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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 ..."
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Cited by 59 (17 self)
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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, 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.
A Generic Approach to Building User Interfaces for Theorem Provers
 JOURNAL OF SYMBOLIC COMPUTATION
, 1995
"... In this paper, we present the results of an ongoing effort in building user interfaces for proof systems. Our approach is generic: we are not constructiong a user interface for a particular proof system, rather we have developed techniques and tools... ..."
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Cited by 32 (8 self)
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In this paper, we present the results of an ongoing effort in building user interfaces for proof systems. Our approach is generic: we are not constructiong a user interface for a particular proof system, rather we have developed techniques and tools...
Taclets: A New Paradigm for Constructing Interactive Theorem Provers
 CIENCIAS EXACTAS, FÍSICAS Y NATURALES, SERIE A: MATEMÁTICAS, 98(1), 2004. SPECIAL ISSUE ON SYMBOLIC COMPUTATION IN LOGIC AND ARTIFICIAL INTELLIGENCE
, 2004
"... Frameworks for interactive theorem proving give the user explicit control over the construction of proofs based on meta languages that contain dedicated control structures for describing proof construction. Such languages are not easy to master and thus contribute to the already long list of skill ..."
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Cited by 22 (8 self)
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Frameworks for interactive theorem proving give the user explicit control over the construction of proofs based on meta languages that contain dedicated control structures for describing proof construction. Such languages are not easy to master and thus contribute to the already long list of skills required by prospective users of interactive theorem provers. Most users, however, only need a convenient formalism that allows to introduce new rules with minimal overhead. On the the other hand, rules of calculi have not only purely logical content, but contain restrictions on the expected context of rule applications and heuristic information. We suggest a new and minimalist concept for implementing interactive theorem provers called taclet. Their usage can be mastered in a matter of hours, and they are efficiently compiled into the GUI of a prover. We implemented the KeY system, an interactive theorem prover for the full JAVA CARD language based on taclets.
Interactive Theorem Proving: An Empirical Study of User Activity
 Journal of Symbolic Computation
, 1995
"... In this paper the interaction between users and the interactive theorem prover HOL is investigated from a humancomputer interaction perspective. First, we outline three possible views of interaction, and give a brief survey of some current interfaces and how they may be described in terms of the ..."
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Cited by 14 (3 self)
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In this paper the interaction between users and the interactive theorem prover HOL is investigated from a humancomputer interaction perspective. First, we outline three possible views of interaction, and give a brief survey of some current interfaces and how they may be described in terms of these views. Second, we describe and present the results of an empirical study of intermediate and expert HOL users. The results are analysed for evidence in support of the proposed view of proof activity in HOL. We believe that this approach provides a principled basis for the assessment and design of interfaces to theorem provers.
A Full Formalisation of πCalculus Theory in the Calculus of Constructions
, 1997
"... A formalisation of picalculus in the Coq system is presented. Based on a de Bruijn notation for names, our... ..."
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Cited by 14 (0 self)
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A formalisation of picalculus in the Coq system is presented. Based on a de Bruijn notation for names, our...
Assisted proof document authoring
 Mathematical Knowledge Management MKM 2005, LNAI 3863
, 2006
"... Abstract. Recently, significant advances have been made in formalised mathematical texts for large, demanding proofs. But although such large developments are possible, they still take an inordinate amount of effort and time, and there is a significant gap between the resulting formalised machinech ..."
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Abstract. Recently, significant advances have been made in formalised mathematical texts for large, demanding proofs. But although such large developments are possible, they still take an inordinate amount of effort and time, and there is a significant gap between the resulting formalised machinecheckable proof scripts and the corresponding humanreadable mathematical texts. We present an authoring system for formal proof which addresses these concerns. It is based on a central document format which, in the tradition of literate programming, allows one to extract either a formal proof script or a humanreadable document; the two may have differing structure and detail levels, but are developed together in a synchronised way. Additionally, we introduce ways to assist production of the central document, by allowing tools to contribute backflow to update and extend it. Our authoring system builds on the new PG Kit architecture for Proof General, bringing the extra advantage that it works in a uniform interface, generically across various interactive theorem provers. 1
Encoding Natural Semantics in Coq
 In Proc. AMAST, LNCS 936
, 1995
"... . We address here the problem of automatically translating the Natural Semantics of programming languages to Coq, in order to prove formally general properties of languages. Natural Semantics [18] is a formalism for specifying semantics of programming languages inspired by Plotkin's Structural ..."
