helm/www/lambdadelta/specification.html

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   8     <meta name="author" content="Ferruccio Guidi" />
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  22     <div class="head1">The Formal Systems of the λδ (\lambda\delta) Family</div>
  23     <div class="spacer">
  24       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
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  29     <div xmlns:ld="http://lambdadelta.info/" class="text">
  30       <table cellpadding="4" cellspacing="0">
  31         <tbody>
  32           <tr>
  33             <td class="snns capitalize italic sky">
  34               <a href="http://lambdadelta.info/index.html">home</a>
  35             </td>
  36             <td class="snns capitalize italic magenta">
  37               <a href="http://lambdadelta.info/news.html">news</a>
  38             </td>
  39             <td class="snns capitalize italic white">
  40               <a href="http://lambdadelta.info/specification.html">specification</a>
  41             </td>
  42             <td class="snnn capitalize italic white">
  43               <br />
  44             </td>
  45             <td class="snnn capitalize italic white">
  46               <br />
  47             </td>
  48             <td class="snns capitalize italic orange">
  49               <a href="http://lambdadelta.info/documentation.html">documentation</a>
  50             </td>
  51             <td class="snns capitalize italic green">
  52               <a href="http://lambdadelta.info/implementation.html">implementation</a>
  53             </td>
  54             <td class="ssnn capitalize italic green">
  55               <br />
  56             </td>
  57           </tr>
  58           <tr>
  59             <td class="snns capitalize sky">
  60               <a href="http://lambdadelta.info/index.html#foreword">foreword</a>
  61             </td>
  62             <td class="snns capitalize magenta">
  63               <a href="http://lambdadelta.info/news.html#milestones">milestones</a>
  64             </td>
  65             <td class="snns capitalize white">
  66               <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
  67             </td>
  68             <td class="snnn capitalize white">(<a href="http://lambdadelta.info/ground_2.html">background</a> - <a href="http://lambdadelta.info/basic_2.html">core</a> - <a href="http://lambdadelta.info/apps_2.html">applications</a>)</td>
  69             <td class="snnn capitalize white">
  70               <br />
  71             </td>
  72             <td class="snns capitalize orange">
  73               <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
  74             </td>
  75             <td class="snns capitalize green">
  76               <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
  77             </td>
  78             <td class="ssnn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
  79           </tr>
  80           <tr>
  81             <td class="snss capitalize sky">
  82               <a href="http://lambdadelta.info/index.html#citations">citations</a>
  83             </td>
  84             <td class="snss capitalize magenta">
  85               <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
  86             </td>
  87             <td class="snss capitalize white">
  88               <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
  89             </td>
  90             <td class="snsn capitalize white">(<a href="http://lambdadelta.info/ground_1.html">background</a> - <a href="http://lambdadelta.info/basic_1.html">core</a>)</td>
  91             <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
  92             <td class="snss capitalize orange">
  93               <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
  94             </td>
  95             <td class="snss capitalize green">
  96               <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
  97             </td>
  98             <td class="sssn capitalize green">
  99               <br />
 100             </td>
 101           </tr>
 102         </tbody>
 103       </table>
 104     </div>
 105     <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="specifications">Computer-checked formal specifications <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b15.png" />
 106     </div>
 107     <div xmlns:ld="http://lambdadelta.info/" class="text">
 108       The systems of the λδ family are developed as machine-checked digital specifications,
 109       and are listed in the next table, which includes the major milestones.
 110    </div>
 111     <div xmlns:ld="http://lambdadelta.info/" class="text">
 112       The life cycle of a specification consists of four periods.
 113       <span class="emph alpha">Alpha:</span>
 114       the definitions are designed and the major propositions are proved,
 115       then the calculus is announced with a presentation.
 116       <span class="emph beta">Beta:</span>
 117       major changes and additions may occur before the calculus is released on paper.
 118       <span class="emph gamma">Gamma:</span>
 119       subsequent improvements occur until the specification is completed or superseded,
 120       while major changes and additions are announced and reported on paper.
 121       <span class="emph delta">Delta:</span>
 122       after its conclusion, the specification is modified just for maintenance.
