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Premise Selection for Mathematics by Corpus Analysis and Kernel Methods
"... Smart premise selection is essential when using automated reasoning as a tool for largetheory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learningbased premise ..."
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Cited by 27 (20 self)
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Smart premise selection is essential when using automated reasoning as a tool for largetheory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learningbased premise selection in two ways. First, a newly available minimal dependency analysis of existing highlevel formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing precise data for ATPbased reverification and for training premise selection algorithms. Second, a new machine learning algorithm for premise selection based on kernel methods is proposed and implemented. To evaluate the impact of both techniques, a benchmark consisting of 2078 largetheory mathematical problems is constructed, extending the older MPTP Challenge benchmark. The combined effect of the techniques results in a 50% improvement on the benchmark over the Vampire/SInE stateoftheart system for automated reasoning in large theories.
MaSh: Machine learning for Sledgehammer
 In Sandrine Blazy, Christine PaulinMohring, and David Pichardie, editors, ITP, volume 7998 of Lecture Notes in Computer Science
, 2013
"... Abstract. Sledgehammer integrates automatic theorem provers in the proof assistant Isabelle/HOL. A key component, the relevance filter, heuristically ranks the thousands of facts available and selects a subset, based on syntactic similarity to the current goal. We introduce MaSh, an alternative tha ..."
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Abstract. Sledgehammer integrates automatic theorem provers in the proof assistant Isabelle/HOL. A key component, the relevance filter, heuristically ranks the thousands of facts available and selects a subset, based on syntactic similarity to the current goal. We introduce MaSh, an alternative that learns from successful proofs. New challenges arose from our "zeroclick" vision: MaSh should integrate seamlessly with the users' workflow, so that they benefit from machine learning without having to install software, set up servers, or guide the learning. The underlying machinery draws on recent research in the context of Mizar and HOL Light, with a number of enhancements. MaSh outperforms the old relevance filter on large formalizations, and a particularly strong filter is obtained by combining the two filters.
Stronger Automation for Flyspeck by Feature Weighting and Strategy Evolution
"... Two complementary AI methods are used to improve the strength of the AI/ATP service for proving conjectures over the HOL Light and Flyspeck corpora. First, several schemes for frequencybased feature weighting are explored in combination with distanceweighted knearestneighbor classifier. This resu ..."
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Cited by 18 (16 self)
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Two complementary AI methods are used to improve the strength of the AI/ATP service for proving conjectures over the HOL Light and Flyspeck corpora. First, several schemes for frequencybased feature weighting are explored in combination with distanceweighted knearestneighbor classifier. This results in 16 % improvement (39.0 % to 45.5% Flyspeck problems solved) of the overall strength of the service when using 14 CPUs and 30 seconds. The best premiseselection/ATP combination is improved from 24.2 % to 31.4%, i.e. by 30%. A smaller improvement is obtained by evolving targetted E prover strategies on two particular premise selections, using the Blind Strategymaker (BliStr) system. This raises the performance of the best AI/ATP method from 31.4 % to 34.9%, i.e. by 11%, and raises the current 14CPU power of the service to 46.9%. 1
MizAR 40 for Mizar 40
, 2014
"... As a present to Mizar on its 40th anniversary, we develop an AI/ATP system that in 30 seconds of real time on a 14CPU machine automatically proves 40 % of the theorems in the latest official version of the Mizar Mathematical Library (MML). This is a considerable improvement over previous performa ..."
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Cited by 18 (14 self)
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As a present to Mizar on its 40th anniversary, we develop an AI/ATP system that in 30 seconds of real time on a 14CPU machine automatically proves 40 % of the theorems in the latest official version of the Mizar Mathematical Library (MML). This is a considerable improvement over previous performance of largetheory AI/ATP methods measured on the whole MML. To achieve that, a large suite of AI/ATP methods is employed and further developed. We implement the most useful methods efficiently, to scale them to the 150000 formulas in MML. This reduces the training times over the corpus to 1–3 seconds, allowing a simple practical deployment of the methods in the online automated reasoning service for the Mizar users (MizAR).
HOL(y)Hammer: Online ATP service for HOL Light
 CoRR
"... Abstract. HOL(y)Hammer is an online AI/ATP service for formal (computerunderstandable) 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 tha ..."
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Cited by 8 (7 self)
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Abstract. HOL(y)Hammer is an online AI/ATP service for formal (computerunderstandable) 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 48CPU 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. 1.
Automated reasoning service for HOL Light
 of Lecture Notes in Computer Science
, 2013
"... Abstract. HOL(y)Hammer is an AI/ATP service for formal (computerunderstandable) mathematics encoded in the HOL Light system, in particular for the users of the large Flyspeck library. The service uses several automated reasoning systems combined with several premise selection methods trained on pr ..."
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Cited by 6 (4 self)
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Abstract. HOL(y)Hammer is an AI/ATP service for formal (computerunderstandable) mathematics encoded in the HOL Light system, in particular for the users of the large Flyspeck library. The service uses several automated reasoning systems combined with several premise selection methods trained on previous Flyspeck proofs, to attack a new conjecture that uses the concepts defined in the Flyspeck library. The public online incarnation of the service runs on a 48CPU server, currently employing in parallel for each task 25 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 are discussed, and an initial account of using the system is given. 1
Learningassisted theorem proving with millions of lemmas
, 2014
"... Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and reused in later proofs by formal mathema ..."
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Cited by 5 (3 self)
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Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and reused in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be reused in later proofs. We show that in combination with learningbased relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical li
Developing Corpusbased Translation Methods between Informal and Formal Mathematics: Project Description
"... Abstract. The goal of this project4 is to (i) accumulate annotated informal/formal mathematical corpora suitable for training semiautomated translation between informal and formal mathematics by statistical machinetranslation methods, (ii) to develop such methods oriented at the formalization ta ..."
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Abstract. The goal of this project4 is to (i) accumulate annotated informal/formal mathematical corpora suitable for training semiautomated translation between informal and formal mathematics by statistical machinetranslation methods, (ii) to develop such methods oriented at the formalization task, and in particular (iii) to combine such methods with learningassisted automated reasoning that will serve as a strong semantic component. We describe these ideas, the initial set of corpora, and some initial experiments done over them. 1
Hammering towards QED
"... This paper surveys the emerging methods to automate reasoning over large libraries developed with formal proof assistants. We call these methods hammers. They give the authors of formal proofs a strong “onestroke ” tool for discharging difficult lemmas without the need for careful and detailed manu ..."
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Cited by 3 (3 self)
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This paper surveys the emerging methods to automate reasoning over large libraries developed with formal proof assistants. We call these methods hammers. They give the authors of formal proofs a strong “onestroke ” tool for discharging difficult lemmas without the need for careful and detailed manual programming of proof search. The main ingredients underlying this approach are efficient automatic theorem provers that can cope with hundreds of axioms, suitable translations of the proof assistant’s logic to the logic of the automatic provers, heuristic and learning methods that select relevant facts from large libraries, and methods that reconstruct the automatically found proofs inside the proof assistants. We outline the history of these methods, explain the main issues and techniques, and show their strength on several large benchmarks. We also discuss the relation of this technology to the QED Manifesto and consider its implications for QEDlike efforts.