Inductive-data-type Systems

In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the last two authors presented a combined language made of a (strongly normalizing) algebraic rewrite system and a typed lambda-calculus enriched by pattern-matching definitions following a certain format, called the "General Schema", which generalizes the usual recursor definitions for natural numbers and similar "basic inductive types". This combined language was shown to be strongly normalizing. The purpose of this paper is to reformulate and extend the General Schema in order to make it easily extensible, to capture a more general class of inductive types, called "strictly positive", and to ease the strong normalization proof of the resulting system. This result provides a computation model for the combination of an algebraic specification language based on abstract data types and of a strongly typed functional language with strictly positive inductive types.Comment: Theoretical Computer Science (2002

Dependent Inductive and Coinductive Types are Fibrational Dialgebras

In this paper, I establish the categorical structure necessary to interpret dependent inductive and coinductive types. It is well-known that dependent type theories \`a la Martin-L\"of can be interpreted using fibrations. Modern theorem provers, however, are based on more sophisticated type systems that allow the definition of powerful inductive dependent types (known as inductive families) and, somewhat limited, coinductive dependent types. I define a class of functors on fibrations and show how data type definitions correspond to initial and final dialgebras for these functors. This description is also a proposal of how coinductive types should be treated in type theories, as they appear here simply as dual of inductive types. Finally, I show how dependent data types correspond to algebras and coalgebras, and give the correspondence to dependent polynomial functors.Comment: In Proceedings FICS 2015, arXiv:1509.0282

Near real time seismic data from the coastal ocean

A moored-buoy system for collecting near real-time seismic data from the coastal ocean has been developed and will be deployed for its initial field trial in the fall of 2016. The technology that makes possible the near real time telemetry of seismic data is the inductive modem technology. This type of data telemetry provides a solution that is convenient, economical, reliable, and flexible. We present results of a prototype system that demonstrate the feasibility of this concept. It will transmit continuous data at a rate of about 1000 bps to a radio link in the surface buoy. A GPS receiver on the surface buoy will be configured to perform accurate and synchronized timestamps on the seismic data on the sea surface, which will make it possible to include data from these undersea systems in the existing seismic data network. Power to operate the system will be supplied by solar panels and rechargeable batteries on the surface buoy and batteries on OBS.Peer ReviewedPostprint (published version

Semantics for first-order affine inductive data types via slice categories

Affine type systems are substructural type systems where copying of information is restricted, but discarding of information is permissible at all types. Such type systems are well-suited for describing quantum programming languages, because copying of quantum information violates the laws of quantum mechanics. In this paper, we consider a first-order affine type system with inductive data types and present a novel categorical semantics for it. The most challenging aspect of this interpretation comes from the requirement to construct appropriate discarding maps for our data types which might be defined by mutual/nested recursion. We show how to achieve this for all types by taking models of a first-order linear type system whose atomic types are discardable and then presenting an additional affine interpretation of types within the slice category of the model with the tensor unit. We present some concrete categorical models for the language ranging from classical to quantum. Finally, we discuss potential ways of dualising and extending our methods and using them for interpreting coalgebraic and lazy data types

Machinery Transportation Management: Case Study of 'Plant-trailer' H&S Incidents

Purpose – The purpose of this paper is to investigate causal agents of health and safety (H&S)incidents among “plant-trailers” (as used by construction and utility contractors to transport mechanical machinery); including the relationship(s) of such incidents to routine safety inspections and, plant maintenance functions. Design/methodology/approach – H&S plant-trailer incident data, from a collaborating UK-based case study utility company are analysed using inductive, interpretative and descriptive statistical methods. Findings – Principal incident occurrences relate to trailer wheels, wheel bearings, tyres and braking systems. All forms of incidents observed harbour significant risk and especially, if they occur during travel on public highways. Derived recommendations for incident mitigation and Control, suggest a requirement for improved human behaviour, machinery inspection regimes and maintenance systems. Research limitations/implications – The findings will be valuable to academia as a basis for advancing this new research subject, both empirically and internationally. Direction is offered in this respect. Practical implications – Recommendations will be of practical relevance to machinery management practitioners generally and to plant-trailer stakeholders more Specifically. For the latter, the study encourages introspective consideration of plant-trailer H&S systems. Originality/value – No previous research has targeted these issues relating to plant-trailers. Keywords Risk, Inspection, Maintenance, Machinery, H&S, Trailers Paper type Case stud

Dependently Typed Languages in Statix

Static type systems can greatly enhance the quality of programs, but implementing a type checker that is both expressive and user-friendly is challenging and error-prone. The Statix meta-language (part of the Spoofax language workbench) aims to make this task easier by automatically deriving a type checker from a declarative specification of a type system. However, so far Statix has not been used to implement dependent types, which is a class of type systems which require evaluation of terms during type checking. In this paper, we present an implementation of a simple dependently typed language in Statix, and discuss how to extend it with several common features such as inductive data types, universes, and inference of implicit arguments. While we encountered some challenges in the implementation, our conclusion is that Statix is already usable as a tool for implementing dependent types

Towards Constructive Hybrid Semantics

With hybrid systems becoming ever more pervasive, the underlying semantic challenges emerge in their entirety. The need for principled semantic foundations has been recognized previously in the case of discrete computation and discrete data, with subsequent implementations in programming languages and proof assistants. Hybrid systems, contrastingly, do not directly fit into the classical semantic paradigms due to the presence of quite specific "non-programmable" features, such as Zeno behaviour and the inherent indispensable reliance on a notion of continuous time. Here, we analyze the phenomenon of hybrid semantics from a constructive viewpoint. In doing so, we propose a monad-based semantics, generic over a given ordered monoid representing the time domain, hence abstracting from the monoid of constructive reals. We implement our construction as a higher inductive-inductive type in the recent cubical extension of the Agda proof assistant, significantly using state-of-the-art advances of homotopy type theory. We show that classically, i.e. under the axiom of choice, our construction admits a charaterization in terms of directed sequence completion