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 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="ssns capitalize italic green">
  49               <a href="http://lambdadelta.info/implementation.html">implementation</a>
  50             </td>
  51           </tr>
  52           <tr>
  53             <td class="snns capitalize sky">
  54               <a href="http://lambdadelta.info/index.html#foreword">foreword</a>
  55             </td>
  56             <td class="snns capitalize magenta">
  57               <a href="http://lambdadelta.info/news.html#milestones">milestones</a>
  58             </td>
  59             <td class="snns capitalize orange">
  60               <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
  61             </td>
  62             <td class="snns capitalize green">
  63               <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
  64             </td>
  65             <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>
  66             <td class="ssns capitalize green">
  67               <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
  68             </td>
  69           </tr>
  70           <tr>
  71             <td class="snss capitalize sky">
  72               <a href="http://lambdadelta.info/index.html#citations">citations</a>
  73             </td>
  74             <td class="snss capitalize magenta">
  75               <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
  76             </td>
  77             <td class="snss capitalize orange">
  78               <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
  79             </td>
  80             <td class="snss capitalize green">
  81               <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
  82             </td>
  83             <td class="snsn capitalize green">
  84               <br />
  85             </td>
  86             <td class="ssss capitalize green">
  87               <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
  88             </td>
  89           </tr>
  90         </tbody>
  91       </table>
  92     </div>
  93
  94    <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" />
  95     </div>
  96    <div xmlns:ld="http://lambdadelta.info/" class="text">
  97       λδ is developed as a machine-checked digital specification.
  98       It comes in several versions listed in the next table,
  99       which includes the major milestones.
 100    </div>
 101    <div xmlns:ld="http://lambdadelta.info/" class="text">
 102       The life cycle of a specification consists of four periods.
 103       <span class="emph alpha">Alpha:</span>
 104       the definitions are designed and the major propositions are proved,
 105       then the calculus is announced with a presentation.
 106       <span class="emph beta">Beta:</span>
 107       major changes and additions may occur before the calculus is released on paper.
 108       <span class="emph gamma">Gamma:</span>
 109       subsequent improvements occur until the specification is completed or superseded,
 110       while major changes and additions are announced and reported on paper.
 111       <span class="emph delta">Delta:</span>
 112       after its conclusion, the specification is modified just for maintenance.
 113    </div>
 114    <div xmlns:ld="http://lambdadelta.info/" class="text">
 115       <table cellpadding="4" cellspacing="0">
 116         <tbody>
 117           <tr>
 118             <td class="snns top capitalize italic gray">version</td>
 119             <td class="snnn top capitalize italic gray">name</td>
 120             <td class="snnn top capitalize italic gray">developed with</td>
 121             <td class="snnn top capitalize italic gray">stage</td>
 122             <td class="snnn top capitalize italic gray">started</td>
 123             <td class="snnn top capitalize italic gray">announced</td>
 124             <td class="snnn top capitalize italic gray">released</td>
 125             <td class="ssnn top capitalize italic gray">concluded</td>
 126           </tr>
 127           <tr>
 128             <td class="snns top orange">
 129               <a href="http://lambdadelta.info/specification.html#v2">Version 2</a>
 130             </td>
 131             <td class="snnn top orange">"basic_2"</td>
 132             <td class="snnn top orange">
 133               <a href="http://matita.cs.unibo.it/">Matita 0.99.2</a>
 134             </td>
 135             <td class="snnn top orange">"A"</td>
 136             <td class="snnn top orange">April 2011</td>
 137             <td class="snnn top orange">June 2014</td>
 138             <td class="snnn top orange">October 2014</td>
 139             <td class="ssnn top orange" />
 140           </tr>
 141           <tr>
 142             <td class="snns top orange">Abandoned</td>
 143             <td class="snnn top orange" />
 144             <td class="snnn top orange">
 145               <a href="http://coq.inria.fr/">Coq 7.3.1</a>
 146             </td>
 147             <td class="snnn top orange" />
 148             <td class="snnn top orange">March 2008</td>
 149             <td class="snnn top orange" />
 150             <td class="snnn top orange" />
 151             <td class="ssnn top orange">February 2011</td>
 152           </tr>
 153           <tr>
 154             <td class="snss top red">
 155               <a href="http://lambdadelta.info/specification.html#v1">Version 1</a>
 156             </td>
 157             <td class="snsn top red">"basic_1"</td>
 158             <td class="snsn top red">
 159               <a href="http://coq.inria.fr/">Coq 7.3.1</a>
 160             </td>
 161             <td class="snsn top red" />
 162             <td class="snsn top red">May 2004</td>
 163             <td class="snsn top red">December 2005</td>
 164             <td class="snsn top red">November 2006</td>
 165             <td class="sssn top red">May 2008</td>
 166           </tr>
 167         </tbody>
 168       </table>
 169     </div>
 170
 171
 172
 173    <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v2">
 174       <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b4.png" /> λδ version 2 (active)</div>
 175    <div xmlns:ld="http://lambdadelta.info/" class="text">
 176       The formal specification of λδ version 2
 177       is available in the following formats:
 178    </div>
 179
 180    <ul xmlns:ld="http://lambdadelta.info/" id="source2">
 181       <li>
 182       <div class="text">
 183          <a href="http://lambdadelta.info/download/lambdadelta_2.tar.gz">lambdadelta_2 for Matita 0.99.2</a>
 184          (revised <span class="emph gamma">2014-10</span>).
