From 985a25a12cfe091bf687b3a0960ad4876e845a71 Mon Sep 17 00:00:00 2001
From: Florian Rabe <florian.rabe@gmail.com>
Date: Fri, 13 Jul 2018 21:50:36 +0100
Subject: [PATCH] no message

---
 events/Dubois.pdf       | Bin 0 -> 278504 bytes
 events/Gonthier.pptx    | Bin 0 -> 2253675 bytes
 events/Shankar.pdf      | Bin 0 -> 139960 bytes
 events/Smith.ppt        | Bin 0 -> 1031168 bytes
 events/Tetrapod-2018.md |  18 +-
 events/Thiery.html      | 523 ++++++++++++++++++++++++++++++++++++++++
 6 files changed, 532 insertions(+), 9 deletions(-)
 create mode 100644 events/Dubois.pdf
 create mode 100644 events/Gonthier.pptx
 create mode 100644 events/Shankar.pdf
 create mode 100644 events/Smith.ppt
 create mode 100644 events/Thiery.html

diff --git a/events/Dubois.pdf b/events/Dubois.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..dfe233f9ec9af7999e316350867428fa2c68921b
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diff --git a/events/Smith.ppt b/events/Smith.ppt
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diff --git a/events/Tetrapod-2018.md b/events/Tetrapod-2018.md
index 38f6739..3dbbf75 100644
--- a/events/Tetrapod-2018.md
+++ b/events/Tetrapod-2018.md
@@ -35,14 +35,14 @@ Of particular interest are
 
 #### Invited speakers and topics
 
-| Speaker           | Modularity in...         |
-| ----------------- | ------------------------ |
-| Catherine Dubois  | Proof Checking           |
-| Georges Gonthier  | Large Proofs             |
-| Till Mossakowski  | Ontologies               |
-| Natarajan Shankar | Proof Assistants         |
-| Doug Smith        | Software Synthesis       |
-| Nicolas M. Thiery | Mathematical Computation |
+| Speaker           | Modularity in...         | Slides                 |
+| ----------------- | ------------------------ | ---------------------- |
+| Catherine Dubois  | Proof Checking           | [slides](Dubois.pdf)   |
+| Georges Gonthier  | Large Proofs             | [slides](Gonthier.pptx)|
+| Till Mossakowski  | Ontologies               |                        |
+| Natarajan Shankar | Proof Assistants         | [slides](Shankar.pdf)  |
+| Doug Smith        | Software Synthesis       | [slides](Smith.ppt)    |
+| Nicolas M. Thiery | Mathematical Computation | [slides](Thiery.html)  |
 
 #### Call for Opinions
 
@@ -177,7 +177,7 @@ ically, the early knowledge applications in a derivation introduce the overall a
 architectural structure and then many more knowledge applications are applied to improve
 performance and to fit the design to the target computational substrate.
