helm/www/lambdadelta/implementation.html

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