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2010): Asynchronous Proof Processing with Isabelle/Scala and Isabelle/jEdit
 In: 9th International Workshop On User Interfaces for Theorem Provers (UITP 2010), Electronic Notes in Theoretical Computer Science, Elsevier. Available at http://www4.in.tum.de/~wenzelm/papers/ asyncisabellescala.pdf
"... After several decades, most proof assistants are still centered around TTYbased interaction in a tight readevalprint loop. Even wellknown Emacs modes for such provers follow this synchronous model based on single commands with immediate response, meaning that the editor waits for the prover afte ..."
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After several decades, most proof assistants are still centered around TTYbased interaction in a tight readevalprint loop. Even wellknown Emacs modes for such provers follow this synchronous model based on single commands with immediate response, meaning that the editor waits for the prover after each command. There have been some attempts to reimplement prover interfaces in big IDE frameworks, while keeping the old interaction model. Can we do better than that? Ten years ago, the Isabelle/Isar proof language already emphasized the idea of proof document (structured text) instead of proof script (sequence of commands), although the implementation was still emulating TTY interaction in order to be able to work with the then emerging Proof General interface. After some recent reworking of Isabelle internals, to support parallel processing of theories and proofs, the original idea of structured document processing has surfaced again. Isabelle versions from 2009 or later already provide some support for interactive proof documents with asynchronous checking, which awaits to be connected to a suitable editor framework or fullscale IDE. The remaining problem is how to do that systematically, without having to specify and implement complex protocols for prover interaction.
A web interface for matita
 In Proceedings of Intelligent Computer Mathematics (CICM 2012
"... This article describes a prototype implementation of a web interface for the Matita proof assistant [2]. The motivations behind our work are similar to those of several recent, related efforts [7, 9, 1, 8] (see also [6]). In particular: 1. creation of a web collaborative working environment for inte ..."
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This article describes a prototype implementation of a web interface for the Matita proof assistant [2]. The motivations behind our work are similar to those of several recent, related efforts [7, 9, 1, 8] (see also [6]). In particular: 1. creation of a web collaborative working environment for interactive theorem proving, aimed at fostering knowledgeintensive cooperation, content creation and management; 2. exploitation of the markup in order to enrich the document with several kinds of annotations or active elements; annotations may have both a presentational/hypertextual nature, aimed to improve the quality of the proof script as a human readable document, or a more semantic nature, aimed to help the system in its processing (or reprocessing) of the script; 3. platform independence with respect to operating systems, and wider accessibility also for users using devices with limited resources; 4. overcoming the installation issues typical of interactive provers, also in view of attracting a wider audience, especially in the mathematical community.
HOL(y)Hammer: Online ATP service for HOL Light
 CoRR
"... Abstract. HOL(y)Hammer is an online AI/ATP service for formal (computerunderstandable) mathematics encoded in the HOL Light system. The service allows its users to upload and automatically process an arbitrary formal development (project) based on HOL Light, and to attack arbitrary conjectures tha ..."
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Abstract. HOL(y)Hammer is an online AI/ATP service for formal (computerunderstandable) mathematics encoded in the HOL Light system. The service allows its users to upload and automatically process an arbitrary formal development (project) based on HOL Light, and to attack arbitrary conjectures that use the concepts defined in some of the uploaded projects. For that, the service uses several automated reasoning systems combined with several premise selection methods trained on all the project proofs. The projects that are readily available on the server for such query answering include the recent versions of the Flyspeck, Multivariate Analysis and Complex Analysis libraries. The service runs on a 48CPU server, currently employing in parallel for each task 7 AI/ATP combinations and 4 decision procedures that contribute to its overall performance. The system is also available for local installation by interested users, who can customize it for their own proof development. An Emacs interface allowing parallel asynchronous queries to the service is also provided. The overall structure of the service is outlined, problems that arise and their solutions are discussed, and an initial account of using the system is given. 1.
Proof Assistants: history, ideas and future
"... In this paper we will discuss the fundamental ideas behind proof assistants: What are they and what is a proof anyway? We give a short history of the main ideas, emphasizing the way they ensure the correctness of the mathematics formalized. We will also briefly discuss the places where proof assista ..."
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In this paper we will discuss the fundamental ideas behind proof assistants: What are they and what is a proof anyway? We give a short history of the main ideas, emphasizing the way they ensure the correctness of the mathematics formalized. We will also briefly discuss the places where proof assistants are used and how we envision their extended use in the future. While being an introduction into the world of proof assistants and the main issues behind them, this paper is also a position paper that pushes the further use of proof assistants. We believe that these systems will become the future of mathematics, where definitions, statements, computations and proofs are all available in a computerized form. An important application is and will be in computer supported modelling and verification of systems. But their is still along road ahead and we will indicate what we believe is needed for the further proliferation of proof assistants.
Teaching logic using a stateoftheart proof assistant
, 2007
"... This article describes the system ProofWeb that is currently being developed in Nijmegen and Amsterdam for teaching logic to undergraduate computer science students. This system is based on the higher order proof assistant Coq, and is made available to the students through an interactive web interfa ..."
