Higher Order Implementation of Kahn Networks in Maude: Alternating Bit Protocol

We implement Kahn networks in Maude system by using behavioural theory of streams and encoding higher order function types. As an example we implement the alternating bit protocol in our framework

Coiterative Morphisms: Interactive Equational Reasoning for Bisimulation, using Coalgebras

ter: SEN 3 Abstract: We study several techniques for interactive equational reasoning with the bisimulation equivalence. Our work is based on a modular library, formalised in Coq, that axiomatises weakly final coalgebras and bisimulation. As a theory we derive some coalgebraic schemes and an associated coinduction principle. This will help in interactive proofs by coinduction, modular derivation of congruence and co-fixed point equations and enables an extensional treatment of bisimulation. Finally we present a version of the lambda-coinduction proof principle in our framework

An exercise in coinduction: Moessner's theorem

We present a coinductive proof of Moessner’s theorem. This theorem describes the construction of the stream (1^n,2^n,3^, ...) (for n > 0) out of the stream of natural numbers by repeatedly dropping and summing elements. Our formalisation consists of a direct translation of the operational description of Moessner’s procedure into the equivalence of - in essence - two functional programs. Our proof fully exploits the circularity that is present in Moessner’s procedure and is more elementary than existing proofs. As such, it serves as a non-trivial illustration of the relevance and power of coinduction

From coinductive proofs to exact real arithmetic: theory and applications

Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. We discuss several examples including the extraction of programs for polynomials up to degree two and the definite integral of continuous maps

Termination Casts: A Flexible Approach to Termination with General Recursion

This paper proposes a type-and-effect system called Teqt, which distinguishes terminating terms and total functions from possibly diverging terms and partial functions, for a lambda calculus with general recursion and equality types. The central idea is to include a primitive type-form "Terminates t", expressing that term t is terminating; and then allow terms t to be coerced from possibly diverging to total, using a proof of Terminates t. We call such coercions termination casts, and show how to implement terminating recursion using them. For the meta-theory of the system, we describe a translation from Teqt to a logical theory of termination for general recursive, simply typed functions. Every typing judgment of Teqt is translated to a theorem expressing the appropriate termination property of the computational part of the Teqt term.Comment: In Proceedings PAR 2010, arXiv:1012.455

From bioavailability science to regulation of organic chemicals

The bioavailability of organic chemicals in soil and sediment is an important area of scientific investigation for environmental scientists, although this area of study remains only partially recognized by regulators and industries working in the environmental sector. Regulators have recently started to consider bioavailability within retrospective risk assessment frameworks for organic chemicals; by doing so, realistic decision-making with regard to polluted environments can be achieved, rather than relying on the traditional approach of using total-extractable concentrations. However, implementation remains difficult because scientific developments on bioavailability are not always translated into ready-to-use approaches for regulators. Similarly, bioavailability remains largely unexplored within prospective regulatory frameworks that address the approval and regulation of organic chemicals. This article discusses bioavailability concepts and methods, as well as possible pathways for the implementation of bioavailability into risk assessment and regulation; in addition, this article offers a simple, pragmatic and justifiable approach for use within retrospective and prospective risk assessment

Formalising Exact Arithmetic in Type Theory

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Formalising Exact Arithmetic. Representations, Algorithms and Proofs

Contains fulltext : 60666.pdf (Publisher’s version ) (Open Access)RU Radboud Universiteit Nijmegen, 27 september 2004Promotor : Barendregt, H.P. Co-promotor : Geuvers, J.H.VI, 195 p