helm/www/lambdadelta/specification.html

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   8     <meta name="author" content="Ferruccio Guidi" />
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  10     <title>\lambda\delta home page</title>
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  21     </div>
  22     <div class="head1">The Formal System λδ (\lambda\delta)</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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  27       <br />
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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       λδ is developed as a machine-checked digital specification.
 109       It comes in several versions listed in the next table,
 110       which includes the major milestones.
 111    </div>
 112     <div xmlns:ld="http://lambdadelta.info/" class="text">
 113       The life cycle of a specification consists of four periods.
 114       <span class="emph alpha">Alpha:</span>
 115       the definitions are designed and the major propositions are proved,
 116       then the calculus is announced with a presentation.
 117       <span class="emph beta">Beta:</span>
 118       major changes and additions may occur before the calculus is released on paper.
 119       <span class="emph gamma">Gamma:</span>
 120       subsequent improvements occur until the specification is completed or superseded,
 121       while major changes and additions are announced and reported on paper.
 122       <span class="emph delta">Delta:</span>
 123       after its conclusion, the specification is modified just for maintenance.
 124    </div>
 125     <div xmlns:ld="http://lambdadelta.info/" class="text">
 126       <table cellpadding="4" cellspacing="0">
 127         <tbody>
 128           <tr>
 129             <td class="snns top capitalize italic gray">version</td>
 130             <td class="snnn top capitalize italic gray">name</td>
 131             <td class="snnn top capitalize italic gray">developed with</td>
 132             <td class="snnn top capitalize italic gray">stage</td>
 133             <td class="snnn top capitalize italic gray">started</td>
 134             <td class="snnn top capitalize italic gray">announced</td>
 135             <td class="snnn top capitalize italic gray">released</td>
 136             <td class="snnn top capitalize italic gray">concluded</td>
 137             <td class="ssnn top capitalize italic gray">references</td>
 138           </tr>
 139           <tr>
 140             <td class="snns top orange">
 141               <a href="http://lambdadelta.info/specification.html#v2">Version 2</a>
 142             </td>
 143             <td class="snnn top orange">"basic_2"</td>
 144             <td class="snnn top orange">
 145               <a href="http://matita.cs.unibo.it/">Matita 0.99.2</a>
 146             </td>
 147             <td class="snns top orange">"A2"</td>
 148             <td class="snnn top orange">October 2015</td>
 149             <td class="snnn top orange" />
 150             <td class="snnn top orange" />
 151             <td class="snnn top orange" />
 152             <td class="ssnn top orange">
 153               <br />
 154             </td>
 155           </tr>
 156           <tr>
 157             <td class="nnns top orange">
 158               <br />
 159             </td>
 160             <td class="nnnn top orange">
 161               <br />
 162             </td>
 163             <td class="nnnn top orange">
 164               <br />
 165             </td>
 166             <td class="snns top orange">"A1"</td>
 167             <td class="snnn top orange">April 2011</td>
 168             <td class="snnn top orange">June 2014</td>
 169             <td class="snnn top orange">October 2014</td>
 170             <td class="snnn top orange">August 2015</td>
 171             <td class="ssnn top orange">
 172               <a href="http://lambdadelta.info/documentation#ldV2a">V2a</a>
 173               <a href="http://lambdadelta.info/documentation#ldR2c">R2c</a>
 174             </td>
 175           </tr>
 176           <tr>
 177             <td class="snns top orange">Abandoned</td>
 178             <td class="snnn top orange" />
 179             <td class="snnn top orange">
 180               <a href="http://coq.inria.fr/">Coq 7.3.1</a>
 181             </td>
 182             <td class="snnn top orange" />
 183             <td class="snnn top orange">March 2008</td>
 184             <td class="snnn top orange" />
 185             <td class="snnn top orange" />
 186             <td class="snnn top orange">February 2011</td>
 187             <td class="ssnn top orange">
 188               <br />
 189             </td>
 190           </tr>
 191           <tr>
 192             <td class="snss top red">
 193               <a href="http://lambdadelta.info/specification.html#v1">Version 1</a>
 194             </td>
 195             <td class="snsn top red">"basic_1"</td>
 196             <td class="snsn top red">
 197               <a href="http://coq.inria.fr/">Coq 7.3.1</a>
 198             </td>
 199             <td class="snsn top red" />
 200             <td class="snsn top red">May 2004</td>
 201             <td class="snsn top red">December 2005</td>
 202             <td class="snsn top red">November 2006</td>
 203             <td class="snsn top red">May 2008</td>
 204             <td class="sssn top red">
 205               <a href="http://lambdadelta.info/documentation#ldV1a">V1a</a>
 206               <a href="http://lambdadelta.info/documentation#ldJ1a">J1a</a>
 207             </td>
 208           </tr>
 209         </tbody>
 210       </table>
 211     </div>
 212     <div xmlns:ld="http://lambdadelta.info/" class="text">
 213      Informational pages on the specifications are provided.
 214    </div>
 215     <ul xmlns:ld="http://lambdadelta.info/" id="">
 216       <li>
 217         <span class="emph alpha">Notice on displayed numerical acounts:</span>
 218       nodes are counted according to the "intrinsic complexity measure"
 219       [F. Guidi: "Procedural Representation of CIC Proof Terms"
 220       Journal of Automated Reasoning 44(1-2), Springer (February 2010), pp. 53-78].
 221    </li>
 222     </ul>
 223     <ul xmlns:ld="http://lambdadelta.info/" id="">
 224       <li>
 225         <span class="emph alpha">Notice on displayed logical structures:</span>
 226       from the logical standpoint, the source scripts are grouped in "planes"
 227       and these are grouped in "components";
 228       the notation for the relations or functions
 229       introduced in each script, is shown in parentheses (? are placeholders).
