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Matching concepts across HOL libraries [article]

Thibault Gauthier, Cezary Kaliszyk
2014 arXiv   pre-print
In this paper we investigate automatic discovery of similar concepts across libraries of proof assistants.  ...  For the basic concepts, like natural numbers, matching them between libraries is often straightforward, because of mathematical naming conventions.  ...  of the matching constants across libraries.  ... 
arXiv:1405.3906v1 fatcat:t54pk7rj4bfufcccqwul2oqe3e

Matching Concepts across HOL Libraries [chapter]

Thibault Gauthier, Cezary Kaliszyk
2014 Lecture Notes in Computer Science  
In this paper we investigate automatic discovery of similar concepts across libraries of proof assistants.  ...  For the basic concepts, like natural numbers, matching them between libraries is often straightforward, because of mathematical naming conventions.  ...  of the matching constants across libraries.  ... 
doi:10.1007/978-3-319-08434-3_20 fatcat:nzsczwmuyrd7jnoe3ty5alvv34

Sharing HOL4 and HOL Light proof knowledge [article]

Thibault Gauthier, Cezary Kaliszyk
2015 arXiv   pre-print
We evaluate the proposed knowledge-sharing methods by reproving the HOL Light and HOL4 standard libraries.  ...  New proof assistant developments often involve concepts similar to already formalized ones.  ...  Concept Matching Concept matching [6] allows the automatic discovery of concepts from one proof library or proof assistant in another.  ... 
arXiv:1509.03527v1 fatcat:pguhm3mu75bhzi625u63jyaxbi

Sharing HOL4 and HOL Light Proof Knowledge [chapter]

Thibault Gauthier, Cezary Kaliszyk
2015 Lecture Notes in Computer Science  
We evaluate the proposed knowledge-sharing methods by reproving the HOL Light and HOL4 standard libraries.  ...  New proof assistant developments often involve concepts similar to already formalized ones.  ...  Concept Matching Concept matching [6] allows the automatic discovery of concepts from one proof library or proof assistant in another.  ... 
doi:10.1007/978-3-662-48899-7_26 fatcat:tdutfexmfzfdbjxla4mx4yvu7q

JEFL: Joint Embedding of Formal Proof Libraries [article]

Qingxiang Wang, Cezary Kaliszyk
2021 arXiv   pre-print
In this paper, we compare a previously proposed algorithm for matching concepts across libraries with our unsupervised embedding approach that can help us retrieve similar concepts.  ...  The heterogeneous nature of the logical foundations used in different interactive proof assistant libraries has rendered discovery of similar mathematical concepts among them difficult.  ...  The alignments between the concepts across multiple proof libraries or within one library have been useful for tasks including conjecturing [7] , browsing multiple libraries simultaneously [25] , and  ... 
arXiv:2107.10188v1 fatcat:wknmuawpkvdqvopkf5zb3akc4y

Mechanised Separation Algebra [chapter]

Gerwin Klein, Rafal Kolanski, Andrew Boyton
2012 Lecture Notes in Computer Science  
We present an Isabelle/HOL library with a generic type class implementation of separation algebra, develop basic separation logic concepts on top of it, and implement generic automated tactic support that  ...  can be used directly for any instantiation of the library.  ...  In Sec 2 we show the main interface of the separation algebra class in Isabelle/HOL, describe how it differs from Calcagno et al, and which concepts and properties we developed on top.  ... 
doi:10.1007/978-3-642-32347-8_22 fatcat:owtfhgdagngo7f4zwie65p3l2i

Classification of Alignments Between Concepts of Formal Mathematical Systems [chapter]

Dennis Müller, Thibault Gauthier, Cezary Kaliszyk, Michael Kohlhase, Florian Rabe
2017 Lecture Notes in Computer Science  
., integrating theorem provers or reusing services across systems. Notably, even imperfect alignments, i.e. concepts that are very similar rather than identical, can often play very important roles.  ...  We speak of alignment if the same concept occurs in different libraries, possibly with slightly different names, notations, or formal definitions.  ...  Every symbol is assigned a unique way to access it across corpora and across logics.  ... 
doi:10.1007/978-3-319-62075-6_7 fatcat:25nchzaurjbarpg4rkav4xdztu

Meta-Logical Frameworks and Formal Digital Libraries [chapter]

Carsten Schürmann
2008 Lecture Notes in Computer Science  
Thus, I have become very interested on how to share mathematical knowledge and proofs across logic specific boundaries.  ...  The most noteworthy feature of Delphin's dependent type constructors is that binding occurrences of variables are determined by pattern matching, such as A and B .  ... 
doi:10.1007/978-3-540-69149-5_51 fatcat:23jhr6jginasfbdz7fsox4jfim