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This article describes the system ProofWeb that is currently being developed in Nijmegen and Amsterdam for teaching logic to undergraduate computer science students. This system is based on the higher order proof assistant Coq, and is made available to the students through an interactive web interface. Part of this system will be a large database of logic problems. This database will also hold the solutions of the students. This means that the students do not need to install anything to be able to use the system (not even a browser plugin), and that the teachers will be able to centrally track progress of the students. The system makes the full power of Coq available to the students, but simultaneously presents the logic problems in a way that is customary in undergraduate logic courses. Both styles of presenting natural deduction proofs (Gentzen style ‘tree view ’ and Fitch style ‘box view’) are supported. Part of the system is a parser that indicates whether the students used the automation of Coq to solve their problems or that they solved it themselves using only the inference rules of the logic. For these inference rules dedicated tactics for Coq have been developed. The system has already been used in a type theory course, and is currently being further developed in the first year logic course of computer science in Nijmegen.
Accessible Integrated Formal Reasoning Environments in Classroom Instruction of Mathematics
"... Computer science researchers in the programming languages and formal verification communities, among others, have produced a variety of automated assistance and verification tools and techniques for formal reasoning: parsers, evaluators, proofauthoring systems, software verification systems, intera ..."
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Computer science researchers in the programming languages and formal verification communities, among others, have produced a variety of automated assistance and verification tools and techniques for formal reasoning: parsers, evaluators, proofauthoring systems, software verification systems, interactive theorem provers, modelcheckers, static analysis methods, and so on. While there have been notable successes in utilizing
Towards an infrastructure for integrated accessible formal reasoning environments
 In Proc. UITP 2012
"... Computer science researchers in the programming languages and formal verification communities have produced a variety of automated tools and techniques for assisting formal reasoning tasks. However, while there exist notable successes in utilizing these tools to develop safe and secure software and ..."
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Computer science researchers in the programming languages and formal verification communities have produced a variety of automated tools and techniques for assisting formal reasoning tasks. However, while there exist notable successes in utilizing these tools to develop safe and secure software and hardware, both leadingedge advances and basic techniques (such as model checking, state space search, type checking, logical inference and verification, computation of congruence closures, noninterference enforcement, and so on) remain underutilized by large populations of endusers that may benefit from them when they engage in formal reasoning tasks within their own application domains. This may be in part because (1) these tools and techniques are not readily accessible to endusers who are not experts in formal systems or are simply not aware of what is available and how it can be utilized, and (2) these tools and techniques are only valuable when used in conjunction with one another and with appropriate domainspecific libraries and databases. Motivated by these circumstances, we present our ongoing efforts, built on earlier work in developing userfriendly formal verification tools, to develop an infrastructure for assembling userfriendly, interactive, integrated formal reasoning environments that can assist users engaged in routine domainspecific formal reasoning tasks. This infrastructure encompasses a programming language, compilers, and other tools for building up from components, instantiating with domainspecific formal content, and finally delivering such environments in the form of readytouse webbased applications that can run entirely within a standard web browser. We describe current efforts to use such instantiated environments in two application domains: classroom instruction of linear algebra and verifying the correctness of protocols. 1
Web Based GUI for Natural Deduction Proofs In Isabelle
, 2007
"... It is fair to say that the use of interactive theorem provers is mostly limited to experts in the field. This project attributed this mainly to the high barrier of entry associated with using interactive theorem provers, and that most current systems do not aid the user in visualizing proofs. A web ..."
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It is fair to say that the use of interactive theorem provers is mostly limited to experts in the field. This project attributed this mainly to the high barrier of entry associated with using interactive theorem provers, and that most current systems do not aid the user in visualizing proofs. A webbased client/server system with a graphical user interface was designed and implemented that users could use to perform pointandclick natural deduction theorem proving. The system did not require client users to install software in order to perform proofs, as the system was accessible through the use of a web browser. Proofs were visualized in boxstyle notation, and proof construction done by performing pointandclick actions on this. The sound and widely used interactive theorem prover Isabelle was used for verifying the proofs created. The system was deemed as successful, based on the analysis of a user test perfomed.
Noname manuscript No. (will be inserted by the editor) LearningAssisted Automated Reasoning with Flyspeck
"... the date of receipt and acceptance should be inserted later Abstract The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machinelearning premise selection methods trained on the Flyspeck proofs, producing an AI syste ..."
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the date of receipt and acceptance should be inserted later Abstract The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machinelearning premise selection methods trained on the Flyspeck proofs, producing an AI system capable of proving a wide range of mathematical conjectures automatically. The performance of this architecture is evaluated in a bootstrapping scenario emulating the development of Flyspeck from axioms to the last theorem, each time using only the previous theorems and proofs. It is shown that 39 % of the 14185 theorems could be proved in a pushbutton mode (without any highlevel advice and user interaction) in 30 seconds of real time on a fourteenCPU workstation. The necessary work involves: (i) an implementation of sound translations of the HOL Light logic to ATP formalisms: untyped firstorder, polymorphic typed firstorder, and typed higherorder, (ii) export of the dependency information from HOL Light and ATP proofs for the machine learners, and (iii) choice of suitable representations and methods for learning from previous proofs, and their integration as advisors with HOL Light. This work is described and discussed here, and an initial analysis of the body of proofs that were found fully automatically is provided.