A Relational Logic for Higher-Order Programs

Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for reasoning about a broad range of properties, including equivalence and refinement, and specialized notions such as continuity, information flow security or relative cost. In a higher-order setting, relational program verification can be achieved using relational refinement type systems, a form of refinement types where assertions have a relational interpretation. Relational refinement type systems excel at relating structurally equivalent terms but provide limited support for relating terms with very different structures. We present a logic, called Relational Higher Order Logic (RHOL), for proving relational properties of a simply typed $\lambda$-calculus with inductive types and recursive definitions. RHOL retains the type-directed flavour of relational refinement type systems but achieves greater expressivity through rules which simultaneously reason about the two terms as well as rules which only contemplate one of the two terms. We show that RHOL has strong foundations, by proving an equivalence with higher-order logic (HOL), and leverage this equivalence to derive key meta-theoretical properties: subject reduction, admissibility of a transitivity rule and set-theoretical soundness. Moreover, we define sound embeddings for several existing relational type systems such as relational refinement types and type systems for dependency analysis and relative cost, and we verify examples that were out of reach of prior work.Comment: Submitted to ICFP 201

Towards ubiquitous accessibility: capability-based profiles and adaptations, delivered via the semantic web

The continuing proliferation of mobile devices, content and applications presents barriers to the mainstreaming of Assistive Technologies (ATs), despite their potential utility for users in demanding situations or with minor-to-moderate impairments. We have previously proposed that user profiling based on human rather than machine-oriented capabilities, coupled with a shift from conspicuous ATs to considering a broader range of adaptations presents opportunities for platform and AT vendors to support many more users. However there has not been a standard, consistent and, most importantly, straightforward way to deliver these benefits. We propose that this delivery gap can be bridged by using the semantic web and related technologies, so the potential benefits of the capability-based approach may be realised

Metadiscursive practices in introductions. Phraseology and semantic sequences across genres

The study of metadiscursive practices is particularly fruitful in introductory part-genres where the representation of disciplinary discursive procedures plays a major role for the discourse community. The main aim of this paper is to investigate the ways in which some English metadiscursive expressions (forms of self-mention and illocution markers in particular) are used to offer a representation of academic argument in different genres. The paper concentrates on the representation of discourse procedures in introductory moves, looking in particular at how economists identify their research purposes and their discourse space, while providing a definition of their topic or contextualizing their research in current debates. The study is based on two small corpora of article introductions and textbook introductions. The approach adopted looks at phraseology as a perspective integrating meaning, form and function. The phraseological patterns identified are analyzed as sequences of semantic units - involving reference to a textual source, a discourse procedure and a cognitive construct. Cross-generic variation highlights a different lexical range and different lexical combinations in the two corpora examined. This is interpreted in terms of the ethos of the discourse community and the different role played by argument in the two genres

The SIMPSONS project: An integrated Mars transportation system

In response to the Request for Proposal (RFP) for an integrated transportation system network for an advanced Martian base, Frontier Transportation Systems (FTS) presents the results of the SIMPSONS project (Systems Integration for Mars Planetary Surface Operations Networks). The following topics are included: the project background, vehicle design, future work, conclusions, management status, and cost breakdown. The project focuses solely on the surface-to-surface transportation at an advanced Martian base

Extending Equational Monadic Reasoning with Monad Transformers

There is a recent interest for the verification of monadic programs using proof assistants. This line of research raises the question of the integration of monad transformers, a standard technique to combine monads. In this paper, we extend Monae, a Coq library for monadic equational reasoning, with monad transformers and we explain the benefits of this extension. Our starting point is the existing theory of modular monad transformers, which provides a uniform treatment of operations. Using this theory, we simplify the formalization of models in Monae and we propose an approach to support monadic equational reasoning in the presence of monad transformers. We also use Monae to revisit the lifting theorems of modular monad transformers by providing equational proofs and explaining how to patch a known bug using a non-standard use of Coq that combines impredicative polymorphism and parametricity

Vagueness and Formal Fuzzy Logic: Some Criticisms

In the common man reasoning the presence of vague predicates is pervasive and under the name “fuzzy logic in narrow sense” or “formal fuzzy logic” there are a series of attempts to formalize such a kind of phenomenon. This paper is devoted to discussing the limits of these attempts both from a technical point of view and with respect the original and principal task: to define a mathematical model of the vagueness. For example, one argues that, since vagueness is necessarily connected with the intuition of the continuum, we have to look at the order-based topology of the interval [0,1] and not at the discrete topology of the set {0,1}. In accordance, in switching from classical logic to a logic for the vague predicates, we cannot avoid the use of the basic notions of real analysis as, for example, the ones of “approximation“, “convergence“, “continuity“. In accordance, instead of defining the compactness of the logical consequence operator and of the deduction operator in terms of finiteness, we have to define it in terms of continuity. Also, the effectiveness of the deduction apparatus has to be defined by using the tools of constructive real analysis and not the one of recursive arithmetic. This means that decidability and semi-decidability have to be defined by involving effective limit processes and not by finite steps stopping processes

