95 research outputs found
HOL(y)Hammer: Online ATP Service for HOL Light
HOL(y)Hammer is an online AI/ATP service for formal (computer-understandable)
mathematics encoded in the HOL Light system. The service allows its users to
upload and automatically process an arbitrary formal development (project)
based on HOL Light, and to attack arbitrary conjectures that use the concepts
defined in some of the uploaded projects. For that, the service uses several
automated reasoning systems combined with several premise selection methods
trained on all the project proofs. The projects that are readily available on
the server for such query answering include the recent versions of the
Flyspeck, Multivariate Analysis and Complex Analysis libraries. The service
runs on a 48-CPU server, currently employing in parallel for each task 7 AI/ATP
combinations and 4 decision procedures that contribute to its overall
performance. The system is also available for local installation by interested
users, who can customize it for their own proof development. An Emacs interface
allowing parallel asynchronous queries to the service is also provided. The
overall structure of the service is outlined, problems that arise and their
solutions are discussed, and an initial account of using the system is given
Machine Learning of Coq Proof Guidance: First Experiments
We report the results of the first experiments with learning proof
dependencies from the formalizations done with the Coq system. We explain the
process of obtaining the dependencies from the Coq proofs, the characterization
of formulas that is used for the learning, and the evaluation method. Various
machine learning methods are compared on a dataset of 5021 toplevel Coq proofs
coming from the CoRN repository. The best resulting method covers on average
75% of the needed proof dependencies among the first 100 predictions, which is
a comparable performance of such initial experiments on other large-theory
corpora
Syntactic-Semantic Form of Mizar Articles
Mizar Mathematical Library is most appreciated for the wealth of mathematical knowledge it contains. However, accessing this publicly available huge corpus of formalized data is not straightforward due to the complexity of the underlying Mizar language, which has been designed to resemble informal mathematical papers. For this reason, most systems exploring the library are based on an internal XML representation format used by semantic modules of Mizar. This representation is easily accessible, but it lacks certain syntactic information available only in the original human-readable Mizar source files. In this paper we propose a new XML-based format which combines both syntactic and semantic data. It is intended to facilitate various applications of the Mizar library requiring fullest possible information to be retrieved from the formalization files
The use of data-mining for the automatic formation of tactics
This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques
Dependencies in Formal Mathematics: Applications and Extraction for Coq and Mizar
Two methods for extracting detailed formal dependencies from the Coq and
Mizar system are presented and compared. The methods are used for dependency
extraction from two large mathematical repositories: the Coq Repository at
Nijmegen and the Mizar Mathematical Library. Several applications of the
detailed dependency analysis are described and proposed. Motivated by the
different applications, we discuss the various kinds of dependencies that we
are interested in,and the suitability of various dependency extraction methods
Proof in Context -- Web Editing with Rich, Modeless Contextual Feedback
The Agora system is a prototypical Wiki for formal mathematics: a web-based
system for collaborating on formal mathematics, intended to support informal
documentation of formal developments. This system requires a reusable proof
editor component, both for collaborative editing of documents, and for
embedding in the resulting documents. This paper describes the design of
Agora's asynchronous editor, that is generic enough to support different tools
working on editor content and providing contextual information, with
interactive theorem proverss being a special, but important, case described in
detail for the Coq theorem prover.Comment: In Proceedings UITP 2012, arXiv:1307.152
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