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website for IsaGeoCoq

parent 12ccbbaa240f
......@@ -2023,6 +2023,61 @@ abstract =
more interesting proofs.
notify = tjm1983@gmail.com
 
[IsaGeoCoq]
title = Tarski's postulate of parallels implies the 5th postulate of Euclid, the postulate of Playfair and the original postulate of Euclid.
author = Roland Coghetto <mailto:roland_coghetto@hotmail.com>
topic = Mathematics/Geometry
license = LGPL
date = 2021-01-31
notify = roland_coghetto@hotmail.com
abstract =
The GeoCoq library (Main autors: Michael Beeson, Pierre Boutry,
Gabriel Braun, Charly Gries, Julien Narboux) contains a formalization
of geometry using the Coq proof assistant. It contains both proofs
about the foundations of geometry and high-level proofs in the same
style as in high-school. Some theorems also inspired by W.
Schwabhaüser, W. Szmielew and A. Tarski are also formalized with
others ITP (Metamath, Mizar) or ATP. We port a part of the GeoCoq
2.4.0 library within the Isabelle/Hol proof assistant: more precisely,
the files Chap02.v to Chap13_3.v, suma.v as well as the associated
definitions and some useful files for the demonstration of certain
parallel postulates. While the demonstrations in Coq are written in
procedural language, the transcript is done in declarative language
Isar. The synthetic approach of the demonstrations are directly
inspired by those contained in GeoCoq. Some demonstrations are
credited to G.E Martin(<<lemma bet_le__lt:>> in
Ch11_angles.thy, proved by Martin as Theorem 18.17) or Gupta H.N
(Krippen Lemma, proved by Gupta in its PhD in 1965 as Theorem 3.45).
In this work, the proofs are not contructive. The sledeghammer tool
being used to find some demonstrations. The names of the lemmas and
theorems used are kept as far as possible as well as the definitions.
A different translation has been proposed when the name was already
used in Isabel/Hol ("Len" is translated as
"TarskiLen") or that characters were not allowed in
Isabel/Hol ("anga'" in Ch13_angles.v is translated as
"angaP"). For some definitions the highlighting of a
variable has changed the order or the position of the variables
(Midpoint, Out, Inter,...). All the lemmas are valid in
absolute/neutral space defined with Tarski's axioms. It should
be noted that T.J.M. Makarios \cite{afp-Tarskis_Geometry} has begun
some demonstrations of certain proposals mainly those corresponding to
SST chapters 2 and 3. It uses a definition that does not quite
coincide with the definition used in Geocoq and here. As an example,
Makarios introduces the axiom A11 (Axiom of continuity) in the
definition of the locale "Tarski_absolute_space".
Furthermore, the definition of the locale "TarskiAbsolute"
\cite{afp-Poincare_Disc} is not not identical to the one defined in
the "Tarski_neutral_dimensionless" class of GeoCoq. Indeed
this one does not contain the axiom "upper_dimension". In
some cases particular, it is nevertheless to use the axiom
"upper_dimension". The addition of the word "_2D"
in the file indicates its presence. In the last part, it is
formalized that, in the neutral/absolute space, the axiom of the
parallels of the system of Tarski implies the Playfair axiom, the 5th
postulate of euclide and the postulate original from Euclid. These
proofs, which are not constructive, are directly inspired by Pierre
Boutry, Charly Gries, Julien Narboux and Pascal Schreck.
[General-Triangle]
title = The General Triangle Is Unique
author = Joachim Breitner <mailto:mail@joachim-breitner.de>
......@@ -9995,14 +10050,14 @@ abstract =
technique we can effectively harness theorem provers, model finders
and 'hammers' for reasoning with quantified non-classical
logics.