 230    </li>
 231     </ul>
 232     <!-- VERSION 2 =========================================================== -->
 233     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v2">
 234       <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b4.png" /> λδ version 2 (active)</div>
 235     <div xmlns:ld="http://lambdadelta.info/" class="text">
 236       The formal specification of λδ version 2
 237       is available in the following formats:
 238    </div>
 239     <ul xmlns:ld="http://lambdadelta.info/" id="source2">
 240       <li>
 241         <div class="text">
 242           <a href="http://lambdadelta.info/download/lambdadelta_2A1.tar.gz">lambdadelta_2A1 for Matita 0.99.2</a>
 243          (revised <span class="emph gamma">2014-10</span>).
 244          Source scripts.
 245          <a href="http://lambdadelta.info/documentation.html#ldR2c">Documentation (R2c)</a>.
 246       </div>
 247         <div class="text">
 248          The scripts are grouped in directories, first by part, then by component.
 249       </div>
 250         <div class="text">
 251           <span class="emph alpha">Notice:</span>
 252          the scripts are checked by the latest version of Matita from
 253          <a href="http://matita.cs.unibo.it/download.shtml">HELM Subversion repository</a>
 254          at path &lt;trunk/matita/&gt;.
 255       </div>
 256       </li>
 257     </ul>
 258     <div xmlns:ld="http://lambdadelta.info/" class="text">
 259       Informational pages on the parts of the specification:
 260       <a href="http://lambdadelta.info/ground_2.html">Background</a>,
 261       <a href="http://lambdadelta.info/basic_2.html">Core</a>,
 262       <a href="http://lambdadelta.info/apps_2.html">Applications</a>.
 263    </div>
 264     <!-- VERSION 1 =========================================================== -->
 265     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v1">
 266       <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b6.png" /> λδ version 1 (superseded)</div>
 267     <div xmlns:ld="http://lambdadelta.info/" class="text">
 268       The formal specification of λδ version 1
 269       is available in the following formats:
 270    </div>
 271     <ul xmlns:ld="http://lambdadelta.info/" id="source1">
 272       <li>
 273         <div class="text">
 274           <a href="http://lambdadelta.info/download/lambdadelta_1.tar.gz">lambdadelta_1 for Coq 7.3.1</a>
 275          (revised <span class="emph delta">2015-09</span>).
 276          Source scripts.
 277          <a href="http://lambdadelta.info/documentation.html#ldJ1a">Documentation (J1a)</a>.
 278          <ul>
 279             <li>
 280               <span class="emph delta">2015 January 15.</span>
 281             17 new lemmas and former lemma "eq_nat_dec" renamed as "nat_dec_neg".
 282          </li>
 283           </ul>
 284         </div>
 285         <div class="text">
 286          The scripts are grouped in directories, one for each part.
 287       </div>
 288       </li>
 289     </ul>
 290     <ul xmlns:ld="http://lambdadelta.info/" id="static1">
 291       <li>
 292         <a href="http://lambdadelta.info/static/matita/lambdadelta/">lambdadelta_1 for Matita 0.5</a>
 293       (revised <span class="emph delta">2011-09</span>).
 294       Static HTML pages generated by the <a href="http://helm.cs.unibo.it/">HELM</a> rendering engine.
 295       <ul>
 296           <li>
 297             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/pr3/pr3/pr3_confluence.con.html">
 298             Confluence of reduction</a>
 299          (Church-Rosser property).
 300       </li>
 301           <li>
 302             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_correct.con.html">
 303             Correctness of types</a>.
 304       </li>
 305           <li>
 306             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_unique.con.html">
 307             Uniqueness of types up to conversion</a>.
 308       </li>
 309           <li>
 310             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/pr3/ty3_sred_pr3.con.html">
 311             Subject reduction of the type assignment</a>.
 312       </li>
 313           <li>
 314             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/arity_props/ty3_sn3.con.html">
 315             Strong normalization of the typed terms</a>.
 316       </li>
 317           <li>
 318             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/dec/ty3_inference.con.html">
 319             Decidability of the type inference problem</a>.
 320       </li>
 321         </ul>
 322       </li>
 323     </ul>
 324     <ul xmlns:ld="http://lambdadelta.info/" id="dynamic1">
 325       <li>
 326         <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/">
 327          lambdadelta_1 for Matita 0.5</a>
 328       (revised <span class="emph delta">2011-09</span>).
 329       <a href="http://helm.cs.unibo.it/">HELM</a> directory.
 330       <span class="emph alpha">Notice: the HELM rendering engine is offline.</span>
 331       </li>
 332     </ul>
 333     <div xmlns:ld="http://lambdadelta.info/" class="text">
 334       Informational pages on the parts of the specification:
 335       <a href="http://lambdadelta.info/ground_1.html">Background</a>,
 336       <a href="http://lambdadelta.info/basic_1.html">Core</a>.
 337    </div>
 338     <div class="spacer">
 339       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
 340     </div>
 341     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 342       <br />
 343     </div>
 344     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 345       <a href="http://validator.w3.org/check?uri=referer">
 346         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
 347       </a>
 348       <a href="http://jigsaw.w3.org/css-validator/check/referer">
 349         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
 350       </a>
 351       <a href="http://www.w3.org/XML/">
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 353       </a>
 354       <a href="http://www.w3.org/Graphics/PNG/">
 355         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
 356       </a>
 357       <a href="http://www.anybrowser.org/campaign/">
 358         <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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 361     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 362       <br />
 363     </div>
 364     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Thu, 10 Dec 2015 16:21:42 +0100</div>
 365   </body>
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