 
-#### Modularity in Mathematical Computation
+#### Modularity in Mathematical Computation (Nicolas Thiery)
 Over the last decades, a huge amount of computational software was
 developed for pure mathematics, in particular to support research and
 education. As for any complex ecosystem of software components, the
diff --git a/events/Thiery.html b/events/Thiery.html
new file mode 100644
index 0000000..ef5b48d
--- /dev/null
+++ b/events/Thiery.html
@@ -0,0 +1,523 @@
+<!DOCTYPE html>
+
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+
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+    <meta name="mobile-web-app-capable" content="yes">
+    <title>
+        Modularity in Mathematical Computation - HackMD
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+    <div id="doc" class="markdown-body container-fluid"><h1 id="Modularity-in-Mathematical-Computation" style=""><a class="anchor hidden-xs" href="#Modularity-in-Mathematical-Computation" title="Modularity-in-Mathematical-Computation"><span class="octicon octicon-link"></span></a>Modularity in Mathematical Computation</h1><p>Nicolas M. Thiéry et al.</p><p>Tetrapod: Modular Knowledge workshop</p><p>FLoC 2018, Oxford, July 13th of 2018</p><h2 id="A-collaborative-document" style=""><a class="anchor hidden-xs" href="#A-collaborative-document" title="A-collaborative-document"><span class="octicon octicon-link"></span></a>A collaborative document</h2><p><strong>Please connect to:</strong></p><p><a href="https://tinyurl.com/tetrapod-2018-computation" target="_blank">https://tinyurl.com/tetrapod-2018-computation</a></p><hr><h2 id="Participants" style=""><a class="anchor hidden-xs" href="#Participants" title="Participants"><span class="octicon octicon-link"></span></a>Participants</h2><ul>
+<li>Georges Gonthier (Inria Saclay)</li>
+<li>Florian Rabe (FAU Erlangen-Nürnberg, LRI, Univ. Paris Sud)</li>
+<li>Dennis Müller (FAU Erlangen-Nürnberg)</li>
+<li>Jeremy Gibbons (University of Oxford), local observer and gate-crasher</li>
+<li>Jacques Carette (McMaster University) System designer and developper</li>
+<li>Nicolas M. Thiéry (LRI, Univ. Paris Sud) Practionner, SageMath dev</li>
+</ul><hr><h2 id="Abstract" style=""><a class="anchor hidden-xs" href="#Abstract" title="Abstract"><span class="octicon octicon-link"></span></a>Abstract</h2><p>Over the last decades, a huge amount of computational software was
+developed for pure mathematics, in particular to support research and
+education. As for any complex ecosystem of software components, the
+ability to compose them has a multiplier effect on the expressive
+power, flexibility, and range of applications.</p><p>The purpose of this session is to share experience on the many
+barriers to composability in computational mathematics, and how they
+are being tackled in various communities. Of particular interest will
+be the exploitation of knowledge to leverage some of the barriers.
+feedback from neighbor fields (proofs, data, knowledge) will be most
+welcome.</p><hr><h2 id="Composability" style=""><a class="anchor hidden-xs" href="#Composability" title="Composability"><span class="octicon octicon-link"></span></a>Composability?</h2><p>For this session we focus on the ability to transfer data
+and run procedures across “systems” (two different software, two instances of the same software on different machines, two libraries within a system, …).</p><hr><h3 id="Data-transfers" style=""><a class="anchor hidden-xs" href="#Data-transfers" title="Data-transfers"><span class="octicon octicon-link"></span></a>Data transfers</h3><ul>
+<li>
+<p><strong>Goal</strong>: Transfer an object O from system <code>A</code> to system <code>B</code></p>
+</li>
+<li>
+<p><strong>Requirements</strong>:</p>
+<ul>
+<li>
