MIZAR in MathWiki Adam Naumowicz adamn@mizar.org Institute of - - PowerPoint PPT Presentation

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MIZAR in MathWiki Adam Naumowicz adamn@mizar.org Institute of - - PowerPoint PPT Presentation

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MIZAR in MathWiki Adam Naumowicz adamn@mizar.org Institute of Computer Science University of Bialystok, Poland MathWiki task inventory MathWiki TYPES Workshop, Edinburgh, November 1, 2007 Adam Naumowicz, Institute of Comp. Sci., University of

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SLIDE 1

MIZAR in MathWiki

Adam Naumowicz

adamn@mizar.org

Institute of Computer Science University of Bialystok, Poland

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SLIDE 2

MathWiki task inventory

MathWiki TYPES Workshop, Edinburgh, November 1, 2007 Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –2–

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SLIDE 3

Interactive proof interface

MathWiki TYPES Workshop, Edinburgh, November 1, 2007 Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –3–

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SLIDE 4

Interactive proof interface

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MIZAR is a command line (“batch”) tool

– “lazy interaction” – stepwise refinement

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –3-a–

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SLIDE 5

Interactive proof interface

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MIZAR is a command line (“batch”) tool

– “lazy interaction” – stepwise refinement

  • processing incomplete proofs is done in a “natural” way

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –3-b–

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SLIDE 6

Interactive proof interface

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MIZAR is a command line (“batch”) tool

– “lazy interaction” – stepwise refinement

  • processing incomplete proofs is done in a “natural” way
  • a local database can be created and distributed among users

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –3-c–

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SLIDE 7

Interactive proof interface

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MIZAR is a command line (“batch”) tool

– “lazy interaction” – stepwise refinement

  • processing incomplete proofs is done in a “natural” way
  • a local database can be created and distributed among users
  • several collaborative projects (CCL, JORDAN)

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –3-d–

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SLIDE 8

Online working environment

MathWiki TYPES Workshop, Edinburgh, November 1, 2007 Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –4–

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SLIDE 9

Online working environment

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MIZAR on-line processors, e.g. http://www.wakasato.org/mizar/

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –4-a–

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SLIDE 10

Online working environment

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MIZAR on-line processors, e.g. http://www.wakasato.org/mizar/
  • binary distribution on several platforms - fairly easy to install!

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –4-b–

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SLIDE 11

Online working environment

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MIZAR on-line processors, e.g. http://www.wakasato.org/mizar/
  • binary distribution on several platforms - fairly easy to install!
  • moderate resources required

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –4-c–

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SLIDE 12

Online working environment

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MIZAR on-line processors, e.g. http://www.wakasato.org/mizar/
  • binary distribution on several platforms - fairly easy to install!
  • moderate resources required
  • most advanced interface - Emacs-mode by Josef Urban

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –4-d–

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SLIDE 13

Online working environment

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MIZAR on-line processors, e.g. http://www.wakasato.org/mizar/
  • binary distribution on several platforms - fairly easy to install!
  • moderate resources required
  • most advanced interface - Emacs-mode by Josef Urban
  • hybrid solution is probably most feasible (on/off-line work)

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –4-e–

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SLIDE 14

Database management

MathWiki TYPES Workshop, Edinburgh, November 1, 2007 Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –5–

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SLIDE 15

Database management

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MML is subject to constant revisions!

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –5-a–

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SLIDE 16

Database management

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MML is subject to constant revisions!

– e.g. the arithmetic of real numbers – better formulation – employing new features (adjectives)

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –5-b–

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SLIDE 17

Database management

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MML is subject to constant revisions!

– e.g. the arithmetic of real numbers – better formulation – employing new features (adjectives)

  • integrity

– e.g. two approaches to lattice theory

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –5-c–

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SLIDE 18

Database management

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MML is subject to constant revisions!

– e.g. the arithmetic of real numbers – better formulation – employing new features (adjectives)

  • integrity

– e.g. two approaches to lattice theory

  • notations

– 120 different +’s – overloading and redefinitions

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –5-d–

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SLIDE 19

Database management

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MML is subject to constant revisions!

– e.g. the arithmetic of real numbers – better formulation – employing new features (adjectives)

  • integrity

– e.g. two approaches to lattice theory

  • notations

– 120 different +’s – overloading and redefinitions

  • Encyclopedia of Mathematics in Mizar (EMM) - better organised

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –5-e–

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SLIDE 20

Database management

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • MML is subject to constant revisions!

