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22 <div class="head1">The Formal Systems of the λδ (\lambda\delta) Family</div>
24 <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
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30 <table cellpadding="4" cellspacing="0">
33 <td class="snns capitalize italic sky">
34 <a href="http://lambdadelta.info/home.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/home.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#helena">helena</a>
78 <td class="ssnn capitalize green">
79 <a href="http://lambdadelta.info/osn/">Open Symbolic Notation (OSN)</a>
83 <td class="snss capitalize sky">
84 <a href="http://lambdadelta.info/home.html#citations">citations</a>
86 <td class="snss capitalize magenta">
87 <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
89 <td class="snss capitalize white">
90 <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
92 <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>
93 <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
94 <td class="snss capitalize orange">
95 <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
97 <td class="snss capitalize green">
98 <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
100 <td class="sssn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
105 <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="specifications">Computer-checked formal specifications <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b15.png" />
107 <div xmlns:ld="http://lambdadelta.info/" class="text">
108 The systems of the λδ family are developed as machine-checked digital specifications,
109 and are listed in the next table, which includes the major milestones.
111 <div xmlns:ld="http://lambdadelta.info/" class="text">
112 The life cycle of a specification consists of four periods.
113 <span class="emph alpha">Alpha:</span>
114 the definitions are designed and the major propositions are proved,
115 then the calculus is announced with a presentation.
116 <span class="emph beta">Beta:</span>
117 major changes and additions may occur before the calculus is released on paper.
118 <span class="emph gamma">Gamma:</span>
119 subsequent improvements occur until the specification is completed or superseded,
120 while major changes and additions are announced and reported on paper.
121 <span class="emph delta">Delta:</span>
122 after its conclusion, the specification is modified just for maintenance.
