Programming and proving with classical types

The propositions-as-types correspondence is ordinarily presen- ted as linking the metatheory of typed λ-calculi and the proof theory of intuitionistic logic. Griffin observed that this correspondence could be extended to classical logic through the use of control operators. This observation set off a flurry of further research, leading to the development of Parigot’s λμ-calculus. In this work, we use the λμ-calculus as the foundation for a system of proof terms for classical first-order logic. In particular, we define an extended call-by-value λμ-calculus with a type system in correspondence with full classical logic. We extend the language with polymorphic types, add a host of data types in ‘direct style’, and prove several metatheoretical properties. All of our proofs and definitions are mechanised in Isabelle/HOL, and we automatically obtain an inter- preter for a system of proof terms cum programming language—called μML—using Isabelle’s code generation mechanism. Atop our proof terms, we build a prototype LCF-style interactive theorem prover—called μTP— for classical first-order logic, capable of synthesising μML programs from completed tactic-driven proofs. We present example closed μML programs with classical tautologies for types, including some inexpressible as closed programs in the original λμ-calculus, and some example tactic-driven μTP proofs of classical tautologies

Verifying Strong Eventual Consistency in Distributed Systems

Data replication is used in distributed systems to maintain up-to-date copies of shared data across multiple computers in a network. However, despite decades of research, algorithms for achieving consistency in replicated systems are still poorly understood. Indeed, many published algorithms have later been shown to be incorrect, even some that were accompanied by supposed mechanised proofs of correctness. In this work, we focus on the correctness of Conflict-free Replicated Data Types (CRDTs), a class of algorithm that provides strong eventual consistency guarantees for replicated data. We develop a modular and reusable framework in the Isabelle/HOL interactive proof assistant for verifying the correctness of CRDT algorithms. We avoid correctness issues that have dogged previous mechanised proofs in this area by including a network model in our formalisation, and proving that our theorems hold in all possible network behaviours. Our axiomatic network model is a standard abstraction that accurately reflects the behaviour of real-world computer networks. Moreover, we identify an abstract convergence theorem, a property of order relations, which provides a formal definition of strong eventual consistency. We then obtain the first machine-checked correctness theorems for three concrete CRDTs: the Replicated Growable Array, the Observed-Remove Set, and an Increment-Decrement Counter. We find that our framework is highly reusable, developing proofs of correctness for the latter two CRDTs in a few hours and with relatively little CRDT-specific code

Interleaving anomalies in collaborative text editors

Collaborative text editors allow two or more users to concurrently edit a shared document without merge conflicts. Such systems require an algorithm to provide convergence, ensuring all clients that have seen the same set of document edits are in the same state. Unfortunately convergence alone does not guarantee that a collaborative text editor is usable. Several published algorithms for collaborative text editing exhibit an undesirable anomaly in which concurrently inserted portions of text with a well-defined order may be randomly interleaved on a character-by-character basis, resulting in an unreadable jumble of letters. Although this anomaly appears to be known informally by some researchers in the field, we are not aware of any published work that fully explains or addresses it. We show that several algorithms suffer from this problem, explain its cause, and also identify a lesser variant of the anomaly that occurs in another algorithm. Moreover, we propose a specification of collaborative text editing that rules out the anomaly, and show how to prevent the lesser anomaly from occurring in one particular algorithm.The Boeing Company and EPSRC “REMS: Rigorous Engineering for Mainstream Systems” programme grant (EP/K008528)

A Highly-Available Move Operation for Replicated Trees

Replicated tree data structures are a fundamental building block of distributed filesystems, such as Google Drive and Dropbox, and collaborative applications with a JSON or XML data model. These systems need to support a move operation that allows a subtree to be moved to a new location within the tree. However, such a move operation is difficult to implement correctly if different replicas can concurrently perform arbitrary move operations, and we demonstrate bugs in Google Drive and Dropbox that arise with concurrent moves. In this paper we present a CRDT algorithm that handles arbitrary concurrent modifications on trees, while ensuring that the tree structure remains valid (in particular, no cycles are introduced), and guaranteeing that all replicas converge towards the same consistent state. Our algorithm requires no synchronous coordination between replicas, making it highly available in the face of network partitions. We formally prove the correctness of our algorithm using the Isabelle/HOL proof assistant, and evaluate the performance of our formally verified implementation in a geo-replicated setting.The Boeing Company; EPSRC “REMS: Rigorous Engineering for Mainstream Systems” programme grant (EP/K008528); Leverhulme Trust Early Career Fellowship, Isaac Newton Trust; Nokia Bell Labs

