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The Lattice of Topological Domains: An Example of Mizar Development
"... We present the complete development of the theory of topological domains (regular sets) in the Mizar formalism. It enveloped the latticetheoretic foundations of the theory of domains that was given in [23] and in [12]. The aim is to present the main result in [11] concerning certain characteriza ..."
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of all useful notions and the all theorems which are necessary to the explanations. The development presented here uses extracts of articles in the Main Mizar Library (MML), which have been fully checked by the PC Mizar System (Version 3.37). Therefore, we formulate only all definitions and all
Some Features of the Mizar Language
 ESPRIT Workshop
, 1993
"... Preface. It is impossible, in a short article, to present completely the Mizar language. I have chosen some topics that seem to be interesting or give some insight into our work. I devoted a large part of this presentation to the technical problems related to the lexical analysis (tokenization), ide ..."
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Cited by 8 (0 self)
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) is a small scientic society (about 40 members, 4 circles, three in Poland, one in Japan) based in Poland and called usually in English { the Mizar Society. The main activity of SUM is the collection of Mizar articles. The Library Committee
Mizar as a tool for teaching mathematics
 in Proc. of Mizar 30 workshop, Bia̷lowie˙za
, 2004
"... Abstract. The Mizar system is a proof–assistant based on classical logic. A substantial body of Mizar texts (the Mizar Mathematical Library) has been developed in various areas of mathematics. It has been quite natural to expect using Mizar as a tool for teaching mathematics; the experience in this ..."
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Abstract. The Mizar system is a proof–assistant based on classical logic. A substantial body of Mizar texts (the Mizar Mathematical Library) has been developed in various areas of mathematics. It has been quite natural to expect using Mizar as a tool for teaching mathematics; the experience
MIZAR Verification of Generic Algebraic Algorithms
, 1997
"... Although generic programming founds more and more attention  nowadays generic programming languages as well as generic libraries exist  there are hardly approaches for the verification of generic algorithms or generic libraries. This thesis deals with generic algorithms in the field of computer ..."
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algebra. We propose the Mizar system as a theorem prover capable of verifying generic algorithms on an appropriate abstract level. The main advantage of the Mizar theorem prover is its special input language that enables textbook style presentation of proofs. For generic versions of Brown/Henrici addition
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
Mizar: An impression
, 1999
"... This note presents an introduction to the Mizar system, followed by a brief comparison between Mizar and Coq. Appended are a Mizar grammar and an annotated example of a complete Mizar article. 1 What It Is Mizar is a system for representing mathematical proof in a computer such that a program can ch ..."
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Cited by 11 (5 self)
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surprisingly well is to study the Mizar syntax (see appendix B on page 16 for a context free grammar) and for specific constructions to search the Mizar library for examples. 2
Dynamics of mitochondrial DNA evolution in animals: amplification and sequencing with conserved primers.
 Proc. Natl. Acad. Sci. USA
, 1989
"... ABSTRACT With a standard set of primers directed toward conserved regions, we have used the polymerase chain reaction to amplify homologous segments of mtDNA from more than 100 animal species, including mammals, birds, amphibians, fishes, and some invertebrates. Amplification and direct sequencing ..."
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Cited by 310 (3 self)
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7). Although the indirect assessment of sequence variation obtained with the restriction endonuclease method is known to have many drawbacks, § sequence data have been difficult to obtain. The construction and screening of clone libraries has been too tedious and have demanded too much expertise for routine
Automated reasoning and presentation support for formalizing mathematics in Mizar
 In Autexier et al
"... Abstract. This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for firstorder automated reasoning. The main di ..."
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Cited by 15 (10 self)
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Abstract. This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for firstorder automated reasoning. The main
Functional Data Structures
, 1996
"... this paper. Note that the cons operation supplied by this library is strict, not lazy. In fact, the only lazy operations in this library are ++ (infix append) and reverse. 2 FIFO Queues Stacks and queues are usually the first two data structures studied by beginning computer science students. The ty ..."
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Cited by 283 (4 self)
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this paper. Note that the cons operation supplied by this library is strict, not lazy. In fact, the only lazy operations in this library are ++ (infix append) and reverse. 2 FIFO Queues Stacks and queues are usually the first two data structures studied by beginning computer science students
Reconstruction of the Mizar type system in the HOL Light system
 WDS Proceedings of Contributed Papers: Part I – Mathematics and Computer Sciences
, 2010
"... Abstract. The Mizar system is a system for formalization of mathematics. It contains a relatively sophisticated and rich type system, which makes formalization of mathematics in Mizar more intuitive than in other systems. On the other hand, the Mizar type system is very complex and together with ob ..."
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with obscure implementation of the Mizar verifier there is concern about correctness of the Mizar system. One of the possible solutions is to translate the Mizar Math Library (MML) to other systems for formalization of mathematics and reverify MML in them. The HOL Light system has been chosen and the necessary
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