helm/www/lambdadelta/specification.html

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  22     <div class="head1">The Formal Systems of the λδ (\lambda\delta) Family</div>
  23     <div class="spacer">
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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/home.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/home.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#helena">helena</a>
  77             </td>
  78             <td class="ssnn capitalize green">
  79               <a href="http://lambdadelta.info/osn/">Open Symbolic Notation (OSN)</a>
  80             </td>
  81           </tr>
  82           <tr>
  83             <td class="snss capitalize sky">
  84               <a href="http://lambdadelta.info/home.html#citations">citations</a>
  85             </td>
  86             <td class="snss capitalize magenta">
  87               <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
  88             </td>
  89             <td class="snss capitalize white">
  90               <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
  91             </td>
  92             <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>
  93             <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
  94             <td class="snss capitalize orange">
  95               <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
  96             </td>
  97             <td class="snss capitalize green">
  98               <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
  99             </td>
 100             <td class="sssn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</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="[butterfly]" title="\lambda\delta 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">stage</td>
 131             <td class="snnn top capitalize italic gray">developed with</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 yellow">
 140               <a href="http://lambdadelta.info/specification.html#v3">Version 3</a>
 141             </td>
 142             <td class="snnn top yellow">"basic_3"</td>
 143             <td class="snnn top yellow" />
 144             <td class="snnn top yellow" />
 145             <td class="snnn top yellow" />
 146             <td class="snnn top yellow" />
 147             <td class="snnn top yellow" />
 148             <td class="snnn top yellow" />
 149             <td class="ssnn top yellow">
 150               <a href="http://lambdadelta.info/documentation.html#ldJ3a">J3a</a>
 151             </td>
 152           </tr>
 153           <tr>
 154             <td class="snns top orange">
 155               <a href="http://lambdadelta.info/specification.html#v2">Version 2</a>
 156             </td>
 157             <td class="snnn top orange">"basic_2"</td>
 158             <td class="snns top orange">"A2"</td>
 159             <td class="snnn top orange">
 160               <a href="http://matita.cs.unibo.it/">Matita 0.99.3</a>
 161             </td>
 162             <td class="snnn top orange">October 2015</td>
 163             <td class="snnn top orange" />
 164             <td class="snnn top orange" />
 165             <td class="snnn top orange" />
 166             <td class="ssnn top orange" />
 167           </tr>
 168           <tr>
 169             <td class="nnns top orange">
 170               <br />
 171             </td>
 172             <td class="nnnn top orange">
 173               <br />
 174             </td>
 175             <td class="snns top orange">"A1"</td>
 176             <td class="snnn top orange">
 177               <a href="http://matita.cs.unibo.it/">Matita 0.99.2</a>
 178             </td>
 179             <td class="snnn top orange">April 2011</td>
 180             <td class="snnn top orange">June 2014</td>
 181             <td class="snnn top orange">October 2014</td>
 182             <td class="snnn top orange">August 2015</td>
 183             <td class="ssnn top orange">
 184               <a href="http://lambdadelta.info/documentation.html#ldV2a">V2a</a>
 185               <a href="http://lambdadelta.info/documentation.html#ldR2c">R2c</a>
 186             </td>
 187           </tr>
 188           <tr>
 189             <td class="snns top orange">Abandoned</td>
 190             <td class="snnn top orange" />
 191             <td class="snnn top orange" />
 192             <td class="snnn top orange">
 193               <a href="http://coq.inria.fr/">Coq 7.3.1</a>
 194             </td>
 195             <td class="snnn top orange">March 2008</td>
 196             <td class="snnn top orange" />
 197             <td class="snnn top orange" />
 198             <td class="snnn top orange">February 2011</td>
 199             <td class="ssnn top orange" />
 200           </tr>
 201           <tr>
 202             <td class="snss top red">
 203               <a href="http://lambdadelta.info/specification.html#v1">Version 1</a>
 204             </td>
 205             <td class="snsn top red">"basic_1"</td>
 206             <td class="snsn top red" />
 207             <td class="snsn top red">
 208               <a href="http://coq.inria.fr/">Coq 7.3.1</a>
 209             </td>
 210             <td class="snsn top red">May 2004</td>
 211             <td class="snsn top red">December 2005</td>
 212             <td class="snsn top red">November 2006</td>
 213             <td class="snsn top red">May 2008</td>
 214             <td class="sssn top red">
 215               <a href="http://lambdadelta.info/documentation.html#ldV1a">V1a</a>
 216               <a href="http://lambdadelta.info/documentation.html#ldJ1a">J1a</a>