– e.g. the arithmetic of real numbers – better formulation – employing new features (adjectives)

  • integrity

– e.g. two approaches to lattice theory

  • notations

– 120 different +’s – overloading and redefinitions

  • Encyclopedia of Mathematics in Mizar (EMM) - better organised
  • dividing into classical/abstract parts or arithmetic-dependent/arithmetic-independent parts

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –5-f–

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SLIDE 21

Contents

MathWiki TYPES Workshop, Edinburgh, November 1, 2007 Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –6–

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SLIDE 22

Contents

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • Mizar Mathematical Library (version 4.87.985) includes:

– 985 articles written by 198 authors – 45002 theorems – 8524 definitions – 753 schemes – 7511 registrations – 6320 symbols

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –6-a–

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SLIDE 23

Contents

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • Mizar Mathematical Library (version 4.87.985) includes:

– 985 articles written by 198 authors – 45002 theorems – 8524 definitions – 753 schemes – 7511 registrations – 6320 symbols

  • refereeing process started in 2006 (“human judgement what is good and what is not”)

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –6-b–

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SLIDE 24

Contents

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • Mizar Mathematical Library (version 4.87.985) includes:

– 985 articles written by 198 authors – 45002 theorems – 8524 definitions – 753 schemes – 7511 registrations – 6320 symbols

  • refereeing process started in 2006 (“human judgement what is good and what is not”)
  • traditional refereeing - “positive” (printing costs, not easy access, only most important

results are published) - Why should that be accepted?

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –6-c–

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SLIDE 25

Contents

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • Mizar Mathematical Library (version 4.87.985) includes:

– 985 articles written by 198 authors – 45002 theorems – 8524 definitions – 753 schemes – 7511 registrations – 6320 symbols

  • refereeing process started in 2006 (“human judgement what is good and what is not”)
  • traditional refereeing - “positive” (printing costs, not easy access, only most important

results are published) - Why should that be accepted?

  • MML refereeing policy - “negative” (only really poor articles are rejected) - Why should

that be rejected?

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –6-d–

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SLIDE 26

Contents

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • Mizar Mathematical Library (version 4.87.985) includes:

– 985 articles written by 198 authors – 45002 theorems – 8524 definitions – 753 schemes – 7511 registrations – 6320 symbols

  • refereeing process started in 2006 (“human judgement what is good and what is not”)
  • traditional refereeing - “positive” (printing costs, not easy access, only most important

results are published) - Why should that be accepted?

  • MML refereeing policy - “negative” (only really poor articles are rejected) - Why should

that be rejected?

  • Freek’s proposal (preliminaries section)

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –6-e–

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SLIDE 27

Contents

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • Mizar Mathematical Library (version 4.87.985) includes:

– 985 articles written by 198 authors – 45002 theorems – 8524 definitions – 753 schemes – 7511 registrations – 6320 symbols

  • refereeing process started in 2006 (“human judgement what is good and what is not”)
  • traditional refereeing - “positive” (printing costs, not easy access, only most important

results are published) - Why should that be accepted?

  • MML refereeing policy - “negative” (only really poor articles are rejected) - Why should

that be rejected?

  • Freek’s proposal (preliminaries section)
  • authorship issues

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –6-f–

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SLIDE 28

Semantics aspects

MathWiki TYPES Workshop, Edinburgh, November 1, 2007 Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –7–

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SLIDE 29

Semantics aspects

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • Formalized Mathematics: http://fm.mizar.org/

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –7-a–

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SLIDE 30

Semantics aspects

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • Formalized Mathematics: http://fm.mizar.org/
  • Journal of Formalized Mathematics: http://mizar.org/JFM/

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –7-b–

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SLIDE 31

Semantics aspects

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • Formalized Mathematics: http://fm.mizar.org/
  • Journal of Formalized Mathematics: http://mizar.org/JFM/
  • XML-based semantic presentation:

http://lipa.ms.mff.cuni.cz/˜urban/xmlmml/html_abstr.4.87.985/

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –7-c–

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SLIDE 32

Semantics aspects

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • Formalized Mathematics: http://fm.mizar.org/
  • Journal of Formalized Mathematics: http://mizar.org/JFM/
  • XML-based semantic presentation:

http://lipa.ms.mff.cuni.cz/˜urban/xmlmml/html_abstr.4.87.985/

  • MMLQuery search language/engine: http://mmlquery.mizar.org/

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –7-d–

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SLIDE 33

Common proof language

MathWiki TYPES Workshop, Edinburgh, November 1, 2007 Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –8–

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SLIDE 34

Common proof language

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • PA languages should still evolve in the direction of the natural language (to reduce the de

Bruijn factor)

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –8-a–

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SLIDE 35

Common proof language

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • PA languages should still evolve in the direction of the natural language (to reduce the de

Bruijn factor) – adjectives, binders, ellipsis, etc.

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –8-b–

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SLIDE 36

Common proof language

MathWiki TYPES Workshop, Edinburgh, November 1, 2007

  • PA languages should still evolve in the direction of the natural language (to reduce the de

Bruijn factor) – adjectives, binders, ellipsis, etc.

  • we should support translations (translation into a language should be done by its “naitive”

users), parallel developments, cross-linking facilities, etc.

Adam Naumowicz, Institute of Comp. Sci., University of Bialystok –8-c–