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50
Automated reasoning in higherorder logic using the TPTP THF infrastructure
 J. of Formalized Reasoning
, 2010
"... Articulate Software The Thousands of Problems for Theorem Provers (TPTP) problem library is the basis of a well known and well established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems. The extension of the TPTP from firstorder form (F ..."
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Cited by 16 (12 self)
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Articulate Software The Thousands of Problems for Theorem Provers (TPTP) problem library is the basis of a well known and well established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems. The extension of the TPTP from firstorder form (FOF) logic to typed higherorder form (THF) logic has provided a basis for new development and application of ATP systems for higherorder logic. Key developments have been the specification of the THF language, the addition of higherorder problems to the TPTP, the development of the TPTP THF infrastructure, several ATP systems for higherorder logic, and the use of higherorder ATP in a range of domains. This paper surveys these developments. 1.
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 ..."
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Cited by 8 (6 self)
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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
A constructive and formal proof of Lebesgue's Dominated Convergence Theorem in the interactive theorem prover Matita
, 2008
"... We present a formalisation of a constructive proof of Lebesgue’s Dominated Convergence Theorem given by Sacerdoti Coen and Zoli in [SZ]. The proof is done in the abstract setting of ordered uniformities, also introduced by the two authors as a simplification of Weber’s lattice uniformities given in ..."
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Cited by 7 (4 self)
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We present a formalisation of a constructive proof of Lebesgue’s Dominated Convergence Theorem given by Sacerdoti Coen and Zoli in [SZ]. The proof is done in the abstract setting of ordered uniformities, also introduced by the two authors as a simplification of Weber’s lattice uniformities given in [Web91, Web93]. The proof is fully constructive, in the sense that it is done in Bishop’s style and, under certain assumptions, it is also fully predicative. The formalisation is done in the Calculus of (Co)Inductive Constructions using the interactive theorem prover Matita [ASTZ07]. It exploits some peculiar features of Matita and an advanced technique to represent algebraic hierarchies previously introduced by the authors in [ST07]. Moreover, we introduce a new technique to cope with duality to halve the formalisation effort.
READEVALPRINT in parallel and asynchronous proofchecking
 In: User Interfaces for Theorem Provers (UITP 2012). EPTCS (2013
"... The LCF tradition of interactive theorem proving, which was started by Milner in the 1970ies, appears to be tied to the classic READEVALPRINTLOOP of sequential and synchronous evaluation of prover commands. We break up this loop and retrofit the readevalprint phases into a model of parallel an ..."
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Cited by 5 (5 self)
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The LCF tradition of interactive theorem proving, which was started by Milner in the 1970ies, appears to be tied to the classic READEVALPRINTLOOP of sequential and synchronous evaluation of prover commands. We break up this loop and retrofit the readevalprint phases into a model of parallel and asynchronous proof processing. Thus we explain some key concepts behind the implementation of the Isabelle/Scala layer for prover interaction and integration, and the Isabelle/jEdit Prover IDE as frontend technology. We hope to open up the scientific discussion about nontrivial interaction models for ITP systems again, and help getting other oldschool proofassistants on a similar track.
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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Cited by 4 (2 self)
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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.
A BIDIRECTIONAL REFINEMENT ALGORITHM FOR THE CALCULUS OF (CO)INDUCTIVE CONSTRUCTIONS
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Smart matching
"... One of the most annoying aspects in the formalization of mathematics is the need of transforming notions to match a given, existing result. This kind of transformations, often based on a conspicuous background knowledge in the given scientific domain (mostly expressed in the form of equalities or ..."
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Cited by 3 (3 self)
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One of the most annoying aspects in the formalization of mathematics is the need of transforming notions to match a given, existing result. This kind of transformations, often based on a conspicuous background knowledge in the given scientific domain (mostly expressed in the form of equalities or isomorphisms), are usually implicit in the mathematical discourse, and it would be highly desirable to obtain a similar behaviour in interactive provers. The paper describes the superpositionbased implementation of this feature inside the Matita interactive theorem prover, focusing in particular on the so called smart application tactic, supporting smart matching between a goal and a given result.
Declarative Representation of Proof Terms
"... Abstract. We present a declarative language inspired by the pseudonatural language used in Matita for the explanation of proof terms. We show how to compile the language to proof terms and how to automatically generate declarative scripts from proof terms. Then we investigate the relationship betwee ..."
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Cited by 2 (1 self)
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Abstract. We present a declarative language inspired by the pseudonatural language used in Matita for the explanation of proof terms. We show how to compile the language to proof terms and how to automatically generate declarative scripts from proof terms. Then we investigate the relationship between the two translations, identifying the amount of proof structure preserved by compilation and regeneration of declarative scripts. 1
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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Cited by 2 (0 self)
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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
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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Cited by 2 (2 self)
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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