Chiral Polymerization in Open Systems From Chiral-Selective Reaction Rates

We investigate the possibility that prebiotic homochirality can be achieved exclusively through chiral-selective reaction rate parameters without any other explicit mechanism for chiral bias. Specifically, we examine an open network of polymerization reactions, where the reaction rates can have chiral-selective values. The reactions are neither autocatalytic nor do they contain explicit enantiomeric cross-inhibition terms. We are thus investigating how rare a set of chiral-selective reaction rates needs to be in order to generate a reasonable amount of chiral bias. We quantify our results adopting a statistical approach: varying both the mean value and the rms dispersion of the relevant reaction rates, we show that moderate to high levels of chiral excess can be achieved with fairly small chiral bias, below 10%. Considering the various unknowns related to prebiotic chemical networks in early Earth and the dependence of reaction rates to environmental properties such as temperature and pressure variations, we argue that homochirality could have been achieved from moderate amounts of chiral selectivity in the reaction rates.Comment: 15 pages, 6 figures, accepted for publication in Origins of Life and Evolution of Biosphere

Counting all dyons in N =4 string theory

For dyons in heterotic string theory compactified on a six-torus, with electric charge vector Q and magnetic charge vector P, the positive integer I = g.c.d.(Q \wedge P) is an invariant of the U-duality group. We propose the microscopic theory for computing the spectrum of all dyons for all values of I, generalizing earlier results that exist only for the simplest case of I=1. Our derivation uses a combination of arguments from duality, 4d-5d lift, and a careful analysis of fermionic zero modes. The resulting degeneracy agrees with the black hole degeneracy for large charges and with the degeneracy of field-theory dyons for small charges. It naturally satisfies several physical requirements including integrality and duality invariance. As a byproduct, we also derive the microscopic (0,4) superconformal field theory relevant for computing the spectrum of five-dimensional Strominger-Vafa black holes in ALE backgrounds and count the resulting degeneracies

Reversible Keap1 inhibitors are preferential pharmacological tools to modulate cellular mitophagy

Mitophagy orchestrates the autophagic degradation of dysfunctional mitochondria preventing their pathological accumulation and contributing to cellular homeostasis. We previously identified a novel chemical tool (hereafter referred to as PMI), which drives mitochondria into autophagy without collapsing their membrane potential (ΔΨm). PMI is an inhibitor of the protein-protein interaction (PPI) between the transcription factor Nrf2 and its negative regulator, Keap1 and is able to up-regulate the expression of autophagy-associated proteins, including p62/SQSTM1. Here we show that PMI promotes mitochondrial respiration, leading to a superoxide-dependent activation of mitophagy. Structurally distinct Keap1-Nrf2 PPI inhibitors promote mitochondrial turnover, while covalent Keap1 modifiers, including sulforaphane (SFN) and dimethyl fumarate (DMF), are unable to induce a similar response. Additionally, we demonstrate that SFN reverses the effects of PMI in co-treated cells by reducing the accumulation of p62 in mitochondria and subsequently limiting their autophagic degradation. This study highlights the unique features of Keap1-Nrf2 PPI inhibitors as inducers of mitophagy and their potential as pharmacological agents for the treatment of pathological conditions characterized by impaired mitochondrial quality control

Genetic variation and recombination of RdRp and HSP 70h genes of Citrus tristeza virus isolates from orange trees showing symptoms of citrus sudden death disease

