14 research outputs found
Advanced Proof Viewing in ProofTool
Sequent calculus is widely used for formalizing proofs. However, due to the
proliferation of data, understanding the proofs of even simple mathematical
arguments soon becomes impossible. Graphical user interfaces help in this
matter, but since they normally utilize Gentzen's original notation, some of
the problems persist. In this paper, we introduce a number of criteria for
proof visualization which we have found out to be crucial for analyzing proofs.
We then evaluate recent developments in tree visualization with regard to these
criteria and propose the Sunburst Tree layout as a complement to the
traditional tree structure. This layout constructs inferences as concentric
circle arcs around the root inference, allowing the user to focus on the
proof's structural content. Finally, we describe its integration into ProofTool
and explain how it interacts with the Gentzen layout.Comment: In Proceedings UITP 2014, arXiv:1410.785
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
The Tactician (extended version): A Seamless, Interactive Tactic Learner and Prover for Coq
We present Tactician, a tactic learner and prover for the Coq Proof
Assistant. Tactician helps users make tactical proof decisions while they
retain control over the general proof strategy. To this end, Tactician learns
from previously written tactic scripts and gives users either suggestions about
the next tactic to be executed or altogether takes over the burden of proof
synthesis. Tactician's goal is to provide users with a seamless, interactive,
and intuitive experience together with robust and adaptive proof automation. In
this paper, we give an overview of Tactician from the user's point of view,
regarding both day-to-day usage and issues of package dependency management
while learning in the large. Finally, we give a peek into Tactician's
implementation as a Coq plugin and machine learning platform.Comment: 19 pages, 2 figures. This is an extended version of a paper published
in CICM-2020. For the project website, see https://coq-tactician.github.i
PaMpeR: Proof Method Recommendation System for Isabelle/HOL
Deciding which sub-tool to use for a given proof state requires expertise
specific to each ITP. To mitigate this problem, we present PaMpeR, a Proof
Method Recommendation system for Isabelle/HOL. Given a proof state, PaMpeR
recommends proof methods to discharge the proof goal and provides qualitative
explanations as to why it suggests these methods. PaMpeR generates these
recommendations based on existing hand-written proof corpora, thus transferring
experienced users' expertise to new users. Our evaluation shows that PaMpeR
correctly predicts experienced users' proof methods invocation especially when
it comes to special purpose proof methods.Comment: An anonymized version of this paper has been submitted to a Computer
Science conference in April 201
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Automating the Formal Verification of Software
Formally verified correctness is one of the most desirable properties of software systems. Despite great progress made toward verification via interactive proof assistants, such as Coq and Isabelle/HOL, such verification remains one of the most effort-intensive (and often prohibitively difficult) software development activities. Recent work has created tools that automatically synthesize proofs either through reasoning using precomputed facts or using machine learning to model proofs and then perform biased search through the proof space. However, models in existing tools fail to capture the richness present in proofs, such as the information the programmer has access to when writing proofs and the natural language contained within variable names. Furthermore, these prior models do not make use of variations in the learning process and advances in large language models.
In this dissertation, I develop tools to improve proof synthesis and to enable fully automating more verification. I first present TacTok, a proof-synthesis tool that models proofs using both the partial proof written thus far and the semantics of the proof state. I then present Diva, a proof-synthesis tool that controls the learning process to produce a diverse set of models and, due to the unique nature of proof synthesis (the existence of the theorem prover, an oracle that infallibly judges a proof’s correctness), efficiently combines these models to improve the overall proving power. I then present Passport, a proof-synthesis tool that systematically explores different ways of encoding identifiers in proofs to improve synthesis. Finally, I present Baldur, a proof-synthesis tool that uses transformer-based pretrained large language models fine-tuned on proofs to generate and repair whole proofs at once, rather than one step at a time.
This dissertation contributes new ideas for improving automated proof synthesis and empirically demonstrates that the improvement is significant on large benchmarks consisting of open-source software projects
Automated Deduction – CADE 28
This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions