this paper we describe a new, categorical approach to normalization in typed -

Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on simulations of low-level machine models. By contrast, we develop a more structural approach. We show how high-level functional programs can be mapped compositionally (i.e. in a syntax-directed fashion) into a simple kind of automata which are immediately seen to be reversible. The size of the automaton is linear in the size of the functional term. In mathematical terms, we are building a concrete model of functional computation. This construction stems directly from ideas arising in Geometry of Interaction and Linear Logic—but can be understood without any knowledge of these topics. In fact, it serves as an excellent introduction to them. At the same time, an interesting logical delineation between reversible and irreversible forms of computation emerges from our analysis. 1

We address the task of enabling naive users in a practical context to define, comprehend and use knowledge bases for representing part-whole information. This work is part of a larger effort whose target users were ecologists who had little experience in mathematics, computing, and artificial intelligence, but who wished to build computer simulation models of ecological systems. The ecological domain has a rich variety of part-whole information. This includes individuals, populations and sub-populations, as well as composite entities. We note the special requirements deriving from the need to satisfy naive users and show how various existing approaches are insufficient. We describe a novel representation, based on the typed lambda calculus which covers the above range of part-whole relationships in a flexible, uniform framework. We emphasise the role of the typed lambda calculus in particular, and more generally, how a careful description of the ontology founding our repres...

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