Theorem proving system supporting both interactive proof development and some degree of automation have become quite successful in sizable applications in recent years (e.g. Isabelle/Bali or VerifiCard). Typical examples of this kind of semi-automated reasoning systems include Coq, PVS, HOL, and Isabelle. Despite this success in actually formalizing parts of mathematics and computer science, there are still obstacles in addressing a broad range of people. Paradoxically, none of the existing semi-automated reasoning systems have an adequate primary notion of proof that is amenable to human understanding (for communication, or just maintenance). The Intelligible semi-automated reasoning (Isar) approach to readable formal proof documents sets out to bridge the semantic gap between internal notions of proof given by state-of-the-art interactive theorem proving systems and an appropriate level of abstraction for user-level work. The Isar formal proof language has been designed to satisfy quite contradictory requirements, being both ’declarative’ and immediately ’executable’, by virtue of the Isar/VM interpreter. Compared to existing declarative theorem proving systems (like Mizar), Isar avoids several shortcomings: it is based on a few basic principles only, it is quite independent of the underlying logic, and integrates a broad range of automated proof methods. Interactive proof development is supported directly as well. The Isabelle system offers Isar as an alternative proof language interface layer, beyond traditional tactic scripts. The Isabelle/Isar system provides an interpreter for the Isar formal proof document language. Isabelle/Isar input consists either of proper document constructors, or improper auxiliary commands (for diagnostics, exploration etc.). Proof texts consisting of proper document constructors only admit a purely static reading, thus being intelligible later without requiring dynamic replay that is so typical for traditional proof scripts. Any of the Isabelle/Isar commands may be executed in single-steps, so basically the interpreter has a proof text debugger already built-in. The Isar subsystem is tightly integrated into the Isabelle/Pure meta-logic implementation. Theories, theorems, proof procedures etc. may be used interchangeably between Isabelle-classic proof scripts and Isabelle/Isar documents. Isar is as generic as Isabelle, able to support a wide range of object-logics. The current end-user setup is mainly for Isabelle/HOL. Together with the Isabelle/Isar instantiation of Proof General, a generic (X)Emacs interface for interactive proof assistants, we arrive at a reasonable environment for live proof document editing. Thus proof texts may be developed incrementally by issuing proper document constructors, including forward and backward tracing of partial documents; intermediate states may be inspected by diagnostic commands.

References in zbMATH (referenced in 145 articles , 1 standard article )

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  1. Maletzky, Alexander: A generic and executable formalization of signature-based Gröbner basis algorithms (2021)
  2. Berghammer, Rudolf; Furusawa, Hitoshi; Guttmann, Walter; Höfner, Peter: Relational characterisations of paths (2020)
  3. Hernández-Orozco, Santiago; Hernández-Quiroz, Francisco; Zenil, Hector; Sieg, Wilfried: Shortening of proof length is elusive for theorem provers (2020)
  4. Schlichtkrull, Anders; Blanchette, Jasmin; Traytel, Dmitriy; Waldmann, Uwe: Formalizing Bachmair and Ganzinger’s ordered resolution prover (2020)
  5. Bentkamp, Alexander; Blanchette, Jasmin Christian; Klakow, Dietrich: A formal proof of the expressiveness of deep learning (2019)
  6. Gunther, Emmanuel; Pagano, Miguel; Sánchez Terraf, Pedro: First steps towards a formalization of forcing (2019)
  7. Kaliszyk, Cezary; Pąk, Karol: Semantics of Mizar as an Isabelle object logic (2019)
  8. Kunčar, Ondřej; Popescu, Andrei: A consistent foundation for Isabelle/HOL (2019)
  9. Lammich, Peter; Sefidgar, S. Reza: Formalizing network flow algorithms: a refinement approach in Isabelle/HOL (2019)
  10. Marmsoler, Diego; Gidey, Habtom Kashay: Interactive verification of architectural design patterns in FACTum (2019)
  11. Paulson, Lawrence C.; Nipkow, Tobias; Wenzel, Makarius: From LCF to Isabelle/HOL (2019)
  12. Stojanović-Ðurđević, Sana: From informal to formal proofs in Euclidean geometry (2019)
  13. Bauereiß, Thomas; Pesenti Gritti, Armando; Popescu, Andrei; Raimondi, Franco: CoSMed: a confidentiality-verified social media platform (2018)
  14. Blanchette, Jasmin Christian; Fleury, Mathias; Lammich, Peter; Weidenbach, Christoph: A verified SAT solver framework with learn, forget, restart, and incrementality (2018)
  15. Eberl, Manuel; Haslbeck, Max W.; Nipkow, Tobias: Verified analysis of random binary tree structures (2018)
  16. Jensen, Alexander Birch; Larsen, John Bruntse; Schlichtkrull, Anders; Villadsen, Jørgen: Programming and verifying a declarative first-order prover in Isabelle/HOL (2018)
  17. Rabe, Florian: A modular type reconstruction algorithm (2018)
  18. Schlichtkrull, Anders: Formalization of the resolution calculus for first-order logic (2018)
  19. Bentkamp, Alexander; Blanchette, Jasmin Christian; Klakow, Dietrich: A formal proof of the expressiveness of deep learning (2017)
  20. Biendarra, Julian; Blanchette, Jasmin Christian; Bouzy, Aymeric; Desharnais, Martin; Fleury, Mathias; Hölzl, Johannes; Kunčar, Ondřej; Lochbihler, Andreas; Meier, Fabian; Panny, Lorenz; Popescu, Andrei; Sternagel, Christian; Thiemann, René; Traytel, Dmitriy: Foundational (co)datatypes and (co)recursion for higher-order logic (2017)

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