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.

Untangle sustainable development goal 8 through data visualization and HCI methods

Following the approval of the 2030 Agenda for Sustainable Development in 2015, sustainability became a hotly debated topic. In order to build a better and more sustainable future by 2030, this agenda addressed several global issues, including inequality, climate change, peace, and justice, in the form of 17 Sustainable Development Goals (SDGs), that should be understood and pursued by nations, corporations, institutions, and individuals. In this thesis, we researched how to exploit and integrate Human-Computer Interaction (HCI) and Data Visualization to promote knowledge and awareness about SDG 8, which wants to encourage lasting, inclusive, and sustainable economic growth, full and productive employment, and decent work for all. In particular, we focused on three targets: green economy, sustainable tourism, employment, decent work for all, and social protection. The primary goal of this research is to determine whether HCI approaches may be used to create and validate interactive data visualization that can serve as helpful decision-making aids for specific groups and raise their knowledge of public-interest issues. To accomplish this goal, we analyzed four case studies. In the first two, we wanted to promote knowledge and awareness about green economy issues: we investigated the Human-Building Interaction inside a Smart Campus and the dematerialization process inside a University. In the third, we focused on smart tourism, investigating the relationship between locals and tourists to create meaningful connections and promote more sustainable tourism. In the fourth, we explored the industry context to highlight sustainability policies inside well-known companies. This research focuses on the hypothesis that interactive data visualization tools can make communities aware of sustainability aspects related to SDG8 and its targets. The research questions addressed are two: "how to promote awareness about SDG8 and its targets through interactive data visualizations?" and "to what extent are these interactive data visualizations effective?".

Teaching informatics to novices: big ideas and the necessity of optimal guidance

This thesis reports on the two main areas of our research: introductory programming as the traditional way of accessing informatics and cultural teaching informatics through unconventional pathways. The research on introductory programming aims to overcome challenges in traditional programming education, thus increasing participation in informatics. Improving access to informatics enables individuals to pursue more and better professional opportunities and contribute to informatics advancements. We aimed to balance active, student-centered activities and provide optimal support to novices at their level. Inspired by Productive Failure and exploring the concept of notional machine, our work focused on developing Necessity Learning Design, a design to help novices tackle new programming concepts. Using this design, we implemented a learning sequence to introduce arrays and evaluated it in a real high-school context. The subsequent chapters discuss our experiences teaching CS1 in a remote-only scenario during the COVID-19 pandemic and our collaborative effort with primary school teachers to develop a learning module for teaching iteration using a visual programming environment. The research on teaching informatics principles through unconventional pathways, such as cryptography, aims to introduce informatics to a broader audience, particularly younger individuals that are less technical and professional-oriented. It emphasizes the importance of understanding informatics's cultural and scientific aspects to focus on the informatics societal value and its principles for active citizenship. After reflecting on computational thinking and inspired by the big ideas of science and informatics, we describe our hands-on approach to teaching cryptography in high school, which leverages its key scientific elements to emphasize its social aspects. Additionally, we present an activity for teaching public-key cryptography using graphs to explore fundamental concepts and methods in informatics and mathematics and their interdisciplinarity. In broadening the understanding of informatics, these research initiatives also aim to foster motivation and prime for more professional learning of informatics.