+<p><strong>A communication channel</strong>: shared memory, disk, pipe, (web)socket, …</p>
+</li>
+<li>
+<p><strong>A communication protocol</strong></p>
+</li>
+<li>
+<p><strong>Serialization / Deserialization</strong>: conversion to/from a string of bytes</p>
+</li>
+<li>
+<p><strong>A format specification</strong>; e.g. XML (syntax) + OpenMath content dictionary (semantic)</p>
+</li>
+<li>
+<p><strong>Format conversion</strong></p>
+<ul>
+<li>
+<p><strong>syntax</strong>: e.g.: JSON  &lt;-&gt;  XML</p>
+</li>
+<li>
+<p><strong>adaptation</strong>: <code>DihedralGroup(4)</code> &lt;-&gt; <code>DihedralGroup(8)</code></p>
+</li>
+<li>
+<p><strong>change of representation (codec)</strong>: recursive &lt;-&gt; sparse polynomial</p>
+</li>
+</ul>
+<p>Idealy: applying a theory morphism to guarantee semantic preservation</p>
+</li>
+</ul>
+</li>
+</ul><hr><h3 id="Procedure-calls" style=""><a class="anchor hidden-xs" href="#Procedure-calls" title="Procedure-calls"><span class="octicon octicon-link"></span></a>Procedure calls</h3><ul>
+<li>
+<p><strong>Goal</strong>: From <code>B</code> request the computation <code>f(a,b,c)</code> in <code>A</code></p>
+</li>
+<li>
+<p><strong>Requirements</strong>:</p>
+<ul>
+<li>
+<p><strong>Data transfers</strong>: send <code>a</code>,<code>b</code>,<code>c</code> to <code>A</code>, receive back the result</p>
+</li>
+<li>
+<p><strong>Procedure call</strong>: bindings, remote procedure calls, …</p>
+</li>
+<li>
+<p><strong>An API specification</strong>: syntax and semantic of <code>f</code> in <code>A</code>?</p>
+</li>
+<li>
+<p><strong>Adapting the API in B to the API in A</strong>: <code>Size(A)</code> &lt;-&gt; <code>A.cardinality()</code></p>
+<p>Idealy: applying a theory morphism to guarantee semantic preservation</p>
+</li>
+</ul>
+</li>
+</ul><hr><h2 id="Barriers-faced-by-the-computational-pure-maths-community" style=""><a class="anchor hidden-xs" href="#Barriers-faced-by-the-computational-pure-maths-community" title="Barriers-faced-by-the-computational-pure-maths-community"><span class="octicon octicon-link"></span></a>Barriers faced by the computational pure maths community?</h2><hr><h3 id="Semantic-barriers" style=""><a class="anchor hidden-xs" href="#Semantic-barriers" title="Semantic-barriers"><span class="octicon octicon-link"></span></a>Semantic barriers</h3><ul>
+<li>
+<p><strong>Many kinds of objects</strong>:</p>
+<p>E.g. thousands in Sage, compared to “matrices of floats” in Matlab</p>
+</li>
+<li>
+<p><strong>Many data representations</strong>, with very different algorithmic complexity</p>
+<p>E.g. for polynomials: sparse, dense, recursive, straight line
+program, evaluation, …</p>
+</li>
+<li>
+<p>Objects at different levels of abstraction</p>
+</li>
+<li>
+<p><strong>Few core concepts</strong></p>
+<p>addition, multiplication commutativity</p>
+</li>
+<li>
+<p>… but <strong>many interesting ways to combine them</strong>:</p>
+<p>Groups, Fields, graded commutative algebras, …</p>
+</li>
+<li>
+<p>A <strong>large variety of use cases</strong></p>
+<p>speed maniacs, flexibility fans, composability devouts</p>
+</li>
+</ul><hr><h4 id="The-good-news"><a class="anchor hidden-xs" href="#The-good-news" title="The-good-news"><span class="octicon octicon-link"></span></a>The good news</h4><ul>
+<li>
+<p>Formal level: <strong>best effort is ok</strong></p>
+</li>
+<li>
+<p>No requirements to define the maths behind</p>
+</li>
+</ul><hr><h3 id="Social-barriers" style=""><a class="anchor hidden-xs" href="#Social-barriers" title="Social-barriers"><span class="octicon octicon-link"></span></a>Social barriers</h3><ul>
+<li>
+<p><strong>Closed science</strong> and the <strong>Montaigu-Capulet syndrome</strong></p>
+<p>(won’t use code from / share code with XXX for political reasons)</p>
+</li>
+<li>