[CSP_RefTK]
title = The HOL-CSP Refinement Toolkit
author = Safouan Taha <mailto:safouan.taha@lri.fr>, Burkhart Wolff <https://www.lri.fr/~wolff/>, Lina Ye <mailto:lina.ye@lri.fr>
topic = Computer science/Concurrency/Process calculi, Computer science/Semantics
date = 2020-11-19
notify = wolff@lri.fr
abstract =
abstract =
We use a formal development for CSP, called HOL-CSP2.0, to analyse a
family of refinement notions, comprising classic and new ones. This
analysis enables to derive a number of properties that allow to deepen
......@@ -10026,7 +10081,7 @@ author = Susannah Mansky <mailto:sjohnsn2@illinois.edu>
topic = Computer science/Programming languages/Language definitions
date = 2021-01-11
notify = sjohnsn2@illinois.edu, susannahej@gmail.com
abstract =
abstract =
We extend Jinja to include static fields, methods, and instructions,
and dynamic class initialization, based on the Java SE 8
specification. This includes extension of definitions and proofs. This
......
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<title>Tarski's postulate of parallels implies the 5th postulate of Euclid, the postulate of Playfair and the original postulate of Euclid. - Archive of Formal Proofs
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<h1> <font class="first">T</font>arski's
postulate
of
parallels
implies
the
<font class="first">5</font>th
postulate
of
<font class="first">E</font>uclid,
the
postulate
of
<font class="first">P</font>layfair
and
the
original
postulate
of
<font class="first">E</font>uclid.
</h1>
<p>&nbsp;</p>
<table width="80%" class="data">
<tbody>
<tr>
<td class="datahead" width="20%">Title:</td>
<td class="data" width="80%">Tarski's postulate of parallels implies the 5th postulate of Euclid, the postulate of Playfair and the original postulate of Euclid.</td>
</tr>
<tr>
<td class="datahead">
Author:
</td>
<td class="data">
Roland Coghetto (roland_coghetto /at/ hotmail /dot/ com)
</td>
</tr>
<tr>
<td class="datahead">Submission date:</td>
<td class="data">2021-01-31</td>
</tr>
<tr>
<td class="datahead" valign="top">Abstract:</td>
<td class="abstract mathjax_process">
The GeoCoq library (Main autors: Michael Beeson, Pierre Boutry,
Gabriel Braun, Charly Gries, Julien Narboux) contains a formalization
of geometry using the Coq proof assistant. It contains both proofs
about the foundations of geometry and high-level proofs in the same
style as in high-school. Some theorems also inspired by W.
Schwabhaüser, W. Szmielew and A. Tarski are also formalized with
others ITP (Metamath, Mizar) or ATP. We port a part of the GeoCoq
2.4.0 library within the Isabelle/Hol proof assistant: more precisely,
the files Chap02.v to Chap13_3.v, suma.v as well as the associated
definitions and some useful files for the demonstration of certain
parallel postulates. While the demonstrations in Coq are written in
procedural language, the transcript is done in declarative language
Isar. The synthetic approach of the demonstrations are directly
inspired by those contained in GeoCoq. Some demonstrations are
credited to G.E Martin(<<lemma bet_le__lt:>> in
Ch11_angles.thy, proved by Martin as Theorem 18.17) or Gupta H.N
(Krippen Lemma, proved by Gupta in its PhD in 1965 as Theorem 3.45).
In this work, the proofs are not contructive. The sledeghammer tool
being used to find some demonstrations. The names of the lemmas and
theorems used are kept as far as possible as well as the definitions.
A different translation has been proposed when the name was already
used in Isabel/Hol ("Len" is translated as
"TarskiLen") or that characters were not allowed in
Isabel/Hol ("anga'" in Ch13_angles.v is translated as
"angaP"). For some definitions the highlighting of a
variable has changed the order or the position of the variables
(Midpoint, Out, Inter,...). All the lemmas are valid in
absolute/neutral space defined with Tarski's axioms. It should
be noted that T.J.M. Makarios \cite{afp-Tarskis_Geometry} has begun
some demonstrations of certain proposals mainly those corresponding to
SST chapters 2 and 3. It uses a definition that does not quite
coincide with the definition used in Geocoq and here. As an example,
Makarios introduces the axiom A11 (Axiom of continuity) in the
definition of the locale "Tarski_absolute_space".