 217             </td>
 218           </tr>
 219         </tbody>
 220       </table>
 221     </div>
 222     <div xmlns:ld="http://lambdadelta.info/" class="text">
 223      Informational pages on the specifications are provided.
 224    </div>
 225     <ul xmlns:ld="http://lambdadelta.info/" id="notice1">
 226       <li>
 227         <span class="emph alpha">Notice on displayed numerical acounts:</span>
 228       nodes are counted according to the "intrinsic complexity measure"
 229       [F. Guidi: "Procedural Representation of CIC Proof Terms"
 230       Journal of Automated Reasoning 44(1-2), Springer (February 2010), pp. 53-78].
 231    </li>
 232     </ul>
 233     <ul xmlns:ld="http://lambdadelta.info/" id="notice2">
 234       <li>
 235         <span class="emph alpha">Notice on displayed logical structures:</span>
 236       from the logical standpoint, the source scripts are grouped in "planes"
 237       and these are grouped in "components";
 238       the notation for the relations or functions
 239       introduced in each script, is shown in parentheses (? are placeholders).
 240    </li>
 241     </ul>
 242     <!-- VERSION 3 =========================================================== -->
 243     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v3">
 244       <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b8.png" /> λδ version 3 (proposed)</div>
 245     <div xmlns:ld="http://lambdadelta.info/" class="text">
 246       The formal specification of λδ version 3
 247       is forthcoming.
 248    </div>
 249     <!-- VERSION 2 =========================================================== -->
 250     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v2">
 251       <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png" /> λδ version 2 (active)</div>
 252     <div xmlns:ld="http://lambdadelta.info/" class="text">
 253       The formal specification of λδ version 2
 254       is available in the following formats:
 255    </div>
 256     <ul xmlns:ld="http://lambdadelta.info/" id="source2">
 257       <li>
 258         <div class="text">
 259           <a href="http://lambdadelta.info/download/lambdadelta_2A1.tar.gz">lambdadelta_2A1 for Matita 0.99.2</a>
 260          (revised <span class="emph gamma">2014-10</span>).
 261          Source scripts [Svn revision: 12964].
 262          <a href="http://lambdadelta.info/documentation.html#ldR2c">Documentation (R2c)</a>.
 263       </div>
 264         <div class="text">
 265          The scripts are grouped in directories, first by part, then by component.
 266       </div>
 267         <div class="text">
 268           <span class="emph alpha">Notice:</span>
 269          the scripts are checked by the latest version of Matita from
 270          <a href="http://matita.cs.unibo.it/download.shtml">HELM Subversion repository</a>
 271          at path &lt;trunk/matita/&gt;.
 272       </div>
 273       </li>
 274     </ul>
 275     <div xmlns:ld="http://lambdadelta.info/" class="text">
 276       Informational pages on the parts of the specification:
 277       <a href="http://lambdadelta.info/ground_2.html">Background</a>,
 278       <a href="http://lambdadelta.info/basic_2.html">Core</a>,
 279       <a href="http://lambdadelta.info/apps_2.html">Applications</a>.
