Results 1  10
of
25
User Interaction with the Matita Proof Assistant
 Journal of Automated Reasoning, Special
, 2006
"... Abstract. Matita is a new, documentcentric, tacticbased interactive theorem prover. This paper focuses on some of the distinctive features of the user interaction with Matita, mostly characterized by the organization of the library as a searchable knowledge base, the emphasis on a highquality not ..."
Abstract

Cited by 63 (17 self)
 Add to MetaCart
(Show Context)
Abstract. Matita is a new, documentcentric, tacticbased interactive theorem prover. This paper focuses on some of the distinctive features of the user interaction with Matita, mostly characterized by the organization of the library as a searchable knowledge base, the emphasis on a highquality notational rendering, and the complex interplay between syntax, presentation, and semantics.
Recognition and Retrieval of Mathematical Expressions
 INTERNATIONAL JOURNAL ON DOCUMENT ANALYSIS AND RECOGNITION
"... Document recognition and retrieval technologies complement one another, providing improved access to increasingly large document collections. While recognition and retrieval of textual information is fairly mature, with widespread availability of Optical Character Recognition (OCR) and textbased ..."
Abstract

Cited by 31 (10 self)
 Add to MetaCart
Document recognition and retrieval technologies complement one another, providing improved access to increasingly large document collections. While recognition and retrieval of textual information is fairly mature, with widespread availability of Optical Character Recognition (OCR) and textbased search engines, recognition and retrieval of graphics such as images, figures, tables, diagrams, and mathematical expressions are in comparatively early stages of research. This paper surveys the state of the art in recognition and retrieval of mathematical expressions, organized around four key problems in math retrieval (query construction, normalization, indexing, and relevance feedback), and four key problems in math recognition (detecting expressions, detecting and classifying symbols, analyzing symbol layout, and constructing a representation of meaning). Of special interest is the machine learning problem of jointly optimizing the component algorithms in a math recognition system, and developing effective indexing, retrieval and relevance feedback algorithms for math retrieval. Another important open problem is developing user interfaces that seamlessly integrate recognition and retrieval. Activity in these important research areas is increasing, in part because math notation provides an excellent domain for studying problems common to many document and graphics recognition and retrieval applications, and also because mature applications will likely provide substantial benefits for education, research, and mathematical literacy.
The Matita Interactive Theorem Prover
"... Abstract. Matita is an interactive theorem prover being developed by the Helm team at the University of Bologna. Its stable version 0.5.x may be downloaded at ..."
Abstract

Cited by 21 (9 self)
 Add to MetaCart
(Show Context)
Abstract. Matita is an interactive theorem prover being developed by the Helm team at the University of Bologna. Its stable version 0.5.x may be downloaded at
E.: Methods to Access and Retrieve Mathematical Content in ACTIVEMATH
 ICMS 2006. LNCS
, 2006
"... Abstract. This article describes how mathematical content items and formulæ are processed, retrieved, and accessed in ActiveMath. Central to the retrieval and access is a search tool which allows for searching text, attributes, relations and formulæ, and presenting items. The search tool has been ev ..."
Abstract

Cited by 14 (3 self)
 Add to MetaCart
Abstract. This article describes how mathematical content items and formulæ are processed, retrieved, and accessed in ActiveMath. Central to the retrieval and access is a search tool which allows for searching text, attributes, relations and formulæ, and presenting items. The search tool has been evaluated according to the standard measures of precision and recall as well as for usability. We report results of these evaluations. 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 ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
(Show Context)
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.
Crafting a Proof Assistant
"... Abstract. Proof assistants are complex applications whose development has never been properly systematized or documented. This work is a contribution in this direction, based on our experience with the development of Matita: a new interactive theorem prover based—as Coq—on the Calculus of Inductive ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
(Show Context)
Abstract. Proof assistants are complex applications whose development has never been properly systematized or documented. This work is a contribution in this direction, based on our experience with the development of Matita: a new interactive theorem prover based—as Coq—on the Calculus of Inductive Constructions (CIC). In particular, we analyze its architecture focusing on the dependencies of its components, how they implement the main functionalities, and their degree of reusability. The work is a first attempt to provide a ground for a more direct comparison between different systems and to highlight the common functionalities, not only in view of reusability but also to encourage a more systematic comparison of different softwares and architectural solutions. 1
Spurious disambiguation errors and how to get rid of them
 Journal of mathematics in computer science
, 2008
"... Abstract. The disambiguation approach to the input of formulae enables users of mathematical assistants to type correct formulae in a terse syntax close to the usual ambiguous mathematical notation. When it comes to incorrect formulae however, far too many typing errors are generated; among them we ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
(Show Context)
Abstract. The disambiguation approach to the input of formulae enables users of mathematical assistants to type correct formulae in a terse syntax close to the usual ambiguous mathematical notation. When it comes to incorrect formulae however, far too many typing errors are generated; among them we want to present only errors related to the formula interpretation meant by the user, hiding errors related to other interpretations. We study disambiguation errors and how to classify them into the spurious and genuine error classes. To this end we give a general presentation of the classes of disambiguation algorithms and efficient disambiguation algorithms. We also quantitatively assess the quality of the presented error classification criteria benchmarking them in the setting of a formal development of constructive algebra.
Extending full text search engine for mathematical content
 Towards Digital Mathematics Library. Birmingham, United Kingdom, July
, 2008
"... Abstract. The WWW became the main resource of mathematical knowledge. Currently available full text search engines can be used on these documents but they are deficient in almost all cases. By applying axioms, equal transformations, and by using different notation each formula can be expressed in ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
Abstract. The WWW became the main resource of mathematical knowledge. Currently available full text search engines can be used on these documents but they are deficient in almost all cases. By applying axioms, equal transformations, and by using different notation each formula can be expressed in numerous ways. Most of these documents do not contain semantic information; therefore, precise mathematical interpretation is impossible. On the other hand, semantic information can help to give more precise information. In this work we address these issues and present a new technique how to search for mathematical formulae in realworld mathematical documents, but still offering an extensible level of mathematical awareness. It exploits the advantages of full text search engine and stores each formula not only once but in several generalised representations. Because it is designed as an extension, any full text search engine can adopt it. Based on the proposed theory we developed EgoMath—new mathematical search engine. Experiments with EgoMath over two document sets, containing semantic information, showed that this technique can be used to build a fullyfledged mathematical search engine. Key words: mathematical discourse, language processing, mathematical searching, full text search engine, indexing 1
Recycling Proof Patterns in Coq: Case Studies
 Journal Mathematics in Computer Science, accepted
, 2014
"... Abstract. Development of Interactive Theorem Provers has led to the creation of big libraries and varied infrastructures for formal proofs. However, despite (or perhaps due to) their sophistication, the reuse of libraries by nonexperts or across domains is a challenge. In this paper, we provide de ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
Abstract. Development of Interactive Theorem Provers has led to the creation of big libraries and varied infrastructures for formal proofs. However, despite (or perhaps due to) their sophistication, the reuse of libraries by nonexperts or across domains is a challenge. In this paper, we provide detailed case studies and evaluate the machinelearning tool ML4PG built to interactively datamine the electronic libraries of proofs, and to provide user guidance on the basis of proof patterns found in the existing libraries.