helm/www/lambdadelta/implementation.html

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   5     <meta content="text/html; charset=UTF-8" http-equiv="content-type"><title>λδ home page</title>
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   7     <meta content="Ferruccio Guidi" name="author">
   8     <meta content="The formal system λδ" name="description">
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  11       <br>
  12       <a href="http://lambdadelta.info"><img alt="[Crux Logo]" title="The Crux" src="images/crux_32.png" style="border: 0px solid ; width: 32px; height: 32px;"></a>
  13       <h1>The Formal System λδ (\lambda\delta)<br>
  14       </h1>
  15       <h2>Towards the unification of terms, types, environments and
  16         contexts</h2>
  17       <img style="width: 95%; height: 4px;" alt="[Separator]" title="Separator" src="images/rainbow.png"><br>
  18       <table style="text-align: left; width: 95%; margin-left: auto; margin-right: auto;" border="0" cellpadding="2" cellspacing="20">
  19         <tbody>
  20           <tr>
  21             <td style="vertical-align: top;">
  22               <ul>
  23                 <li><a href="index.html">Foreword</a></li>
  24               </ul>
  25               <ul>
  26                 <li><a href="news.html">News</a></li>
  27               </ul>
  28               <ul>
  29                 <li><a href="documentation.html">Papers</a></li>
  30               </ul>
  31               <ul>
  32                 <li>Resources<br>
  33                 </li>
  34               </ul>
  35             </td>
  36             <td style="vertical-align: top; text-align: left;">
  37               <h3 style="text-align: right;">Computer-checked formal
  38                 specifications <img style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly" src="images/b9.png"></h3>
  39               <span style="font-weight: bold;">Resource
  40                 1</span> below provides for the statically generated <span style="font-weight: bold;">natural language
  41                 representation</span> of
  42               λδ meta-theory (faster rendering w.r.t. resource 2 below).<br>
  43               <span style="font-weight: bold;">Resource 2</span> below
  44               provides
  45               for the dynamically generated <span style="font-weight: bold;">natural
  46                 language representation</span> of
  47               λδ meta-theory (powered by the <a href="http://helm.cs.unibo.it/">HELM</a>
  48               rendering engine).<br>
  49               Remarkably, λδ was born and developed in the digital
  50               format of <span style="font-weight: bold;">resource 3</span>
  51               below, which is not the
  52               formal counterpart of some informal material previously
  53               written on
  54               paper (as it happens for most currently digitalized
  55               Mathematics).<br>
  56               <ol>
  57                 <li><a name="static"></a>F. Guidi: <a style="font-style: italic;" href="static/matita/lambdadelta/">lambdadelta</a>
  58                   (revised <span style="font-weight: bold;">2011-09</span>).
  59                   Formal
  60                   specification for <a href="http://matita.cs.unibo.it/">Matita</a> 0.5
  61                   (HTML pages generated
  62                   by the <a href="http://helm.cs.unibo.it/">HELM</a>
  63                   rendering engine)<br>
  64                   Here are the most relevant theorems proved in the
  65                   formal specification:
  66                   <ul>
  67                     <li><a href="static/matita/lambdadelta/Basic_1/pr3/pr3/pr3_confluence.con.html">Confluence
  68                         of
  69                         reduction</a> (Church-Rosser property).</li>
  70                     <li><a href="static/matita/lambdadelta/Basic_1/ty3/props/ty3_correct.con.html">Correctness
  71                         of
  72                         types</a>.</li>
  73                     <li><a href="static/matita/lambdadelta/Basic_1/ty3/props/ty3_unique.con.html">Uniqueness
  74                         of
  75                         types
  76                         up
  77                         to
  78                         conversion</a>.<br>
  79                     </li>
  80                     <li><a href="static/matita/lambdadelta/Basic_1/ty3/pr3/ty3_sred_pr3.con.html">Subject
  81                         reduction
  82                         of
  83                         the
  84                         type
  85                         assignment</a>.</li>
  86                     <li><a href="static/matita/lambdadelta/Basic_1/ty3/arity_props/ty3_sn3.con.html">Strong
  87                         normalization
  88                         of
  89                         the
  90                         typed
  91                         terms</a>.</li>
  92                     <li><a href="static/matita/lambdadelta/Basic_1/ty3/dec/ty3_inference.con.html">Decidability
  93                         of
  94                         the
  95                         type
  96                         inference
  97                         problem</a>.<br>
  98                       <br>
  99                     </li>
 100                   </ul>
 101                 </li>
 102                 <li><a name="dynamic"></a>F. Guidi: <a style="font-style: italic;" 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/">lambdadelta</a>
 103                   (revised <span style="font-weight: bold;">2011-09</span>).
