helm/www/lambda_delta/implementation.html

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   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 with the proof assistant <a
  63  href="http://matita.cs.unibo.it/">Matita</a> 0.5 (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 with the proof assistant <a
 114  href="http://matita.cs.unibo.it/">Matita</a> 0.5 (<a
 115  href="http://helm.cs.unibo.it/">HELM</a> directory).<br>
 116           <br>
 117         </li>
 118         <li><a name="source"></a>F. Guidi: <a
 119  href="download/lambda_delta_1.tar.gz"><span
 120  style="font-style: italic;">lambda_delta_1</span></a> (revised <span
 121  style="font-weight: bold;">2011-09</span>).
 122 Formal specification with the proof assistant <span
 123  style="font-weight: bold;">Coq 7.3.1</span> (source
 124 proof scripts). <a href="#bibtex">BibTeX entry</a>.<br>
 125         </li>
 126       </ol>
 127       <h3 style="text-align: right;">Tools <img
 128  style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
 129  src="download/b5.png"></h3>
 130       <a name="lddl"></a><img style="width: 32px; height: 32px;"
 131  alt="[Crux Logo]" title="The Crux" src="download/crux_32.png"><span
 132  style="font-weight: bold;"> </span>The <span
 133  style="font-weight: bold;"><span style="text-decoration: underline;">λδ
 134 Digital
 135 Library
 136 (LDDL)</span></span> is part of <a href="http://helm.cs.unibo.it/">HELM</a>
 137 and contains a set of
 138 resources expressed in λδ.<br>
 139       <ul>
 140         <li><span style="font-weight: bold;">Contents:</span> Landau's "<span
 141  style="font-style: italic;">Grundlagen der Analysis</span>" (from
 142 Jutting's specification in <a href="http://www.win.tue.nl/automath/">Automath</a>).<br>
 143           <span style="font-weight: bold;"></span></li>
 144       </ul>
 145       <ul>
 146         <li><span style="font-weight: bold;">Access:</span> <a
 147  href="static/lddl/">static pages</a> (updated <span
 148  style="font-weight: bold;">2011-09</span>), <a
 149  href="download/lddl.tar.bz2">data set</a> (updated <span
 150  style="font-weight: bold;">2011-09</span>), <a
 151  href="http://lambda-delta.info/xml">HELM server URL</a>
 152 (updated <span style="font-weight: bold;">2011-09</span>).</li>
 153       </ul>
 154       <ul>
 155         <li><span style="font-weight: bold;">Examples:</span> <a
 156  href="static/lddl/brg_si/grundlagen/l/e/st/eq/landau/n/rt/rp/r/c/8283/t234.ld.html">Grundlagen's
 157 definition
 158 "t234"</a> (in "basic_rg" λδ), <a
 159  href="static/lddl/crg_si/grundlagen/l/e/st/eq/landau/n/rt/rp/r/c/8283/t234.ld.html">Grundlagen's
 160 definition
 161 "t234"</a> (in "complete_rg" λδ).<br>
 162         </li>
 163       </ul>
 164       <br>
 165       <a name="helena"></a><span style="font-weight: bold;"><img
 166  style="width: 32px; height: 32px;" alt="[Helena Logo]" title="Helena"
