The use of interactive theorem provers to establish the correctness of critical parts of a software development or for formalising mathematics is becoming more common and feasible in practice. However, most mature theorem provers lack a direct treatment of partial and general recursive functions; overcoming this weakness has been the objective of intensive research during the last decades. In t...

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Euclidean and Similarity group of transformations. We leverage on the representational power of convolutional neural networks to compute these geometric quantities. In comparison with axiomatic constructions, we show that the invariants approximated by the learning architectures...

— We present hère some facts about recursive function theory that we describe in an abstract jorm; for this we use hère fibered catégories. A first approach ofthis was made by P. Mulry by using of topos theory. Out of the results find hère, we give the first steps towards the treatment of partiality in an abstract form. Résumé. — Nous donnons ici quelques résultats sur les fonctions récursives ...

From a Gebserian perspective. this chapter explores the spatializing sense of partial fulfillment in Husserlian phenomenological intuition. This involves the complete fulfillment of the sense of partiality and also implicates the sense of apodicticity. necessity. certainty. and probability. To enter this investigation. I not only draw on several writers. including Husserl. but I also attempt an...

Natural language techniques have been employed in attempts to automatically translate legal texts, and specifically contracts, into formal models that allow automatic reasoning. However, such techniques suffer from incomplete coverage, typically resulting in parts of the text being left uninterpreted, and which, in turn, may result in the formal models failing to identify potential problems due...

We describe an executable specification of the Java Virtual Machine (JVM) within the Coq proof assistant. The principal features of the development are that it is executable, meaning that it can be tested against a real JVM to gain confidence in the correctness of the specification; and that it has been written with heavy use of dependent types, this is both to structure the model in a useful w...

Aortic arch surgery remains a complex surgical operation that necessitates specific neuroprotection strategies. Various approaches, such as hypothermic circulatory arrest (HCA), retrograde cerebral perfusion, and antegrade selective cerebral perfusion (aSCP), have each enjoyed periods of popularity. However, while the overall surgical approach tend to favour HCA with aSCP, technical factors, su...

Good tools can bring mechanical verification to programs written in mainstream functional languages. We use hs-to-coq to translate significant portions of Haskell’s containers library into Coq, and verify it against specifications that we derive from a variety of sources including type class laws, the library’s test suite, and interfaces from Coq’s standard library. Our work shows that it is fe...

Situations can be used to model context of agents’ actions in heterogeneous P2P data integration system. They are the crucial concept in the situation theory and are suitable to cope with data, metadata, information partiality, open-world and non-monotonic reasoning in knowledgebase systems. In the SIXP2P system agents can ask and answer queries, which are propagated to their partners and are e...

The question addressed is: Is there need, in health care, for one consolidated science of production? For responding to this question, the classical science of production is reviewed and the current approaches to production and service in healthcare are analysed as for their evolution and current status. It is found that these current movements are not self-aware of the restrictions deriving fr...