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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="snnn top capitalize italic gray">concluded</td>
137 <td class="ssnn top capitalize italic gray">references</td>
140 <td class="snns top orange">
141 <a href="http://lambdadelta.info/specification.html#v2">Version 2</a>
143 <td class="snnn top orange">"basic_2"</td>
144 <td class="snnn top orange">
145 <a href="http://matita.cs.unibo.it/">Matita 0.99.2</a>
147 <td class="snns top orange">"A2"</td>
148 <td class="snnn top orange">October 2015</td>
149 <td class="snnn top orange" />
150 <td class="snnn top orange" />
151 <td class="snnn top orange" />
152 <td class="ssnn top orange">
157 <td class="nnns top orange">
160 <td class="nnnn top orange">
163 <td class="nnnn top orange">
166 <td class="snns top orange">"A1"</td>
167 <td class="snnn top orange">April 2011</td>
168 <td class="snnn top orange">June 2014</td>
169 <td class="snnn top orange">October 2014</td>
170 <td class="snnn top orange">August 2015</td>
171 <td class="ssnn top orange">
172 <a href="http://lambdadelta.info/documentation#ldV2a">V2a</a>
173 <a href="http://lambdadelta.info/documentation#ldR2c">R2c</a>
177 <td class="snns top orange">Abandoned</td>
178 <td class="snnn top orange" />
179 <td class="snnn top orange">
180 <a href="http://coq.inria.fr/">Coq 7.3.1</a>
182 <td class="snnn top orange" />
183 <td class="snnn top orange">March 2008</td>
184 <td class="snnn top orange" />
185 <td class="snnn top orange" />
186 <td class="snnn top orange">February 2011</td>
187 <td class="ssnn top orange">
192 <td class="snss top red">
193 <a href="http://lambdadelta.info/specification.html#v1">Version 1</a>
195 <td class="snsn top red">"basic_1"</td>
196 <td class="snsn top red">
197 <a href="http://coq.inria.fr/">Coq 7.3.1</a>
199 <td class="snsn top red" />
200 <td class="snsn top red">May 2004</td>
201 <td class="snsn top red">December 2005</td>
202 <td class="snsn top red">November 2006</td>
203 <td class="snsn top red">May 2008</td>
204 <td class="sssn top red">
205 <a href="http://lambdadelta.info/documentation#ldV1a">V1a</a>
206 <a href="http://lambdadelta.info/documentation#ldJ1a">J1a</a>
212 <div xmlns:ld="http://lambdadelta.info/" class="text">
213 Informational pages on the specifications are provided.
215 <ul xmlns:ld="http://lambdadelta.info/" id="">
217 <span class="emph alpha">Notice on displayed numerical acounts:</span>
218 nodes are counted according to the "intrinsic complexity measure"
219 [F. Guidi: "Procedural Representation of CIC Proof Terms"
220 Journal of Automated Reasoning 44(1-2), Springer (February 2010), pp. 53-78].
223 <ul xmlns:ld="http://lambdadelta.info/" id="">
225 <span class="emph alpha">Notice on displayed logical structures:</span>
226 from the logical standpoint, the source scripts are grouped in "planes"
227 and these are grouped in "components";
228 the notation for the relations or functions
229 introduced in each script, is shown in parentheses (? are placeholders).
232 <!-- VERSION 2 =========================================================== -->
233 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v2">
234 <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b4.png" /> λδ version 2 (active)</div>
235 <div xmlns:ld="http://lambdadelta.info/" class="text">
236 The formal specification of λδ version 2
237 is available in the following formats:
239 <ul xmlns:ld="http://lambdadelta.info/" id="source2">
242 <a href="http://lambdadelta.info/download/lambdadelta_2A1.tar.gz">lambdadelta_2A1 for Matita 0.99.2</a>
243 (revised <span class="emph gamma">2014-10</span>).
245 <a href="http://lambdadelta.info/documentation.html#ldR2c">Documentation (R2c)</a>.
248 The scripts are grouped in directories, first by part, then by component.
251 <span class="emph alpha">Notice:</span>
252 the scripts are checked by the latest version of Matita from
253 <a href="http://matita.cs.unibo.it/download.shtml">HELM Subversion repository</a>
254 at path <trunk/matita/>.
258 <div xmlns:ld="http://lambdadelta.info/" class="text">
259 Informational pages on the parts of the specification:
260 <a href="http://lambdadelta.info/ground_2.html">Background</a>,
261 <a href="http://lambdadelta.info/basic_2.html">Core</a>,
262 <a href="http://lambdadelta.info/apps_2.html">Applications</a>.
264 <!-- VERSION 1 =========================================================== -->
265 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v1">
266 <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b6.png" /> λδ version 1 (superseded)</div>
267 <div xmlns:ld="http://lambdadelta.info/" class="text">
268 The formal specification of λδ version 1
269 is available in the following formats:
271 <ul xmlns:ld="http://lambdadelta.info/" id="source1">
274 <a href="http://lambdadelta.info/download/lambdadelta_1.tar.gz">lambdadelta_1 for Coq 7.3.1</a>
275 (revised <span class="emph delta">2015-09</span>).
277 <a href="http://lambdadelta.info/documentation.html#ldJ1a">Documentation (J1a)</a>.
280 <span class="emph delta">2015 January 15.</span>
281 17 new lemmas and former lemma "eq_nat_dec" renamed as "nat_dec_neg".
286 The scripts are grouped in directories, one for each part.
290 <ul xmlns:ld="http://lambdadelta.info/" id="static1">
292 <a href="http://lambdadelta.info/static/matita/lambdadelta/">lambdadelta_1 for Matita 0.5</a>
293 (revised <span class="emph delta">2011-09</span>).
294 Static HTML pages generated by the <a href="http://helm.cs.unibo.it/">HELM</a> rendering engine.
297 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/pr3/pr3/pr3_confluence.con.html">
298 Confluence of reduction</a>
299 (Church-Rosser property).
302 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_correct.con.html">
303 Correctness of types</a>.
306 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_unique.con.html">
307 Uniqueness of types up to conversion</a>.
310 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/pr3/ty3_sred_pr3.con.html">
311 Subject reduction of the type assignment</a>.
314 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/arity_props/ty3_sn3.con.html">
315 Strong normalization of the typed terms</a>.
318 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/dec/ty3_inference.con.html">
319 Decidability of the type inference problem</a>.
324 <ul xmlns:ld="http://lambdadelta.info/" id="dynamic1">
326 <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/">
327 lambdadelta_1 for Matita 0.5</a>
328 (revised <span class="emph delta">2011-09</span>).
329 <a href="http://helm.cs.unibo.it/">HELM</a> directory.
330 <span class="emph alpha">Notice: the HELM rendering engine is offline.</span>
333 <div xmlns:ld="http://lambdadelta.info/" class="text">
334 Informational pages on the parts of the specification:
335 <a href="http://lambdadelta.info/ground_1.html">Background</a>,
336 <a href="http://lambdadelta.info/basic_1.html">Core</a>.
339 <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
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364 <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Thu, 10 Dec 2015 16:21:42 +0100</div>