A general theory of syntax with bindings

In this thesis we give a general theory of syntax with bindings. We address the problem from a mathematical point of view and at the same time we give a formalization, in the Isabelle/HOL proof assistant. Our theory uses explicit names for variables, and then deals with alpha-equivalence classes, remaining intuitive and close to informal mathematics, although being fully formalized and sound in classical high-order logic. In this sense it can be regarded as a generalization of nominal logic. Our end product can be used to construct complex binding patterns and binding-aware datatypes, including non-well-founded and infinitely branching types, in a modular fashion. We provide definitions of the fundamental operators on terms (free variables, alpha-equivalence, and capture-avoiding substitution) and reasoning and definition principles, obeying Barendregt’s convention. We present our work as a thinking process that starts from some desiderata, and then evolves in different formalization stages for the general theory. We start by taking a “universal algebra” approach, modelling syntaxes via algebraic-style binding signatures, which we employ in a substantial case study on formal reasoning: Church-Rosser and standardization theorems for lamda-calculus. This solution proves itself too restrictive, so we refine it into a more flexible one, which constitutes the main original contribution of this thesis: We construct a universe of functors on sets that handle bindings on a general, flexible and modular level. Our functors do not commit to any a priori syntactic format, cater for codatatypes in addition to datatypes, and are supported by powerful definition and reasoning principles. They generalize the bounded natural functors (BNFs), which have been previously implemented in Isabelle/HOL to support (co)datatypes

Multimode synthesis procedure for microwave filters based on thick inductive windows

For several types of microwave filters for space application it is important to manufacture hardware without tuning elements. For this to be possible, one needs a systematic procedure to codvert ideal elements, such as resonators and impedance inverters, into actual waveguide lengths and discontinuities. The situation is further complicated by the fact that waveguide discontinuities excite higher order modes that interacting with each other can have very strong effects. In this paper we first outline the theory behind a very efficient computer code for the simulation of microwave filters based on thick inductive windows. Then we describe in detail a step-by-step procedure that, based on the code developed, allows for the rapid design of this class of microwave filters without any tuning elements. Two actual examples of design are also discussed and comparisons presented between measurements and simulations

A formalized general theory of syntax with bindings

We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying numbers of inputs, quotiented to alpha-equivalence and sorted according to a binding signature. The theory includes a rich collection of properties of the standard operators on terms, such as substitution and freshness. It also includes induction and recursion principles and support for semantic interpretation, all tailored for smooth interaction with the bindings and the standard operators

Subnormalizers and solvability in finite groups

For a finite group $G$, we study the probability $sp(G)$ that, given two elements $x,y \in G$, the cyclic subgroup $\langle x \rangle$ is subnormal in the subgroup $\langle x, y \rangle$. This can be seen as an intermediate invariant between the probability that two elements generate a nilpotent subgroup and the probability that two elements generate a solvable subgroup. We prove that $sp(G) \leq 1/6$ for every nonsolvable group $G$

«Wir haben jetzt die Demokratie, das ist kompliziert genug». Zur Krise demokratischer Systeme und Auflösung des Politischen in «Munin oder Chaos im Kopf» von Monika Maron: [«Now we have democracy, that is complicated enough». On the crisis of democratic systems and the decline of politics in «Munin or Chaos in the Head» by Monika Maron]

In the light of the profound changes that have affected both the political scenario and the political role and forms of engagement of literature over the past thirty years, Monika Maron’s novel Munin oder Chaos im Kopf (2018) seems particularly topical. If analysed through Hannah Arendt’s remarks on the nature of politics and Zygmunt Bauman’s thoughts on our “besieged” society, the narrator’s shocking experience can be seen as both the consequence and the reflection of a failure of our democratic systems, as well as of our traditional idea of politics itself

Sintesi di tesi di laurea - Università degli Studi di Firenze - Facoltà di Ingegneria - Corso di Laurea in Ingegneria Edile RECUPERO ARCHITETTONICO E STRUTTURALE DELL’OSPEDALE VECCHIO SAN GIUSEPPE DI EMPOLI PER LA REALIZZAZIONE DI UN POLIAULE UNIVERSITARIO Autore: Valentina COCULO, Andrea GHERI Relatori: Prof. Arch. Frida BAZZOCCHI - Prof. Ing. Maurizio ORLANDO - Prof. Ing. Paolo SPINELLI Prof. Ing. Paolo FORABOSCHI - Arch. Francesca CAPECCHI Data di laurea: 9 Aprile 2008

La tesi degli ingg. Gheri e Coculo tratta di un intervento per il riuso di un edificio storico importante, l’Ospedale San Giuseppe nel centro di Empoli. La proposta progettuale integra in modo organico le tematiche architettoniche, strutturali ed impiantistiche, nel pieno rispetto dei vincoli della Soprintendenza per i Beni e le Attività Culturali della Regione Toscana, a cui l’organismo edilizio è sottoposto. La progettazione architettonica muove da una approfondita analisi storica del complesso ospedaliero e da un’analisi sistematica dei fattori tipologici e prevede il ripristino della configurazione morfologica originaria e la trasformazione dell’edificio in un poliaule per la didattica universitaria. Il progetto strutturale propone tecniche innovative per il rafforzamento dei sistemi voltati esistenti, per l’analisi dei quali sono utilizzati e confrontati vari metodi di calcolo. La tesi rappresenta un ottimo esempio di progettazione integrata e segna una strada da seguire nella concezione degli interventi per il riuso di edifici storici esistenti in muratura. Prof. Ing. Paolo SPINELL