A Mobile Application for Self-Guided Study of Formal Reasoning

Abstract

In this work, we introduce AXolotl, a self-study aid designed to guide students through the basics of formal reasoning and term manipulation. Unlike most of the existing study aids for formal reasoning, AXolotl is an Android-based application with a simple touch-based interface. Part of the design goal was to minimize the possibility of user errors which distract from the learning process. Such as typos or inconsistent application of the provided rules. The system includes a zoomable proof viewer which displays the progress made so far and allows for storage of the completed proofs as a JPEG or L A T E X file. The software is available on the google play store and comes with a small library of problems. Additional problems may be opened in AXolotl using a simple input language. Currently, AXolotl supports problems that can be solved using rules which transform a single expression into a set of expressions. This covers educational scenarios found in our first-semester introduction to logic course and helps bridge the gap between propositional and first-order reasoning. Future developments will include rewrite rules which take a set of expressions and return a set of expressions, as well as a quantified first-order extension.

A Proof Tree Builder for Sequent Calculus and Hoare Logic

“…Its syntax, semantics, and proof system are all formalized in the Isabelle proof assistant [23], so students can see "behind the scenes", dig into the definitions all the way down, and verify the resulting proof in Isabelle. AXolotl [6] is an educational tool that can handle Hilbert style, sequent style and natural deduction proofs. Their tool allows restricting the allowed rules for a given problem, hence helping the student focus on the rules that are relevant to the problem.…”

Towards an Accessible Mathematics Working Environment Based on Isabelle/VSCode

“…At high-school teaching proof is limited, so strong efforts are required at the Secondary-Tertiary-Transition. There are many initiatives to support academic education in mathematical proof by software tools [1,5,6,9,12] and their number increases rapidly in the present, particularly in the field of computer science. Since the initiatives are driven by proactive lecturers, success is promising.…”

“…The joint project thoroughly investigated the demand for such software, detailed the user requirements and technical feasibility and present all together in this paper. Technical feasibility has been checked at the Isabelle Workshop 6 , details have been documented in [42] and now the project is underway to look for international cooperation with the relevant academic institutions.…”

Evolution of SASyLF 2008-2021

“…The researcher (Cerna) recognized that students often struggle with unification and substitution in rule application and includes several aids to help students bridge the conceptual gap. Recently the tool has been ported to work as a mobile application [7].…”