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+ <head>
+ <meta content="text/html; charset=UTF-8" http-equiv="content-type">
+ <title>lambdadelta home page</title>
+ <meta content="Ferruccio Guidi" name="author">
+ <meta content="The formal system lambdadelta" name="description">
+ <link rel="shortcut icon" href="download/crux_16.ico">
+ </head>
+ <body>
+ <div style="text-align: center;">
+ <br>
+ <a href="http://lambdadelta.info"><img alt="[Crux Logo]"
+ title="The Crux" src="download/crux_32.png" style="border: 0px
+ solid ; width: 32px; height: 32px;"></a>
+ <h1>The Formal System λδ (lambdadelta)<br>
+ </h1>
+ <h2>Towards the unification of terms, types, environments and
+ contexts</h2>
+ <img style="width: 95%; height: 4px;" alt="[Separator]"
+ title="Separator" src="download/rainbow.png"><br>
+ <table style="text-align: left; width: 95%; margin-left: auto;
+ margin-right: auto;" border="0" cellpadding="2" cellspacing="20">
+ <tbody>
+ <tr>
+ <td style="vertical-align: top;">
+ <ul>
+ <li><a href="index.html">Foreword</a></li>
+ </ul>
+ <ul>
+ <li><a href="news.html">News</a></li>
+ </ul>
+ <ul>
+ <li><a href="documentation.html">Papers</a></li>
+ </ul>
+ <ul>
+ <li>Resources<br>
+ </li>
+ </ul>
+ </td>
+ <td style="vertical-align: top; text-align: left;">
+ <h3 style="text-align: right;">Computer-checked formal
+ specifications <img style="width: 37px; height: 37px;"
+ alt="[Butterfly]" title="Butterfly"
+ src="download/b9.png"></h3>
+ <span style="font-weight: bold;">Resource
+ 1</span> below provides for the statically generated <span
+ style="font-weight: bold;">natural language
+ representation</span> of
+ λδ meta-theory (faster rendering w.r.t. resource 2 below).<br>
+ <span style="font-weight: bold;">Resource 2</span> below
+ provides
+ for the dynamically generated <span style="font-weight:
+ bold;">natural
+ language representation</span> of
+ λδ meta-theory (powered by the <a
+ href="http://helm.cs.unibo.it/">HELM</a>
+ rendering engine).<br>
+ Remarkably, λδ was born and developed in the digital
+ format of <span style="font-weight: bold;">resource 3</span>
+ below, which is not the
+ formal counterpart of some informal material previously
+ written on
+ paper (as it happens for most currently digitalized
+ Mathematics).<br>
+ <ol>
+ <li><a name="static"></a>F. Guidi: <a
+ style="font-style: italic;"
+ href="static/matita/lambdadelta/">lambdadelta</a>
+ (revised <span style="font-weight: bold;">2011-09</span>).
+ Formal
+ specification for <a
+ href="http://matita.cs.unibo.it/">Matita</a> 0.5
+ (HTML pages generated
+ by the <a href="http://helm.cs.unibo.it/">HELM</a>
+ rendering engine)<br>
+ Here are the most relevant theorems proved in the
+ formal specification:
+ <ul>
+ <li><a
+href="static/matita/lambdadelta/Basic_1/pr3/pr3/pr3_confluence.con.html">Confluence
+ of
+ reduction</a> (Church-Rosser property).</li>
+ <li><a
+ href="static/matita/lambdadelta/Basic_1/ty3/props/ty3_correct.con.html">Correctness
+ of
+ types</a>.</li>
+ <li><a
+ href="static/matita/lambdadelta/Basic_1/ty3/props/ty3_unique.con.html">Uniqueness
+ of
+ types
+ up
+ to
+ conversion</a>.<br>
+ </li>
+ <li><a
+ href="static/matita/lambdadelta/Basic_1/ty3/pr3/ty3_sred_pr3.con.html">Subject
+ reduction
+ of
+ the
+ type
+ assignment</a>.</li>
+ <li><a
+href="static/matita/lambdadelta/Basic_1/ty3/arity_props/ty3_sn3.con.html">Strong
+ normalization
+ of
+ the
+ typed
+ terms</a>.</li>
+ <li><a
+ href="static/matita/lambdadelta/Basic_1/ty3/dec/ty3_inference.con.html">Decidability
+ of
+ the
+ type
+ inference
+ problem</a>.<br>
+ <br>
+ </li>
+ </ul>
+ </li>
+ <li><a name="dynamic"></a>F. Guidi: <a
+ style="font-style: italic;"
+href="http://mowgli.cs.unibo.it:58080/apply?keys=RT&xmluri=http://helm.cs.unibo.it/helm//html/folder/index.html&prop.media-type=text/html&param.thmedia-type=text/html&param.thkeys=T1%2CT2%2CL%2CE&param.embedkeys=d_c%2CTC1%2CHC2%2CL&param.thencoding=UTF-8&prop.encoding=UTF-8&prop.doctype-public=-//W3C//DTD%20XHTML%201.0%20Transitional//EN&param.doctype-public=-//W3C//DTD%20XHTML%201.0%20Transitional//EN&param.encoding=UTF-8&param.media-type=text/html&param.keys=d_c%2CC1%2CHC2%2CL&profile=default&param.profile=default&param.CICURI=theory:/matita/lambdadelta/">lambdadelta</a>
+ (revised <span style="font-weight: bold;">2011-09</span>).
+ Formal
+ specification for <a
+ href="http://matita.cs.unibo.it/">Matita</a> 0.5 (<a
+ href="http://helm.cs.unibo.it/">HELM</a> directory).<br>
+ <br>
+ </li>
+ <li><a name="ldp1"></a>F. Guidi: <a
+ href="download/lambdadelta_1.tar.gz"><span
+ style="font-style: italic;">lambdadelta_1</span></a>
+ (revised <span style="font-weight: bold;">2011-09</span>).
+Formal
+ specification for <span style="font-weight: bold;">Coq
+ 7.3.1</span>
+ (source
+ proof scripts). <a href="#bibtex">BibTeX entry</a>.<br>
+ </li>
+ </ol>
+ <h3 style="text-align: right;">Tools <img style="width:
+ 37px; height: 37px;" alt="[Butterfly]"
+ title="Butterfly" src="download/b5.png"></h3>
+ <a name="lddl"></a><img style="width: 32px; height: 32px;"
+ alt="[Crux Logo]" title="The Crux"
+ src="download/crux_32.png"><span style="font-weight:
+ bold;"> </span>The <span style="font-weight: bold;"><span
+ style="text-decoration: underline;">λδ
+ Digital
+ Library
+ (LDDL)</span></span> is part of <a
+ href="http://helm.cs.unibo.it/">HELM</a>
+ and contains a set of
+ resources expressed in λδ.<br>
+ <ul>
+ <li><span style="font-weight: bold;">Contents:</span>
+ Landau's "<span style="font-style: italic;">Grundlagen
+ der Analysis</span>" (from
+ Jutting's specification in <a
+ href="http://www.win.tue.nl/automath/">Automath</a>).<br>
+ <span style="font-weight: bold;"></span></li>
+ </ul>
+ <ul>
+ <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>
+ (updated <span style="font-weight: bold;">2011-09</span>).</li>
+ </ul>
+ <ul>
+ <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
+ definition
+ "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
+ definition
+ "t234"</a> (in "complete_rg" λδ).<br>
+ </li>
+ </ul>
+ <br>
+ <a name="helena"></a><span style="font-weight: bold;"><img
+ style="width: 32px; height: 32px;" alt="[Helena Logo]"
+ title="Helena" src="download/helena_32.png"> <span
+ style="text-decoration: underline;">Helena</span></span>
+ is a λδ
+ processor,
+ implemented in <a href="http://caml.inria.fr/">Caml</a>
+ as a part of
+ the <a href="http://helm.cs.unibo.it/">HELM</a> software,
+ meant for
+ testing the stable features of the calculus as well as the
+ unstable
+ ones.<br>
+ The processor source code is available in the directory <a
+href="http://helm.cs.unibo.it/websvn/listing.php?repname=helm&path=%2Ftrunk%2Fhelm%2Fsoftware%2Fhelena%2F&rev=0&sc=0">/trunk/helm/software/helena/</a>
+ of the <a
+ href="http://helm.cs.unibo.it/software/index.html">HELM
+ Svn
+ repository</a>. The Svn revisions containing the stable
+ versions
+ of Helena are indicated below. <br>
+ <ul>
+ <li><span style="font-weight: bold;">Version 0.8.2.</span>
+ In
+ progress.<br>
+ </li>
+ </ul>
+ <ul>
+ <li><span style="font-weight: bold;">Version 0.8.1
+ (2010-11).</span>
+ Exploits a subset of "complete_rg" λδ as the
+ intermediate language.
+ Features importation from ".hln" files containing λδ
+ textual syntax.
+ The overall validation speed of the "<span
+ style="font-style: italic;">Grundlagen
+ der
+ Analysis</span>" increases of 22% with respect to
+ version 0.8.0. [Svn
+ revision: 11032] (<a
+ href="download/helena_0.8.1.tar.gz">archived
+ source code</a>)
+ <ul>
+ <li><span style="font-weight: bold;">2009-12.</span>
+ Helena
+ appears in F. Wiedijk's <a
+ href="http://www.cs.ru.nl/%7Efreek/digimath/index.html#helena">index
+of
+computer
+ math systems</a>.</li>
+ </ul>
+ </li>
+ </ul>
+ <ul>
+ <li><a style=" font-weight: bold;"
+ href="documentation.html#ldp6">Version 0.8.0</a><span
+ style="font-weight: bold;"> (2009-09).</span>
+ Supports
+ "basic_rg" λδ with naive implementation of
+ impredicative sort
+ inclusion. Features
+ importation from <a
+ href="http://www.win.tue.nl/automath/">Automath</a>
+ and exportation to <a href="http://www.w3.org/XML/">XML</a>.
+ [Svn
+ revision: 10304] (<a
+ href="download/helena_0.8.0.tar.gz">archived
+ source code</a>)<br>
+ <ul>
+ <li><span style="font-weight: bold;">2009-09.</span>
+ Jutting's specification of Landau's "<span
+ style="font-style: italic;">Grundlagen
+ der
+ Analysis</span>" enters λδ Digital Library.<br>
+ <span style="font-weight: bold;"></span></li>
+ <li><span style="font-weight: bold;">2009-06.</span>
+ Jutting's specification of Landau's "<span
+ style="font-style: italic;">Grundlagen
+ der
+ Analysis</span>" is
+ successfully processed, enabling sort inclusion<span
+ style="font-weight: bold;"></span>.</li>
+ </ul>
+ </li>
+ </ul>
+ <h3 style="text-align: right;">Other resources <img
+ style="width: 37px; height: 37px;" alt="[Butterfly]"
+ title="Butterfly" src="download/b4.png"></h3>
+ <ul>
+ <li><a name="bibtex"></a>A
+ BibTeX database of λδ documentation: <a
+ href="download/lambdadelta.bib"><span
+ style="font-style: italic;">lambdadelta.bib</span></a>,
+ <a style="font-style: italic;"
+ href="download/lambdadelta.txt">lambdadelta.txt</a>
+ (revised <span style="font-weight: bold;">2011-09</span>).</li>
+ </ul>
+ <ul>
+ <li>A <a href="http://www.jedsoft.org/jed/">Jed mode</a>
+ for
+ editing ".hln" files (containing λδ textual syntax): <a
+ style="font-style: italic;"
+ href="download/helena.sl">helena.sl</a>
+ (revised <span style="font-weight: bold;">2010-11</span>).</li>
+ </ul>
+ <ul>
+ <li>A <a href="http://www.jedsoft.org/jed/">Jed mode</a>
+ for
+ editing ".aut" files (containing <a
+ href="http://www.win.tue.nl/automath/">Automath</a>
+ textual syntax): <a style="font-style: italic;"
+ href="download/automath.sl">automath.sl</a>
+ (revised <span style="font-weight: bold;">2008-07</span>).</li>
+ </ul>
+ <ul>
+ <li>A logo for λδ: <a href="images/crux_177.png"><span
+ style="font-style: italic;">crux_177.png</span></a>
+ (revised <span style="font-weight: bold;">2012-09</span>).<br>
+ </li>
+ </ul>
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ <br>
+ <a href="http://validator.w3.org/check?uri=referer"><img
+ alt="[Valid HTML 4.01 Transitional]" title="Valid HTML 4.01
+ Transitional" src="http://www.w3.org/Icons/valid-html401"
+ style="border: 0px solid ; width: 88px; height: 31px;"></a> <a
+ href="http://www.anybrowser.org/campaign/"><img alt="[Use Any
+ Browser Here]" title="Use Any Browser Here"
+ src="download/globe_trans.png" style="border: 0px solid ;
+ width: 147px; height: 42px;"></a> <img style="width: 88px;
+ height: 31px;" alt="[PNG Used Here]" title="PNG Used Here"
+ src="download/PNGnow2.png"><br>
+ <br>
+ Last update 2012-12-01 by <a
+ href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio
+ Guidi</a><br>
+ </div>
+ </body>
+</html>