Lucas-Interpretation on Isabelle's Functions

Abstract

Software tools of Automated Reasoning are too sophisticated for general use in mathematics education and respective reasoning, while Lucas-Interpretation provides a general concept for integrating such tools into educational software with the purpose to reliably and flexibly check formal input of students. This paper gives the first technically concise description of Lucas-Interpretation at the occasion of migrating a prototype implementation to the function package of the proof assistant Isabelle. The description shows straightforward adaptations of Isabelle's programming language and shows, how simple migration of the interpreter was, since the design (before the function package has been introduced to Isabelle) recognised appropriateness of Isabelle's terms as middle end. The paper gives links into the code in an open repository as invitation to readers for re-using the prototyped code or adopt the general concept. And since the prototype has been designed before the function package was implemented, the paper is an opportunity for recording lessons learned from Isabelle's development of code structure.

Towards an Accessible Mathematics Working Environment Based on Isabelle/VSCode

“…Our case study will focus the "what" in the so-called "specification phase", which in general is considered more difficult to cope with automation by software than the "how" in the so-called "solution phase". Our expectation in the latter phase is documented in [28] and more generally in [27].…”

“…Creating such user guidance automatically is a conceptual challenge. For the "solve phase" this is accomplished by Lucas-Interpretation [28] 11 For the "specification phase" such user guidance is described in the subsequent section §4. This addresses the aspect of "interactive model" of problem solving.…”

“…3. Methods comprise a guard, as mentioned at the end of §4.3, and a program, which supports interactive construction of a solution for the specified problem [28]. While an optimal structure for collections of methods is still unclear, the ISAC prototype collects them in a tree the same way as problems.…”

“…Browser support, using generic HTML/CSS/JavaScript technology. • The ISAC project 15 implements a concept of "Next-Step Guidance" [28] of mathematical reasoning, based on Isabelle theory content [21]. It was historically built on the Isabelle commandline with add-on Java GUI (now discontinued).…”

Interactive Formal Specification for Mathematical Problems of Engineers

“…Since its beginnings more than two decades ago the ISAC project strives for a generally usable system for mathematics education, which might cover a major part of educational scenarios, posing and solving problems which can best be tackled by mathematical methods. This paper presents the second part of a concise description of the prototype that has been developed in the course of the project, the description of the so-called specify-phase, while the first part describing the solve-phase is already published [15].…”