Axiom musings ... The Lean Mathematical Library
Tim Daly <[email protected]> Sat, 2 Jul 2022 05:18:58 -0400
| Newsgroups | gmane.comp.mathematics.axiom.devel |
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| Message-ID | <CAJn5L=Jd2Z-zLgEw5guJ20ED445m8rmcA7Q67H6YEQt19u=zhQ@mail.gmail.com> |
--000000000000d5dd8d05e2cefe48 Content-Type: multipart/alternative; boundary="000000000000d5dd8b05e2cefe46" --000000000000d5dd8b05e2cefe46 Content-Type: text/plain; charset="UTF-8" Axiom has a category structure (Axiom's kind, not the math kind). The Axiom SANE branch is trying to structure definitions and axioms to benefit from Lean's research. In this paper, The Lean Mathematical Library https://arxiv.org/pdf/1910.09336.pdf on page 4, there is a graph of the Lean structure hierarchy. This differs considerably from Axiom's structure. How can these work together? There is a bit of design issue here. On the plus side, LEAN's structure has an underlying set of proofs. We would really like to leverage this effort. On the minus side, reorganizing Axiom's category hierarchy to match this would undercut most of the existing code. How to get the benefit and avoid the damage is currently a major design consideration. At the moment I'm leaning (pun intended) toward a parallel structure. Conceptually that would mean that SANE would only explicitly reference certain LEAN theorems directly and inherit the rest through the LEAN structure. Unfortunately Axiom's category hierarchy is somewhat ad-hoc and may not be strictly valid in some cases. Research is SUCH fun :-) Tim --000000000000d5dd8b05e2cefe46 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable <div dir=3D"ltr"><div>Axiom has a category structure (Axiom's kind, not= the math kind).</div><div>The Axiom SANE branch is trying to structure def= initions and axioms</div><div>to benefit from Lean's research.</div><di= v><br></div><div>In this paper, The Lean Mathematical Library</div><div><a = href=3D"https://arxiv.org/pdf/1910.09336.pdf">https://arxiv.org/pdf/1910.09= 336.pdf</a></div><div>on page 4, there is a graph of the Lean structure hie= rarchy.</div><div>This differs considerably from Axiom's structure.</di= v><div><br></div><div>How can these work together? There is a bit of design= issue here.</div><div><br></div><div>On the plus side, LEAN's structur= e has an underlying set of proofs.</div><div>We would really like to levera= ge this effort.<br></div><div><br></div><div>On the minus side, reorganizin= g Axiom's category hierarchy</div><div>to match this would undercut mos= t of the existing code.</div><div><br></div><div>How to get the benefit and= avoid the damage is currently</div><div>a major design consideration. At t= he moment I'm leaning</div><div>(pun intended) toward a parallel struct= ure. Conceptually <br></div><div>that would mean that SANE would only expli= citly reference</div><div>certain LEAN theorems directly and inherit the re= st through</div><div>the LEAN structure. Unfortunately Axiom's category= hierarchy</div><div>is somewhat ad-hoc and may not be strictly valid in so= me cases.</div><div><br></div><div>Research is SUCH fun :-)<br></div><div><= br></div><div>Tim<br></div></div> --000000000000d5dd8b05e2cefe46-- --000000000000d5dd8d05e2cefe48 Content-Type: image/png; name="LEANStructureHierarchy.png" Content-Disposition: attachment; filename="LEANStructureHierarchy.png" Content-Transfer-Encoding: base64 Content-ID: <f_l53nvg8s0> X-Attachment-Id: f_l53nvg8s0 iVBORw0KGgoAAAANSUhEUgAAA4YAAAIXCAYAAADAPkBfAAAh/XpUWHRSYXcgcHJvZmlsZSB0eXBl IGV4aWYAAHjapZtpdhy5joX/cxW9BM7DcsDpnN5BL7+/y0z72a7qN5wulyVZSkUwCOAOINKd//nv 6/6L/1pv3eXSeh21ev7LI49ofNH95z97H4PP7+P7r1efvt/97fsuNB/fV5Fv6SXp5y98/jt8n1eE +P3++nwOxvfLLxca5/uD+fsP7Huh2L83+H7/e1ufwucGfn8vZN8Lpfi9c/78e37vXEdvvz7C9/f0 +OH7+f11+pBTi7XU0DIfc/St1cHXPfrc2Lethcb1/cXvBf/8t/vx0sia4kkh+fexf1aZ9Dcm43N7 HyOv86m8rysfSyqfx3WEjCVw4fHd2++jajd/25sfn/+P/9y/81jfdPgt3D+/+qaB+/GD0X5G5bc0 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