 123    </div>
 124     <div xmlns:ld="http://lambdadelta.info/" class="text">
 125       <table cellpadding="4" cellspacing="0">
 126         <tbody>
 127           <tr>
 128             <td class="snns top capitalize italic gray">version</td>
 129             <td class="snnn top capitalize italic gray">name</td>
 130             <td class="snnn top capitalize italic gray">developed with</td>
 131             <td class="snnn top capitalize italic gray">stage</td>
 132             <td class="snnn top capitalize italic gray">started</td>
 133             <td class="snnn top capitalize italic gray">announced</td>
 134             <td class="snnn top capitalize italic gray">released</td>
 135             <td class="snnn top capitalize italic gray">concluded</td>
 136             <td class="ssnn top capitalize italic gray">references</td>
 137           </tr>
 138           <tr>
 139             <td class="snns top orange">
 140               <a href="http://lambdadelta.info/specification.html#v2">Version 2</a>
 141             </td>
 142             <td class="snnn top orange">"basic_2"</td>
 143             <td class="snnn top orange">
 144               <a href="http://matita.cs.unibo.it/">Matita 0.99.2</a>
 145             </td>
 146             <td class="snns top orange">"A2"</td>
 147             <td class="snnn top orange">October 2015</td>
 148             <td class="snnn top orange" />
 149             <td class="snnn top orange" />
 150             <td class="snnn top orange" />
 151             <td class="ssnn top orange">
 152               <br />
 153             </td>
 154           </tr>
 155           <tr>
 156             <td class="nnns top orange">
 157               <br />
 158             </td>
 159             <td class="nnnn top orange">
 160               <br />
 161             </td>
 162             <td class="nnnn top orange">
 163               <br />
 164             </td>
 165             <td class="snns top orange">"A1"</td>
 166             <td class="snnn top orange">April 2011</td>
 167             <td class="snnn top orange">June 2014</td>
 168             <td class="snnn top orange">October 2014</td>
 169             <td class="snnn top orange">August 2015</td>
 170             <td class="ssnn top orange">
 171               <a href="http://lambdadelta.info/documentation#ldV2a">V2a</a>
 172               <a href="http://lambdadelta.info/documentation#ldR2c">R2c</a>
 173             </td>
 174           </tr>
 175           <tr>
 176             <td class="snns top orange">Abandoned</td>
 177             <td class="snnn top orange" />
 178             <td class="snnn top orange">
 179               <a href="http://coq.inria.fr/">Coq 7.3.1</a>
 180             </td>
 181             <td class="snnn top orange" />
 182             <td class="snnn top orange">March 2008</td>
 183             <td class="snnn top orange" />
 184             <td class="snnn top orange" />
 185             <td class="snnn top orange">February 2011</td>
 186             <td class="ssnn top orange">
 187               <br />
 188             </td>
 189           </tr>
 190           <tr>
 191             <td class="snss top red">
 192               <a href="http://lambdadelta.info/specification.html#v1">Version 1</a>
 193             </td>
 194             <td class="snsn top red">"basic_1"</td>
 195             <td class="snsn top red">
 196               <a href="http://coq.inria.fr/">Coq 7.3.1</a>
 197             </td>
 198             <td class="snsn top red" />
 199             <td class="snsn top red">May 2004</td>
 200             <td class="snsn top red">December 2005</td>
 201             <td class="snsn top red">November 2006</td>
 202             <td class="snsn top red">May 2008</td>
 203             <td class="sssn top red">
 204               <a href="http://lambdadelta.info/documentation#ldV1a">V1a</a>
 205               <a href="http://lambdadelta.info/documentation#ldJ1a">J1a</a>
 206             </td>
 207           </tr>
 208         </tbody>
 209       </table>
 210     </div>
 211     <div xmlns:ld="http://lambdadelta.info/" class="text">
 212      Informational pages on the specifications are provided.
 213    </div>
 214     <ul xmlns:ld="http://lambdadelta.info/" id="">
 215       <li>
 216         <span class="emph alpha">Notice on displayed numerical acounts:</span>
 217       nodes are counted according to the "intrinsic complexity measure"
 218       [F. Guidi: "Procedural Representation of CIC Proof Terms"
 219       Journal of Automated Reasoning 44(1-2), Springer (February 2010), pp. 53-78].
 220    </li>
 221     </ul>
 222     <ul xmlns:ld="http://lambdadelta.info/" id="">
 223       <li>
 224         <span class="emph alpha">Notice on displayed logical structures:</span>
 225       from the logical standpoint, the source scripts are grouped in "planes"
 226       and these are grouped in "components";
 227       the notation for the relations or functions
 228       introduced in each script, is shown in parentheses (? are placeholders).
 229    </li>
 230     </ul>
 231     <!-- VERSION 2 =========================================================== -->
 232     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v2">
 233       <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b4.png" /> λδ version 2 (active)</div>
 234     <div xmlns:ld="http://lambdadelta.info/" class="text">
 235       The formal specification of λδ version 2
 236       is available in the following formats:
 237    </div>
 238     <ul xmlns:ld="http://lambdadelta.info/" id="source2">
 239       <li>
 240         <div class="text">
 241           <a href="http://lambdadelta.info/download/lambdadelta_2A1.tar.gz">lambdadelta_2A1 for Matita 0.99.2</a>
 242          (revised <span class="emph gamma">2014-10</span>).
 243          Source scripts.
 244          <a href="http://lambdadelta.info/documentation.html#ldR2c">Documentation (R2c)</a>.
 245       </div>
 246         <div class="text">
 247          The scripts are grouped in directories, first by part, then by component.
 248       </div>
 249         <div class="text">
 250           <span class="emph alpha">Notice:</span>
 251          the scripts are checked by the latest version of Matita from
 252          <a href="http://matita.cs.unibo.it/download.shtml">HELM Subversion repository</a>
 253          at path &lt;trunk/matita/&gt;.
