- <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>
- </ul>
- <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
+ <a href="http://lambda-delta.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 (lambda_delta)<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/lambda_delta/">lambda_delta</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/lambda_delta/Basic_1/pr3/pr3/pr3_confluence.con.html">Confluence
+ of
+ reduction</a> (Church-Rosser property).</li>
+ <li><a
+ href="static/matita/lambda_delta/Basic_1/ty3/props/ty3_correct.con.html">Correctness
+ of
+ types</a>.</li>
+ <li><a
+ href="static/matita/lambda_delta/Basic_1/ty3/props/ty3_unique.con.html">Uniqueness
+ of
+ types
+ up
+ to
+ conversion</a>.<br>
+ </li>
+ <li><a
+ href="static/matita/lambda_delta/Basic_1/ty3/pr3/ty3_sred_pr3.con.html">Subject
+ reduction
+ of
+ the
+ type
+ assignment</a>.</li>
+ <li><a
+href="static/matita/lambda_delta/Basic_1/ty3/arity_props/ty3_sn3.con.html">Strong
+ normalization
+ of
+ the
+ typed
+ terms</a>.</li>
+ <li><a
+ href="static/matita/lambda_delta/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/lambda_delta/">lambda_delta</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/lambda_delta_1.tar.gz"><span
+ style="font-style: italic;">lambda_delta_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://lambda-delta.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