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Inspired from the recent developments in theories of non-wellfounded syntax (coinductively defined languages) and of syntax with binding operators, the structure of algebras of wellfounded and non-wellfounded terms is studied for a very general notion of signature permitting both simple variable binding operators as well as operators of explicit substitution. This is done in an extensional mathematical setting of initial algebras and final coalgebras of endofunctors on a functor category. The main technical tool is a novel concept of heterogeneous substitution systems.

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A new approach to inhabitation problems in simply typed lambda-calculus is shown, dealing with both decision and counting problems. This approach works by exploiting a representation of the search space generated by a given inhabitation problem, which is in terms of a lambda-calculus for proof search that the authors developed recently. The representation may be seen as extending the Curry–Howard representation of proofs by lambda terms. Our methodology reveals inductive descriptions of the decision problems, driven by the syntax of the proof-search expressions, and produces simple, recursive decision procedures and counting functions. These allow to predict the number of inhabitants by testing the given type for syntactic criteria. This new approach is comprehensive and robust: based on the same syntactic representation, we also derive the state-of-the-art coherence theorems ensuring uniqueness of inhabitants.

Nested datatypes are families of datatypes that are indexed over all types such that the constructors may relate different family members (unlike the homogeneous lists). Moreover, the argument types of the constructors refer to indices given by expressions in which the family name may occur. Especially in this case of true nesting, termination of functions that traverse these data structures is far from being obvious. A joint paper with A. Abel and T. Uustalu (Theor. Comput. Sci., 333 (1-2), 2005, pp. 3-66) proposed iteration schemes that guarantee termination not by structural requirements but just by polymorphic typing. They are generic in the sense that no specific syntactic form of the underlying datatype "functor" is required. However, there was no induction principle for the verification of the programs thus obtained, although they are well known in the usual model of initial algebras on endofunctor categories. The new contribution is a representation of nested datatypes in intensional type theory (more specifically, in the calculus of inductive constructions) that is still generic and covers true nesting, guarantees termination of all expressible programs, and has an induction principle that allows to prove functoriality of monotonicity witnesses (maps for nested datatypes) and naturality properties of iteratively defined polymorphic functions.

This study investigates the individual magnetic field exposures at 16 2/3 and 50 Hz of 1952 people, selected from the Bavarian population. Personal flux density meters ("Field Watcher FW2A") were worn by the participants for 24 h. Every second, the flux density was recorded for both frequencies and for the three spatial axes (dynamic range per axis: several nT up to 100 microT at 50 Hz, 150 microT at 16 2/3 Hz). For 50 Hz fields, the mean of the 1,952 individual means was 0.101 microT and that of the individual medians was 0.047 microT. High level exposures occurred mainly during working hours. Only 2.4% of the subjects showed individual medians higher than 0.2 microT. About 53% of all volunteers were working on the day of recording. Levels for craftsmen (n = 148; mean individual mean: 0.166 microT) were generally higher than those for office workers (n = 624; mean individual mean: 0.107 microT). Flux densities exceeding 100 microT at 50 Hz were measured in 31 persons. The total time with such extreme exposures amounts to nearly 21 min, less than 0.001% of the total time for all measurements (5.3 years). To our knowledge, this is the first exposure study where 16 2/3 Hz magnetic fields (caused by electrified railways) have additionally been monitored over 24 h. For persons living next to railway lines, the mean individual mean (0.156 microT) and mean individual median (0.102 microT) were calculated. Over all, the mean exposures are only 0.1% of the magnetic flux density limit for 50 Hz (100 microT) and about 0.05% of the limit (300 microT) for 16 2/3 Hz recommended by the International Commission on Non-Ionizing Radiation Protection.

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