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3 <head>
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5   <title>lambda_delta home page</title>
6   <meta content="Ferruccio Guidi" name="author">
7   <meta content="The formal system lambda_delta" name="description">
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10 <body>
11 <div style="text-align: center;">
12 <br>
13 <a href="http://lambda-delta.info"><img alt="[Crux Logo]"
14  title="The Crux" src="download/crux_32.png"
15  style="border: 0px solid ; width: 32px; height: 32px;"></a>
16 <h1>The Formal System λδ (lambda_delta)<br>
17 </h1>
18 <h2>Towards the unification of terms, types, environments and contexts</h2>
19 <img style="width: 95%; height: 4px;" alt="[Separator]"
20  title="Separator" src="download/rainbow.png"><br>
21 <table
22  style="text-align: left; width: 95%; margin-left: auto; margin-right: auto;"
23  border="0" cellpadding="2" cellspacing="20">
24   <tbody>
25     <tr>
26       <td style="vertical-align: top;">
27       <ul>
28         <li><a href="index.html">Foreword</a></li>
29       </ul>
30       <ul>
31         <li>News</li>
32       </ul>
33       <ul>
34         <li><a href="documentation.html">Papers</a></li>
35       </ul>
36       <ul>
37         <li><a href="implementation.html">Resources</a><br>
38         </li>
39       </ul>
40       </td>
41       <td style="vertical-align: top; text-align: left;">
42       <h3 style="text-align: right;">News <img
43  style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
44  src="download/b5.png"></h3>
45       <ul>
46         <li><span style="font-weight: bold;">September 2011.</span> The
47 denomination "lambda-delta" changes to "lambda_delta".</li>
48         <ul>
49           <li>The character "-" is reserved in λδ textual syntax
50 (recognized by <span style="font-style: italic;">Helena 0.8.1</span>).<br>
51           </li>
52           <li>Eventually, the occurrences of the character "-" will be
53 replaced by "_" in all λδ-related identifiers.</li>
54           <li>In particular, this refactoring involves file names and
55 path names.</li>
56           <li>The permanent λδ URL is sheduled to become <span
57  style="font-style: italic;">http://lambda_delta.info</span> on December 2012.<br>
58           </li>
59         </ul>
60       </ul>
61       <ul>
62         <li><span style="font-weight: bold;">April 2011.</span> The
63 specification of λδ version 2 is restarted in <a
64  href="http://matita.cs.unibo.it/">Matita 0.5</a>.</li>
65         <ul>
66           <li><a href="ld_basic_2.html">Here</a> is a page about the
67 specification.<br>
68           </li>
69         </ul>
70       </ul>
71       <ul>
72         <li><span style="font-weight: bold;">December 2010.</span>
73 Permanent λδ URL acquired: <a href="http://lambda-delta.info">http://lambda-delta.info</a>
74 (pointing at this site). <br>
75           <span style="font-weight: bold;"></span></li>
76       </ul>
77       <ul>
78         <li><span style="font-weight: bold;">November 2010.</span> <span
79  style="font-style: italic;">Helena 0.8.1</span> is released. <br>
80         </li>
81       </ul>
82       <ul>
83         <li><span style="font-weight: bold;">September 2009.</span> <span
84  style="font-style: italic;">Helena 0.8.0</span> is released and the <a
85  href="implementation.html#lddl">λδ Digital Library</a> is
86 started.<br>
87           <span style="font-weight: bold;"></span></li>
88       </ul>
89       <ul>
90         <li><span style="font-weight: bold;">June 2009.</span> <span
91  style="font-style: italic;">Helena</span>, A <a
92  href="implementation.html#helena">validator for </a><a
93  href="implementation.html#helena">λδ</a><span
94  style="font-style: italic;"></span>, <span style="font-style: italic;"></span>is
95 available
96 as
97 a
98 part
99 of
100 the
101           <a href="http://helm.cs.unibo.it/">HELM</a> software. <br>
102         </li>
103       </ul>
104       <span style="font-weight: bold;"></span>
105       <ul>
106         <li><span style="font-weight: bold;">September 2008.</span>
107 This site is online.<br>
108         </li>
109       </ul>
110       <span style="font-weight: bold;"></span>
111       <ul>
112         <li><span style="font-weight: bold;">July 2008.</span> <a
113  href="documentation.html#tocl1">First journal paper on λδ</a> accepted
114 for publication.</li>
115       </ul>
116       <ul>
117         <li><span style="font-weight: bold;">July 2008.</span> First <a
118  href="http://helm.cs.unibo.it/procedural/">procedural
119 reconstruction</a> in <a href="http://matita.cs.unibo.it/">Matita 0.5</a>
120 of the <a href="implementation.html#source">λδ proof scripts in
121 Coq 7.3.1</a>.<br>
122         </li>
123       </ul>
124       <ul>
125         <li><span style="font-weight: bold;">June 2008.</span> The <a
126  href="implementation.html#static">HTML
127 pages of the specification of λδ in Matita 0.5</a> are online.<br>
128           <span style="font-weight: bold;"></span></li>
129       </ul>
130       <ul>
131         <li><span style="font-weight: bold;">March 2008.</span> The
132 specification of λδ version 2 begins in Coq 7.3.1 (false start).
133 <!--          <ul>
134             <li>native type assignment with new rules for application: <span
135  style="font-style: italic;">nty</span> (it replaces <span
136  style="font-style: italic;">ty3</span>);<br>
137             </li>
138             <li>parallel conversion on focalized terms: <span
139  style="font-style: italic;">fpcs</span> (it replaces <span
140  style="font-style: italic;"></span><span style="font-style: italic;">pc3</span>);
141               <br>
142             </li>
143             <li>new weak parallel reduction on environments: <span
144  style="font-style: italic;">wcpr</span> <span
145  style="font-style: italic;"></span>(it is based on <span
146  style="font-style: italic;">fpr</span> and replaces <span
147  style="font-style: italic;">wcpr0</span>);&nbsp; <br>
148             </li>
149             <li>parallel reduction on focalized terms: <span
150  style="font-style: italic;">fpr</span> and <span
151  style="font-style: italic;">fprs</span> (they replace <span
152  style="font-style: italic;"></span><span style="font-style: italic;"></span><span
153  style="font-style: italic;">pr2</span>, <span
154  style="font-style: italic;">pr3</span>); <br>
155             </li>
156           </ul>
157           <ul>
158             <li>new thinning relation: <span
159  style="font-style: italic;">drop</span>
160 (it replaces the old <span style="font-style: italic;">drop</span>, <span
161  style="font-style: italic;">clear</span>, <span
162  style="font-style: italic;">getl</span>, <span
163  style="font-style: italic;">cimp</span>, <span
164  style="font-style: italic;">drop1</span>);</li>
165             <li>new shift function: <span style="font-style: italic;">shift</span>:
166 (it
167 replaces
168
169               <span style="font-style: italic;">app1</span>);</li>
170             <li>new length function for environments: <span
171  style="font-style: italic;">clen</span>;<br>
172             </li>
173             <li>new relocation function: <span
174  style="font-style: italic;">lift</span> (it replaces old <span
175  style="font-style: italic;">lift</span>, <span
176  style="font-style: italic;">lift1</span>);<br>
177             </li>
178             <li>new term structure with polarity indicators and no
179 distinction between binding and flat items;</li>
180             <li>new general theory of relocation (comprises new
181 relocation functions: <span style="font-style: italic;">s</span>, <span
182  style="font-style: italic;">r</span>);</li>
183             <li>we removed context-free reduction and conversion (<span
184  style="font-style: italic;">pr0</span>, <span
185  style="font-style: italic;">pr1</span>, <span
186  style="font-style: italic;">pc1</span>);<br>
187             </li>
188             <li>we removed greedy substitution (<span
189  style="font-style: italic;"></span><span style="font-style: italic;">csubst0</span>,
190               <span style="font-style: italic;">csubst1</span>, <span
191  style="font-style: italic;">fsubst0</span>, <span
192  style="font-style: italic;">subst0</span>, <span
193  style="font-style: italic;">subst1</span>);<br>
194             </li>
195             <li>we removed level indicators on environments (<span
196  style="font-style: italic;">cbk</span>).</li>
197           </ul>
198 --> </li>
199       </ul>
200       <ul>
201         <li><span style="font-weight: bold;">September 2007.</span>
202 The <a href="implementation.html#dynamic">specification of λδ in
203 Matita 0.4</a> is online.<br>
204         </li>
205       </ul>
206       <ul>
207         <li><span style="font-weight: bold;">December 2005.</span> <a
208  href="documentation.html#bologna1">First communication on λδ</a>.<br>
209         </li>
210       </ul>
211       <ul>
212         <li><span style="font-weight: bold;">May 2004.</span> The <a
213  href="implementation.html#source">specification of λδ in
214 Coq 7.3.1</a> begins.<br>
215         </li>
216       </ul>
217       <h3 style="text-align: right;">Visibility <img
218  style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
219  src="download/b4.png"></h3>
220       <ul>
221         <li><span style="font-weight: bold;">November 2010.</span>
222 The <a href="http://www.google.com/">Google</a>
223 search <span style="color: rgb(255, 0, 0);">formal system lambda delta</span>
224 gives 8 resources about λδ as the first results.<br>
225         </li>
226       </ul>
227       <ul>
228         <li><span style="font-weight: bold;">November 2010.</span>
229 The <a href="http://www.yahoo.com/">Yahoo</a>
230 search <span style="color: rgb(255, 0, 0);">formal system lambda delta</span>
231 gives 4 resources and 2 sub-resources about λδ as the first results.</li>
232       </ul>
233       </td>
234     </tr>
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250 Last update 2011-10-03 by <a href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio
251 Guidi</a><br>
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