124 <div xmlns:ld="http://lambdadelta.info/" class="text">
125 <table cellpadding="4" cellspacing="0">
128 <td class="snns top capitalize italic gray">version</td>
129 <td class="snnn top capitalize italic gray">name</td>
130 <td class="snnn top capitalize italic gray">stage</td>
131 <td class="snnn top capitalize italic gray">developed with</td>
132 <td class="snnn top capitalize italic gray">started</td>
133 <td class="snnn top capitalize italic gray">announced</td>
134 <td class="snnn top capitalize italic gray">released</td>
135 <td class="snnn top capitalize italic gray">concluded</td>
136 <td class="ssnn top capitalize italic gray">references</td>
139 <td class="snns top yellow">
140 <a href="http://lambdadelta.info/specification.html#v3">Version 3</a>
142 <td class="snnn top yellow">"basic_3"</td>
143 <td class="snnn top yellow" />
144 <td class="snnn top yellow" />
145 <td class="snnn top yellow" />
146 <td class="snnn top yellow" />
147 <td class="snnn top yellow" />
148 <td class="snnn top yellow" />
149 <td class="ssnn top yellow">
150 <a href="http://lambdadelta.info/documentation#ldJ3a">J3a</a>
154 <td class="snns top orange">
155 <a href="http://lambdadelta.info/specification.html#v2">Version 2</a>
157 <td class="snnn top orange">"basic_2"</td>
158 <td class="snns top orange">"A2"</td>
159 <td class="snnn top orange">
160 <a href="http://matita.cs.unibo.it/">Matita 0.99.3</a>
162 <td class="snnn top orange">October 2015</td>
163 <td class="snnn top orange" />
164 <td class="snnn top orange" />
165 <td class="snnn top orange" />
166 <td class="ssnn top orange" />
169 <td class="nnns top orange">
172 <td class="nnnn top orange">
175 <td class="snns top orange">"A1"</td>
176 <td class="snnn top orange">
177 <a href="http://matita.cs.unibo.it/">Matita 0.99.2</a>
179 <td class="snnn top orange">April 2011</td>
180 <td class="snnn top orange">June 2014</td>
181 <td class="snnn top orange">October 2014</td>
182 <td class="snnn top orange">August 2015</td>
183 <td class="ssnn top orange">
184 <a href="http://lambdadelta.info/documentation#ldV2a">V2a</a>
185 <a href="http://lambdadelta.info/documentation#ldR2c">R2c</a>
189 <td class="snns top orange">Abandoned</td>
190 <td class="snnn top orange" />
191 <td class="snnn top orange" />
192 <td class="snnn top orange">
193 <a href="http://coq.inria.fr/">Coq 7.3.1</a>
195 <td class="snnn top orange">March 2008</td>
196 <td class="snnn top orange" />
197 <td class="snnn top orange" />
198 <td class="snnn top orange">February 2011</td>
199 <td class="ssnn top orange" />
202 <td class="snss top red">
203 <a href="http://lambdadelta.info/specification.html#v1">Version 1</a>
205 <td class="snsn top red">"basic_1"</td>
206 <td class="snsn top red" />
207 <td class="snsn top red">
208 <a href="http://coq.inria.fr/">Coq 7.3.1</a>
210 <td class="snsn top red">May 2004</td>
211 <td class="snsn top red">December 2005</td>
212 <td class="snsn top red">November 2006</td>
213 <td class="snsn top red">May 2008</td>
214 <td class="sssn top red">
215 <a href="http://lambdadelta.info/documentation#ldV1a">V1a</a>
216 <a href="http://lambdadelta.info/documentation#ldJ1a">J1a</a>
222 <div xmlns:ld="http://lambdadelta.info/" class="text">
223 Informational pages on the specifications are provided.
225 <ul xmlns:ld="http://lambdadelta.info/" id="notice1">
227 <span class="emph alpha">Notice on displayed numerical acounts:</span>
228 nodes are counted according to the "intrinsic complexity measure"
229 [F. Guidi: "Procedural Representation of CIC Proof Terms"
230 Journal of Automated Reasoning 44(1-2), Springer (February 2010), pp. 53-78].
233 <ul xmlns:ld="http://lambdadelta.info/" id="notice2">
235 <span class="emph alpha">Notice on displayed logical structures:</span>
236 from the logical standpoint, the source scripts are grouped in "planes"
237 and these are grouped in "components";
238 the notation for the relations or functions
239 introduced in each script, is shown in parentheses (? are placeholders).
242 <!-- VERSION 3 =========================================================== -->
243 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v3">
244 <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b8.png" /> λδ version 3 (proposed)</div>
245 <div xmlns:ld="http://lambdadelta.info/" class="text">
246 The formal specification of λδ version 3
249 <!-- VERSION 2 =========================================================== -->
250 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v2">
251 <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png" /> λδ version 2 (active)</div>
252 <div xmlns:ld="http://lambdadelta.info/" class="text">
253 The formal specification of λδ version 2
254 is available in the following formats:
256 <ul xmlns:ld="http://lambdadelta.info/" id="source2">
259 <a href="http://lambdadelta.info/download/lambdadelta_2A1.tar.gz">lambdadelta_2A1 for Matita 0.99.2</a>
260 (revised <span class="emph gamma">2014-10</span>).
262 <a href="http://lambdadelta.info/documentation.html#ldR2c">Documentation (R2c)</a>.
265 The scripts are grouped in directories, first by part, then by component.
268 <span class="emph alpha">Notice:</span>
269 the scripts are checked by the latest version of Matita from
270 <a href="http://matita.cs.unibo.it/download.shtml">HELM Subversion repository</a>
271 at path <trunk/matita/>.
275 <div xmlns:ld="http://lambdadelta.info/" class="text">
276 Informational pages on the parts of the specification:
277 <a href="http://lambdadelta.info/ground_2.html">Background</a>,
278 <a href="http://lambdadelta.info/basic_2.html">Core</a>,
279 <a href="http://lambdadelta.info/apps_2.html">Applications</a>.
281 <!-- VERSION 1 =========================================================== -->
282 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v1">
283 <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b6.png" /> λδ version 1 (superseded)</div>
284 <div xmlns:ld="http://lambdadelta.info/" class="text">
285 The formal specification of λδ version 1
286 is available in the following formats:
288 <ul xmlns:ld="http://lambdadelta.info/" id="source1">
291 <a href="http://lambdadelta.info/download/lambdadelta_1.tar.gz">lambdadelta_1 for Coq 7.3.1</a>
292 (revised <span class="emph delta">2015-09</span>).
294 <a href="http://lambdadelta.info/documentation.html#ldJ1a">Documentation (J1a)</a>.
297 <span class="emph delta">2015 January 15.</span>
298 17 new lemmas and former lemma "eq_nat_dec" renamed as "nat_dec_neg".
303 The scripts are grouped in directories, one for each part.
307 <ul xmlns:ld="http://lambdadelta.info/" id="static1">
309 <a href="http://lambdadelta.info/static/matita/lambdadelta/">lambdadelta_1 for Matita 0.5</a>
310 (revised <span class="emph delta">2011-09</span>).
311 Static HTML pages generated by the <a href="http://helm.cs.unibo.it/">HELM</a> rendering engine.
314 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/pr3/pr3/pr3_confluence.con.html">
315 Confluence of reduction</a>
316 (Church-Rosser property).
319 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_correct.con.html">
320 Correctness of types</a>.
323 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_unique.con.html">
324 Uniqueness of types up to conversion</a>.
327 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/pr3/ty3_sred_pr3.con.html">
328 Subject reduction of the type assignment</a>.
331 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/arity_props/ty3_sn3.con.html">
332 Strong normalization of the typed terms</a>.
335 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/dec/ty3_inference.con.html">
336 Decidability of the type inference problem</a>.
341 <ul xmlns:ld="http://lambdadelta.info/" id="dynamic1">
343 <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/">
344 lambdadelta_1 for Matita 0.5</a>
345 (revised <span class="emph delta">2011-09</span>).
346 <a href="http://helm.cs.unibo.it/">HELM</a> directory.
347 <span class="emph alpha">Notice: the HELM rendering engine is offline.</span>
350 <div xmlns:ld="http://lambdadelta.info/" class="text">
351 Informational pages on the parts of the specification:
352 <a href="http://lambdadelta.info/ground_1.html">Background</a>,
353 <a href="http://lambdadelta.info/basic_1.html">Core</a>.
356 <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
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381 <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Wed, 05 Apr 2017 18:05:16 +0200</div>