 185          Source scripts.
 186       </div>
 187       <div class="text">
 188          The scripts are grouped in directories, first by part, then by component.
 189       </div>
 190       <div class="text">
 191          <span class="emph alpha">Notice:</span>
 192          the scripts are checked by the latest version of Matita from
 193          <a href="http://matita.cs.unibo.it/download.shtml">HELM Subversion repository</a>
 194          at path &lt;trunk/matita/&gt;.
 195       </div>
 196    </li>
 197     </ul>
 198
 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
 219
 220
 221    <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v1">
 222       <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b6.png" /> λδ version 1 (superseded)</div>
 223    <div xmlns:ld="http://lambdadelta.info/" class="text">
 224       The formal specification of λδ version 1
 225       is available in the following formats:
 226    </div>
 227
 228    <ul xmlns:ld="http://lambdadelta.info/" id="source1">
 229       <li>
 230       <div class="text">
 231          <a href="http://lambdadelta.info/download/lambdadelta_1.tar.gz">lambdadelta_1 for Coq 7.3.1</a>
 232          (revised <span class="emph delta">2012-10</span>).
 233          Source scripts.
 234       </div>
 235       <div class="text">
 236          The scripts are grouped in directories, one for each part.
 237       </div>
 238    </li>
 239     </ul>
 240
 241    <ul xmlns:ld="http://lambdadelta.info/" id="static1">
 242       <li>
 243       <a href="http://lambdadelta.info/static/matita/lambdadelta/">lambdadelta_1 for Matita 0.5</a>
 244       (revised <span class="emph delta">2011-09</span>).
 245       Static HTML pages generated by the <a href="http://helm.cs.unibo.it/">HELM</a> rendering engine.
 246       <ul>
 247           <li>
 248          <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/pr3/pr3/pr3_confluence.con.html">
 249             Confluence of reduction</a>
 250          (Church-Rosser property).
 251       </li>
 252           <li>
 253          <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_correct.con.html">
 254             Correctness of types</a>.
 255       </li>
 256           <li>
 257          <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_unique.con.html">
 258             Uniqueness of types up to conversion</a>.
 259       </li>
 260           <li>
 261          <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/pr3/ty3_sred_pr3.con.html">
 262             Subject reduction of the type assignment</a>.
 263       </li>
 264           <li>
 265          <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/arity_props/ty3_sn3.con.html">
 266             Strong normalization of the typed terms</a>.
 267       </li>
 268           <li>
 269          <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/dec/ty3_inference.con.html">
 270             Decidability of the type inference problem</a>.
 271       </li>
 272         </ul>
 273    </li>
 274     </ul>
 275
 276    <ul xmlns:ld="http://lambdadelta.info/" id="dynamic1">
 277       <li>
 278       <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/">
 279          lambdadelta_1 for Matita 0.5</a>
 280       (revised <span class="emph delta">2011-09</span>).
 281       <a href="http://helm.cs.unibo.it/">HELM</a> directory.
 282       <span class="emph alpha">Notice: the HELM rendering engine is offline.</span>
 283    </li>
 284     </ul>
 285
 286    <div class="spacer">
 287       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
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 297         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
 298       </a>
 299       <a href="http://www.w3.org/XML/">
 300         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
 301       </a>
 302       <a href="http://www.w3.org/Graphics/PNG/">
 303         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
 304       </a>
 305       <a href="http://www.anybrowser.org/campaign/">
 306         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
 307       </a>
 308     </div>
 309     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 310       <br />
 311     </div>
 312     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Tue, 28 Oct 2014 17:45:56 +0100</div>
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