+<p><strong>Tight man power resources</strong></p>
+<p>Severel hundreds of thousands use computer algebra; hundreds implement it; a handful are
+officially paid full time for it.</p>
+</li>
+<li>
+<p><strong>Mastering math &amp; computer science</strong>?</p>
+</li>
+<li>
+<p><strong>High level of math specialization required when writing code</strong></p>
+<p>E.g. thousands of people use Gröbner bases; a handful know how to
+implement them right</p>
+</li>
+<li>
+<p>Pieces of software that took decades to develop</p>
+<p>We can’t afford to reimplement them; yet we can’t afford to not reimplement them (to learn from one’s mistakes and benefit from technology advances!)</p>
+</li>
+<li>
+<p>A fragmented community</p>
+</li>
+</ul><hr><h3 id="Technical-barriers" style=""><a class="anchor hidden-xs" href="#Technical-barriers" title="Technical-barriers"><span class="octicon octicon-link"></span></a>Technical barriers</h3><ul>
+<li>
+<p><strong>Systems written in different languages / idioms</strong></p>
+<p>C, C++, Python 2/3, Java, Javascript, Julia, GAP, Singular,
+Macaulay, Maple, Mathematica, MuPAD, Magma, Axiom/Aldor, Haskell, ML, Agda, …</p>
+</li>
+<li>
+<p><strong>Systems written using different frameworks / API</strong></p>
+</li>
+<li>
+<p><strong>Packaging barriers</strong></p>
+</li>
+<li>
+<p>Tendency for <strong>large old systems</strong>: 10-30 years, <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-1-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><msup><mn>10</mn><mn>6</mn></msup></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1" style="width: 1.727em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.455em; height: 0px; font-size: 116%;"><span style="position: absolute; clip: rect(1.399em, 1001.46em, 2.608em, -1000em); top: -2.425em; left: 0em;"><span class="mrow" id="MathJax-Span-2"><span class="msubsup" id="MathJax-Span-3"><span style="display: inline-block; position: relative; width: 1.429em; height: 0px;"><span style="position: absolute; clip: rect(3.159em, 1000.96em, 4.171em, -1000em); top: -3.987em; left: 0em;"><span class="mn" id="MathJax-Span-4" style="font-family: MathJax_Main;">10</span><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="position: absolute; top: -4.38em; left: 1em;"><span class="mn" id="MathJax-Span-5" style="font-size: 70.7%; font-family: MathJax_Main;">6</span><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.425em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.088em; border-left: 0px solid; width: 0px; height: 1.153em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>10</mn><mn>6</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-1">10^6</script></span> lines of code</p>
+<ul>
+<li>
+<p>lots of <strong>technical debt</strong>; <strong>slow evolution</strong></p>
+</li>
+<li>
+<p><strong>Lack of modularity</strong>, <strong>large dependencies</strong></p>
+<p>E.g. having to install SageMath to use just a few of its lines</p>
+</li>
+</ul>
+</li>
+</ul><hr><h2 id="Some-case-studies-and-tentative-solutions" style=""><a class="anchor hidden-xs" href="#Some-case-studies-and-tentative-solutions" title="Some-case-studies-and-tentative-solutions"><span class="octicon octicon-link"></span></a>Some case studies and tentative solutions</h2><hr><h3 id="OpenMath" style=""><a class="anchor hidden-xs" href="#OpenMath" title="OpenMath"><span class="octicon octicon-link"></span></a>OpenMath</h3><ul>
+<li>
+<p><strong>Goal</strong>: standardized serialization format to exchange data across systems</p>
+</li>
+<li>
+<p><strong>Syntax</strong>: XML, json, binary</p>
+</li>
+<li>
+<p><strong>Semantic</strong>: defined by content dictionaries (CD)</p>
+</li>
+<li>
+<p><strong>Hard problem</strong>: agreeing on CD’s for polynomials was already hard; scaling?</p>