 280    </div>
 281     <!-- VERSION 1 =========================================================== -->
 282     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v1">
 283       <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b6.png" /> λδ version 1 (superseded)</div>
 284     <div xmlns:ld="http://lambdadelta.info/" class="text">
 285       The formal specification of λδ version 1
 286       is available in the following formats:
 287    </div>
 288     <ul xmlns:ld="http://lambdadelta.info/" id="source1">
 289       <li>
 290         <div class="text">
 291           <a href="http://lambdadelta.info/download/lambdadelta_1.tar.gz">lambdadelta_1 for Coq 7.3.1</a>
 292          (revised <span class="emph delta">2015-09</span>).
 293          Source scripts.
 294          <a href="http://lambdadelta.info/documentation.html#ldJ1a">Documentation (J1a)</a>.
 295          <ul>
 296             <li class="">
 297               <span class="emph delta">2015 January 15.</span>
 298             17 new lemmas and former lemma "eq_nat_dec" renamed as "nat_dec_neg".
 299          </li>
 300           </ul>
 301         </div>
 302         <div class="text">
 303          The scripts are grouped in directories, one for each part.
 304       </div>
 305       </li>
 306     </ul>
 307     <ul xmlns:ld="http://lambdadelta.info/" id="static1">
 308       <li>
 309         <a href="http://lambdadelta.info/static/matita/lambdadelta/">lambdadelta_1 for Matita 0.5</a>
 310       (revised <span class="emph delta">2011-09</span>).
 311       Static HTML pages generated by the <a href="http://helm.cs.unibo.it/">HELM</a> rendering engine.
 312       <ul>
 313           <li class="">
 314             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/pr3/pr3/pr3_confluence.con.html">
 315             Confluence of reduction</a>
 316          (Church-Rosser property).
 317       </li>
 318           <li class="">
 319             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_correct.con.html">
 320             Correctness of types</a>.
 321       </li>
 322           <li class="">
 323             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_unique.con.html">
 324             Uniqueness of types up to conversion</a>.
 325       </li>
 326           <li class="">
 327             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/pr3/ty3_sred_pr3.con.html">
 328             Subject reduction of the type assignment</a>.
 329       </li>
 330           <li class="">
 331             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/arity_props/ty3_sn3.con.html">
 332             Strong normalization of the typed terms</a>.
 333       </li>
 334           <li class="">
 335             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/dec/ty3_inference.con.html">
 336             Decidability of the type inference problem</a>.
 337       </li>
 338         </ul>
 339       </li>
 340     </ul>
 341     <ul xmlns:ld="http://lambdadelta.info/" id="dynamic1">
 342       <li>
 343         <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/">
 344          lambdadelta_1 for Matita 0.5</a>
 345       (revised <span class="emph delta">2011-09</span>).
 346       <a href="http://helm.cs.unibo.it/">HELM</a> directory.
 347       <span class="emph alpha">Notice: the HELM rendering engine is offline.</span>
 348       </li>
 349     </ul>
 350     <div xmlns:ld="http://lambdadelta.info/" class="text">
 351       Informational pages on the parts of the specification:
 352       <a href="http://lambdadelta.info/ground_1.html">Background</a>,
 353       <a href="http://lambdadelta.info/basic_1.html">Core</a>.
 354    </div>
 355     <div class="spacer">
 356       <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
 357     </div>
 358     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 359       <br />
 360     </div>
 361     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 362       <a href="http://validator.w3.org/check?uri=referer">
 363         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
 364       </a>
 365       <a href="http://jigsaw.w3.org/css-validator/check/referer">
 366         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
 367       </a>
 368       <a href="http://www.w3.org/XML/">
 369         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
 370       </a>
 371       <a href="http://www.w3.org/Graphics/PNG/">
 372         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
 373       </a>
 374       <a href="http://www.anybrowser.org/campaign/">
 375         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
 376       </a>
 377     </div>
 378     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 379       <br />
 380     </div>
 381     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Fri, 24 Nov 2017 21:00:00 +0100</div>
 382   </body>
 383 </html>