Towards lightweight front-end for Isabelle/Isar

This work describes an attempt to assemble a lightweight prototype front-end for verifying propositional logic proofs that relies on the Isabelle/Isar proof authoring and verification system. This prototype serves as an opportunity to become familiar with some of Isabelle/Isar's verification capabilities and limitations, and provides a starting point for future work incorporating Isabelle/Isar as one of the underlying component tools in the Aartifact accessible integrated environment for formal modelling and verification

Isabelle for Philosophers

This is an introduction to the Isabelle proof assistant aimed at philosophers and their students

A formally verified proof of the prime number theorem

The prime number theorem, established by Hadamard and de la Vall'ee Poussin independently in 1896, asserts that the density of primes in the positive integers is asymptotic to 1 / ln x. Whereas their proofs made serious use of the methods of complex analysis, elementary proofs were provided by Selberg and Erd"os in 1948. We describe a formally verified version of Selberg's proof, obtained using the Isabelle proof assistant.Comment: 23 page

A User-friendly Interface for a Lightweight Verification System

User-friendly interfaces can play an important role in bringing the benefits of a machine-readable representation of formal arguments to a wider audience. The "aartifact" system is an easy-to-use lightweight verifier for formal arguments that involve logical and algebraic manipulations of common mathematical concepts. The system provides validation capabilities by utilizing a database of propositions governing common mathematical concepts. The "aartifact" system's multi-faceted interactive user interface combines several approaches to user-friendly interface design: (1) a familiar and natural syntax based on existing conventions in mathematical practice, (2) a real-time keyword-based lookup mechanism for interactive, context-sensitive discovery of the syntactic idioms and semantic concepts found in the system's database of propositions, and (3) immediate validation feedback in the form of reformatted raw input. The system's natural syntax and database of propositions allow it to meet a user's expectations in the formal reasoning scenarios for which it is intended. The real-time keyword-based lookup mechanism and validation feedback allow the system to teach the user about its capabilities and limitations in an immediate, interactive, and context-aware manner

Automation for interactive proof: First prototype

AbstractInteractive theorem provers require too much effort from their users. We have been developing a system in which Isabelle users obtain automatic support from automatic theorem provers (ATPs) such as Vampire and SPASS. An ATP is invoked at suitable points in the interactive session, and any proof found is given to the user in a window displaying an Isar proof script. There are numerous differences between Isabelle (polymorphic higher-order logic with type classes, natural deduction rule format) and classical ATPs (first-order, untyped, and clause form). Many of these differences have been bridged, and a working prototype that uses background processes already provides much of the desired functionality

Mining the Archive of Formal Proofs

International audienceThe Archive of Formal Proofs is a vast collection of computer-checked proofs developed using the proof assistant Isabelle. We perform an in-depth analysis of the archive, looking at various properties of the proof developments, including size, dependencies, and proof style. This gives some insights into the nature of formal proofs