+</li>
+</ul><p>After twenty years, little adoption</p><hr><h3 id="The-Math-in-the-Middle-approach" style=""><a class="anchor hidden-xs" href="#The-Math-in-the-Middle-approach" title="The-Math-in-the-Middle-approach"><span class="octicon octicon-link"></span></a>The Math-in-the-Middle approach</h3><ul>
+<li>
+<p><strong>Goals</strong>:</p>
+<ul>
+<li>
+<p>Separate <strong>serialization</strong> from <strong>adaptation</strong></p>
+</li>
+<li>
+<p>Separate <strong>binding</strong> from <strong>adaptation</strong></p>
+</li>
+<li>
+<p>Separate the treatment of each system</p>
+</li>
+</ul>
+</li>
+<li>
+<p><strong>Approach</strong>:</p>
+<ul>
+<li>
+<p>A central math ontology</p>
+</li>
+<li>
+<p>Formalize each systems by aligning to the central ontology</p>
+</li>
+</ul>
+</li>
+</ul><hr><h3 id="Categories-in-GAP-Axiom-MuPAD-SageMath" style=""><a class="anchor hidden-xs" href="#Categories-in-GAP-Axiom-MuPAD-SageMath" title="Categories-in-GAP-Axiom-MuPAD-SageMath"><span class="octicon octicon-link"></span></a>Categories in GAP, Axiom, MuPAD, SageMath</h3><ul>
+<li>
+<p><strong>Barrier</strong>: compose building blocks <code>A1</code> and <code>A2</code> into modular generic code <code>B</code>: <code>f(a1, a2)</code></p>
+</li>
+<li>
+<p><strong>Requirements</strong>: <strong>uniform modular API</strong> + <strong>method resolution mechanism</strong></p>
+<p>Remember: few core concepts, hundreds of interesting combinations</p>
+</li>
+<li>
+<p><strong>Approaches</strong>:</p>
+<ul>
+<li>
+<p>Axiom, MuPAD: OOP with large hierarchies of abstract classes (categories)</p>
+</li>
+<li>
+<p>SageMath:</p>
+<ul>
+<li>same, but even larger</li>
+<li>based on standard OOP (Python) + infrastructure to scale</li>
+<li>embed semantic knowledge at single point of truth;
+exploit it to automatically generate the class hierarchy</li>
+</ul>
+</li>
+<li>
+<p>GAP: bespoke method resolution mechanism</p>
+</li>
+</ul>
+</li>
+</ul><hr><h3 id="Case-Study-libsemigroups-a-library-for-computing-with-semigroups" style=""><a class="anchor hidden-xs" href="#Case-Study-libsemigroups-a-library-for-computing-with-semigroups" title="Case-Study-libsemigroups-a-library-for-computing-with-semigroups"><span class="octicon octicon-link"></span></a>Case Study: libsemigroups:, a library for computing with semigroups</h3><p>Author: James B. Mitchel et al.</p><ul>
+<li>
+<p><strong>Problems</strong></p>
+<ul>
+<li>
+<p>Speeding GAP’s semigroup package while increasing its availability</p>
+</li>
+<li>
+<p>Use a low-level library <code>A</code> from a system <code>B</code> written in a different language</p>
+</li>
+</ul>
+</li>
+<li>
+<p><strong>Approach</strong></p>
+<ul>
+<li>
+<p>Rewrite as a standalone templated C++ library</p>
+</li>
+<li>
+<p>API: many iterations until converging to a natural API (no memory management, …)</p>
+</li>
+<li>
+<p>Bindings: from Python: on-the-fly binding using cppyy (also tried Cython, Pybind11, …)</p>
+</li>
+<li>
+<p>Adaptation: a thin layer for now; could use alignments</p>
+</li>
+</ul>
+</li>
+</ul><hr><h3 id="Case-Study-the-Sage--GAP-interface" style=""><a class="anchor hidden-xs" href="#Case-Study-the-Sage--GAP-interface" title="Case-Study-the-Sage--GAP-interface"><span class="octicon octicon-link"></span></a>Case Study: the Sage / GAP interface</h3><ul>
+<li>
+<p><strong>Problem</strong></p>
+<p>Use funtionalities from a system <code>A</code> in a system <code>B</code> written in a different language</p>
+</li>
+<li>
+<p><strong>Data exchange</strong></p>
+<ul>
+<li>
+<p>Objects returned as references (handles):</p>
+<ul>
+<li>Few conversions</li>
+<li>Reduced overhead</li>
+<li>Manipulate from B objects of A with no native representation in B</li>
+</ul>
+</li>
+</ul>
+</li>
+<li>
+<p><strong>Binding</strong></p>
+<ul>
