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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  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="ssnn top capitalize italic gray">concluded</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="snnn top orange">"A"</td>
 147             <td class="snnn top orange">April 2011</td>
 148             <td class="snnn top orange">June 2014</td>
 149             <td class="snnn top orange">October 2014</td>
 150             <td class="ssnn top orange" />
 151           </tr>
 152           <tr>
 153             <td class="snns top orange">Abandoned</td>
 154             <td class="snnn top orange" />
 155             <td class="snnn top orange">
 156               <a href="http://coq.inria.fr/">Coq 7.3.1</a>
 157             </td>
 158             <td class="snnn top orange" />
 159             <td class="snnn top orange">March 2008</td>
 160             <td class="snnn top orange" />
 161             <td class="snnn top orange" />
 162             <td class="ssnn top orange">February 2011</td>
 163           </tr>
 164           <tr>
 165             <td class="snss top red">
 166               <a href="http://lambdadelta.info/specification.html#v1">Version 1</a>
 167             </td>
 168             <td class="snsn top red">"basic_1"</td>
 169             <td class="snsn top red">
 170               <a href="http://coq.inria.fr/">Coq 7.3.1</a>
 171             </td>
 172             <td class="snsn top red" />
 173             <td class="snsn top red">May 2004</td>
 174             <td class="snsn top red">December 2005</td>
 175             <td class="snsn top red">November 2006</td>
 176             <td class="sssn top red">May 2008</td>
 177           </tr>
 178         </tbody>
 179       </table>
 180     </div>
 181     <div xmlns:ld="http://lambdadelta.info/" class="text">
 182      Informational pages on the specifications are provided.
 183    </div>
 184     <ul xmlns:ld="http://lambdadelta.info/" id="">
 185       <li>
 186         <span class="emph alpha">Notice on displayed numerical acounts:</span>
 187       nodes are counted according to the "intrinsic complexity measure"
 188       [F. Guidi: "Procedural Representation of CIC Proof Terms"
 189       Journal of Automated Reasoning 44(1-2), Springer (February 2010), pp. 53-78].
 190    </li>
 191     </ul>
 192     <ul xmlns:ld="http://lambdadelta.info/" id="">
 193       <li>
 194         <span class="emph alpha">Notice on displayed logical structures:</span>
 195       from the logical standpoint, the source scripts are grouped in "planes"
 196       and these are grouped in "components";
 197       the notation for the relations or functions
 198       introduced in each script, is shown in parentheses (? are placeholders).
 199    </li>
 200     </ul>
 201     <!-- VERSION 2 =========================================================== -->
 202     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v2">
 203       <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b4.png" /> λδ version 2 (active)</div>
 204     <div xmlns:ld="http://lambdadelta.info/" class="text">
 205       The formal specification of λδ version 2
 206       is available in the following formats:
 207    </div>
 208     <ul xmlns:ld="http://lambdadelta.info/" id="source2">
 209       <li>
 210         <div class="text">
 211           <a href="http://lambdadelta.info/download/lambdadelta_2.tar.gz">lambdadelta_2 for Matita 0.99.2</a>
 212          (revised <span class="emph gamma">2014-10</span>).
 213          Source scripts.
 214       </div>
 215         <div class="text">
 216          The scripts are grouped in directories, first by part, then by component.
 217       </div>
 218         <div class="text">
 219           <span class="emph alpha">Notice:</span>
 220          the scripts are checked by the latest version of Matita from
 221          <a href="http://matita.cs.unibo.it/download.shtml">HELM Subversion repository</a>
 222          at path &lt;trunk/matita/&gt;.
 223       </div>
 224       </li>
 225     </ul>
 226     <div xmlns:ld="http://lambdadelta.info/" class="text">
 227       Informational pages on the parts of the specification:
 228       <a href="http://lambdadelta.info/ground_2.html">Background</a>,
 229       <a href="http://lambdadelta.info/basic_2.html">Core</a>,
 230       <a href="http://lambdadelta.info/apps_2.html">Applications</a>.
 231    </div>
 232     <!-- VERSION 1 =========================================================== -->
 233     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v1">
 234       <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b6.png" /> λδ version 1 (superseded)</div>
 235     <div xmlns:ld="http://lambdadelta.info/" class="text">
 236       The formal specification of λδ version 1
 237       is available in the following formats:
 238    </div>
 239     <ul xmlns:ld="http://lambdadelta.info/" id="source1">
 240       <li>
 241         <div class="text">
 242           <a href="http://lambdadelta.info/download/lambdadelta_1.tar.gz">lambdadelta_1 for Coq 7.3.1</a>
 243          (revised <span class="emph delta">2015-09</span>).
 244          Source scripts.
 245          <ul>
 246             <li>
 247               <span class="emph delta">2015 January 15.</span>
 248             17 new lemmas and former lemma "eq_nat_dec" renamed as "nat_dec_neg".
 249          </li>
 250           </ul>
 251         </div>
 252         <div class="text">
 253          The scripts are grouped in directories, one for each part.
 254       </div>
 255       </li>
 256     </ul>
 257     <ul xmlns:ld="http://lambdadelta.info/" id="static1">
 258       <li>
 259         <a href="http://lambdadelta.info/static/matita/lambdadelta/">lambdadelta_1 for Matita 0.5</a>
 260       (revised <span class="emph delta">2011-09</span>).
 261       Static HTML pages generated by the <a href="http://helm.cs.unibo.it/">HELM</a> rendering engine.
 262       <ul>
 263           <li>
 264             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/pr3/pr3/pr3_confluence.con.html">
 265             Confluence of reduction</a>
 266          (Church-Rosser property).
 267       </li>
 268           <li>
 269             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_correct.con.html">
 270             Correctness of types</a>.
 271       </li>
 272           <li>
 273             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_unique.con.html">
 274             Uniqueness of types up to conversion</a>.
 275       </li>
 276           <li>
 277             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/pr3/ty3_sred_pr3.con.html">
 278             Subject reduction of the type assignment</a>.
 279       </li>
 280           <li>
 281             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/arity_props/ty3_sn3.con.html">
 282             Strong normalization of the typed terms</a>.
 283       </li>
 284           <li>
 285             <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/dec/ty3_inference.con.html">
 286             Decidability of the type inference problem</a>.
 287       </li>
 288         </ul>
 289       </li>
 290     </ul>
 291     <ul xmlns:ld="http://lambdadelta.info/" id="dynamic1">
 292       <li>
 293         <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/">
 294          lambdadelta_1 for Matita 0.5</a>
 295       (revised <span class="emph delta">2011-09</span>).
 296       <a href="http://helm.cs.unibo.it/">HELM</a> directory.
 297       <span class="emph alpha">Notice: the HELM rendering engine is offline.</span>
 298       </li>
 299     </ul>
 300     <div xmlns:ld="http://lambdadelta.info/" class="text">
 301       Informational pages on the parts of the specification:
 302       <a href="http://lambdadelta.info/ground_1.html">Background</a>,
 303       <a href="http://lambdadelta.info/basic_1.html">Core</a>.
 304    </div>
 305     <div class="spacer">
 306       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
 307     </div>
 308     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 309       <br />
 310     </div>
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 321       <a href="http://www.w3.org/Graphics/PNG/">
 322         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
 323       </a>
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 327     </div>
 328     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 329       <br />
 330     </div>
 331     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sun, 11 Oct 2015 17:42:23 +0200</div>
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