<p>Abstract</p> <p>Background</p> <p>Citrus sudden death (CSD), a disease that rapidly kills orange trees, is an emerging threat to the Brazilian citrus industry. Although the causal agent of CSD has not been definitively determined, based on the disease's distribution and symptomatology it is suspected that the agent may be a new strain of <it>Citrus tristeza virus </it>(CTV). CTV genetic variation was therefore assessed in two Brazilian orange trees displaying CSD symptoms and a third with more conventional CTV symptoms.</p> <p>Results</p> <p>A total of 286 RNA-dependent-RNA polymerase (RdRp) and 284 heat shock protein 70 homolog (HSP70h) gene fragments were determined for CTV variants infecting the three trees. It was discovered that, despite differences in symptomatology, the trees were all apparently coinfected with similar populations of divergent CTV variants. While mixed CTV infections are common, the genetic distance between the most divergent population members observed (24.1% for RdRp and 11.0% for HSP70h) was far greater than that in previously described mixed infections. Recombinants of five distinct RdRp lineages and three distinct HSP70h lineages were easily detectable but respectively accounted for only 5.9 and 11.9% of the RdRp and HSP70h gene fragments analysed and there was no evidence of an association between particular recombinant mosaics and CSD. Also, comparisons of CTV population structures indicated that the two most similar CTV populations were those of one of the trees with CSD and the tree without CSD.</p> <p>Conclusion</p> <p>We suggest that if CTV is the causal agent of CSD, it is most likely a subtle feature of population structures within mixed infections and not merely the presence (or absence) of a single CTV variant within these populations that triggers the disease.</p

Helicobacter pylori chronic infection and mucosal inflammation switches the human gastric glycosylation pathways

Helicobacter pylori exploits host glycoconjugates to colonize the gastric niche. Infection can persist for decades promoting chronic inflammation, and in a subset of individuals lesions can silently progress to cancer. This study shows that H. pylori chronic infection and gastric tissue inflammation result in a remodeling of the gastric glycophenotype with increased expression of sialyl-Lewis a/x antigens due to transcriptional up-regulation of the B3GNT5, B3GALT5, and FUT3 genes. We observed that H. pylori infected individuals present a marked gastric local pro-inflammatory signature with significantly higher TNF-a levels and demonstrated that TNF-induced activation of the NF-kappaB pathway results in B3GNT5 transcriptional up-regulation. Furthermore, we show that this gastric glycosylation shift, characterized by increased sialylation patterns, favors SabA-mediated H. pylori attachment to human inflamed gastric mucosa. This study provides novel clinically relevant insights into the regulatory mechanisms underlying H. pylori modulation of host glycosylation machinery, and phenotypic alterations crucial for life-long infection. Moreover, the biosynthetic pathways here identified as responsible for gastric mucosa increased sialylation, in response to H. pylori infection, can be exploited as drug targets for hindering bacteria adhesion and counteract the infection chronicity.IPATIMUP integrates the i3S Research Unit, which is partially supported by FCT, the Portuguese Foundation for Science and Technology (PEst C/SAU/LA0003/2013). This work is funded by FEDER funds through the Operational Programme for Competitiveness Factors-COMPETE (NORTE 07 0124 FEDER 000024; FCOMP-01-0124-FEDER028188; FCOMP-01-0124-FEDER 041276) and National Funds through the FCT-Foundation for Science and Technology (EXPL/CTM-BIO/0762/2013, PTDC/BBB-EBI/0786/2012) and acknowledges support by the EuropeanUnion (Seventh Framework Programme GastricGlycoExplorer project, grant number 316929). Grants were received from FCT, POPH (Programa Operacional Potencial Humano) and FSE (Fundo Social Europeu) (SFRH/BPD/75871/2011 to AM;SFRH/SINTD/60034/2009 to RMP; SFRH/BPD/84084/2012 to RMF; SFRH/BPD/89764/2012 to PO). AM acknowledges EMBO for a Short-Term Fellowship (EMBO ASTF 330-212). Transcript analysis was funded by NIH (grant P41GM103490) to KWM