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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.
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.
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.
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
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
UITP 2010 Narrating Formal Proof (Work in Progress)
"... Building on existing work in proxying interaction with proof assistants, we have previously developed a proof movie. We have now considered the problem of how to augment this movie data structure to support commentary on formal proof development. In this setting, we have studied extracting commentar ..."
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Building on existing work in proxying interaction with proof assistants, we have previously developed a proof movie. We have now considered the problem of how to augment this movie data structure to support commentary on formal proof development. In this setting, we have studied extracting commentary from an online text by Pierce et al. [11]. Keywords: Coursebooks, Proof Assistants, Proof Communication
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.
Ideas for a MathWiki Editor
"... We present some functional and nonfunctional requirements and wishes for a webbased editor for formalized mathematics, in particular for use in the MathWiki project at RU Nijmegen [13]. We discuss possible implementation alternatives, and argue for a holistic design of the entire wiki with editor ..."
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We present some functional and nonfunctional requirements and wishes for a webbased editor for formalized mathematics, in particular for use in the MathWiki project at RU Nijmegen [13]. We discuss possible implementation alternatives, and argue for a holistic design of the entire wiki with editor features in mind. 1