Isabelle/PIDE as Platform for Educational Tools

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.Comment: In Proceedings THedu'11, arXiv:1202.453

Compensation methods to support generic graph editing: A case study in automated verification of schema requirements for an advanced transaction model

Compensation plays an important role in advanced transaction models, cooperative work, and workflow systems. However, compensation operations are often simply written as a^−1 in transaction model literature. This notation ignores any operation parameters, results, and side effects. A schema designer intending to use an advanced transaction model is expected (required) to write correct method code. However, in the days of cut-and-paste, this is much easier said than done. In this paper, we demonstrate the feasibility of using an off-the-shelf theorem prover (also called a proof assistant) to perform automated verification of compensation requirements for an OODB schema. We report on the results of a case study in verification for a particular advanced transaction model that supports cooperative applications. The case study is based on an OODB schema that provides generic graph editing functionality for the creation, insertion, and manipulation of nodes and links

Proof in Context -- Web Editing with Rich, Modeless Contextual Feedback

The Agora system is a prototypical Wiki for formal mathematics: a web-based system for collaborating on formal mathematics, intended to support informal documentation of formal developments. This system requires a reusable proof editor component, both for collaborative editing of documents, and for embedding in the resulting documents. This paper describes the design of Agora's asynchronous editor, that is generic enough to support different tools working on editor content and providing contextual information, with interactive theorem proverss being a special, but important, case described in detail for the Coq theorem prover.Comment: In Proceedings UITP 2012, arXiv:1307.152

Compensation methods to support cooperative applications: A case study in automated verification of schema requirements for an advanced transaction model

Compensation plays an important role in advanced transaction models, cooperative work and workflow systems. A schema designer is typically required to supply for each transaction another transaction to semantically undo the effects of . Little attention has been paid to the verification of the desirable properties of such operations, however. This paper demonstrates the use of a higher-order logic theorem prover for verifying that compensating transactions return a database to its original state. It is shown how an OODB schema is translated to the language of the theorem prover so that proofs can be performed on the compensating transactions

Interactive Simplifier Tracing and Debugging in Isabelle

The Isabelle proof assistant comes equipped with a very powerful tactic for term simplification. While tremendously useful, the results of simplifying a term do not always match the user's expectation: sometimes, the resulting term is not in the form the user expected, or the simplifier fails to apply a rule. We describe a new, interactive tracing facility which offers insight into the hierarchical structure of the simplification with user-defined filtering, memoization and search. The new simplifier trace is integrated into the Isabelle/jEdit Prover IDE.Comment: Conferences on Intelligent Computer Mathematics, 201

Asynchronous processing of Coq documents: from the kernel up to the user interface

The work described in this paper improves the reactivity of the Coq system by completely redesigning the way it processes a formal document. By subdividing such work into independent tasks the system can give precedence to the ones of immediate interest for the user and postpones the others. On the user side, a modern interface based on the PIDE middleware aggregates and present in a consistent way the output of the prover. Finally postponed tasks are processed exploiting modern, parallel, hardware to offer better scalability.Comment: in Proceedings of ITP, Aug 2015, Nanjing, Chin