helm/www/lambda_delta/implementation.html

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   5   <title>lambda_delta home page</title>
   6   <meta content="Ferruccio Guidi" name="author">
   7   <meta content="The formal system lambda_delta" name="description">
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  13 <a href="http://lambda-delta.info"><img alt="[Crux Logo]"
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  16 <h1>The Formal System λδ (lambda_delta)<br>
  17 </h1>
  18 <h2>Towards the unification of terms, types, environments and contexts</h2>
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  27       <ul>
  28         <li><a href="index.html">Foreword</a></li>
  29       </ul>
  30       <ul>
  31         <li><a href="news.html">News</a></li>
  32       </ul>
  33       <ul>
  34         <li><a href="documentation.html">Papers</a></li>
  35       </ul>
  36       <ul>
  37         <li>Resources<br>
  38         </li>
  39       </ul>
  40       </td>
  41       <td style="vertical-align: top; text-align: left;">
  42       <h3 style="text-align: right;">Computer-checked formal
  43 specifications <img style="width: 37px; height: 37px;"
  44  alt="[Butterfly]" title="Butterfly" src="download/b9.png"></h3>
  45       <span style="font-weight: bold;">Resource
  46 1</span> below provides for the statically generated <span
  47  style="font-weight: bold;">natural language representation</span> of
  48 λδ meta-theory (faster rendering w.r.t. resource 2 below).<br>
  49       <span style="font-weight: bold;">Resource 2</span> below provides
  50 for the dynamically generated <span style="font-weight: bold;">natural
  51 language representation</span> of
  52 λδ meta-theory (powered by the <a href="http://helm.cs.unibo.it/">HELM</a>
  53 rendering engine).<br>
  54 Remarkably, λδ was born and developed in the digital format of <span
  55  style="font-weight: bold;">resource 3</span> below, which is not the
  56 formal counterpart of some informal material previously written on
  57 paper (as it happens for most currently digitalized Mathematics).<br>
  58       <ol>
  59         <li><a name="static"></a>F. Guidi: <a
  60  style="font-style: italic;" href="static/matita/lambda_delta/">lambda_delta</a>
  61 (revised <span style="font-weight: bold;">2011-09</span>). Formal
  62 specification for <a href="http://matita.cs.unibo.it/">Matita</a> 0.5
  63 (HTML pages generated
  64 by the <a href="http://helm.cs.unibo.it/">HELM</a>
  65 rendering engine)<br>
  66 Here are the most relevant theorems proved in the formal specification:
  67           <ul>
  68             <li><a
  69  href="static/matita/lambda_delta/Basic_1/pr3/pr3/pr3_confluence.con.html">Confluence
  70 of
  71 reduction</a> (Church-Rosser property).</li>
  72             <li><a
  73  href="static/matita/lambda_delta/Basic_1/ty3/props/ty3_correct.con.html">Correctness
  74 of
  75 types</a>.</li>
  76             <li><a
  77  href="static/matita/lambda_delta/Basic_1/ty3/props/ty3_unique.con.html">Uniqueness
  78 of
  79 types
  80 up
  81 to
  82 conversion</a>.<br>
  83             </li>
  84             <li><a
  85  href="static/matita/lambda_delta/Basic_1/ty3/pr3/ty3_sred_pr3.con.html">Subject
  86 reduction
  87 of
  88 the
  89 type
  90 assignment</a>.</li>
  91             <li><a
  92  href="static/matita/lambda_delta/Basic_1/ty3/arity_props/ty3_sn3.con.html">Strong
  93 normalization
  94 of
  95 the
  96 typed
  97 terms</a>.</li>
  98             <li><a
  99  href="static/matita/lambda_delta/Basic_1/ty3/dec/ty3_inference.con.html">Decidability
 100 of
 101 the
 102 type
 103 inference
 104 problem</a>.<br>
 105               <br>
 106             </li>
 107           </ul>
 108         </li>
 109         <li><a name="dynamic"></a>F. Guidi: <a
 110  style="font-style: italic;"
 111  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/lambda_delta/">lambda_delta</a>
 112 (revised <span style="font-weight: bold;">2011-09</span>). Formal
 113 specification for <a href="http://matita.cs.unibo.it/">Matita</a> 0.5 (<a
 114  href="http://helm.cs.unibo.it/">HELM</a> directory).<br>
 115           <br>
 116         </li>
 117         <li><a name="source"></a>F. Guidi: <a
 118  href="download/lambda_delta_1.tar.gz"><span style="font-style: italic;">lambda_delta_1</span></a>
 119 (revised <span style="font-weight: bold;">2011-09</span>).
 120 Formal specification for <span style="font-weight: bold;">Coq 7.3.1</span>
 121 (source
 122 proof scripts). <a href="#bibtex">BibTeX entry</a>.<br>
 123         </li>
 124       </ol>
 125       <h3 style="text-align: right;">Tools <img
 126  style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
 127  src="download/b5.png"></h3>
 128       <a name="lddl"></a><img style="width: 32px; height: 32px;"
 129  alt="[Crux Logo]" title="The Crux" src="download/crux_32.png"><span
 130  style="font-weight: bold;"> </span>The <span
 131  style="font-weight: bold;"><span style="text-decoration: underline;">λδ
 132 Digital
 133 Library
 134 (LDDL)</span></span> is part of <a href="http://helm.cs.unibo.it/">HELM</a>
 135 and contains a set of
 136 resources expressed in λδ.<br>
 137       <ul>
 138         <li><span style="font-weight: bold;">Contents:</span> Landau's "<span
 139  style="font-style: italic;">Grundlagen der Analysis</span>" (from
 140 Jutting's specification in <a href="http://www.win.tue.nl/automath/">Automath</a>).<br>
 141           <span style="font-weight: bold;"></span></li>
 142       </ul>
 143       <ul>
 144         <li><span style="font-weight: bold;">Access:</span> <a
 145  href="static/lddl/">static pages</a> (updated <span
 146  style="font-weight: bold;">2011-09</span>), <a
 147  href="download/lddl.tar.bz2">data set</a> (updated <span
 148  style="font-weight: bold;">2011-09</span>), <a
 149  href="http://lambda-delta.info/xml">HELM server URL</a>
 150 (updated <span style="font-weight: bold;">2011-09</span>).</li>
 151       </ul>
 152       <ul>
 153         <li><span style="font-weight: bold;">Examples:</span> <a
 154  href="static/lddl/brg_si/grundlagen/l/e/st/eq/landau/n/rt/rp/r/c/8283/t234.ld.html">Grundlagen's
 155 definition
 156 "t234"</a> (in "basic_rg" λδ), <a
 157  href="static/lddl/crg_si/grundlagen/l/e/st/eq/landau/n/rt/rp/r/c/8283/t234.ld.html">Grundlagen's
 158 definition
 159 "t234"</a> (in "complete_rg" λδ).<br>
 160         </li>
 161       </ul>
 162       <br>
 163       <a name="helena"></a><span style="font-weight: bold;"><img
 164  style="width: 32px; height: 32px;" alt="[Helena Logo]" title="Helena"
 165  src="download/helena_32.png"> <span
 166  style="text-decoration: underline;">Helena</span></span> is a λδ
 167 processor,
 168 implemented in <a href="http://caml.inria.fr/">Caml</a> as a part of
 169 the <a href="http://helm.cs.unibo.it/">HELM</a> software, meant for
 170 testing the stable features of the calculus as well as the unstable
 171 ones.<br>
 172 The processor source code is available in the directory <a
 173  href="http://helm.cs.unibo.it/websvn/listing.php?repname=helm&amp;path=%2Ftrunk%2Fhelm%2Fsoftware%2Fhelena%2F&amp;rev=0&amp;sc=0">/trunk/helm/software/helena/</a>
