Book available: “All about Proofs, Proofs for All”

As a result of the APPA workshop at Vienna Summer of Logic 2014, there is now a book available with the collected contributions by the invited experts (including myself). It is edited by Bruno Woltzenlogel Paleo and David Delahaye, and is published by College Publications. Here is a copy of the abstract from it:

The development of new and improved proof systems, proof formats and proof search methods is one of the most essential goals of Logic. But what is a proof? What makes a proof better than another? How can a proof be found efficiently? How can a proof be used? Logicians from different communities usually provide radically different answers to such questions. Their principles may be folklore within their own communities but are often unknown to outsiders.

This book provides a snapshot of the current state of the art in proof search and proof production as implemented in contemporary automated reasoning tools such as SAT-solvers, SMT-solvers, first-order and higher-order automated theorem provers and proof assistants. Furthermore, various trends in proof theory, such as the calculus of inductive constructions, deduction modulo, deep inference, foundational proof certificates and cut-elimination, are surveyed; and applications of formal proofs are illustrated in the areas of cryptography, verification and mathematical proof mining.

Experts in these topics were invited to present tutorials about proofs during the Vienna Summer of Logic and the chapters in this book reflect their tutorials. Therefore, each chapter is intended to be accessible not only to experts but also to novice researchers from all fields of Logic.

My contribution to the book is a chapter on “Interactive Theorem Proving — from the perspective of Isabelle/Isar”, with the following abstract:

Interactive Theorem Proving (ITP) has a long tradition, going back to the 1970s when interaction was introduced as a concept in computing. The main provers in use today can be traced back over 20–30 years of development. As common traits there are usually strong logical systems at the bottom, with many layers of add-on tools around the logical core, and big applications of formalized mathematics or formal methods. There is a general attitude towards flexibility and open-endedness in the combination of logical tools: typical interactive provers use automated provers and disprovers routinely in their portfolio.

The subsequent exposition of ITP takes Isabelle/Isar as the focal point to explain concepts of the greater “LCF family”, which includes Coq and various HOL systems. Isabelle itself shares much of the relatively simple logical foundations of HOL, but follows Coq in the ambition to deliver a sophisticated system to end-users, without requiring self-assembly of individual parts. Isabelle today is probably the most advanced proof assistant concerning its architecture and extra-logical infrastructure.

The Isar aspect of Isabelle refers first to the structured language for human-readable and machine-checkable proof documents, but also to the Isabelle architecture that emerged around the logical framework in the past 10 years. Thus Isabelle/Isar provides extra structural integrity beyond the core logical framework, with native support for parallel proof processing and asynchronous interaction in its Prover IDE (PIDE).

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