome, increased beneficial taxa of bacteria and elevated cecal short chain fatty acid and hippocampal scyllo-inositol. E3FAD mice had altered metabolism related to tryptophan and tyrosine, while E4FAD mice had changes in the tricarboxylic acid cycle, pentose phosphate pathway, and bile acids. Differences were found in levels of brain metabolites related to oxidative stress, and levels of Claudin-1 and Claudin-5 BBB tight junction expression. DISCUSSION: We found that inulin had many similar beneficial effects in the gut and brain for both E3FAD and E4FAD mice, which may be protective for brain functions and reduce risk for neurodegeneration. . E3FAD and E4FAD mice also had distinct responses in several metabolic pathways, suggesting an APOE-dependent nutrigenetic effects in modulating systemic metabolism and neuroprotection

A coinductive semantics of the Unlimited Register Machine

We exploit (co)inductive specifications and proofs to approach the evaluation of low-level programs for the Unlimited Register Machine (URM) within the Coq system, a proof assistant based on the Calculus of (Co)Inductive Constructions type theory. Our formalization allows us to certify the implementation of partial functions, thus it can be regarded as a first step towards the development of a workbench for the formal analysis and verification of both converging and diverging computations

Friends with benefits: implementing corecursion in foundational proof assistants

We introduce AmiCo, a tool that extends a proof assistant, Isabelle/HOL, with flexible function definitions well beyond primitive corecursion. All definitions are certified by the assistant’s inference kernel to guard against inconsistencies. A central notion is that of friends: functions that preserve the productivity of their arguments and that are allowed in corecursive call contexts. As new friends are registered, corecursion benefits by becoming more expressive. We describe this process and its implementation, from the user’s specification to the synthesis of a higher-order definition to the registration of a friend. We show some substantial case studies where our approach makes a difference