 104                   Formal
 105                   specification for <a href="http://matita.cs.unibo.it/">Matita</a> 0.5 (<a href="http://helm.cs.unibo.it/">HELM</a> directory).<br>
 106                   <br>
 107                 </li>
 108                 <li><a name="ldp1"></a>F. Guidi: <a href="download/lambdadelta_1.tar.gz"><span style="font-style: italic;">lambdadelta_1</span></a>
 109                   (revised <span style="font-weight: bold;">2011-09</span>).
 110 Formal
 111                   specification for <span style="font-weight: bold;">Coq
 112                     7.3.1</span>
 113                   (source
 114                   proof scripts). <a href="#bibtex">BibTeX entry</a>.<br>
 115                 </li>
 116               </ol>
 117               <h3 style="text-align: right;">Tools <img style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly" src="images/b5.png"></h3>
 118               <a name="lddl"></a><img style="width: 32px; height: 32px;" alt="[Crux Logo]" title="The Crux" src="images/crux_32.png"><span style="font-weight: bold;"> </span>The <span style="font-weight: bold;"><span style="text-decoration: underline;">λδ
 119                   Digital
 120                   Library
 121                   (LDDL)</span></span> is part of <a href="http://helm.cs.unibo.it/">HELM</a>
 122               and contains a set of
 123               resources expressed in λδ.<br>
 124               <ul>
 125                 <li><span style="font-weight: bold;">Contents:</span>
 126                   Landau's "<span style="font-style: italic;">Grundlagen
 127                     der Analysis</span>" (from
 128                   Jutting's specification in <a href="http://www.win.tue.nl/automath/">Automath</a>).<br>
 129                   <span style="font-weight: bold;"></span></li>
 130               </ul>
 131               <ul>
 132                 <li><span style="font-weight: bold;">Access:</span> <a href="static/lddl/">static pages</a> (updated <span style="font-weight: bold;">2011-09</span>), <a href="download/lddl.tar.bz2">data set</a> (updated <span style="font-weight: bold;">2011-09</span>), <a href="http://lambdadelta.info/xml">HELM server URL</a>
 133                   (updated <span style="font-weight: bold;">2011-09</span>).</li>
 134               </ul>
 135               <ul>
 136                 <li><span style="font-weight: bold;">Examples:</span> <a href="static/lddl/brg_si/grundlagen/l/e/st/eq/landau/n/rt/rp/r/c/8283/t234.ld.html">Grundlagen's
 137                     definition
 138                     "t234"</a> (in "basic_rg" λδ), <a href="static/lddl/crg_si/grundlagen/l/e/st/eq/landau/n/rt/rp/r/c/8283/t234.ld.html">Grundlagen's
 139                     definition
 140                     "t234"</a> (in "complete_rg" λδ).<br>
 141                 </li>
 142               </ul>
 143               <br>
 144               <a name="helena"></a><span style="font-weight: bold;"><img style="width: 32px; height: 32px;" alt="[Helena Logo]" title="Helena" src="images/helena_32.png"> <span style="text-decoration: underline;">Helena</span></span>
 145               is a λδ
 146               processor,
 147               implemented in <a href="http://caml.inria.fr/">Caml</a>
 148               as a part of
 149               the <a href="http://helm.cs.unibo.it/">HELM</a> software,
 150               meant for
 151               testing the stable features of the calculus as well as the
 152               unstable
 153               ones.<br>
 154               The processor source code is available in the directory <a 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>
 155               of the <a href="http://helm.cs.unibo.it/software/index.html">HELM
 156                 Svn
 157                 repository</a>. The Svn revisions containing the stable
 158               versions
 159               of&nbsp; Helena are indicated below. <br>
 160               <ul>
 161                 <li><span style="font-weight: bold;">Version 0.8.2.</span>
 162                   In
 163                   progress.<br>
 164                 </li>
 165               </ul>
 166               <ul>
 167                 <li><span style="font-weight: bold;">Version 0.8.1
 168                     (2010-11).</span>
 169                   Exploits a subset of "complete_rg" λδ as the
 170                   intermediate language.