Myths and Legends in High-Performance Computing

In this thought-provoking article, we discuss certain myths and legends that are folklore among members of the high-performance computing community. We gathered these myths from conversations at conferences and meetings, product advertisements, papers, and other communications such as tweets, blogs, and news articles within and beyond our community. We believe they represent the zeitgeist of the current era of massive change, driven by the end of many scaling laws such as Dennard scaling and Moore's law. While some laws end, new directions are emerging, such as algorithmic scaling or novel architecture research. Nevertheless, these myths are rarely based on scientific facts, but rather on some evidence or argumentation. In fact, we believe that this is the very reason for the existence of many myths and why they cannot be answered clearly. While it feels like there should be clear answers for each, some may remain endless philosophical debates, such as whether Beethoven was better than Mozart. We would like to see our collection of myths as a discussion of possible new directions for research and industry investment

Generalized ordinal analysis and reflection principles in set theory

It is widely claimed that the natural axiom systems\unicode{x2013}including the large cardinal axioms\unicode{x2013}form a well-ordered hierarchy. Yet, as is well-known, it is possible to exhibit non-linearity and ill-foundedness by means of \emph{ad hoc} constructions. In this paper we formulate notions of proof-theoretic strength based on set-theoretic reflection principles. We prove that they coincide with orderings on theories given by the generalized ordinal analysis of Pohlers. Accordingly, these notions of proof-theoretic strength engender genuinely well-ordered hierarchies. The reflection principles considered in this paper are formulated relative to G\"odel's constructible universe; we conclude with generalizations to other inner models.Comment: 36 page

Hyper Hoare Logic: (Dis-)Proving Program Hyperproperties (extended version)

Hoare logics are proof systems that allow one to formally establish properties of computer programs. Traditional Hoare logics prove properties of individual program executions (so-called trace properties, such as functional correctness). Hoare logic has been generalized to prove also properties of multiple executions of a program (so-called hyperproperties, such as determinism or non-interference). These program logics prove the absence of (bad combinations of) executions. On the other hand, program logics similar to Hoare logic have been proposed to disprove program properties (e.g., Incorrectness Logic), by proving the existence of (bad combinations of) executions. All of these logics have in common that they specify program properties using assertions over a fixed number of states, for instance, a single pre- and post-state for functional properties or pairs of pre- and post-states for non-interference. In this paper, we present Hyper Hoare Logic, a generalization of Hoare logic that lifts assertions to properties of arbitrary sets of states. The resulting logic is simple yet expressive: its judgments can express arbitrary trace- and hyperproperties over the terminating executions of a program. By allowing assertions to reason about sets of states, Hyper Hoare Logic can reason about both the absence and the existence of (combinations of) executions, and, thereby, supports both proving and disproving program (hyper-)properties within the same logic. In fact, we prove that Hyper Hoare Logic subsumes the properties handled by numerous existing correctness and incorrectness logics, and can express hyperproperties that no existing Hoare logic can. We also prove that Hyper Hoare Logic is sound and complete, and admits powerful compositionality rules. All our technical results have been proved in Isabelle/HOL

You Get What You Need: An Examination of Purpose‐Based Inheritance Reasoning in Undergraduates, Preschoolers, and Biological Experts

This set of seven experiments examines reasoning about the inheritance and acquisition of physical properties in preschoolers, undergraduates, and biology experts. Participants ( N =  390) received adoption vignettes in which a baby animal was born to one parent but raised by a biologically unrelated parent, and they judged whether the offspring would have the same property as the birth or rearing parent. For each vignette, the animal parents had contrasting values on a physical property dimension (e.g., the birth parent had a short tail; the rearing parent had a long tail). Depending on the condition, the distinct properties had distinct functions (“function‐predictive”) were associated with distinct habitats (“habitat‐predictive”), or had no implications (“non‐predictive”). Undergraduates' bias to view properties as inherited from the birth parent was reduced in the function‐ and habitat‐predictive conditions. This result indicates a purpose‐based view of inheritance, whereby animals can acquire properties that serve a purpose in their environment. This stance was not found in experts or preschoolers. We discuss the results in terms of how undergraduates' purpose‐based inheritance reasoning develops and relates to larger‐scale misconceptions about Darwinian evolutionary processes, and implications for biology education.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106669/1/cogs12097.pd