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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">
8     <link rel="shortcut icon" href="download/crux_16.ico">
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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" style="border: 0px
15           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
19         contexts</h2>
20       <img style="width: 95%; height: 4px;" alt="[Separator]"
21         title="Separator" src="download/rainbow.png"><br>
22       <table style="text-align: left; width: 95%; margin-left: auto;
23         margin-right: auto;" 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 style="width:
43                   37px; height: 37px;" alt="[Butterfly]"
44                   title="Butterfly" src="download/b5.png"></h3>
45               <ul>
46                 <li><span style="font-weight: bold;">September 2011.</span>
47                   The
48                   denomination "lambda-delta" changes to "lambda_delta".
49                 <ul>
50                   <li>The character "-" is reserved in λδ textual syntax
51                     (recognized by <span style="font-style: italic;">Helena
52                       0.8.1</span>).
53                   </li>
54                   <li>Eventually, the occurrences of the character "-"
55                     will be
56                     replaced by "_" in all λδ-related identifiers.</li>
57                   <li>In particular, this refactoring involves file
58                     names and
59                     path names.</li>
60                   <li>The permanent λδ URL is sheduled to become <span
61                       style="font-style: italic;">http://lambda_delta.info</span>
62                     on
63                     December 2012.<br>
64                   </li>
65                 </ul></li>
66               </ul>
67               <ul>
68                 <li><span style="font-weight: bold;">April 2011.</span>
69                   The
70                   specification of λδ version 2 and related topics is
71                   restarted in <a href="http://matita.cs.unibo.it/">Matita
72                     0.5</a>.
73                 <ul>
74                   <li><a href="apps_2.html">Here</a> is a page about
75                     the
76                     topics related to the specification (Applications).</li>
77                   <li><a href="basic_2.html">Here</a> is a page about
78                     the
79                     specification (Core).
80                   </li>
81                 </ul></li>
82               </ul>
83               <ul>
84                 <li><span style="font-weight: bold;">December 2010.</span>
85                   Permanent λδ URL acquired: <a
86                     href="http://lambda-delta.info">http://lambda-delta.info</a>
87                   (pointing at this site). <br>
88                   <span style="font-weight: bold;"></span></li>
89               </ul>
90               <ul>
91                 <li><span style="font-weight: bold;">November 2010.</span>
92                   <span style="font-style: italic;">Helena 0.8.1</span>
93                   is released. <br>
94                 </li>
95               </ul>
96               <ul>
97                 <li><span style="font-weight: bold;">September 2009.</span>
98                   <span style="font-style: italic;">Helena 0.8.0</span>
99                   is released and the <a
100                     href="implementation.html#lddl">λδ Digital Library</a>
101                   is
102                   started.<br>
103                   <span style="font-weight: bold;"></span></li>
104               </ul>
105               <ul>
106                 <li><span style="font-weight: bold;">June 2009.</span> <span
107                     style="font-style: italic;">Helena</span>, a <a
108                     href="implementation.html#helena">validator for λδ
109                     version 2</a>, is
110                   available
111                   as
112                   a
113                   part
114                   of
115                   the <a href="http://helm.cs.unibo.it/">HELM</a>
116                   software. <br>
117                 </li>
118               </ul>
119               <span style="font-weight: bold;"></span>
120               <ul>
121                 <li><span style="font-weight: bold;">September 2008.</span>
122                   This site is online.<br>
123                 </li>
124               </ul>
125               <span style="font-weight: bold;"></span>
126               <ul>
127                 <li><span style="font-weight: bold;">July 2008.</span> <a
128                     href="documentation.html#ldp5">First journal paper
129                     on λδ</a> accepted
130                   for publication.</li>
131               </ul>
132               <ul>
133                 <li><span style="font-weight: bold;">July 2008.</span>
134                   First <a href="http://helm.cs.unibo.it/procedural/">procedural
135                     reconstruction</a> for <a
136                     href="http://matita.cs.unibo.it/">Matita 0.5</a>
137                   of the <a href="implementation.html#ldp1">λδ proof
138                     scripts for
139                     Coq 7.3.1</a>.<br>
140                 </li>
141               </ul>
142               <ul>
143                 <li><span style="font-weight: bold;">June 2008.</span>
144                   The <a href="implementation.html#static">HTML
145                     pages of the specification of λδ version 1 for
146                     Matita 0.5</a> are
147                   online.<br>
148                   <span style="font-weight: bold;"></span></li>
149               </ul>
150               <ul>
151                 <li><span style="font-weight: bold;">March 2008.</span>
152                   The
153                   specification of λδ version 2 is started with Coq
154                   7.3.1 (false start).
155                   <!--          <ul>
156             <li>native type assignment with new rules for application: <span
157  style="font-style: italic;">nty</span> (it replaces <span
158  style="font-style: italic;">ty3</span>);<br>
159             </li>
160             <li>parallel conversion on focalized terms: <span
161  style="font-style: italic;">fpcs</span> (it replaces <span
162  style="font-style: italic;"></span><span style="font-style: italic;">pc3</span>);
163               <br>
164             </li>
165             <li>new weak parallel reduction on environments: <span
166  style="font-style: italic;">wcpr</span> <span
167  style="font-style: italic;"></span>(it is based on <span
168  style="font-style: italic;">fpr</span> and replaces <span
169  style="font-style: italic;">wcpr0</span>);&nbsp; <br>
170             </li>
171             <li>parallel reduction on focalized terms: <span
172  style="font-style: italic;">fpr</span> and <span
173  style="font-style: italic;">fprs</span> (they replace <span
174  style="font-style: italic;"></span><span style="font-style: italic;"></span><span
175  style="font-style: italic;">pr2</span>, <span
176  style="font-style: italic;">pr3</span>); <br>
177             </li>
178           </ul>
179           <ul>
180             <li>new thinning relation: <span
181  style="font-style: italic;">drop</span>
182 (it replaces the old <span style="font-style: italic;">drop</span>, <span
183  style="font-style: italic;">clear</span>, <span
184  style="font-style: italic;">getl</span>, <span
185  style="font-style: italic;">cimp</span>, <span
186  style="font-style: italic;">drop1</span>);</li>
187             <li>new shift function: <span style="font-style: italic;">shift</span>:
188 (it
189 replaces
190
191               <span style="font-style: italic;">app1</span>);</li>
192             <li>new length function for environments: <span
193  style="font-style: italic;">clen</span>;<br>
194             </li>
195             <li>new relocation function: <span
196  style="font-style: italic;">lift</span> (it replaces old <span
197  style="font-style: italic;">lift</span>, <span
198  style="font-style: italic;">lift1</span>);<br>
199             </li>
200             <li>new term structure with polarity indicators and no
201 distinction between binding and flat items;</li>
202             <li>new general theory of relocation (comprises new
203 relocation functions: <span style="font-style: italic;">s</span>, <span
204  style="font-style: italic;">r</span>);</li>
205             <li>we removed context-free reduction and conversion (<span
206  style="font-style: italic;">pr0</span>, <span
207  style="font-style: italic;">pr1</span>, <span
208  style="font-style: italic;">pc1</span>);<br>
209             </li>
210             <li>we removed greedy substitution (<span
211  style="font-style: italic;"></span><span style="font-style: italic;">csubst0</span>,
212               <span style="font-style: italic;">csubst1</span>, <span
213  style="font-style: italic;">fsubst0</span>, <span
214  style="font-style: italic;">subst0</span>, <span
215  style="font-style: italic;">subst1</span>);<br>
216             </li>
217             <li>we removed level indicators on environments (<span
218  style="font-style: italic;">cbk</span>).</li>
219           </ul>
220 --> </li>
221               </ul>
222               <ul>
223                 <li><span style="font-weight: bold;">September 2007.</span>
224                   The <a href="implementation.html#dynamic">specification
225                     of λδ version
226                     1 for
227                     Matita 0.4</a> is online.</li>
228               </ul>
229               <ul>
230                 <li><span style="font-weight: bold;">November 2006.</span>
231                   <a href="documentation.html#ldp3">λδ version
232                     1</a> is released.</li>
233               </ul>
234               <ul>
235                 <li><span style="font-weight: bold;">December 2005.</span>
236                   <a href="documentation.html#ldt1">First communication
237                     on λδ</a>.<br>
238                 </li>
239               </ul>
240               <ul>
241                 <li><span style="font-weight: bold;">May 2004.</span>
242                   The <a href="implementation.html#ldp1">specification
243                     of λδ version 1</a> is
244                   started with Coq 7.3.1.<br>
245                 </li>
246               </ul>
247               <h3 style="text-align: right;">Visibility <img
248                   style="width: 37px; height: 37px;" alt="[Butterfly]"
249                   title="Butterfly" src="download/b4.png"></h3>
250               <ul>
251                 <li><span style="font-weight: bold;">February 2012.</span>
252                   The <a href="http://www.google.com/">Google</a>
253                   search for <span style="color: rgb(255, 0, 0);">formal
254                     system lambda
255                     delta</span>
256                   gives 5 resources about λδ in the first 6 results.<br>
257                 </li>
258               </ul>
259               <ul>
260                 <li><span style="font-weight: bold;">February 2012.</span>
261                   The <a href="http://www.yahoo.com/">Yahoo</a>
262                   search <span style="color: rgb(255, 0, 0);">formal
263                     system lambda delta</span>
264                   gives this site as the first result.</li>
265               </ul>
266             </td>
267           </tr>
268         </tbody>
269       </table>
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281       <br>
282       Last update 2012-04-16 by <a
283         href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio
284         Guidi</a><br>
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