helm/www/lambdadelta/implementation.html

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   6     <meta content="text/html; charset=UTF-8" http-equiv="content-type"><title>λδ home page</title>
   7
   8     <meta content="Ferruccio Guidi" name="author">
   9     <meta content="The formal system λδ" name="description">
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  12       <br>
  13       <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>
  14       <h1>The Formal System λδ (\lambda\delta)<br>
  15       </h1>
  16       <h2>Towards the unification of terms, types, environments and
  17         contexts</h2>
  18       <img style="width: 95%; height: 4px;" alt="[Separator]" title="Separator" src="images/rainbow.png"><br>
  19       <table style="text-align: left; width: 95%; margin-left: auto; margin-right: auto;" border="0" cellpadding="2" cellspacing="20">
  20         <tbody>
  21           <tr>
  22             <td style="vertical-align: top;">
  23               <ul>
  24                 <li><a href="index.html">Foreword</a></li>
  25               </ul>
  26               <ul>
  27                 <li><a href="news.html">News</a></li>
  28               </ul>
  29               <ul>
  30                 <li><a href="documentation.html">Papers</a></li>
  31               </ul>
  32               <ul>
  33                 <li>Resources<br>
  34                 </li>
  35               </ul>
  36             </td>
  37             <td style="vertical-align: top; text-align: left;">
  38               <h3 style="text-align: right;">Computer-checked formal
  39                 specifications <img style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly" src="images/b9.png"></h3>
  40               <span style="font-weight: bold;">Resource
  41                 1</span> below provides for the statically generated <span style="font-weight: bold;">natural language
  42                 representation</span> of
  43               λδ meta-theory (faster rendering w.r.t. resource 2 below).<br>
  44               <span style="font-weight: bold;">Resource 2</span> below
  45               provides
  46               for the dynamically generated <span style="font-weight: bold;">natural
  47                 language representation</span> of
  48               λδ meta-theory (powered by the <a href="http://helm.cs.unibo.it/">HELM</a>
  49               rendering engine).<br>
  50               Remarkably, λδ was born and developed in the digital
  51               format of <span style="font-weight: bold;">resource 3</span>
  52               below, which is not the
  53               formal counterpart of some informal material previously
  54               written on
  55               paper (as it happens for most currently digitalized
  56               Mathematics).<br>
  57               <ol>
  58                 <li><a name="static"></a>F. Guidi: <a style="font-style: italic;" href="static/matita/lambdadelta/">lambdadelta</a>
  59                   (revised <span style="font-weight: bold;">2011-09</span>).
  60                   Formal
  61                   specification for <a href="http://matita.cs.unibo.it/">Matita</a> 0.5
  62                   (HTML pages generated
  63                   by the <a href="http://helm.cs.unibo.it/">HELM</a>
  64                   rendering engine)<br>
  65                   Here are the most relevant theorems proved in the
  66                   formal specification:
  67                   <ul>
  68                     <li><a href="static/matita/lambdadelta/Basic_1/pr3/pr3/pr3_confluence.con.html">Confluence
  69                         of
  70                         reduction</a> (Church-Rosser property).</li>
  71                     <li><a href="static/matita/lambdadelta/Basic_1/ty3/props/ty3_correct.con.html">Correctness
  72                         of
  73                         types</a>.</li>
  74                     <li><a href="static/matita/lambdadelta/Basic_1/ty3/props/ty3_unique.con.html">Uniqueness
  75                         of
  76                         types
  77                         up
  78                         to
  79                         conversion</a>.<br>
  80                     </li>
  81                     <li><a href="static/matita/lambdadelta/Basic_1/ty3/pr3/ty3_sred_pr3.con.html">Subject
  82                         reduction
  83                         of
  84                         the
  85                         type
  86                         assignment</a>.</li>
  87                     <li><a href="static/matita/lambdadelta/Basic_1/ty3/arity_props/ty3_sn3.con.html">Strong
  88                         normalization
  89                         of
  90                         the
  91                         typed
  92                         terms</a>.</li>
  93                     <li><a href="static/matita/lambdadelta/Basic_1/ty3/dec/ty3_inference.con.html">Decidability
  94                         of
  95                         the
  96                         type
  97                         inference
  98                         problem</a>.<br>
  99                       <br>
 100                     </li>
 101                   </ul>
 102                 </li>
 103                 <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>
 104                   (revised <span style="font-weight: bold;">2011-09</span>).
 105                   Formal
 106                   specification for <a href="http://matita.cs.unibo.it/">Matita</a> 0.5 (<a href="http://helm.cs.unibo.it/">HELM</a> directory).<br>
 107                   <br>
 108                 </li>
 109                 <li><a name="ldp1"></a>F. Guidi: <a href="download/lambdadelta_1.tar.gz"><span style="font-style: italic;">lambdadelta_1</span></a>
 110                   (revised <span style="font-weight: bold;">2012-10</span>).
 111 Formal
 112                   specification for <span style="font-weight: bold;">Coq
 113                     7.3.1</span>
 114                   (source
 115                   proof scripts). <a href="#bibtex">BibTeX entry</a>.<br>
 116                 </li>
 117               </ol>
 118               <h3 style="text-align: right;">Tools <img style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly" src="images/b5.png"></h3>
 119               <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
 120                   Digital
 121                   Library
 122                   (LDDL)</span></span> is part of <a href="http://helm.cs.unibo.it/">HELM</a>
 123               and contains a set of
 124               resources expressed in λδ.<br>
 125               <ul>
 126                 <li><span style="font-weight: bold;">Contents:</span>
 127                   Landau's "<span style="font-style: italic;">Grundlagen
 128                     der Analysis</span>" (from
 129                   Jutting's specification in <a href="http://www.win.tue.nl/automath/">Automath</a>).<br>
 130                   <span style="font-weight: bold;"></span></li>
 131               </ul>
 132               <ul>
 133                 <li><span style="font-weight: bold;">Access:</span> <a href="static/lddl/">static pages</a> (updated <span style="font-weight: bold;">2012-10</span>), <a href="download/lddl.tar.bz2">data set</a> (updated <span style="font-weight: bold;">2012-10</span>), <a href="http://lambdadelta.info/xml">HELM server URL</a>
 134                   (updated <span style="font-weight: bold;">2012-10</span>).</li>
 135               </ul>
 136               <ul>
 137                 <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
 138                     definition
 139                     "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
 140                     definition
 141                     "t234"</a> (in "complete_rg" λδ).<br>
 142                 </li>
 143               </ul>
 144               <br>
 145               <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>
 146               is a λδ
 147               processor,
 148               implemented in <a href="http://caml.inria.fr/">Caml</a>
 149               as a part of
 150               the <a href="http://helm.cs.unibo.it/">HELM</a> software,
 151               meant for
 152               testing the stable features of the calculus as well as the
 153               unstable
 154               ones.<br>
 155               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>
 156               of the <a href="http://helm.cs.unibo.it/software/index.html">HELM
 157                 Svn
 158                 repository</a>. The Svn revisions containing the stable
 159               versions
 160               of&nbsp; Helena are indicated below. <br>
 161               <ul>
 162                 <li><span style="font-weight: bold;">Version 0.8.2.</span>
 163                   In
 164                   progress.<br>
 165                 </li>
 166               </ul>
 167               <ul>
 168                 <li><span style="font-weight: bold;">Version 0.8.1
 169                     (2010-11).</span>
 170                   Exploits a subset of "complete_rg" λδ as the
 171                   intermediate language.
 172                   Features importation from ".hln" files containing λδ
 173                   textual syntax.
 174                   The overall validation speed of the "<span style="font-style: italic;">Grundlagen
 175                     der
 176                     Analysis</span>" increases of 22% with respect to
 177                   version 0.8.0. [Svn
 178                   revision: 11032] (<a href="download/helena_0.8.1.tar.gz">archived
 179                     source code</a>)
 180                   <ul>
 181                     <li><span style="font-weight: bold;">2009-12.</span>
 182                       Helena
 183                       appears in&nbsp;F. Wiedijk's <a href="http://www.cs.ru.nl/%7Efreek/digimath/index.html#helena">index
 184 of
 185 computer
 186                         math systems</a>.</li>
 187                   </ul>
 188                 </li>
 189               </ul>
 190               <ul>
 191                 <li><a style="font-weight: bold;" href="documentation.html#ldp6">Version 0.8.0</a><span style="font-weight: bold;"> (2009-09).</span>
 192                   Supports
 193                   "basic_rg" λδ with naive implementation of
 194                   impredicative sort
 195                   inclusion. Features
 196                   importation from <a href="http://www.win.tue.nl/automath/">Automath</a>
 197                   and exportation to <a href="http://www.w3.org/XML/">XML</a>.
 198                   [Svn
 199                   revision: 10304] (<a href="download/helena_0.8.0.tar.gz">archived
 200                     source code</a>)<br>
 201                   <ul>
 202                     <li><span style="font-weight: bold;">2009-09.</span>
 203                       Jutting's specification of Landau's "<span style="font-style: italic;">Grundlagen
 204                         der
 205                         Analysis</span>" enters λδ Digital Library.<br>
 206                       <span style="font-weight: bold;"></span></li>
 207                     <li><span style="font-weight: bold;">2009-06.</span>
 208                       Jutting's specification of Landau's "<span style="font-style: italic;">Grundlagen
 209                         der
 210                         Analysis</span>" is
 211                       successfully processed, enabling sort inclusion<span style="font-weight: bold;"></span>.</li>
 212                   </ul>
 213                 </li>
 214               </ul>
 215               <h3 style="text-align: right;">Other resources <img style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly" src="images/b4.png"></h3>
 216               <ul>
 217                 <li><a name="bibtex"></a>A
 218                   BibTeX database of λδ documentation: <a href="download/lambdadelta.bib"><span style="font-style: italic;">lambdadelta.bib</span></a>,
 219                   <a style="font-style: italic;" href="download/lambdadelta.txt">lambdadelta.txt</a>
 220                   (revised <span style="font-weight: bold;">2012-10</span>).</li>
 221               </ul>
 222               <ul>
 223                 <li>A <a href="http://www.jedsoft.org/jed/">Jed mode</a>
 224                   for
 225                   editing ".hln" files (containing λδ textual syntax): <a style="font-style: italic;" href="download/helena.sl">helena.sl</a>
 226                   (revised <span style="font-weight: bold;">2010-11</span>).</li>
 227               </ul>
 228               <ul>
 229                 <li>A <a href="http://www.jedsoft.org/jed/">Jed mode</a>
 230                   for
 231                   editing ".aut" files (containing <a href="http://www.win.tue.nl/automath/">Automath</a>
 232                   textual syntax): <a style="font-style: italic;" href="download/automath.sl">automath.sl</a>
 233                   (revised <span style="font-weight: bold;">2008-07</span>).</li>
 234               </ul>
 235               <ul>
 236                 <li>A logo for λδ: <a href="images/crux_177.png"><span style="font-style: italic;">crux_177.png</span></a>
 237                   (revised <span style="font-weight: bold;">2012-09</span>).<br>
 238                 </li>
 239               </ul>
 240             </td>
 241           </tr>
 242         </tbody>
 243       </table>
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 248       <br>
 249       Last update 2012-12-02 by <a href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio
 250         Guidi</a><br>
 251     </div>
 252
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