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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  22     <div class="head1">The Formal System λδ (\lambda\delta)</div>
  23     <div class="spacer">
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  27       <br />
  28     </div>
  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 orange">
  40               <a href="http://lambdadelta.info/documentation.html">documentation</a>
  41             </td>
  42             <td class="snns capitalize italic green">
  43               <a href="http://lambdadelta.info/specification.html">specification</a>
  44             </td>
  45             <td class="snnn capitalize italic green">
  46               <br />
  47             </td>
  48             <td class="snns capitalize italic green">
  49               <a href="http://lambdadelta.info/implementation.html">implementation</a>
  50             </td>
  51             <td class="ssnn capitalize italic green">
  52               <br />
  53             </td>
  54           </tr>
  55           <tr>
  56             <td class="snns capitalize sky">
  57               <a href="http://lambdadelta.info/index.html#foreword">foreword</a>
  58             </td>
  59             <td class="snns capitalize magenta">
  60               <a href="http://lambdadelta.info/news.html#milestones">milestones</a>
  61             </td>
  62             <td class="snns capitalize orange">
  63               <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
  64             </td>
  65             <td class="snns capitalize green">
  66               <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
  67             </td>
  68             <td class="snnn capitalize green">(<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="snns capitalize green">
  70               <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
  71             </td>
  72             <td class="ssnn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
  73           </tr>
  74           <tr>
  75             <td class="snss capitalize sky">
  76               <a href="http://lambdadelta.info/index.html#citations">citations</a>
  77             </td>
  78             <td class="snss capitalize magenta">
  79               <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
  80             </td>
  81             <td class="snss capitalize orange">
  82               <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
  83             </td>
  84             <td class="snss capitalize green">
  85               <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
  86             </td>
  87             <td class="snsn capitalize green">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
  88             <td class="snss capitalize green">
  89               <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
  90             </td>
  91             <td class="sssn capitalize green">
  92               <br />
  93             </td>
  94           </tr>
  95         </tbody>
  96       </table>
  97     </div>
  98     <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/b5.png" />
  99     </div>
 100     <div xmlns:ld="http://lambdadelta.info/" class="text">
 101       λδ is developed as a machine-checked digital specification.
 102       It comes in several versions listed in the next table,
 103       which includes the major milestones.
 104    </div>
 105     <div xmlns:ld="http://lambdadelta.info/" class="text">
 106       The life cycle of a specification consists of four periods.
 107       <span class="emph alpha">Alpha:</span>
 108       the definitions are designed and the major propositions are proved,
 109       then the calculus is announced with a presentation.
 110       <span class="emph beta">Beta:</span>
 111       major changes and additions may occur before the calculus is released on paper.
 112       <span class="emph gamma">Gamma:</span>
 113       subsequent improvements occur until the specification is completed or superseded,
 114       while major changes and additions are announced and reported on paper.
 115       <span class="emph delta">Delta:</span>
 116       after its conclusion, the specification is modified just for maintenance.
 117    </div>
 118     <div xmlns:ld="http://lambdadelta.info/" class="text">
 119       <table cellpadding="4" cellspacing="0">
 120         <tbody>
 121           <tr>
 122             <td class="snns top capitalize italic gray">version</td>
 123             <td class="snnn top capitalize italic gray">name</td>
 124             <td class="snnn top capitalize italic gray">developed with</td>
 125             <td class="snnn top capitalize italic gray">stage</td>
 126             <td class="snnn top capitalize italic gray">started</td>
 127             <td class="snnn top capitalize italic gray">announced</td>
 128             <td class="snnn top capitalize italic gray">released</td>
 129             <td class="ssnn top capitalize italic gray">concluded</td>
 130           </tr>
 131           <tr>
 132             <td class="snns top orange">
 133               <a href="http://lambdadelta.info/specification.html#v2">Version 2</a>
 134             </td>
 135             <td class="snnn top orange">"basic_2"</td>
 136             <td class="snnn top orange">
 137               <a href="http://matita.cs.unibo.it/">Matita 0.99.2</a>
 138             </td>
 139             <td class="snnn top orange">"A"</td>
 140             <td class="snnn top orange">April 2011</td>
 141             <td class="snnn top orange">June 2014</td>
 142             <td class="snnn top orange">October 2014</td>
 143             <td class="ssnn top orange" />
 144           </tr>
 145           <tr>
 146             <td class="snns top orange">Abandoned</td>
 147             <td class="snnn top orange" />
 148             <td class="snnn top orange">
 149               <a href="http://coq.inria.fr/">Coq 7.3.1</a>
 150             </td>
 151             <td class="snnn top orange" />
 152             <td class="snnn top orange">March 2008</td>
 153             <td class="snnn top orange" />
 154             <td class="snnn top orange" />
 155             <td class="ssnn top orange">February 2011</td>
 156           </tr>
 157           <tr>
 158             <td class="snss top red">
 159               <a href="http://lambdadelta.info/specification.html#v1">Version 1</a>
 160             </td>
 161             <td class="snsn top red">"basic_1"</td>
 162             <td class="snsn top red">
 163               <a href="http://coq.inria.fr/">Coq 7.3.1</a>
 164             </td>
 165             <td class="snsn top red" />
 166             <td class="snsn top red">May 2004</td>
 167             <td class="snsn top red">December 2005</td>
 168             <td class="snsn top red">November 2006</td>
 169             <td class="sssn top red">May 2008</td>
 170           </tr>
 171         </tbody>
 172       </table>
 173     </div>
 174     <!-- VERSION 2 =========================================================== -->
 175     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v2">
 176       <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b4.png" /> λδ version 2 (active)</div>
 177     <div xmlns:ld="http://lambdadelta.info/" class="text">
 178       The formal specification of λδ version 2
 179       is available in the following formats:
 180    </div>
 181     <ul xmlns:ld="http://lambdadelta.info/" id="source2">
 182       <li>
 183         <div class="text">
 184           <a href="http://lambdadelta.info/download/lambdadelta_2.tar.gz">lambdadelta_2 for Matita 0.99.2</a>
 185          (revised <span class="emph gamma">2014-10</span>).