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. We address here the problem of automatically translating the Natural Semantics of programming languages to Coq, in order to prove formally general properties of languages. Natural Semantics [18] is a formalism for specifying semantics of programming languages inspired by Plotkin's Structural Operational Semantics [22]. The Coq proof development system [12], based on the Calculus of Constructions extended with inductive types (CCind), provides mechanized support including tactics for building goaldirected proofs. Our representation of a language in Coq is inAEuenced by the encoding of logics used by Church [6] and in the Edinburgh Logical Framework (ELF) [15, 3]. 1 Introduction The motivation for our work is the need for an environment to help develop proofs in Natural Semantics. The interactive programming environment generator Centaur [17] allows us to compile a Natural Semantics speciøcation of a given language into executable code (typecheckers, evaluators, compilers, program t...
Interactive Theorem Proving with Schematic Theory Specific Rules
 Fakultät für Informatik, Universität Karlsruhe, 2000b. URL http://www.keyproject.org/doc/2000/stsr.ps.gz
, 2000
"... . This paper presents a framework to make interactive proving over abstract data types (rst order logic plus induction) more comfortable. A language of schematic rules is introduced, yielding the ability to write, to use, and even to verify these rules for any abstract data type and its theory. ..."
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. This paper presents a framework to make interactive proving over abstract data types (rst order logic plus induction) more comfortable. A language of schematic rules is introduced, yielding the ability to write, to use, and even to verify these rules for any abstract data type and its theory. The language allows to express the functionality of a rule easily and clearly. Nearly all potential rule applications are coupled with the occurrence of certain terms or formulas. One can prove with these rules simply by mouse clicks on these terms and formulas. The rule language is expressive enough to describe even complex induction rules. Nevertheless, the correctness of a rule can be veried within the same theory without use of explicit higher order logic or of a translation to some kind of meta level. So, in each state of a proof, new rules can be introduced, whenever required, and proven. 1 Introduction An abstract data type can have a rich signature and a complex theory. ...
Mathematics and Proof Presentation in Pcoq
 IN: PROCEEDINGS OF PROOF TRANSFORMATION AND PRESENTATION AND PROOF COMPLEXITIES (PTP’01
, 2001
"... PCOQ is the latest product in a decadelong effort to produce graphical userinterfaces for proof systems. It inherits many characteristics from the previous CTCOQ system... ..."
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Cited by 9 (1 self)
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PCOQ is the latest product in a decadelong effort to produce graphical userinterfaces for proof systems. It inherits many characteristics from the previous CTCOQ system...
Interactive theorem proving with tasks
 Electronic Notes in Theoretical Computer Science 103 (2004
, 2004
"... Interactive theorem proving systems for mathematics require user interfaces which allow for user interaction that is as natural as possible. However, this interaction is often limited by the traditional calculi underlying most theorem proving systems. This is particularly problematic with respect to ..."
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Cited by 8 (6 self)
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Interactive theorem proving systems for mathematics require user interfaces which allow for user interaction that is as natural as possible. However, this interaction is often limited by the traditional calculi underlying most theorem proving systems. This is particularly problematic with respect to the application of assertions and intuitive presentation of proof states. In this paper we show how a more flexible user interaction can be realized when traditional calculi for classical logic are replaced by a less restrictive reasoning engine, the recently developed CORE [2] system. We describe the task level which is built on top of the CORE system and combines the Proof by Pointing approach [5] with a flexible mechanism for the application of assertions that avoids decomposition and abstracts from the syntactical form of an assertion. We demonstrate how proof steps that are difficult to implement in other systems, like forward application of assertions, are quite naturally supported by the underlying CORE system and are therefore straightforward to realize at the task level.