 174 of the <a href="http://helm.cs.unibo.it/software/index.html">HELM Svn
 175 repository</a>. The Svn revisions containing the stable versions
 176 of&nbsp; Helena are indicated below. <br>
 177       <ul>
 178       </ul>
 179       <ul>
 180         <li><span style="font-weight: bold;">Version 0.8.2.</span> In
 181 progress.<br>
 182         </li>
 183       </ul>
 184       <ul>
 185         <li><span style="font-weight: bold;">Version 0.8.1 (2010-11).</span>
 186 Exploits a subset of "complete_rg" λδ as the intermediate language.
 187 Features importation from ".hln" files containing λδ textual syntax.
 188 The overall validation speed of the "<span style="font-style: italic;">Grundlagen
 189 der
 190 Analysis</span>" increases of 22% with respect to version 0.8.0. [Svn
 191 revision: 11032] (<a href="download/helena_0.8.1.tar.gz">archived
 192 source code</a>)
 193           <ul>
 194             <li><span style="font-weight: bold;">2009-12.</span> Helena
 195 appears in&nbsp;F. Wiedijk's <a
 196  href="http://www.cs.ru.nl/%7Efreek/digimath/index.html#helena">index
 197 of
 198 computer math systems</a>.</li>
 199           </ul>
 200         </li>
 201       </ul>
 202       <ul>
 203         <li><a style="font-weight: bold;"
 204  href="documentation.html#ublcs-2009-16">Version 0.8.0</a><span
 205  style="font-weight: bold;"> (2009-09).</span> Supports
 206 "basic_rg" λδ with naive implementation of impredicative sort
 207 inclusion. Features
 208 importation from <a href="http://www.win.tue.nl/automath/">Automath</a>
 209 and exportation to <a href="http://www.w3.org/XML/">XML</a>. [Svn
 210 revision: 10304] (<a href="download/helena_0.8.0.tar.gz">archived
 211 source code</a>)<br>
 212           <ul>
 213             <li><span style="font-weight: bold;">2009-09.</span>
 214 Jutting's specification of Landau's "<span style="font-style: italic;">Grundlagen
 215 der
 216 Analysis</span>" enters λδ Digital Library.<br>
 217               <span style="font-weight: bold;"></span></li>
 218             <li><span style="font-weight: bold;">2009-06.</span>
 219 Jutting's specification of Landau's "<span style="font-style: italic;">Grundlagen
 220 der
 221 Analysis</span>" is
 222 successfully processed, enabling sort inclusion<span
 223  style="font-weight: bold;"></span>.</li>
 224           </ul>
 225         </li>
 226       </ul>
 227       <h3 style="text-align: right;">Other resources <img
 228  style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
 229  src="download/b4.png"></h3>
 230       <ul>
 231         <li><a name="bibtex"></a>A
 232 BibTeX database of λδ documentation: <a
 233  href="download/lambda_delta.bib"><span style="font-style: italic;">lambda_delta.bib</span></a>,
 234
 235
 236
 237           <a style="font-style: italic;"
 238  href="download/lambda_delta.txt">lambda_delta.txt</a> (revised <span
 239  style="font-weight: bold;">2011-09</span>).</li>
 240       </ul>
 241       <ul>
 242         <li>A <a href="http://www.jedsoft.org/jed/">Jed mode</a> for
 243 editing ".hln" files (containing λδ textual syntax): <a
 244  style="font-style: italic;" href="download/helena.sl">helena.sl</a>
 245 (revised <span style="font-weight: bold;">2010-11</span>).</li>
 246       </ul>
 247       <ul>
 248         <li>A <a href="http://www.jedsoft.org/jed/">Jed mode</a> for
 249 editing ".aut" files (containing <a
 250  href="http://www.win.tue.nl/automath/">Automath</a> textual syntax): <a
 251  style="font-style: italic;" href="download/automath.sl">automath.sl</a>
 252 (revised <span style="font-weight: bold;">2008-07</span>).</li>
 253       </ul>
 254       <ul>
 255         <li>A logo for "basic" λδ: <a href="download/bld.pdf"><span
 256  style="font-style: italic;">bld.pdf</span></a> (revised <span
 257  style="font-weight: bold;">2008-07</span>).<br>
 258         </li>
 259       </ul>
 260       </td>
 261     </tr>
 262   </tbody>
 263 </table>
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 277 Last update 2012-02-21 by <a href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio
 278 Guidi</a><br>
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