There are many ways to teach proof competence. Students try to use “perfect” proofs from textbooks or experts to create their own proofs in exercises, and they often fail. In particular, many students struggle with properly understanding the structure of proofs. We believe that—for the education of Computer Science students who are used to programming—it is natural to use proof assistants to learn to develop and write proofs. In addition, the immediate feedback from proof assistants helps students to check their proofs for correctness and completeness.

However, proof assistants are not made for beginners. Moreover, learning formal and mathematical language at the same time is often overwhelming. We develop the web interface ProofBuddy based on the proof assistant Isabelle as a tool that (also) targets for beginners. We chose Isabelle, because we assume that the proximity of its Isar language to natural/mathematical language supports the learning process. Pedagogically, we experiment with a setting in which students constantly switch between pen-and-paper-proofs and their formal counterparts. ProofBuddy is designed to support this back-and-forth approach.

In the talk, I report on the architecture and the user interface of ProofBuddy, give a short introduction to Isar within ProofBuddy and present our pedagogical approach.

Blind Signatures are a useful primitive for privacy preserving applications such as electronic payments, e-voting, anonymous credentials, and more.

However, existing practical blind signature schemes based on standard assumptions require either pairings or lattices. We present the first practical construction of a round-optimal blind signature in the random oracle model based on standard assumptions without resorting to pairings or lattices. In particular, our construction is secure under the strong RSA assumption and DDH (in pairing-free groups). For our construction, we provide a NIZK-friendly signature based on strong RSA, and efficiently instantiate a variant of Fischlin's generic framework (CRYPTO'06). Our Blind Signature scheme has signatures of size 4.28 KB and communication cost 10.98 KB. On the way, we develop techniques that might be of independent interest. In particular, we provide efficient *relaxed* range-proofs for large ranges with subversion zero-knowledge and compact commitments to elements of arbitrary groups.

Joint work with Michael Reichle and Ky Nguyen.

The Ahlbrandt-Ziegler result in model theory asserts that a countably categorical theory is characterised, up to bi-interpretability, by the topological automorphism group of its (unique) countable model, thus permitting a study of these theories by group-theoretic properties.

Removing the countable categoricity assumption necessitates using topological groupoids rather than groups. We will describe a groupoidal generalisation of the Ahlbrandt-Ziegler result using topos theory.

Our result extends the results in the topos-theoretic literature of Awodey, Butz, Caramello, Forssell and Moerdijk, while being orthogonal to the parallel generalisation of Ben Yaacov.

We will start a new series of non-permanent weekly seminars with an introduction section, during which everyone can briefly share their name, background, and research topic (if desired). This is a casual and friendly setting, so don't be shy!

After the session, we will have some refreshment and play some games, everyone is welcome.

Session types are a typed approach to ensure the communication correctness of message-passing programs. They have been extensively studied from a theoretical standpoint, and have been also incorporated into diverse programming languages and models.

Perhaps surprisingly, there is no single, canonical session type system, but many. It is fair to say that expressiveness has been key to the success and impact of session types: enhancing the expressivity of typed processes and/or the properties enforced by typing is often a strong motivation for developing new typed frameworks.

In this rich and diverse context, rigorously contrasting different variants of session types from an expressiveness perspective is a fascinating and non-trivial challenge. In this talk I introduce session types briefly and overview some recent works related to their expressiveness; they cover various angles, including “propositions-as-sessions”, i.e., the Curry-Howard correspondence between session types and linear logic.

Büchi's seminal 1962 paper established the decidability of the monadic second-order (MSO) theory of the structure (Nat; <), and in so doing brought to light the profound connections between mathematical logic and automata theory. This talk presents our recent results on the decidability of expansions (Nat; <, P1, …, Pd) for various unary predicates P1, …, Pd. We focus in particular on predicates of arithmetic origin, such as Pow-k (powers of k) and N-k (k-th powers). The following is a representative sample of the results yielded by our techniques, which combine automata theory, algebra, number theory, dynamical systems, and combinatorics:

- The MSO theory of (Nat; <, Pow-2, Pow-3) is decidable.

- The MSO theory of (Nat; <, Pow-2, Pow-3, Pow-6) is decidable.

- The MSO theory of (Nat; <, Pow-2, Pow-3, Pow-5) is decidable subject to Schanuel's conjecture.

- The MSO theory of (Nat; <, Squares, Pow-4) is decidable.

- The MSO theory of (Nat; <; Squares, Pow-2) is Turing-equivalent to the MSO theory of (Nat; <, S), where S is the unary predicate corresponding to the binary expansion of s = sqrt(2). As s is widely believed to be a weakly normal number, the corresponding MSO theory is in turn expected to be decidable.

The talk will give an overview of our techniques in general, and the automata theory and algebra that enable the above results in particular.

Dans ce premier exposé basé sur l’article « Univalence in simplicial sets » (https://arxiv.org/abs/1203.2553) je détaillerai la notion de « fibration universelle » qui en est l’ingrédient essentiel. J’examinerai en parallèle ce que devient une telle construction lorsqu’on remplace les ensembles simpliciaux par le cadre beaucoup plus simple des ensembles tout court.

Smart contracts are programs that run on an interpreter cobbled together from a massively distributed network of mutually untrusting computers. Unsurprisingly, the unruly nature of the underlying execution engine has a profound impact on the behavior of the interpreter and thus the semantics of smart contracts.

Caught once again by my incurable curiosity, I have set out to delineate precisely what set smart contracts aside in the realm of programming languages.

This talk reports on some early results, modeling the semantics of smart contracts in a type-theoretic and monadic framework. The objective of this work is to support formal reasoning at the protocol level (that is, starting from a specification free from programming error).

We shall strive to stay on track and in good taste: the presentation will not cover any financial aspect of smart contracts.