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Formal Proof
, 2008
"... There remains but one course for the recovery of a sound and healthy condition—namely, that the entire work of the understanding be commenced afresh, and the mind itself be from the very outset not left to take its own course, but guided at every step; and the business be done as if by machinery. ..."
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Cited by 27 (1 self)
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There remains but one course for the recovery of a sound and healthy condition—namely, that the entire work of the understanding be commenced afresh, and the mind itself be from the very outset not left to take its own course, but guided at every step; and the business be done as if by machinery.
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).
PRocH: Proof reconstruction for HOL Light
 Accepted for CADE
"... Abstract. PRocH3 is a proof reconstruction tool that imports in HOL Light proofs produced by ATPs on the recently developed translation of HOL Light and Flyspeck problems to ATP formats. PRocH combines several reconstruction methods in parallel, but the core improvement over previous methods is obt ..."
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Abstract. PRocH3 is a proof reconstruction tool that imports in HOL Light proofs produced by ATPs on the recently developed translation of HOL Light and Flyspeck problems to ATP formats. PRocH combines several reconstruction methods in parallel, but the core improvement over previous methods is obtained by replaying in the HOL logic the detailed inference steps recorded in the ATP (TPTP) proofs, using several internal HOL Light inference methods. These methods range from fast variable matching and more involved rewriting, to full firstorder theorem proving using the MESON tactic. The system is described and its performance is evaluated here on a large set of Flyspeck problems. 1 Introduction, Motivation
TFF1: The TPTP typed firstorder form with rank1 polymorphism
"... The TPTP World is a wellestablished infrastructure for automatic theorem provers. It defines several concrete syntaxes, notably an untyped firstorder form (FOF) and a typed firstorder form (TFF0), that have become de facto standards in the automated reasoning community. This paper introduces the ..."
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The TPTP World is a wellestablished infrastructure for automatic theorem provers. It defines several concrete syntaxes, notably an untyped firstorder form (FOF) and a typed firstorder form (TFF0), that have become de facto standards in the automated reasoning community. This paper introduces the TFF1 format, an extension of TFF0 with rank1 polymorphism. It presents its syntax, typing rules, and semantics, as well as a sound and complete translation to TFF0. The format is designed to be easy to process by existing reasoning tools that support MLstyle polymorphism. It opens the door to useful middleware, such as monomorphizers and other translation tools that encode polymorphism in FOF or TFF0. Ultimately, the hope is that TFF1 will be implemented in popular automatic theorem provers.
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.
Formal mathematics on display: A wiki for Flyspeck
 In Carette et al
"... Abstract. The Agora system is a prototype “Wiki for Formal Mathematics”, with an aim to support developing and documenting large formalizations of mathematics in a proof assistant. The functions implemented in Agora include inbrowser editing, strong AI/ATP proof advice, verification, and HTML ren ..."
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Abstract. The Agora system is a prototype “Wiki for Formal Mathematics”, with an aim to support developing and documenting large formalizations of mathematics in a proof assistant. The functions implemented in Agora include inbrowser editing, strong AI/ATP proof advice, verification, and HTML rendering. The HTML rendering contains hyperlinks and provides ondemand explanation of the proof state for each proof step. In the present paper we show the prototype Flyspeck Wiki as an instance of Agora for HOL Light formalizations. The wiki can be used for formalizations of mathematics and for writing informal wiki pages about mathematics. Such informal pages may contain islands of formal text, which is used here for providing an initial crosslinking between Hales’s informal Flyspeck book, and the formal Flyspeck development. The Agora platform intends to address distributed wikistyle collaboration on large formalization projects, in particular both the aspect of immediate editing, verification and rendering of formal code, and the aspect of gradual and mutual refactoring and correspondence of the initial informal text and its formalization. Here, we highlight these features within the Flyspeck Wiki. 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