Published: 10th March 2023
DOI: 10.4204/EPTCS.375
ISSN: 2075-2180


Proceedings 11th International Workshop on
Theorem Proving Components for Educational Software
Haifa, Israel, 11 August 2022

Edited by: Pedro Quaresma, João Marcos and Walther Neuper

Invited Talk: Satisfiability Modulo Theories in an Undergraduate Class
Yoni Zohar
Computer Assisted Proofs and Automated Methods in Mathematics Education
Thierry Noah Dana-Picard
A Rule Based Theorem Prover: an Introduction to Proofs in Secondary Schools
Joana Teles, Vanda Santos and Pedro Quaresma
ANITA: Analytic Tableau Proof Assistant
Davi Romero Vasconcelos
A Proof Tree Builder for Sequent Calculus and Hoare Logic
Joomy Korkut
On Exams with the Isabelle Proof Assistant
Frederik Krogsdal Jacobsen and Jørgen Villadsen
Automated Grading of Automata with ACL2s
Ankit Kumar, Andrew Walter and Panagiotis Manolios
Towards an Accessible Mathematics Working Environment Based on Isabelle/VSCode
Klaus Miesenberger, Walther Neuper, Bernhard Stöger and Makarius Wenzel


The ThEdu series pursues the smooth transition from an intuitive way of doing mathematics at secondary school to a more formal approach to the subject in STEM education, while favouring software support for this transition by exploiting the power of theorem-proving technologies. What follows is a brief description of how the present volume contributes to this enterprise.

The 11th International Workshop on Theorem Proving Components for Educational Software (ThEdu'22), was a satellite event of the 8th Federated Logic Conference (FLoC 2022), July 31-August 12, 2022, Haifa, Israel. ThEdu'22 was a vibrant workshop, with two invited talks, by Thierry Dana-Picard (Jerusalem College of Technology, Jerusalem, Israel) and by Yoni Zohar (Bar Ilan University, Tel Aviv, Israel), and four regular contributions. An open call for papers was then issued, and it attracted seven submissions. Those submissions have been accepted by our reviewers, who jointly produced at least three careful reports on each of the contributions. The resulting revised papers are collected in the present volume.

The contributions in this volume are a faithful representation of the wide spectrum of ThEdu, ranging from those more focused on the automated deduction research, not losing track of the possible applications in an educational setting, to those focused on the applications, in educational settings, of automated deduction tools and methods.

Yoni Zohar reported on his experience in teaching an automated reasoning class focused on SMT, in his invited talk, the abstract of which is here contained in HTML format only. Thierry Dana-Picard, in a comprehensive article covering the area of Computer Algebra Systems (CAS) and Dynamic Geometry Systems (DGS) and their connections with automated reasoning, presents tools and methods for high-school mathematics education, in particular geometry, discussing the transformation of Mathematics Education into an exploration-discovery-conjecture-proof scheme, avoiding usage as a black box. At the same school level, Joana Teles, Vanda Santos and Pedro Quaresma discuss the possible use of the deductive database method for geometry in a 7th year class (≈12 year-old students), with a specifically designed set of rules, as a way to motivate students for deductive reasoning and to exhibit the beauty of mathematical proof. The teaching for formal reasoning at the university level is addressed by several authors presenting several systems with different goals. Davi Vasconcelos presents the system ANITA (Analytic Tableau Proof Assistant), developed for teaching analytic tableaux to computer science students. The tool is written in Python and may be used either as a desktop application or as a Web application. Joomy Korkut presents a Web-based pedagogical proof assistant, the Proof Tree Builder that may be applied to sequent calculus and Hoare logic proofs. With an intuitive interface, the system can be used to lessen the burden of manual production of proof trees. Frederik Krogsdal Jacobsen and Jørgen Villadsen present an approach for testing student learning outcomes in a course on automated reasoning using the Isabelle proof assistant. The approach allows teachers to test both general understanding of formal proofs in various logical proof systems and understanding of proofs, in particular, in the higher-order logic of Isabelle/HOL. Ankit Kumar, Andrew Walter and Panagiotis Manolios present the Automatic Automata Checker (A2C), an open-source library that enables one to construct executable automata using definitions that mimic those found in standard textbooks. Instructors can conveniently specify solutions in the form of their own constructions with the system generating actionable feedback, which helps students better understand the material. Finally, Klaus Miesenberger, Walther Neuper, Bernhard Stöger and Makarius Wenzel describe plans for a project, made in close collaboration between experts in accessibility of studies for visually impaired individuals with experts in developing educational mathematics software and experts in designing and implementing interactive proof assistants. This way they come back to one of the initial goals of ThEdu, namely to support early mathematics education with formal mathematics software.

For their help in reviewing the papers, the editors would like to thank the other members of the Programme Committee of ThEdu'22: Francisco Botana (University of Vigo at Pontevedra, Spain); David Cerna (Czech Academy of Sciences Institute of Computer Science, Czech Republic); Filip Marić (University of Belgrade, Serbia); Adolfo Neto (UTFPR, Brazil); Giselle Reis (Carnegie Mellon University Qatar, Qatar); Vanda Santos (University of Aveiro, Portugal); Anders Schlichtkrull, Aalborg University, Denmark; Wolfgang Schreiner (Research Institute for Symbolic Computation (RISC), Austria); M. Pilar Vélez (Nebrija University, Spain) and Jørgen Villadsen (Technical University of Denmark, Denmark).

We, the volume editors, hope that this collection of papers will further promote the development of theorem-proving based software, and that it will allow to improve the mutual understanding between computer scientists, mathematicians and stakeholders in education.

While this volume goes to press, the next edition of the ThEdu workshop is being prepared: ThEdu'23 will be a satellite event of the 29th international Conference on Automated Deduction (CADE 2023), July 1-4, 2023, Rome, Italy.

PC Chairs:
João Marcos (UFRN, Federal University of Rio Grande do Norte, Brazil)
Walther Neuper (JKU, Johannes Kepler University, Linz, Austria)
Pedro Quaresma (University of Coimbra, Portugal)

Satisfiability Modulo Theories in an Undergraduate Class

Yoni Zohar (Bar Ilan University, Tel Aviv, Israel)

Satisfiability Modulo Theories (SMT) solvers are widely used in various applications, most prominently verification of hardware and software. They are focused on the task of checking the satisfiability of first-order formulas over a wide range of background theories. Currently, mainstream SMT-solvers offer easy to use APIs and textual interfaces, and are accessible even to users with little logical background. Nevertheless, their algorithms are based on interesting and varied theoretical subjects.

For these reasons, SMT as a field is a good candidate for introducing automated reasoning and logic to students with little or no background in logic: its wide applicability provides a great motivation to study them, the solvers' accessibility offers hands-on exercises and the logical foundations contain a wide variety of topics of different levels and depth.

In this talk I will describe my experience in teaching an automated reasoning class focused on SMT. I will describe my original hypotheses and plans before the class, what happened during the class, and some reflections that occurred in the process.