Syntax for free: representing syntax with binding using parametricity

We show that, in a parametric model of polymorphism, the type ∀ α. ((α → α) → α) → (α → α → α) → α is isomorphic to closed de Bruijn terms. That is, the type of closed higher-order abstract syntax terms is isomorphic to a concrete representation. To demonstrate the proof we have constructed a model of parametric polymorphism inside the Coq proof assistant. The proof of the theorem requires parametricity over Kripke relations. We also investigate some variants of this representation

The treatment of skin ulcers in patients with systemic sclerosis

Systemic Sclerosis (Ssc) is a complex disease of the connective tissue, characterized by progressive thickening and fibrosis of the skin and the internal organs and by diffused damage of the microvascular system. The fibrosis ones of the skin associated to the characteristic vascular alterations lead to the genesis of ulcers, more or less extended, often multiple, peripheral localization, chronic course, painful, able to influence patient's quality of life. Indeed, immunity reactivity, the thinning and the loss of elasticity of the skin, the peripheral neurological damage and the eventual drug assumption that can reduce regenerative/reparative abilities, can easy chronicizzate an ulcer and become infected complicating still more the patient disease, rendering more difficult the cure often, ulcer evolves to gangrene, and in some cases, in amputation too. For all these reasons, we have begun to study ulcers therapy (local and systemic), considering this activity it leave integrating of the charitable distance of the sclerodermico patient, putting to point on strategy both diagnostic and therapeutic, but above all with the primary scope, if possible, is to prevent ulcers, in contrary case, to alleviate the pain and to render the quality of the life of the patient better

On CSP and the Algebraic Theory of Effects

We consider CSP from the point of view of the algebraic theory of effects, which classifies operations as effect constructors or effect deconstructors; it also provides a link with functional programming, being a refinement of Moggi's seminal monadic point of view. There is a natural algebraic theory of the constructors whose free algebra functor is Moggi's monad; we illustrate this by characterising free and initial algebras in terms of two versions of the stable failures model of CSP, one more general than the other. Deconstructors are dealt with as homomorphisms to (possibly non-free) algebras. One can view CSP's action and choice operators as constructors and the rest, such as concealment and concurrency, as deconstructors. Carrying this programme out results in taking deterministic external choice as constructor rather than general external choice. However, binary deconstructors, such as the CSP concurrency operator, provide unresolved difficulties. We conclude by presenting a combination of CSP with Moggi's computational {\lambda}-calculus, in which the operators, including concurrency, are polymorphic. While the paper mainly concerns CSP, it ought to be possible to carry over similar ideas to other process calculi

Generic Fibrational Induction

This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs' elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, a sound induction rule that is generic over all inductive types, polynomial or not. Our induction rule is generic over the kinds of properties to be proved as well: like Hermida and Jacobs, we work in a general fibrational setting and so can accommodate very general notions of properties on inductive types rather than just those of a particular syntactic form. We establish the soundness of our generic induction rule by reducing induction to iteration. We then show how our generic induction rule can be instantiated to give induction rules for the data types of rose trees, finite hereditary sets, and hyperfunctions. The first of these lies outside the scope of Hermida and Jacobs' work because it is not polynomial, and as far as we are aware, no induction rules have been known to exist for the second and third in a general fibrational framework. Our instantiation for hyperfunctions underscores the value of working in the general fibrational setting since this data type cannot be interpreted as a set.Comment: For Special Issue from CSL 201

Layer by layer - Combining Monads

We develop a method to incrementally construct programming languages. Our approach is categorical: each layer of the language is described as a monad. Our method either (i) concretely builds a distributive law between two monads, i.e. layers of the language, which then provides a monad structure to the composition of layers, or (ii) identifies precisely the algebraic obstacles to the existence of a distributive law and gives a best approximant language. The running example will involve three layers: a basic imperative language enriched first by adding non-determinism and then probabilistic choice. The first extension works seamlessly, but the second encounters an obstacle, which results in a best approximant language structurally very similar to the probabilistic network specification language ProbNetKAT

Operational semantics for signal handling

Signals are a lightweight form of interprocess communication in Unix. When a process receives a signal, the control flow is interrupted and a previously installed signal handler is run. Signal handling is reminiscent both of exception handling and concurrent interleaving of processes. In this paper, we investigate different approaches to formalizing signal handling in operational semantics, and compare them in a series of examples. We find the big-step style of operational semantics to be well suited to modelling signal handling. We integrate exception handling with our big-step semantics of signal handling, by adopting the exception convention as defined in the Definition of Standard ML. The semantics needs to capture the complex interactions between signal handling and exception handling.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244

Right Inferior Frontal Activation During Alcohol-Specific Inhibition Increases With Craving and Predicts Drinking Outcome in Alcohol Use Disorder

Alcohol use disorder (AUD) is characterized by enhanced cue-reactivity and the opposing control processes being insufficient. The ability to inhibit reactions to alcohol-related cues, alcohol-specific inhibition, is thus crucial to AUD; and trainings strengthening this ability might increase treatment outcome. The present study investigated whether neurophysiological correlates of alcohol-specific inhibition (I) vary with craving, (II) predict drinking outcome in AUD and (III) are modulated by alcohol-specific inhibition training. A total of 45 recently abstinent patients with AUD and 25 controls participated in this study. All participants underwent functional magnetic resonance imaging (fMRI) during a Go-NoGo task with alcohol-related as well as neutral conditions. Patients with AUD additionally participated in a double-blind RCT, where they were randomized to either an alcohol-specific inhibition training or an active control condition (non-specific inhibition training). After the training, patients participated in a second fMRI measurement where the Go-NoGo task was repeated. Percentage of days abstinent was assessed as drinking outcome 3 months after discharge from residential treatment. Whole brain analyses indicated that in the right inferior frontal gyrus (rIFG), activation related to alcohol-specific inhibition varied with craving and predicted drinking outcome at 3-months follow-up. This neurophysiological correlate of alcohol-specific inhibition was however not modulated by the training version. Our results suggest that enhanced rIFG activation during alcohol-specific (compared to neutral) inhibition (I) is needed to inhibit responses when craving is high and (II) fosters sustained abstinence in patients with AUD. As alcoholspecific rIFG activation was not affected by the training, future research might investigate whether potential training effects on neurophysiology are better detectable with other methodological approaches

A semantical approach to equilibria and rationality

Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and with the environment. Rational behaviors are achieved not only through conscious reasoning, but also through spontaneous stabilization at equilibrium points. Formal theories of rationality are usually guided by informal intuitions, which are acquired by observing some concrete economic, biological, or network processes. Treating such processes as instances of computation, we reconstruct and refine some basic notions of equilibrium and rationality from the some basic structures of computation. It is, of course, well known that equilibria arise as fixed points; the point is that semantics of computation of fixed points seems to be providing novel methods, algebraic and coalgebraic, for reasoning about them.Comment: 18 pages; Proceedings of CALCO 200