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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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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;">December 2010.</span>
47 Permanent λδ URL acquired: <a href="http://lambda-delta.info">http://lambda-delta.info</a>
48 (pointing at this site). <br>
49           <span style="font-weight: bold;"></span></li>
50       </ul>
51       <ul>
52         <li><span style="font-weight: bold;">November 2010.</span> <span
53  style="font-style: italic;">Helena 0.8.1</span> is released. <br>
54         </li>
55       </ul>
56       <ul>
57         <li><span style="font-weight: bold;">September 2009.</span> <span
58  style="font-style: italic;">Helena 0.8.0</span> is released and the <a
59  href="implementation.html#lddl">λδ Digital Library</a> is
60 started.<br>
61           <span style="font-weight: bold;"></span></li>
62       </ul>
63       <ul>
64         <li><span style="font-weight: bold;">June 2009.</span> <span
65  style="font-style: italic;">Helena</span>, A <a
66  href="implementation.html#helena">validator for </a><a
67  href="implementation.html#helena">λδ</a><span
68  style="font-style: italic;"></span>, <span style="font-style: italic;"></span>is
69 available
70 as a
71 part of the <a href="http://helm.cs.unibo.it/">HELM</a> software. <br>
72         </li>
73       </ul>
74       <span style="font-weight: bold;"></span>
75       <ul>
76         <li><span style="font-weight: bold;">September 2008.</span>
77 This site is online.<br>
78         </li>
79       </ul>
80       <span style="font-weight: bold;"></span>
81       <ul>
82         <li><span style="font-weight: bold;">July 2008.</span> <a
83  href="documentation.html#tocl1">First journal paper on λδ</a> accepted
84 for publication.</li>
85       </ul>
86       <ul>
87         <li><span style="font-weight: bold;">July 2008.</span> First <a
88  href="http://helm.cs.unibo.it/procedural/">procedural
89 reconstruction</a> in <a href="http://matita.cs.unibo.it/">Matita 0.5</a>
90 of the <a href="implementation.html#source">λδ proof scripts in
91 Coq 7.3.1</a>.<br>
92         </li>
93       </ul>
94       <ul>
95         <li><span style="font-weight: bold;">June 2008.</span> The <a
96  href="implementation.html#static">HTML
97 pages of the specification of λδ in Matita 0.5</a> are online.<br>
98           <span style="font-weight: bold;"></span></li>
99       </ul>
100       <ul>
101         <li><span style="font-weight: bold;">March 2008.</span> An
102 improvement of the
103 specification of λδ in Coq 7.3.1 begins:
104           <ul>
105             <li>native type assignment with new rules for application: <span
106  style="font-style: italic;">nty</span> (it replaces <span
107  style="font-style: italic;">ty3</span>);<br>
108             </li>
109             <li>parallel conversion on focalized terms: <span
110  style="font-style: italic;">fpcs</span> (it replaces <span
111  style="font-style: italic;"></span><span style="font-style: italic;">pc3</span>);
112
113
114
115
116
117
118
119               <br>
120             </li>
121             <li>new weak parallel reduction on environments: <span
122  style="font-style: italic;">wcpr</span> <span
123  style="font-style: italic;"></span>(it is based on <span
124  style="font-style: italic;">fpr</span> and replaces <span
125  style="font-style: italic;">wcpr0</span>);&nbsp; <br>
126             </li>
127             <li>parallel reduction on focalized terms: <span
128  style="font-style: italic;">fpr</span> and <span
129  style="font-style: italic;">fprs</span> (they replace <span
130  style="font-style: italic;"></span><span style="font-style: italic;"></span><span
131  style="font-style: italic;">pr2</span>, <span
132  style="font-style: italic;">pr3</span>); <br>
133             </li>
134           </ul>
135           <ul>
136             <li>new thinning relation: <span
137  style="font-style: italic;">drop</span>
138 (it replaces the old <span style="font-style: italic;">drop</span>, <span
139  style="font-style: italic;">clear</span>, <span
140  style="font-style: italic;">getl</span>, <span
141  style="font-style: italic;">cimp</span>, <span
142  style="font-style: italic;">drop1</span>);</li>
143             <li>new shift function: <span style="font-style: italic;">shift</span>:
144 (it
145 replaces
146               <span style="font-style: italic;">app1</span>);</li>
147             <li>new length function for environments: <span
148  style="font-style: italic;">clen</span>;<br>
149             </li>
150             <li>new relocation function: <span
151  style="font-style: italic;">lift</span> (it replaces old <span
152  style="font-style: italic;">lift</span>, <span
153  style="font-style: italic;">lift1</span>);<br>
154             </li>
155             <li>new term structure with polarity indicators and no
156 distinction between binding and flat items;</li>
157             <li>new general theory of relocation (comprises new
158 relocation functions: <span style="font-style: italic;">s</span>, <span
159  style="font-style: italic;">r</span>);</li>
160             <li>we removed context-free reduction and conversion (<span
161  style="font-style: italic;">pr0</span>, <span
162  style="font-style: italic;">pr1</span>, <span
163  style="font-style: italic;">pc1</span>);<br>
164             </li>
165             <li>we removed greedy substitution (<span
166  style="font-style: italic;"></span><span style="font-style: italic;">csubst0</span>,
167
168
169               <span style="font-style: italic;">csubst1</span>, <span
170  style="font-style: italic;">fsubst0</span>, <span
171  style="font-style: italic;">subst0</span>, <span
172  style="font-style: italic;">subst1</span>);<br>
173             </li>
174             <li>we removed level indicators on environments (<span
175  style="font-style: italic;">cbk</span>).</li>
176           </ul>
177         </li>
178       </ul>
179       <ul>
180         <li><span style="font-weight: bold;">September 2007.</span>
181 The <a href="implementation.html#dynamic">specification of λδ in
182 Matita 0.4</a> is online.<br>
183         </li>
184       </ul>
185       <ul>
186         <li><span style="font-weight: bold;">December 2005.</span> <a
187  href="documentation.html#bologna1">First communication on λδ</a>.<br>
188         </li>
189       </ul>
190       <ul>
191         <li><span style="font-weight: bold;">May 2004.</span> The <a
192  href="implementation.html#source">specification of λδ in
193 Coq 7.3.1</a> begins.<br>
194         </li>
195       </ul>
196       <h3 style="text-align: right;">Visibility <img
197  style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
198  src="download/b4.png"></h3>
199       <ul>
200         <li><span style="font-weight: bold;">November 2010.</span> The <a
201  href="http://www.google.com/">Google</a>
202 search <span style="color: rgb(255, 0, 0);">formal system lambda delta</span>
203 gives 8 resources about λδ as the first results.<br>
204         </li>
205       </ul>
206       <ul>
207         <li><span style="font-weight: bold;">November 2010.</span> The <a
208  href="http://www.yahoo.com/">Yahoo</a>
209 search <span style="color: rgb(255, 0, 0);">formal system lambda delta</span>
210 gives 4 resources and 2 sub-resources about λδ as the first results.</li>
211       </ul>
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230 Last update 2010-12-14 by <a href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio
231 Guidi</a><br>
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