Isabelle/PIDE as Platform for Educational Tools

TL;DR

This paper explores using the Isabelle/PIDE platform as a foundation for developing educational tools that make proof assistants more accessible and integrated into math education.

Contribution

It introduces the PIDE platform as a means to enhance proof assistant accessibility for educational purposes, bridging formal logic engines with user-friendly interfaces.

Findings

PIDE enables integration of proof engines with educational tools.

Scala exposes Isabelle's proof engine to JVM-based environments.

Potential for combined mathematical assistants in education.

Abstract

The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have so far been counter-balanced by somewhat inaccessible interaction via the TTY (or minor variations like the well-known Proof General / Emacs interface). Thus the fundamental question of math education tools with fully-formal background theories has often been answered negatively due to accidental weaknesses of existing proof engines. The idea of "PIDE" (which means "Prover IDE") is to integrate existing provers like Isabelle into a larger environment, that facilitates access by end-users and other tools. We use Scala to expose the proof engine in ML to the JVM world, where many user-interfaces, editor frameworks, and educational tools already exist. This shall ultimately lead to combined mathematical assistants, where the logical engine is in the background, without obstructing the view on applications of formal methods, formalized mathematics, and math education in particular.