Making Isabelle Content Accessible in Knowledge Representation Formats [article]

Michael Kohlhase, Florian Rabe, Makarius Wenzel
2020 arXiv   pre-print
The libraries of proof assistants like Isabelle, Coq, HOL are notoriously difficult to interpret by external tools: de facto, only the prover itself can parse and process them adequately.  ...  Concretely we present an integration of PIDE and MMT that allows exporting all Isabelle libraries in OMDoc format.  ...  Alignments [KKMR16] have been used to match pragmatically corresponding concepts defined in different libraries [GK14] .  ... 
arXiv:2005.08884v1 fatcat:tnzdgnb22zedvod3odyj6avqye

Semantic Parsing of Mathematics by Context-based Learning from Aligned Corpora and Theorem Proving [article]

Cezary Kaliszyk, Josef Urban, Jiří Vyskočil
2016 arXiv   pre-print
However, * is almost always associative across all types and interpretations.  ...  We call the latter situation other library theorem (OLT).  ... 
arXiv:1611.09703v1 fatcat:yt5ndgmv4fe5jltqauadt55cbu

The Isabelle Collections Framework [chapter]

Peter Lammich, Andreas Lochbihler
2010 Lecture Notes in Computer Science  
In a case study with tree automata, we demonstrate that the ICF is easy to use and efficient: An ICF based, verified tree automata library outperforms the unverified Timbuk/Taml library by a factor of  ...  The Isabelle Collections Framework (ICF) provides a unified framework for using verified collection data structures in Isabelle/HOL formalizations and generating efficient functional code in ML, Haskell  ...  Red-black trees are taken from the Isabelle/HOL standard library and extended with the iterator concept.  ... 
doi:10.1007/978-3-642-14052-5_24 fatcat:gd22qdlcfbgxfpbuvuijq5h3za

An Isabelle Proof Method Language [chapter]

Daniel Matichuk, Makarius Wenzel, Toby Murray
2014 Lecture Notes in Computer Science  
Isabelle/HOL is a rich library of logical theories and tools on top of Isabelle/Pure.  ...  Matching performs proof search through implicit backtracking across matches, attempting multiple unifications and falling through to other patterns upon failure.  ... 
doi:10.1007/978-3-319-08970-6_25 fatcat:j32ukqtr35di5emlzbcpqlwta4

Experiences from Exporting Major Proof Assistant Libraries [article]

Michael Kohlhase, Florian Rabe
2020 arXiv   pre-print
As a preparatory step, in previous work, we translated the libraries of multiple proof assistants, specifically the ones of Coq, HOL Light, IMPS, Isabelle, Mizar, and PVS into a universal format: OMDoc  ...  The interoperability of proof assistants and the integration of their libraries is a highly valued but elusive goal in the field of theorem proving.  ...  libraries, e.g., to automatically match up Coq records with corresponding Isabelle locales.  ... 
arXiv:2005.03089v1 fatcat:h2dzkdjpprd75eqzk3fausgthq

Making Isabelle Content Accessible in Knowledge Representation Formats

Michael Kohlhase, Florian Rabe, Makarius Wenzel, Assia Mahboubi, Marc Bezem
2020 Types for Proofs and Programs  
The libraries of proof assistants like Isabelle, Coq, HOL are notoriously difficult to interpret by external tools: de facto, only the prover itself can parse and process them adequately.  ...  Concretely we present an integration of PIDE and Mmt that allows exporting all Isabelle libraries in OMDoc format.  ...  HOL-type definitions, inductive types. As discussed in Section 4.2, this is supported by Mmt and would allow a structurally more similar and thus more understandable export.  ... 
doi:10.4230/lipics.types.2019.1 dblp:conf/types/KohlhaseRW19 fatcat:l35sk5hohjahdd54ylxkecxylm

Isabelle Import Infrastructure for the Mizar Mathematical Library [chapter]

Cezary Kaliszyk, Karol Pąk
2018 Lecture Notes in Computer Science  
We present an infrastructure that allows importing an initial part of the Mizar Mathematical Library into the Isabelle/Mizar object logic.  ...  Isabelle already includes a package that allows importing proofs originating from HOL Light and HOL4 [22, 14] as well as one for importing the OpenTheory library articles [11] .  ...  The reason for this in Mizar, is that the concept cannot be used in the definition block.  ... 
doi:10.1007/978-3-319-96812-4_13 fatcat:puwm4uo5xjfxvniy5qn6t2ltou
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