A General Theory of Sharing Graphs

Sharing graphs are the structures introduced by Lamping to implement optimal reductions of lambda calculus. Gonthier’s reformulation of Lamping’s technique inside Geometry of Interaction, and Asperti and Laneve’s work on Interaction Systems have shown that sharing graphs can be used to implement a wide class of calculi. Here, we give a general characterization of sharing graphs independent from the calculus to be implemented. Such a characterization rests on an algebraic semantics of sharing graphs exploiting the methods of Geometry of Interaction. By this semantics we can define an unfolding partial order between proper sharing graphs, whose minimal elements are unshared graphs. The least-shared-instance of a sharing graph is the unique unshared graph that the unfolding partial order associates to it. The algebraic semantics allows to prove that we can associate a semantical read-back to each unshared graph and that such a read-back can be computed via suitable read-back reductions. The result is then lifted to sharing graphs proving that any read-back (or unfolding) reduction of them can be simulated on their least-shared- instances. The sharing graphs defined in this way allow to implement in a distributed and local way any calculus with a global reduction rule in the style of the beta rule of lambda calculus. Also in this case the proof technique is to prove that sharing reductions can be simulated on least-shared-instances. The result is proved under the only assumption that the structures of the calculus have a box nesting property, that is, that two beta redexes may not partially overlap. As a result, we get a sharing graph machine that seems to be the most natural low-level computational model for functional languages. The paper concludes showing that optimality is a by-product of this technique: optimal reductions are lazy reductions of the sharing graph machine. We stress the proof strategy followed in the paper: it is based on an amazing interplay between standard rewriting system properties (strong normalization, confluence, and unique normal form) and algebraic properties definable via the techniques of Geometry of Interaction

Interaction systems I : the theory of optimal reductions

Projet PARAA new class of higher order rewriting systems, called interaction systems is introduced. From one side, interaction systems provide the intuitionistic generalization of Lafont's interaction nets (recall that interaction nets are linear). In particular, we keep the idea of binary interaction and the syntactical bipartition of operators into constructors and destructors. From the other side, interaction systems are the subsystem of Klop's combinatory reduction systems where the Curry-Howard analogy stoll "makes sense". This means that we can associate with every IS a suitable logical (intuitionistic) system ; constructors and destructors respectively correspond to right and left introduction rules, interaction is cut and computation is cut-elimination. Interaction systems have been primarily motivated by the necessity of extending Lamping's optimal graph reduction technique for the l-calculus to other computational constructs than just -reduction. This implementation style can be smootly generalized to arbitrary IS's providing in this way a uniform description of essential rules such as conditionals and recursion The optimal implementation of IS's will be only sketched here (it will eventually be the subject of the forthcoming Part II). The main aim of this paper is to introduce this new class of systems, to discuss the motivations behind its definition and to investigate the theoretical aspect of optimal reductions (in particular, the notion of redex-family)

Reserve Requirements, Currency Substitution, and Seigniorage in the Transition to European Monetary Union

This article considers a transition toward European monetary union that combines increased substitution of currencies and greater monetary, financial, and fiscal policy coordination. It explores how such a transition would affect national inflation and interest rates and required reserve ratios when governments depend in part on seigniorage funding for public expenditures. We find that greater coordination of policies would lead to lower inflation and interest rates but higher reserve-requirement ratios. Because higher reserve-requirement ratios could place European banks at a competititve disadvantage, we conclude that the interaction between reserve requirements and seigniorage concerns makes it less likely that the gradualist approach of the Maastricht treaty is a sustainable means of transition to European union

Towards marginal cost pricing: A comparison of alternative pricing systems

European urban areas are marred by the problems of congestion and environmental degradation due to the prevailing levels of car use. Strong arguments have thus been put forward in support of a policy based on marginal cost pricing (European Commission 1996). Such policy measures – which would force private consumers to pay for a public service that was previously provided «for free» – are, however, notoriously unpopular with the general public and hence also with their elected representatives – the politicians. There is thus an obvious tension between economic theory, which suggests that marginal cost pricing is the welfare maximising solution to urban transport problems, and practical experience, which suggests that such pricing measures are unwanted by the affected population and hence hard to implement through democratic processes. The AFFORD Project for the European Commission has aimed to investigate this paradox and its possible solutions, through a combination of economic analysis, predictive modelling, attitudinal surveys, and an assessment of fiscal and financial measures within a number of case study cities in Europe. In this paper the methodology and results obtained for the Edinburgh case study are reported in detail. The study analyses alternative road pricing instruments and compares their performance against the theoretical first best situation. It discusses the effect of coverage, location, charging mechanism and interaction with other instruments. The paper shows that limited coverage in one mode may lead to a deviation from the user pays principle in other modes, that location is as important as charge levels and that assumptions about the use of revenues are critical in determining the effect on equity and acceptability. Finally the results show that a relatively simple smart card system can come close to providing the economic first best solution, but that this result should be viewed in the context of the model assumptions

Learning curves and changing product attributes: the case of wind turbines

The heuristic concept of learning curves describes cost reductions as a function of cumulative production. A study of the Liberty shipbuilders suggested that product quality and production scale are other relevant factors that affect costs. Significant changes of attributes of a technology must be corrected when assessing the impact of learning-by-doing. We use an engineering-based model to capture the cost changes of wind turbines that can be attributed to changes in turbine size. We estimate the learning curve and turbine size parameters using more than 1500 price points from 1991 to 2003. The fit between model and empirical data confirms the concept

Dividend reductions and signaling in an imputation environment

In contrast to the double taxation system prevailing in the U.S., Australian firms operate within an imputation tax environment with respect to dividend payments. We argue that the dividend imputation tax system increases the signaling potential of dividend reductions and our empirical findings strongly support this view. We find that the size of the dividend reduction is related to the tax credit status of the dividend. Abnormal changes in profitability are negative in the year following dividend reductions and are negatively related to the dividend reduction; similar signaling effects are found in terms of price reactions. The significance levels for the relations between abnormal change in profitability and dividend reductions, and price reactions and dividend reductions are statistically significantly stronger for dividends with associated tax credits. Overall, our study conclusively demonstrates that dividend reductions in Australia have strong signaling power and, as such, our results are at variance with the results obtained in the U.S