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favonia
mechanized
2
mechanized reasoning favonia 1 2 2 2 checked! 2 Peace of - - PowerPoint PPT Presentation
mechanized reasoning favonia 1 2 2 2 checked! 2 Peace of - - PowerPoint PPT Presentation
mechanized reasoning favonia 1 2 2 2 checked! 2 Peace of Mind 3 *photo credit: voltamax@pixabay Dream Everyone can (easily) check their work in computers 4 Notable Projects Four-color theorem
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2
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2
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checked!
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Peace of Mind
*photo credit: voltamax@pixabay
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Dream
Everyone can (easily) check their work in computers
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Notable Projects
Four-color theorem Odd-order (Feit-Thompson) theorem Kepler's conjecture (now theorem)
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6 The diiculty and length of formal proofs are certainly a major cause of the absence
- f any widespread adoption by mathema-
ticians of automated proof checkers.
— Mechanizing Proof by Donald MacKenzie
Challenges
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Good language (abstraction)
Theory
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7
Good language (abstraction)
Theory
Good editor Eicient checker
Engineering
+
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7
Good language (abstraction)
Theory
Good editor Eicient checker
Engineering
+
Community
+
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7
Good language (abstraction)
Theory
Good editor Eicient checker
Engineering
+
Community
+
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Good language (abstraction)
Theory
0, 1, 2, 3, ...
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Good language (abstraction)
Theory
0, 1, 2, 3, ... {}, {{}}, {{},{{}}}, {{},{{}},{{},{{}}}}, ...
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Good language (abstraction)
Theory
0, 1, 2, 3, ... {}, {{}}, {{},{{}}}, {{},{{}},{{},{{}}}}, ... (2, 0) {{{},{{}}},{{},{{},{{}}}}}
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Good language (abstraction)
Theory
0, 1, 2, 3, ... {}, {{}}, {{},{{}}}, {{},{{}},{{},{{}}}}, ... (2, 0) {{{},{{}}},{{},{{},{{}}}}}
Need structural set theory, type theory, or something
Think about Euclid's Elements.
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(material) set theory classical mathematics
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(material) set theory classical mathematics good lang. for mechanization
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(material) set theory classical mathematics good lang. for mechanization
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(material) set theory classical mathematics good lang. for mechanization
insightful even if not for mechanization
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Homotopy Type Theory
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simplicial sets or some model category classical homotopy theory homotopy type theory
(even proofs need to be homotopy-invariant)
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Did we address the issues?
The diiculty and length of formal proofs are certainly a major cause of the absence
- f any widespread adoption by mathema-
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Many results were mechanized, some done without paper proofs.
Did we address the issues?
The diiculty and length of formal proofs are certainly a major cause of the absence
- f any widespread adoption by mathema-
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Many results were mechanized, some done without paper proofs.
Did we address the issues?
Mechanized proofs are not longer.
The diiculty and length of formal proofs are certainly a major cause of the absence
- f any widespread adoption by mathema-
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Blakers-Massey in homotopy type theory
(2012-13)
[Finster, Licata, Lumsdaine]
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Blakers-Massey in homotopy type theory Full mechanization of Blakers-Massey in Agda
(2012-13) (2013)
[Finster, Licata, Lumsdaine] [Licata?] [Favonia]
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Blakers-Massey in homotopy type theory Full mechanization of Blakers-Massey in Agda Un-mechanization into classical theory
(2012-13) (2013) (2014)
unpublished [Rezk] [Finster, Licata, Lumsdaine] [Licata?] [Favonia]
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Blakers-Massey in homotopy type theory Full mechanization of Blakers-Massey in Agda Un-mechanization into classical theory Generalization
(2012-13) (2013) (2014) (2016 or earlier)
Generalization available on arXiv
(2017)
1703.09050 unpublished [Rezk] [Finster, Licata, Lumsdaine] [Licata?] [Favonia]
[Anel, Biedermann, Finster, Joyal]
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13
Blakers-Massey in homotopy type theory Full mechanization of Blakers-Massey in Agda Un-mechanization into classical theory Generalization
(2012-13) (2013) (2014) (2016 or earlier)
Generalization available on arXiv
(2017)
Mechanization published
(2016)
1703.09050 unpublished [Rezk] [Finster, Licata, Lumsdaine] [Licata?] [Favonia] [FFLL]
[Anel, Biedermann, Finster, Joyal]
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Blakers-Massey in homotopy type theory Full mechanization of Blakers-Massey in Agda Un-mechanization into classical theory Generalization Mechanization of the generalization in Agda?
(2012-13) (2013) (2014) (2016 or earlier)
Generalization available on arXiv
(2017)
Mechanization published
(2016)
1703.09050
(2017-?)
unpublished [Rezk] [Finster, Licata, Lumsdaine] [Licata?] [Favonia] [FFLL]
[Anel, Biedermann, Finster, Joyal]
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https://plus.google.com/+UrsSchreiber/posts/Zzjd8KM7K5s
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I will...
Mechanize more theorems Develop new tools (RedPRL, ...) Design new languages
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You can...
Teach me the theorems you want me to mechanize!
I will...
Mechanize more theorems Develop new tools (RedPRL, ...) Design new languages
SLIDE 36
15
You can...
Teach me the theorems you want me to mechanize! Try a modern mechanization tool
I will...
Mechanize more theorems Develop new tools (RedPRL, ...) Design new languages
SLIDE 37
15
You can...
Teach me the theorems you want me to mechanize! Try a modern mechanization tool Send me an email by TODAY if you want to play Hanabi
I will...
Mechanize more theorems Develop new tools (RedPRL, ...) Design new languages