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Knowledge Archives in Theorema: A LogicInternal Approach
"... Archives are implemented as an extension of Theorema for representing mathematical repositories in a natural way. An archive can be conceived as one large formula in a language consisting of higherorder predicate logic together with a few constructs for structuring knowledge: attaching labels to ..."
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Archives are implemented as an extension of Theorema for representing mathematical repositories in a natural way. An archive can be conceived as one large formula in a language consisting of higherorder predicate logic together with a few constructs for structuring knowledge: attaching labels to subhierarchies, disambiguating symbols by the use of namespaces, importing symbols from other namespaces and specifying the domains of categories and functors as namespaces with variable operations. All these constructs are logicinternal in the sense that they have a natural translation to higherorder logic so that certain aspects of Mathematical Knowledge Management can be realized in the object logic itself. There are a variety of operations on archives, though in this paper we can only sketch a few of them: knowledge retrieval and theory exploration, merging and splitting, insertion and translation to predicate logic.
An interactive driver for goal directed proof strategies
 In Proc. of User Interfaces for Theorem Provers
, 2008
"... Interactive Theorem Provers (ITPs) are tools meant to assist the user during the formal development of mathematics. Automatic proof searching procedures are a desirable aid, and most ITPs supply the user with an extensive set of facilities to improve automation. However, the blackbox nature of most ..."
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Interactive Theorem Provers (ITPs) are tools meant to assist the user during the formal development of mathematics. Automatic proof searching procedures are a desirable aid, and most ITPs supply the user with an extensive set of facilities to improve automation. However, the blackbox nature of most automatic procedure conflicts with the interactive nature of these tools: a newcomer running an automatic procedure learns nothing by its execution (especially in case of failure), and a trained user has no opportunities to interactively guide the procedure towards the solution, e.g. pruning wrong or not promising branches of the search tree. In this paper we discuss the implementation of the resolution based automatic procedure of the Matita ITP, explicitly conceived to be interactively driven by the user through a suitable, simple graphical interface. Keywords: Interactive theorem proving, SLD resolution, automation
Spurious Disambiguation Error Detection
"... Abstract. The disambiguation approach to the input of formulae enables the user to type correct formulae in a terse syntax close to the usual ambiguous mathematical notation. When it comes to incorrect formulae we want to present only errors related to the interpretation meant by the user, hiding er ..."
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Abstract. The disambiguation approach to the input of formulae enables the user to type correct formulae in a terse syntax close to the usual ambiguous mathematical notation. When it comes to incorrect formulae we want to present only errors related to the interpretation meant by the user, hiding errors related to other interpretations (spurious errors). We propose a heuristic to recognize spurious errors, which has been integrated with the disambiguation algorithm of [6]. 1
LayoutBased Substitution Tree Indexing and Retrieval for Mathematical Expressions
"... Thanks to my committee members for their insightful guidance and extraordinary patience. Thanks to my experiment participants for their timely assistance. And thanks to everyone who supported me throughout this remarkable journey. ..."
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Thanks to my committee members for their insightful guidance and extraordinary patience. Thanks to my experiment participants for their timely assistance. And thanks to everyone who supported me throughout this remarkable journey.
UITP 2006 Web Interfaces for Proof Assistants
"... This article describes an architecture for creating responsive web interfaces for proof assistants. The architecture combines current web development technologies with the functionality of local prover interfaces, to create an interface that is available completely within a web browser, but resemble ..."
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This article describes an architecture for creating responsive web interfaces for proof assistants. The architecture combines current web development technologies with the functionality of local prover interfaces, to create an interface that is available completely within a web browser, but resembles and behaves like a local one. Security, availability and efficiency issues of the proposed solution are described. A prototype implementation of a web interface for the Coq proof assistant [8] created according to our architecture is presented. Access to the prototype is available on
J Autom Reasoning (2007) 39:109–139 DOI 10.1007/s1081700790705 User Interaction with the Matita Proof Assistant
"... 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, characterized mostly by the organization of the library as a searchable knowledge base, the emphasis on a highquality not ..."
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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, characterized mostly 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.
Distributed Tagging and Annotation of Computer Checked Proofs
"... Users of theorem proving systems often complain about lemma management issues within their own proofs and have even more difficulty locating and reusing appropriate definitions and formalized theorems available from third parties. Both users ’ searches for and understanding of lemmas can be improve ..."
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Users of theorem proving systems often complain about lemma management issues within their own proofs and have even more difficulty locating and reusing appropriate definitions and formalized theorems available from third parties. Both users ’ searches for and understanding of lemmas can be improved by associating relevant metadata with portions of formal proofs. This paper describes an architecture based on web annotation techniques intended to lower the barriers to spurofthemoment and collaborative creation of metadata for formal proofs. The architecture allows user annotations and both userdefined and automatically generated tags to be represented in a unified and proveragnostic way. 1
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"... 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 basedas Coqon the Calculus of Inductiv ..."
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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 basedas Coqon 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 Introduction In contrast with automatic theorem provers, whose internal architecture is inmany cases well documented (see e.g. the detailed description of Vampire in [16]), it is extremely difficult to find good system descriptions for their interactivecounterpart. Traditionally, the only component of these systems that is suitably documented is the kernel, namely the part that is responsible for checking thecorrectness of proofs. Considering that:
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"... 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 basedas Coqon the Calculus of Inductiv ..."
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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 basedas Coqon 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 Introduction In contrast with automatic theorem provers, whose internal architecture is inmany cases well documented (see e.g. the detailed description of Vampire in [16]), it is extremely difficult to find good system descriptions for their interactive counterpart. Traditionally, the only component of the latter systems that is suitably documented is the kernel, namely the part that is responsible for checking thecorrectness of proofs. Considering that: 1. most systems (claim to) satisfy the so called &quot;De Bruijn criterion&quot;, that isthe principle that the correctness of the whole application should depend on