 254       </div>
 255       </li>
 256     </ul>
 257     <div xmlns:ld="http://lambdadelta.info/" class="text">
 258       Informational pages on the parts of the specification:
 259       <a href="http://lambdadelta.info/ground_2.html">Background</a>,
 260       <a href="http://lambdadelta.info/basic_2.html">Core</a>,
 261       <a href="http://lambdadelta.info/apps_2.html">Applications</a>.
 262    </div>
 263     <!-- VERSION 1 =========================================================== -->
 264     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v1">
 265       <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b6.png" /> λδ version 1 (superseded)</div>
 266     <div xmlns:ld="http://lambdadelta.info/" class="text">
 267       The formal specification of λδ version 1
 268       is available in the following formats:
 269    </div>
 270     <ul xmlns:ld="http://lambdadelta.info/" id="source1">
 271       <li>
 272         <div class="text">
 273           <a href="http://lambdadelta.info/download/lambdadelta_1.tar.gz">lambdadelta_1 for Coq 7.3.1</a>
 274          (revised <span class="emph delta">2015-09</span>).
 275          Source scripts.
 276          <a href="http://lambdadelta.info/documentation.html#ldJ1a">Documentation (J1a)</a>.
 277          <ul>
 278             <li>
 279               <span class="emph delta">2015 January 15.</span>
 280             17 new lemmas and former lemma "eq_nat_dec" renamed as "nat_dec_neg".
 281          </li>
 282           </ul>
 283         </div>
 284         <div class="text">
 285          The scripts are grouped in directories, one for each part.
 286       </div>
 287       </li>
 288     </ul>
 289     <ul xmlns:ld="http://lambdadelta.info/" id="static1">
 290       <li>
 291         <a href="http://lambdadelta.info/static/matita/lambdadelta/">lambdadelta_1 for Matita 0.5</a>
 292       (revised <span class="emph delta">2011-09</span>).
 293       Static HTML pages generated by the <a href="http://helm.cs.unibo.it/">HELM</a> rendering engine.
 294       <ul>
 295           <li>
 296             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/pr3/pr3/pr3_confluence.con.html">
 297             Confluence of reduction</a>
 298          (Church-Rosser property).
 299       </li>
 300           <li>
 301             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_correct.con.html">
 302             Correctness of types</a>.
 303       </li>
 304           <li>
 305             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_unique.con.html">
 306             Uniqueness of types up to conversion</a>.
 307       </li>
 308           <li>
 309             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/pr3/ty3_sred_pr3.con.html">
 310             Subject reduction of the type assignment</a>.
 311       </li>
 312           <li>
 313             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/arity_props/ty3_sn3.con.html">
 314             Strong normalization of the typed terms</a>.
 315       </li>
 316           <li>
 317             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/dec/ty3_inference.con.html">
 318             Decidability of the type inference problem</a>.
 319       </li>
 320         </ul>
 321       </li>
 322     </ul>
 323     <ul xmlns:ld="http://lambdadelta.info/" id="dynamic1">
 324       <li>
 325         <a href="http://mowgli.cs.unibo.it:58080/apply?keys=RT&amp;xmluri=http://helm.cs.unibo.it/helm//html/folder/index.html&amp;prop.media-type=text/html&amp;param.thmedia-type=text/html&amp;param.thkeys=T1%2CT2%2CL%2CE&amp;param.embedkeys=d_c%2CTC1%2CHC2%2CL&amp;param.thencoding=UTF-8&amp;prop.encoding=UTF-8&amp;prop.doctype-public=-//W3C//DTD%20XHTML%201.0%20Transitional//EN&amp;param.doctype-public=-//W3C//DTD%20XHTML%201.0%20Transitional//EN&amp;param.encoding=UTF-8&amp;param.media-type=text/html&amp;param.keys=d_c%2CC1%2CHC2%2CL&amp;profile=default&amp;param.profile=default&amp;param.CICURI=theory:/matita/lambdadelta/">
 326          lambdadelta_1 for Matita 0.5</a>
 327       (revised <span class="emph delta">2011-09</span>).
 328       <a href="http://helm.cs.unibo.it/">HELM</a> directory.
 329       <span class="emph alpha">Notice: the HELM rendering engine is offline.</span>
 330       </li>
 331     </ul>
 332     <div xmlns:ld="http://lambdadelta.info/" class="text">
 333       Informational pages on the parts of the specification:
 334       <a href="http://lambdadelta.info/ground_1.html">Background</a>,
 335       <a href="http://lambdadelta.info/basic_1.html">Core</a>.
 336    </div>
 337     <div class="spacer">
 338       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
 339     </div>
 340     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 341       <br />
 342     </div>
 343     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 344       <a href="http://validator.w3.org/check?uri=referer">
 345         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
 346       </a>
 347       <a href="http://jigsaw.w3.org/css-validator/check/referer">
 348         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
 349       </a>
 350       <a href="http://www.w3.org/XML/">
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 352       </a>
 353       <a href="http://www.w3.org/Graphics/PNG/">
 354         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
 355       </a>
 356       <a href="http://www.anybrowser.org/campaign/">
 357         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
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 360     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 361       <br />
 362     </div>
 363     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Wed, 30 Dec 2015 12:08:04 +0100</div>
 364   </body>
 365 </html>