 186          Source scripts.
 187       </div>
 188         <div class="text">
 189          The scripts are grouped in directories, first by part, then by component.
 190       </div>
 191         <div class="text">
 192           <span class="emph alpha">Notice:</span>
 193          the scripts are checked by the latest version of Matita from
 194          <a href="http://matita.cs.unibo.it/download.shtml">HELM Subversion repository</a>
 195          at path &lt;trunk/matita/&gt;.
 196       </div>
 197       </li>
 198     </ul>
 199     <div xmlns:ld="http://lambdadelta.info/" class="text">
 200       Informational pages on the parts of the specification:
 201       <a href="http://lambdadelta.info/ground_2.html">Background</a>,
 202       <a href="http://lambdadelta.info/basic_2.html">Core</a>,
 203       <a href="http://lambdadelta.info/apps_2.html">Applications</a>.
 204    </div>
 205     <div xmlns:ld="http://lambdadelta.info/" class="text">
 206       <span class="emph alpha">Notice on numerical acounts:</span>
 207       nodes are counted according to the "intrinsic complexity measure"
 208       [F. Guidi: "Procedural Representation of CIC Proof Terms"
 209       Journal of Automated Reasoning 44(1-2), Springer (February 2010), pp. 53-78].
 210    </div>
 211     <div xmlns:ld="http://lambdadelta.info/" class="text">
 212       <span class="emph alpha">Notice on displayed logical structures:</span>
 213       from the logical standpoint, the source scripts are grouped in "planes"
 214       and these are grouped in "components";
 215       the notation for the relations or functions
 216       introduced in each script, is shown in parentheses (? are placeholders).
 217    </div>
 218     <!-- VERSION 1 =========================================================== -->
 219     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v1">
 220       <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b6.png" /> λδ version 1 (superseded)</div>
 221     <div xmlns:ld="http://lambdadelta.info/" class="text">
 222       The formal specification of λδ version 1
 223       is available in the following formats:
 224    </div>
 225     <ul xmlns:ld="http://lambdadelta.info/" id="source1">
 226       <li>
 227         <div class="text">
 228           <a href="http://lambdadelta.info/download/lambdadelta_1.tar.gz">lambdadelta_1 for Coq 7.3.1</a>
 229          (revised <span class="emph delta">2012-10</span>).
 230          Source scripts.
 231       </div>
 232         <div class="text">
 233          The scripts are grouped in directories, one for each part.
 234       </div>
 235       </li>
 236     </ul>
 237     <ul xmlns:ld="http://lambdadelta.info/" id="static1">
 238       <li>
 239         <a href="http://lambdadelta.info/static/matita/lambdadelta/">lambdadelta_1 for Matita 0.5</a>
 240       (revised <span class="emph delta">2011-09</span>).
 241       Static HTML pages generated by the <a href="http://helm.cs.unibo.it/">HELM</a> rendering engine.
 242       <ul>
 243           <li>
 244             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/pr3/pr3/pr3_confluence.con.html">
 245             Confluence of reduction</a>
 246          (Church-Rosser property).
 247       </li>
 248           <li>
 249             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_correct.con.html">
 250             Correctness of types</a>.
 251       </li>
 252           <li>
 253             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_unique.con.html">
 254             Uniqueness of types up to conversion</a>.
 255       </li>
 256           <li>
 257             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/pr3/ty3_sred_pr3.con.html">
 258             Subject reduction of the type assignment</a>.
 259       </li>
 260           <li>
 261             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/arity_props/ty3_sn3.con.html">
 262             Strong normalization of the typed terms</a>.
 263       </li>
 264           <li>
 265             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/dec/ty3_inference.con.html">
 266             Decidability of the type inference problem</a>.
 267       </li>
 268         </ul>
 269       </li>
 270     </ul>
 271     <ul xmlns:ld="http://lambdadelta.info/" id="dynamic1">
 272       <li>
 273         <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/">
 274          lambdadelta_1 for Matita 0.5</a>
 275       (revised <span class="emph delta">2011-09</span>).
 276       <a href="http://helm.cs.unibo.it/">HELM</a> directory.
 277       <span class="emph alpha">Notice: the HELM rendering engine is offline.</span>
 278       </li>
 279     </ul>
 280     <div class="spacer">
 281       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
 282     </div>
 283     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 284       <br />
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 286     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
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 288         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
 289       </a>
 290       <a href="http://jigsaw.w3.org/css-validator/check/referer">
 291         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
 292       </a>
 293       <a href="http://www.w3.org/XML/">
 294         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
 295       </a>
 296       <a href="http://www.w3.org/Graphics/PNG/">
 297         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
 298       </a>
 299       <a href="http://www.anybrowser.org/campaign/">
 300         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
 301       </a>
 302     </div>
 303     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 304       <br />
 305     </div>
 306     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Mon, 05 Jan 2015 00:32:03 +0100</div>
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