 167  src="download/helena_32.png"> <span
 168  style="text-decoration: underline;">Helena</span></span> is a λδ
 169 processor,
 170 implemented in <a href="http://caml.inria.fr/">Caml</a> as a part of
 171 the <a href="http://helm.cs.unibo.it/">HELM</a> software, meant for
 172 testing the stable features of the calculus as well as the unstable
 173 ones.<br>
 174 The processor source code is available in the directory <a
 175  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>
 176 of the <a href="http://helm.cs.unibo.it/software/index.html">HELM Svn
 177 repository</a>. The Svn revisions containing the stable versions
 178 of&nbsp; Helena are indicated below. <br>
 179       <ul>
 180         <li><span style="font-weight: bold;">Version 0.8.1 (2010-11).</span>
 181 Exploits a subset of "complete_rg" λδ as the intermediate language.
 182 Features importation from ".hln" files containing λδ textual syntax.
 183 The overall validation speed of the "<span style="font-style: italic;">Grundlagen
 184 der
 185 Analysis</span>" increases of 22% with respect to version 0.8.0. [Svn
 186 revision: 11032] (<a href="download/helena_0.8.1.tar.gz">archived
 187 source code</a>)
 188           <ul>
 189             <li><span style="font-weight: bold;">2009-12.</span> Helena
 190 appears in&nbsp;F. Wiedijk's <a
 191  href="http://www.cs.ru.nl/%7Efreek/digimath/index.html#helena">index of
 192 computer math systems</a>.</li>
 193           </ul>
 194         </li>
 195       </ul>
 196       <ul>
 197         <li><a style="font-weight: bold;"
 198  href="documentation.html#ublcs-2009-16">Version 0.8.0</a><span
 199  style="font-weight: bold;"> (2009-09).</span> Supports
 200 "basic_rg" λδ with naive implementation of impredicative sort
 201 inclusion. Features
 202 importation from <a href="http://www.win.tue.nl/automath/">Automath</a>
 203 and exportation to <a href="http://www.w3.org/XML/">XML</a>. [Svn
 204 revision: 10304] (<a href="download/helena_0.8.0.tar.gz">archived
 205 source code</a>)<br>
 206           <ul>
 207             <li><span style="font-weight: bold;">2009-09.</span>
 208 Jutting's specification of Landau's "<span style="font-style: italic;">Grundlagen
 209 der
 210 Analysis</span>" enters λδ Digital Library.<br>
 211               <span style="font-weight: bold;"></span></li>
 212             <li><span style="font-weight: bold;">2009-06.</span>
 213 Jutting's specification of Landau's "<span style="font-style: italic;">Grundlagen
 214 der
 215 Analysis</span>" is
 216 successfully processed, enabling sort inclusion<span
 217  style="font-weight: bold;"></span>.</li>
 218           </ul>
 219         </li>
 220       </ul>
 221       <h3 style="text-align: right;">Other resources <img
 222  style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
 223  src="download/b4.png"></h3>
 224       <ul>
 225         <li><a name="bibtex"></a>A
 226 BibTeX database of λδ documentation: <a
 227  href="download/lambda_delta.bib"><span style="font-style: italic;">lambda_delta.bib</span></a>,
 228
 229
 230           <a style="font-style: italic;"
 231  href="download/lambda_delta.txt">lambda_delta.txt</a> (revised <span
 232  style="font-weight: bold;">2011-09</span>).</li>
 233       </ul>
 234       <ul>
 235         <li>A <a href="http://www.jedsoft.org/jed/">Jed mode</a> for
 236 editing ".hln" files (containing λδ textual syntax): <a
 237  style="font-style: italic;" href="download/helena.sl">helena.sl</a>
 238 (revised <span style="font-weight: bold;">2010-11</span>).</li>
 239       </ul>
 240       <ul>
 241         <li>A <a href="http://www.jedsoft.org/jed/">Jed mode</a> for
 242 editing ".aut" files (containing <a
 243  href="http://www.win.tue.nl/automath/">Automath</a> textual syntax): <a
 244  style="font-style: italic;" href="download/automath.sl">automath.sl</a>
 245 (revised <span style="font-weight: bold;">2008-07</span>).</li>
 246       </ul>
 247       <ul>
 248         <li>A logo for "basic" λδ: <a href="download/bld.pdf"><span
 249  style="font-style: italic;">bld.pdf</span></a> (revised <span
 250  style="font-weight: bold;">2008-07</span>).<br>
 251         </li>
 252       </ul>
 253       </td>
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 271 Last update 2011-09-09 by <a href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio
 272 Guidi</a><br>
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