Isabelle/PIDE as Platform for Educational Tools
This work addresses the challenge of using formal proof systems in math education by reducing accidental technical barriers, though it is incremental as it builds on existing technologies.
The paper tackles the problem of making LCF-family proof assistants like Isabelle more accessible for educational tools by introducing the Isabelle/PIDE platform, which integrates the proof engine into a JVM-based environment to facilitate user interaction and tool integration.
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.