Theoretical and implementation aspects in the mechanization of the metatheory of programming languages

Interactive theorem provers are tools designed for the certification of formal proofs developed by means of man-machine collaboration. Formal proofs obtained in this way cover a large variety of logical theories, ranging from the branches of mainstream mathematics, to the field of software verification. The border between these two worlds is marked by results in theoretical computer science and proofs related to the metatheory of programming languages. This last field, which is an obvious application of interactive theorem proving, poses nonetheless a serious challenge to the users of such tools, due both to the particularly structured way in which these proofs are constructed, and to difficulties related to the management of notions typical of programming languages like variable binding. This thesis is composed of two parts, discussing our experience in the development of the Matita interactive theorem prover and its use in the mechanization of the metatheory of programming languages. More specifically, part I covers: - the results of our effort in providing a better framework for the development of tactics for Matita, in order to make their implementation and debugging easier, also resulting in a much clearer code; - a discussion of the implementation of two tactics, providing infrastructure for the unification of constructor forms and the inversion of inductive predicates; we point out interactions between induction and inversion and provide an advancement over the state of the art. In the second part of the thesis, we focus on aspects related to the formalization of programming languages. We describe two works of ours: - a discussion of basic issues we encountered in our formalizations of part 1A of the Poplmark challenge, where we apply the extended inversion principles we implemented for Matita; - a formalization of an algebraic logical framework, posing more complex challenges, including multiple binding and a form of hereditary substitution; this work adopts, for the encoding of binding, an extension of Masahiko Sato's canonical locally named representation we designed during our visit to the Laboratory for Foundations of Computer Science at the University of Edinburgh, under the supervision of Randy Pollack.

Analyzing convergence of Agricultural and Rural Areas in the Enlarged EU: The case of Hungary

The fall of the Berlin Wall opened the way for a reform path – the transition process – which accompanied ten former Socialist countries in Central and South Eastern Europe to knock at the EU doors. By the way, at the time of the EU membership several economic and structural weaknesses remained. A tendency towards convergence between the new Member States (NMS) and the EU average income level emerged, together with a spread of inequality at the sub-regional level, mainly driven by the backwardness of the agricultural and rural areas. Several progresses were made in evaluating the policies for rural areas, but a shared definition of rurality is still missing. Numerous indicators were calculated for assessing the effectiveness of the Common Agricultural Policy and Rural Development Policy. Previous analysis on the Central and Eastern European countries found that the characteristics of the most backward areas were insufficiently addressed by the policies enacted; the low data availability and accountability at a sub-regional level, and the deficiencies in institutional planning and implementation represented an obstacle for targeting policies and payments. The next pages aim at providing a basis for understanding the connections between the peculiarities of the transition process, the current development performance of NMS and the EU role, with particular attention to the agricultural and rural areas. Applying a mixed methodological approach (multivariate statistics, non-parametric methods, spatial econometrics), this study contributes to the identification of rural areas and to the analysis of the changes occurred during the EU membership in Hungary, assessing the effect of CAP introduction and its contribution to the convergence of the Hungarian agricultural and rural. The author believes that more targeted – and therefore efficient – policies for agricultural and rural areas require a deeper knowledge of their structural and dynamic characteristics.