+<li>
+<p>Originally: a pexpect interface</p>
+</li>
+<li>
+<p>Now: ABI (direct calls at the C level)</p>
+</li>
+</ul>
+</li>
+</ul><hr><ul>
+<li>
+<p><strong>Adapting</strong></p>
+<ul>
+<li>
+<p>Currently:</p>
+<ul>
+<li>monolithic adapters for some cases (groups, …)</li>
+</ul>
+</li>
+<li>
+<p>In progress:</p>
+<ul>
+<li>
+<p>modular adapters, exploiting the category hierarchy and semantic alignments</p>
+</li>
+<li>
+<p>objects returned as reference + semantic</p>
+</li>
+<li>
+<p>alignment <code>B.cardinality() -&gt; Size(A)</code> attached to the category of sets</p>
+</li>
+<li>
+<p>alignment <code>B.conjugacy_classes() -&gt; ConjugacyClasses(A)</code> attached to the category of groups</p>
+</li>
+</ul>
+</li>
+</ul>
+</li>
+</ul><hr><h2 id="Open-discussion" style=""><a class="anchor hidden-xs" href="#Open-discussion" title="Open-discussion"><span class="octicon octicon-link"></span></a>Open discussion</h2><ul>
+<li>
+<p>How to foster a sustainable and agile ecosystem where (sub)components have their own life cycle, explore new approaches, compete, and happily die when no more relevant.</p>
+</li>
+<li>
+<p>What other barriers do you identify in Computational Math?</p>
+</li>
+<li>
+<p>How do the barriers differ from other areas</p>
+</li>
+<li>
+<p>Other case studies? solutions? approaches?</p>
+</li>
+</ul></div>
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+        <div class="toc"><ul class="nav"><li class=""><a href="#Modularity-in-Mathematical-Computation" title="Modularity in Mathematical Computation">Modularity in Mathematical Computation</a><ul class="nav"><li><a href="#A-collaborative-document" title="A collaborative document">A collaborative document</a></li><li><a href="#Participants" title="Participants">Participants</a></li><li><a href="#Abstract" title="Abstract">Abstract</a></li><li><a href="#Composability" title="Composability?">Composability?</a><ul class="nav"><li><a href="#Data-transfers" title="Data transfers">Data transfers</a></li><li><a href="#Procedure-calls" title="Procedure calls">Procedure calls</a></li></ul></li><li><a href="#Barriers-faced-by-the-computational-pure-maths-community" title="Barriers faced by the computational pure maths community?">Barriers faced by the computational pure maths community?</a><ul class="nav"><li><a href="#Semantic-barriers" title="Semantic barriers">Semantic barriers</a></li><li><a href="#Social-barriers" title="Social barriers">Social barriers</a></li><li><a href="#Technical-barriers" title="Technical barriers">Technical barriers</a></li></ul></li><li><a href="#Some-case-studies-and-tentative-solutions" title="Some case studies and tentative solutions">Some case studies and tentative solutions</a><ul class="nav"><li><a href="#OpenMath" title="OpenMath">OpenMath</a></li><li><a href="#The-Math-in-the-Middle-approach" title="The Math-in-the-Middle approach">The Math-in-the-Middle approach</a></li><li><a href="#Categories-in-GAP-Axiom-MuPAD-SageMath" title="Categories in GAP, Axiom, MuPAD, SageMath">Categories in GAP, Axiom, MuPAD, SageMath</a></li><li><a href="#Case-Study-libsemigroups-a-library-for-computing-with-semigroups" title="Case Study: libsemigroups:, a library for computing with semigroups">Case Study: libsemigroups:, a library for computing with semigroups</a></li><li><a href="#Case-Study-the-Sage--GAP-interface" title="Case Study: the Sage / GAP interface">Case Study: the Sage / GAP interface</a></li></ul></li><li><a href="#Open-discussion" title="Open discussion">Open discussion</a></li></ul></li></ul></div><div class="toc-menu"><a class="expand-toggle" href="#">Expand all</a><a class="back-to-top" href="#">Back to top</a><a class="go-to-bottom" href="#">Go to bottom</a></div>
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