From jan.kofron at d3s.mff.cuni.cz Mon Jun 9 15:17:28 2025 From: jan.kofron at d3s.mff.cuni.cz (Jan Kofron) Date: Mon, 9 Jun 2025 15:17:28 +0200 Subject: Seminar tomorrow Message-ID: Dear all, Let me invite you to another seminar in this semester that will take place tomorrow, Tuesday, June 10, at 14:00 in S4 [1]. Pablo Donato from Grothendieck Institute will talk about "Deep Inference for Graphical Theorem Proving". Please find the details below. [1] https://d3s.mff.cuni.cz/seminar/ Thanks, best regards! Jan ==== Deep Inference for Graphical Theorem Proving Abstract: Contemporary proof assistants such as Rocq, Lean and Agda provide robust frameworks for constructing and verifying formal proofs, and can also be used as very expressive programming languages thanks to their powerful type systems. However their interfaces remain largely textual, and require users to master mathematical logic and functional programming. This poses significant usability barriers, limiting both broader adoption and more exploratory, human-centered forms of reasoning. This talk introduces Proof-by-Action (PbA), a novel paradigm developed in my PhD thesis for interacting with proof assistants through direct manipulation in a graphical user interface. Grounded in the proof-theoretic framework of deep inference, PbA allows users to construct proofs via intuitive gestures?such as clicking and dragging?performed directly on logical statements. A live demonstration in Rocq will showcase the integration of this paradigm into a state-of-the-art proof assistant, enabling gestural proof construction within a trusted backend and a rich library ecosystem. I will then present a more ambitious research direction: replacing the traditional symbolic notations of logic with iconic representations that leverage our spatial intuition. I focus on a long-neglected diagrammatic formalism introduced by C. S. Peirce at the end of the 19th century?existential graphs?and on my intuitionistic extension of them, the Flower Calculus. I will conclude with my latest work toward a Curry-Howard interpretation of existential graphs, which I hope will pave the way for a new kind of interactive programming systems that are both strongly typed and genuinely user-friendly. Bio: Pablo Donato is a postdoctoral researcher in computer science currently based in Paris. His research focuses on the design of graphical proof languages and interactive tools for formal reasoning, with a particular interest in rethinking the user experience of proof assistants and programming systems. During his Ph.D., he developed the Proof-by-Action paradigm, a novel approach to proof construction based on direct manipulation and the proof-theoretic framework of deep inference. He also introduced the Flower Calculus, a diagrammatic system inspired by C. S. Peirce's existential graphs. His goal is to make correct-by-construction programming more feasible by redesigning our notations for the dynamic medium. More information can be found on his website: https://pablogician.refl.fr/. -- Jan Kofron, Ph.D. Associate Professor Department of Distributed and Dependable Systems Faculty of Mathematics and Physics Charles University Malostranske namesti 25 118 00 Praha 1, Czech Republic Phone: +420 95155 4285 http://d3s.mff.cuni.cz/~kofron -------------- next part -------------- A non-text attachment was scrubbed... Name: OpenPGP_signature.asc Type: application/pgp-signature Size: 236 bytes Desc: OpenPGP digital signature URL: