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10 <title>\lambda\delta home page</title>
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22 <div class="head1">The Formal System λδ (\lambda\delta)</div>
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29 <div xmlns:ld="http://lambdadelta.info/" class="text">
30 <table cellpadding="4" cellspacing="0">
33 <td class="snns capitalize italic sky">
34 <a href="http://lambdadelta.info/index.html">home</a>
36 <td class="snns capitalize italic magenta">
37 <a href="http://lambdadelta.info/news.html">news</a>
39 <td class="snns capitalize italic white">
40 <a href="http://lambdadelta.info/specification.html">specification</a>
42 <td class="snnn capitalize italic white">
45 <td class="snnn capitalize italic white">
48 <td class="snns capitalize italic orange">
49 <a href="http://lambdadelta.info/documentation.html">documentation</a>
51 <td class="snns capitalize italic green">
52 <a href="http://lambdadelta.info/implementation.html">implementation</a>
54 <td class="ssnn capitalize italic green">
59 <td class="snns capitalize sky">
60 <a href="http://lambdadelta.info/index.html#foreword">foreword</a>
62 <td class="snns capitalize magenta">
63 <a href="http://lambdadelta.info/news.html#milestones">milestones</a>
65 <td class="snns capitalize white">
66 <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
68 <td class="snnn capitalize white">(<a href="http://lambdadelta.info/ground_2.html">background</a> - <a href="http://lambdadelta.info/basic_2.html">core</a> - <a href="http://lambdadelta.info/apps_2.html">applications</a>)</td>
69 <td class="snnn capitalize white">
72 <td class="snns capitalize orange">
73 <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
75 <td class="snns capitalize green">
76 <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
78 <td class="ssnn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
81 <td class="snss capitalize sky">
82 <a href="http://lambdadelta.info/index.html#citations">citations</a>
84 <td class="snss capitalize magenta">
85 <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
87 <td class="snss capitalize white">
88 <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
90 <td class="snsn capitalize white">(<a href="http://lambdadelta.info/ground_1.html">background</a> - <a href="http://lambdadelta.info/basic_1.html">core</a>)</td>
91 <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
92 <td class="snss capitalize orange">
93 <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
95 <td class="snss capitalize green">
96 <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
98 <td class="sssn capitalize green">
105 <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="specifications">Computer-checked formal specifications <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b15.png" />
107 <div xmlns:ld="http://lambdadelta.info/" class="text">
108 λδ is developed as a machine-checked digital specification.
109 It comes in several versions listed in the next table,
110 which includes the major milestones.
112 <div xmlns:ld="http://lambdadelta.info/" class="text">
113 The life cycle of a specification consists of four periods.
114 <span class="emph alpha">Alpha:</span>
115 the definitions are designed and the major propositions are proved,
116 then the calculus is announced with a presentation.
117 <span class="emph beta">Beta:</span>
118 major changes and additions may occur before the calculus is released on paper.
119 <span class="emph gamma">Gamma:</span>
120 subsequent improvements occur until the specification is completed or superseded,
121 while major changes and additions are announced and reported on paper.
122 <span class="emph delta">Delta:</span>
123 after its conclusion, the specification is modified just for maintenance.
125 <div xmlns:ld="http://lambdadelta.info/" class="text">
126 <table cellpadding="4" cellspacing="0">
129 <td class="snns top capitalize italic gray">version</td>
130 <td class="snnn top capitalize italic gray">name</td>
131 <td class="snnn top capitalize italic gray">developed with</td>
132 <td class="snnn top capitalize italic gray">stage</td>
133 <td class="snnn top capitalize italic gray">started</td>
134 <td class="snnn top capitalize italic gray">announced</td>
135 <td class="snnn top capitalize italic gray">released</td>
136 <td class="ssnn top capitalize italic gray">concluded</td>
139 <td class="snns top orange">
140 <a href="http://lambdadelta.info/specification.html#v2">Version 2</a>
142 <td class="snnn top orange">"basic_2"</td>
143 <td class="snnn top orange">
144 <a href="http://matita.cs.unibo.it/">Matita 0.99.2</a>
146 <td class="snnn top orange">"A"</td>
147 <td class="snnn top orange">April 2011</td>
148 <td class="snnn top orange">June 2014</td>
149 <td class="snnn top orange">October 2014</td>
150 <td class="ssnn top orange" />
153 <td class="snns top orange">Abandoned</td>
154 <td class="snnn top orange" />
155 <td class="snnn top orange">
156 <a href="http://coq.inria.fr/">Coq 7.3.1</a>
158 <td class="snnn top orange" />
159 <td class="snnn top orange">March 2008</td>
160 <td class="snnn top orange" />
161 <td class="snnn top orange" />
162 <td class="ssnn top orange">February 2011</td>
165 <td class="snss top red">
166 <a href="http://lambdadelta.info/specification.html#v1">Version 1</a>
168 <td class="snsn top red">"basic_1"</td>
169 <td class="snsn top red">
170 <a href="http://coq.inria.fr/">Coq 7.3.1</a>
172 <td class="snsn top red" />
173 <td class="snsn top red">May 2004</td>
174 <td class="snsn top red">December 2005</td>
175 <td class="snsn top red">November 2006</td>
176 <td class="sssn top red">May 2008</td>
181 <div xmlns:ld="http://lambdadelta.info/" class="text">
182 Informational pages on the specifications are provided.
184 <ul xmlns:ld="http://lambdadelta.info/" id="">
186 <span class="emph alpha">Notice on displayed numerical acounts:</span>
187 nodes are counted according to the "intrinsic complexity measure"
188 [F. Guidi: "Procedural Representation of CIC Proof Terms"
189 Journal of Automated Reasoning 44(1-2), Springer (February 2010), pp. 53-78].
192 <ul xmlns:ld="http://lambdadelta.info/" id="">
194 <span class="emph alpha">Notice on displayed logical structures:</span>
195 from the logical standpoint, the source scripts are grouped in "planes"
196 and these are grouped in "components";
197 the notation for the relations or functions
198 introduced in each script, is shown in parentheses (? are placeholders).
201 <!-- VERSION 2 =========================================================== -->
202 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v2">
203 <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b4.png" /> λδ version 2 (active)</div>
204 <div xmlns:ld="http://lambdadelta.info/" class="text">
205 The formal specification of λδ version 2
206 is available in the following formats:
208 <ul xmlns:ld="http://lambdadelta.info/" id="source2">
211 <a href="http://lambdadelta.info/download/lambdadelta_2.tar.gz">lambdadelta_2 for Matita 0.99.2</a>
212 (revised <span class="emph gamma">2014-10</span>).
216 The scripts are grouped in directories, first by part, then by component.
219 <span class="emph alpha">Notice:</span>
220 the scripts are checked by the latest version of Matita from
221 <a href="http://matita.cs.unibo.it/download.shtml">HELM Subversion repository</a>
222 at path <trunk/matita/>.
226 <div xmlns:ld="http://lambdadelta.info/" class="text">
227 Informational pages on the parts of the specification:
228 <a href="http://lambdadelta.info/ground_2.html">Background</a>,
229 <a href="http://lambdadelta.info/basic_2.html">Core</a>,
230 <a href="http://lambdadelta.info/apps_2.html">Applications</a>.
232 <!-- VERSION 1 =========================================================== -->
233 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v1">
234 <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b6.png" /> λδ version 1 (superseded)</div>
235 <div xmlns:ld="http://lambdadelta.info/" class="text">
236 The formal specification of λδ version 1
237 is available in the following formats:
239 <ul xmlns:ld="http://lambdadelta.info/" id="source1">
242 <a href="http://lambdadelta.info/download/lambdadelta_1.tar.gz">lambdadelta_1 for Coq 7.3.1</a>
243 (revised <span class="emph delta">2015-01</span>).
247 <span class="emph delta">2015 January 15.</span>
248 17 new lemmas and former lemma "eq_nat_dec" renamed as "nat_dec_neg".
253 The scripts are grouped in directories, one for each part.
257 <ul xmlns:ld="http://lambdadelta.info/" id="static1">
259 <a href="http://lambdadelta.info/static/matita/lambdadelta/">lambdadelta_1 for Matita 0.5</a>
260 (revised <span class="emph delta">2011-09</span>).
261 Static HTML pages generated by the <a href="http://helm.cs.unibo.it/">HELM</a> rendering engine.
264 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/pr3/pr3/pr3_confluence.con.html">
265 Confluence of reduction</a>
266 (Church-Rosser property).
269 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_correct.con.html">
270 Correctness of types</a>.
273 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_unique.con.html">
274 Uniqueness of types up to conversion</a>.
277 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/pr3/ty3_sred_pr3.con.html">
278 Subject reduction of the type assignment</a>.
281 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/arity_props/ty3_sn3.con.html">
282 Strong normalization of the typed terms</a>.
285 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/dec/ty3_inference.con.html">
286 Decidability of the type inference problem</a>.
291 <ul xmlns:ld="http://lambdadelta.info/" id="dynamic1">
293 <a 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/">
294 lambdadelta_1 for Matita 0.5</a>
295 (revised <span class="emph delta">2011-09</span>).
296 <a href="http://helm.cs.unibo.it/">HELM</a> directory.
297 <span class="emph alpha">Notice: the HELM rendering engine is offline.</span>
300 <div xmlns:ld="http://lambdadelta.info/" class="text">
301 Informational pages on the parts of the specification:
302 <a href="http://lambdadelta.info/ground_1.html">Background</a>,
303 <a href="http://lambdadelta.info/basic_1.html">Core</a>.
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331 <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Wed, 02 Sep 2015 17:59:07 +0200</div>