Furthermore, the definition of the locale "TarskiAbsolute"
\cite{afp-Poincare_Disc} is not not identical to the one defined in
the "Tarski_neutral_dimensionless" class of GeoCoq. Indeed
this one does not contain the axiom "upper_dimension". In
some cases particular, it is nevertheless to use the axiom
"upper_dimension". The addition of the word "_2D"
in the file indicates its presence. In the last part, it is
formalized that, in the neutral/absolute space, the axiom of the
parallels of the system of Tarski implies the Playfair axiom, the 5th
postulate of euclide and the postulate original from Euclid. These
proofs, which are not constructive, are directly inspired by Pierre
Boutry, Charly Gries, Julien Narboux and Pascal Schreck.</td>
</tr>
<tr>
<td class="datahead" valign="top">BibTeX:</td>
<td class="formatted">
<pre>@article{IsaGeoCoq-AFP,
author = {Roland Coghetto},
title = {Tarski's postulate of parallels implies the 5th postulate of Euclid, the postulate of Playfair and the original postulate of Euclid.},
journal = {Archive of Formal Proofs},
month = jan,
year = 2021,
note = {\url{https://isa-afp.org/entries/IsaGeoCoq.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
</td>
</tr>
<tr><td class="datahead">License:</td>
<td class="data"><a href="http://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></td></tr>
</tbody>
</table>
<p></p>
<table class="links">
<tbody>
<tr>
<td class="links">
<a href="../browser_info/current/AFP/IsaGeoCoq/outline.pdf">Proof outline</a><br>
<a href="../browser_info/current/AFP/IsaGeoCoq/document.pdf">Proof document</a>
</td>
</tr>
<tr>
<td class="links">
<a href="../browser_info/current/AFP/IsaGeoCoq/index.html">Browse theories</a>
</td></tr>
<tr>
<td class="links">
<a href="../release/afp-IsaGeoCoq-current.tar.gz">Download this entry</a>
</td>
</tr>
<tr><td class="links">Older releases:
None
</td></tr>
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<script src="../script.js"></script>
</body>
</html>
\ No newline at end of file
......@@ -88,6 +88,14 @@ of a scientific journal, is indexed by <a href="http://dblp.uni-trier.de/db/jour
<tr>
<td class="head">2021</td>
</tr>
<tr>
<td class="entry">
2021-01-31: <a href="entries/IsaGeoCoq.html">Tarski's postulate of parallels implies the 5th postulate of Euclid, the postulate of Playfair and the original postulate of Euclid.</a>
<br>
Author:
Roland Coghetto
</td>
</tr>
<tr>
<td class="entry">
2021-01-11: <a href="entries/JinjaDCI.html">JinjaDCI: a Java semantics with dynamic class initialization</a>
......
......@@ -9,7 +9,61 @@
and larger scientific developments, mechanically checked
in the theorem prover Isabelle.
</description>
<pubDate>11 Jan 2021 00:00:00 +0000</pubDate>
<pubDate>31 Jan 2021 00:00:00 +0000</pubDate>
<item>
<title>Tarski's postulate of parallels implies the 5th postulate of Euclid, the postulate of Playfair and the original postulate of Euclid.</title>
<link>https://www.isa-afp.org/entries/IsaGeoCoq.html</link>
<guid>https://www.isa-afp.org/entries/IsaGeoCoq.html</guid>
<dc:creator> Roland Coghetto </dc:creator>
<pubDate>31 Jan 2021 00:00:00 +0000</pubDate>
<description>
The GeoCoq library (Main autors: Michael Beeson, Pierre Boutry,
Gabriel Braun, Charly Gries, Julien Narboux) contains a formalization
of geometry using the Coq proof assistant. It contains both proofs
about the foundations of geometry and high-level proofs in the same
style as in high-school. Some theorems also inspired by W.
Schwabhaüser, W. Szmielew and A. Tarski are also formalized with
others ITP (Metamath, Mizar) or ATP. We port a part of the GeoCoq
2.4.0 library within the Isabelle/Hol proof assistant: more precisely,
the files Chap02.v to Chap13_3.v, suma.v as well as the associated
definitions and some useful files for the demonstration of certain
parallel postulates. While the demonstrations in Coq are written in
procedural language, the transcript is done in declarative language
Isar. The synthetic approach of the demonstrations are directly
inspired by those contained in GeoCoq. Some demonstrations are
credited to G.E Martin(&lt;&lt;lemma bet_le__lt:&gt;&gt; in
Ch11_angles.thy, proved by Martin as Theorem 18.17) or Gupta H.N
(Krippen Lemma, proved by Gupta in its PhD in 1965 as Theorem 3.45).
In this work, the proofs are not contructive. The sledeghammer tool
being used to find some demonstrations. The names of the lemmas and
theorems used are kept as far as possible as well as the definitions.
A different translation has been proposed when the name was already
used in Isabel/Hol (&#34;Len&#34; is translated as
&#34;TarskiLen&#34;) or that characters were not allowed in
Isabel/Hol (&#34;anga&#39;&#34; in Ch13_angles.v is translated as
&#34;angaP&#34;). For some definitions the highlighting of a
variable has changed the order or the position of the variables
(Midpoint, Out, Inter,...). All the lemmas are valid in
absolute/neutral space defined with Tarski&#39;s axioms. It should
be noted that T.J.M. Makarios \cite{afp-Tarskis_Geometry} has begun
some demonstrations of certain proposals mainly those corresponding to
SST chapters 2 and 3. It uses a definition that does not quite
coincide with the definition used in Geocoq and here. As an example,
Makarios introduces the axiom A11 (Axiom of continuity) in the
definition of the locale &#34;Tarski_absolute_space&#34;.
Furthermore, the definition of the locale &#34;TarskiAbsolute&#34;
\cite{afp-Poincare_Disc} is not not identical to the one defined in
the &#34;Tarski_neutral_dimensionless&#34; class of GeoCoq. Indeed
this one does not contain the axiom &#34;upper_dimension&#34;. In
some cases particular, it is nevertheless to use the axiom
&#34;upper_dimension&#34;. The addition of the word &#34;_2D&#34;
in the file indicates its presence. In the last part, it is
formalized that, in the neutral/absolute space, the axiom of the
parallels of the system of Tarski implies the Playfair axiom, the 5th
postulate of euclide and the postulate original from Euclid. These
proofs, which are not constructive, are directly inspired by Pierre
Boutry, Charly Gries, Julien Narboux and Pascal Schreck.</description>
</item>
<item>
<title>JinjaDCI: a Java semantics with dynamic class initialization</title>
<link>https://www.isa-afp.org/entries/JinjaDCI.html</link>
......@@ -577,22 +631,5 @@ we stay in first-order logic this development helps with mechanising
proofs. To demonstrate the applicability of the algebraic framework we
verify the correctness of three basic graph algorithms.</description>
</item>
<item>
<title>A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles</title>
<link>https://www.isa-afp.org/entries/Safe_Distance.html</link>
<guid>https://www.isa-afp.org/entries/Safe_Distance.html</guid>
<dc:creator> Albert Rizaldi, Fabian Immler </dc:creator>
<pubDate>01 Jun 2020 00:00:00 +0000</pubDate>
<description>
The Vienna Convention on Road Traffic defines the safe distance
traffic rules informally. This could make autonomous vehicle liable
for safe-distance-related accidents because there is no clear
definition of how large a safe distance is. We provide a formally
proven prescriptive definition of a safe distance, and checkers which
can decide whether an autonomous vehicle is obeying the safe distance
rule. Not only does our work apply to the domain of law, but it also
serves as a specification for autonomous vehicle manufacturers and for
online verification of path planners.</description>
</item>
</channel>
</rss>
This diff is collapsed.
......@@ -812,6 +812,7 @@
<a href="entries/Triangle.html">Triangle</a> &nbsp;
<a href="entries/Impossible_Geometry.html">Impossible_Geometry</a> &nbsp;
<a href="entries/Tarskis_Geometry.html">Tarskis_Geometry</a> &nbsp;
<a href="entries/IsaGeoCoq.html">IsaGeoCoq</a> &nbsp;
<a href="entries/General-Triangle.html">General-Triangle</a> &nbsp;
<a href="entries/Nullstellensatz.html">Nullstellensatz</a> &nbsp;
<a href="entries/Ptolemys_Theorem.html">Ptolemys_Theorem</a> &nbsp;
......
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