 171                   Features importation from ".hln" files containing λδ
 172                   textual syntax.
 173                   The overall validation speed of the "<span style="font-style: italic;">Grundlagen
 174                     der
 175                     Analysis</span>" increases of 22% with respect to
 176                   version 0.8.0. [Svn
 177                   revision: 11032] (<a href="download/helena_0.8.1.tar.gz">archived
 178                     source code</a>)
 179                   <ul>
 180                     <li><span style="font-weight: bold;">2009-12.</span>
 181                       Helena
 182                       appears in&nbsp;F. Wiedijk's <a href="http://www.cs.ru.nl/%7Efreek/digimath/index.html#helena">index
 183 of
 184 computer
 185                         math systems</a>.</li>
 186                   </ul>
 187                 </li>
 188               </ul>
 189               <ul>
 190                 <li><a style="font-weight: bold;" href="documentation.html#ldp6">Version 0.8.0</a><span style="font-weight: bold;"> (2009-09).</span>
 191                   Supports
 192                   "basic_rg" λδ with naive implementation of
 193                   impredicative sort
 194                   inclusion. Features
 195                   importation from <a href="http://www.win.tue.nl/automath/">Automath</a>
 196                   and exportation to <a href="http://www.w3.org/XML/">XML</a>.
 197                   [Svn
 198                   revision: 10304] (<a href="download/helena_0.8.0.tar.gz">archived
 199                     source code</a>)<br>
 200                   <ul>
 201                     <li><span style="font-weight: bold;">2009-09.</span>
 202                       Jutting's specification of Landau's "<span style="font-style: italic;">Grundlagen
 203                         der
 204                         Analysis</span>" enters λδ Digital Library.<br>
 205                       <span style="font-weight: bold;"></span></li>
 206                     <li><span style="font-weight: bold;">2009-06.</span>
 207                       Jutting's specification of Landau's "<span style="font-style: italic;">Grundlagen
 208                         der
 209                         Analysis</span>" is
 210                       successfully processed, enabling sort inclusion<span style="font-weight: bold;"></span>.</li>
 211                   </ul>
 212                 </li>
 213               </ul>
 214               <h3 style="text-align: right;">Other resources <img style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly" src="images/b4.png"></h3>
 215               <ul>
 216                 <li><a name="bibtex"></a>A
 217                   BibTeX database of λδ documentation: <a href="download/lambdadelta.bib"><span style="font-style: italic;">lambdadelta.bib</span></a>,
 218                   <a style="font-style: italic;" href="download/lambdadelta.txt">lambdadelta.txt</a>
 219                   (revised <span style="font-weight: bold;">2011-09</span>).</li>
 220               </ul>
 221               <ul>
 222                 <li>A <a href="http://www.jedsoft.org/jed/">Jed mode</a>
 223                   for
 224                   editing ".hln" files (containing λδ textual syntax): <a style="font-style: italic;" href="download/helena.sl">helena.sl</a>
 225                   (revised <span style="font-weight: bold;">2010-11</span>).</li>
 226               </ul>
 227               <ul>
 228                 <li>A <a href="http://www.jedsoft.org/jed/">Jed mode</a>
 229                   for
 230                   editing ".aut" files (containing <a href="http://www.win.tue.nl/automath/">Automath</a>
 231                   textual syntax): <a style="font-style: italic;" href="download/automath.sl">automath.sl</a>
 232                   (revised <span style="font-weight: bold;">2008-07</span>).</li>
 233               </ul>
 234               <ul>
 235                 <li>A logo for λδ: <a href="images/crux_177.png"><span style="font-style: italic;">crux_177.png</span></a>
 236                   (revised <span style="font-weight: bold;">2012-09</span>).<br>
 237                 </li>
 238               </ul>
 239             </td>
 240           </tr>
 241         </tbody>
 242       </table>
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 247       <br>
 248       Last update 2012-12-01 by <a href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio
 249         Guidi</a><br>
 250     </div>
 251
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