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8 <meta content="Ferruccio Guidi" name="author">
9 <meta content="The formal system λδ" name="description">
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14 <h1>The Formal System λδ (\lambda\delta)<br>
16 <h2>Towards the unification of terms, types, environments and
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">
22 <td style="vertical-align: top;">
24 <li><a href="index.html">Foreword</a></li>
27 <li><a href="news.html">News</a></li>
30 <li><a href="documentation.html">Papers</a></li>
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
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
55 paper (as it happens for most currently digitalized
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>).
61 specification for <a href="http://matita.cs.unibo.it/">Matita</a> 0.5
63 by the <a href="http://helm.cs.unibo.it/">HELM</a>
65 Here are the most relevant theorems proved in the
68 <li><a href="static/matita/lambdadelta/Basic_1/pr3/pr3/pr3_confluence.con.html">Confluence
70 reduction</a> (Church-Rosser property).</li>
71 <li><a href="static/matita/lambdadelta/Basic_1/ty3/props/ty3_correct.con.html">Correctness
74 <li><a href="static/matita/lambdadelta/Basic_1/ty3/props/ty3_unique.con.html">Uniqueness
81 <li><a href="static/matita/lambdadelta/Basic_1/ty3/pr3/ty3_sred_pr3.con.html">Subject
87 <li><a href="static/matita/lambdadelta/Basic_1/ty3/arity_props/ty3_sn3.con.html">Strong
93 <li><a href="static/matita/lambdadelta/Basic_1/ty3/dec/ty3_inference.con.html">Decidability
103 <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>
104 (revised <span style="font-weight: bold;">2011-09</span>).
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>
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>).
112 specification for <span style="font-weight: bold;">Coq
115 proof scripts). <a href="#bibtex">BibTeX entry</a>.<br>
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
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>
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>
133 <li><span style="font-weight: bold;">Access:</span> <a
134 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>
135 (updated <span style="font-weight: bold;">2012-10</span>).</li>
138 <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
140 "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
142 "t234"</a> (in "complete_rg" λδ).<br>
146 <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>
149 implemented in <a href="http://caml.inria.fr/">Caml</a>
151 the <a href="http://helm.cs.unibo.it/">HELM</a> software,
153 testing the stable features of the calculus as well as the
156 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>
157 of the <a href="http://helm.cs.unibo.it/software/index.html">HELM
159 repository</a>. The Svn revisions containing the stable
161 of Helena are indicated below. <br>
163 <li><span style="font-weight: bold;">Version 0.8.2.</span>
169 <li><span style="font-weight: bold;">Version 0.8.1
171 Exploits a subset of "complete_rg" λδ as the
172 intermediate language.
173 Features importation from ".hln" files containing λδ
175 The overall validation speed of the "<span style="font-style: italic;">Grundlagen
177 Analysis</span>" increases of 22% with respect to
179 revision: 11032] (<a href="download/helena_0.8.1.tar.gz">archived
182 <li><span style="font-weight: bold;">2009-12.</span>
184 appears in F. Wiedijk's <a href="http://www.cs.ru.nl/%7Efreek/digimath/index.html#helena">index
187 math systems</a>.</li>
192 <li><a style="font-weight: bold;" href="documentation.html#ldp6">Version 0.8.0</a><span style="font-weight: bold;"> (2009-09).</span>
194 "basic_rg" λδ with naive implementation of
197 importation from <a href="http://www.win.tue.nl/automath/">Automath</a>
198 and exportation to <a href="http://www.w3.org/XML/">XML</a>.
200 revision: 10304] (<a href="download/helena_0.8.0.tar.gz">archived
203 <li><span style="font-weight: bold;">2009-09.</span>
204 Jutting's specification of Landau's "<span style="font-style: italic;">Grundlagen
206 Analysis</span>" enters λδ Digital Library.<br>
207 <span style="font-weight: bold;"></span></li>
208 <li><span style="font-weight: bold;">2009-06.</span>
209 Jutting's specification of Landau's "<span style="font-style: italic;">Grundlagen
212 successfully processed, enabling sort inclusion<span style="font-weight: bold;"></span>.</li>
216 <h3 style="text-align: right;">Other resources <img style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly" src="images/b4.png"></h3>
218 <li><a name="bibtex"></a>A
219 BibTeX database of λδ documentation: <a href="download/lambdadelta.bib"><span style="font-style: italic;">lambdadelta.bib</span></a>,
220 <a style="font-style: italic;" href="download/lambdadelta.txt">lambdadelta.txt</a>
221 (revised <span style="font-weight: bold;">2012-10</span>).</li>
224 <li>A <a href="http://www.jedsoft.org/jed/">Jed mode</a>
226 editing ".hln" files (containing λδ textual syntax): <a style="font-style: italic;" href="download/helena.sl">helena.sl</a>
227 (revised <span style="font-weight: bold;">2010-11</span>).</li>
230 <li>A <a href="http://www.jedsoft.org/jed/">Jed mode</a>
232 editing ".aut" files (containing <a href="http://www.win.tue.nl/automath/">Automath</a>
233 textual syntax): <a style="font-style: italic;" href="download/automath.sl">automath.sl</a>
234 (revised <span style="font-weight: bold;">2008-07</span>).</li>
237 <li>A logo for λδ: <a href="images/crux_177.png"><span style="font-style: italic;">crux_177.png</span></a>
238 (revised <span style="font-weight: bold;">2012-09</span>).<br>
246 <a href="http://validator.w3.org/check?uri=referer"><img alt="[Valid HTML 4.01 Transitional]" title="Valid HTML 4.01
247 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
248 Browser Here]" title="Use Any Browser Here" src="images/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="images/PNGnow2.png"><br>
250 Last update 2012-12-02 by <a href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio