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22 <div class="head1">The Formal System λδ (\lambda\delta)</div>
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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 orange">
40 <a href="http://lambdadelta.info/documentation.html">documentation</a>
42 <td class="snns capitalize italic green">
43 <a href="http://lambdadelta.info/specification.html">specification</a>
45 <td class="snnn capitalize italic green">
48 <td class="snns capitalize italic green">
49 <a href="http://lambdadelta.info/implementation.html">implementation</a>
51 <td class="ssnn capitalize italic green">
56 <td class="snns capitalize sky">
57 <a href="http://lambdadelta.info/index.html#foreword">foreword</a>
59 <td class="snns capitalize magenta">
60 <a href="http://lambdadelta.info/news.html#milestones">milestones</a>
62 <td class="snns capitalize orange">
63 <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
65 <td class="snns capitalize green">
66 <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
68 <td class="snnn capitalize green">(<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="snns capitalize green">
70 <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
72 <td class="ssnn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
75 <td class="snss capitalize sky">
76 <a href="http://lambdadelta.info/index.html#citations">citations</a>
78 <td class="snss capitalize magenta">
79 <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
81 <td class="snss capitalize orange">
82 <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
84 <td class="snss capitalize green">
85 <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
87 <td class="snsn capitalize green">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
88 <td class="snss capitalize green">
89 <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
91 <td class="sssn capitalize green">
98 <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/b5.png" />
100 <div xmlns:ld="http://lambdadelta.info/" class="text">
101 λδ is developed as a machine-checked digital specification.
102 It comes in several versions listed in the next table,
103 which includes the major milestones.
105 <div xmlns:ld="http://lambdadelta.info/" class="text">
106 The life cycle of a specification consists of four periods.
107 <span class="emph alpha">Alpha:</span>
108 the definitions are designed and the major propositions are proved,
109 then the calculus is announced with a presentation.
110 <span class="emph beta">Beta:</span>
111 major changes and additions may occur before the calculus is released on paper.
112 <span class="emph gamma">Gamma:</span>
113 subsequent improvements occur until the specification is completed or superseded,
114 while major changes and additions are announced and reported on paper.
115 <span class="emph delta">Delta:</span>
116 after its conclusion, the specification is modified just for maintenance.
118 <div xmlns:ld="http://lambdadelta.info/" class="text">
119 <table cellpadding="4" cellspacing="0">
122 <td class="snns top capitalize italic gray">version</td>
123 <td class="snnn top capitalize italic gray">name</td>
124 <td class="snnn top capitalize italic gray">developed with</td>
125 <td class="snnn top capitalize italic gray">stage</td>
126 <td class="snnn top capitalize italic gray">started</td>
127 <td class="snnn top capitalize italic gray">announced</td>
128 <td class="snnn top capitalize italic gray">released</td>
129 <td class="ssnn top capitalize italic gray">concluded</td>
132 <td class="snns top orange">
133 <a href="http://lambdadelta.info/specification.html#v2">Version 2</a>
135 <td class="snnn top orange">"basic_2"</td>
136 <td class="snnn top orange">
137 <a href="http://matita.cs.unibo.it/">Matita 0.99.2</a>
139 <td class="snnn top orange">"A"</td>
140 <td class="snnn top orange">April 2011</td>
141 <td class="snnn top orange">June 2014</td>
142 <td class="snnn top orange">October 2014</td>
143 <td class="ssnn top orange" />
146 <td class="snns top orange">Abandoned</td>
147 <td class="snnn top orange" />
148 <td class="snnn top orange">
149 <a href="http://coq.inria.fr/">Coq 7.3.1</a>
151 <td class="snnn top orange" />
152 <td class="snnn top orange">March 2008</td>
153 <td class="snnn top orange" />
154 <td class="snnn top orange" />
155 <td class="ssnn top orange">February 2011</td>
158 <td class="snss top red">
159 <a href="http://lambdadelta.info/specification.html#v1">Version 1</a>
161 <td class="snsn top red">"basic_1"</td>
162 <td class="snsn top red">
163 <a href="http://coq.inria.fr/">Coq 7.3.1</a>
165 <td class="snsn top red" />
166 <td class="snsn top red">May 2004</td>
167 <td class="snsn top red">December 2005</td>
168 <td class="snsn top red">November 2006</td>
169 <td class="sssn top red">May 2008</td>
174 <!-- VERSION 2 =========================================================== -->
175 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v2">
176 <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b4.png" /> λδ version 2 (active)</div>
177 <div xmlns:ld="http://lambdadelta.info/" class="text">
178 The formal specification of λδ version 2
179 is available in the following formats:
181 <ul xmlns:ld="http://lambdadelta.info/" id="source2">
184 <a href="http://lambdadelta.info/download/lambdadelta_2.tar.gz">lambdadelta_2 for Matita 0.99.2</a>
185 (revised <span class="emph gamma">2014-10</span>).
189 The scripts are grouped in directories, first by part, then by component.
192 <span class="emph alpha">Notice:</span>
193 the scripts are checked by the latest version of Matita from
194 <a href="http://matita.cs.unibo.it/download.shtml">HELM Subversion repository</a>
195 at path <trunk/matita/>.
199 <div xmlns:ld="http://lambdadelta.info/" class="text">
200 Informational pages on the parts of the specification:
201 <a href="http://lambdadelta.info/ground_2.html">Background</a>,
202 <a href="http://lambdadelta.info/basic_2.html">Core</a>,
203 <a href="http://lambdadelta.info/apps_2.html">Applications</a>.
205 <div xmlns:ld="http://lambdadelta.info/" class="text">
206 <span class="emph alpha">Notice on numerical acounts:</span>
207 nodes are counted according to the "intrinsic complexity measure"
208 [F. Guidi: "Procedural Representation of CIC Proof Terms"
209 Journal of Automated Reasoning 44(1-2), Springer (February 2010), pp. 53-78].
211 <div xmlns:ld="http://lambdadelta.info/" class="text">
212 <span class="emph alpha">Notice on displayed logical structures:</span>
213 from the logical standpoint, the source scripts are grouped in "planes"
214 and these are grouped in "components";
215 the notation for the relations or functions
216 introduced in each script, is shown in parentheses (? are placeholders).
218 <!-- VERSION 1 =========================================================== -->
219 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v1">
220 <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b6.png" /> λδ version 1 (superseded)</div>
221 <div xmlns:ld="http://lambdadelta.info/" class="text">
222 The formal specification of λδ version 1
223 is available in the following formats:
225 <ul xmlns:ld="http://lambdadelta.info/" id="source1">
228 <a href="http://lambdadelta.info/download/lambdadelta_1.tar.gz">lambdadelta_1 for Coq 7.3.1</a>
229 (revised <span class="emph delta">2015-01</span>).
233 <span class="emph delta">2015 January 15.</span>
234 17 new lemmas and former lemma "eq_nat_dec" renamed as "nat_dec_neg".
239 The scripts are grouped in directories, one for each part.
243 <ul xmlns:ld="http://lambdadelta.info/" id="static1">
245 <a href="http://lambdadelta.info/static/matita/lambdadelta/">lambdadelta_1 for Matita 0.5</a>
246 (revised <span class="emph delta">2011-09</span>).
247 Static HTML pages generated by the <a href="http://helm.cs.unibo.it/">HELM</a> rendering engine.
250 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/pr3/pr3/pr3_confluence.con.html">
251 Confluence of reduction</a>
252 (Church-Rosser property).
255 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_correct.con.html">
256 Correctness of types</a>.
259 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_unique.con.html">
260 Uniqueness of types up to conversion</a>.
263 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/pr3/ty3_sred_pr3.con.html">
264 Subject reduction of the type assignment</a>.
267 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/arity_props/ty3_sn3.con.html">
268 Strong normalization of the typed terms</a>.
271 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/dec/ty3_inference.con.html">
272 Decidability of the type inference problem</a>.
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280 lambdadelta_1 for Matita 0.5</a>
281 (revised <span class="emph delta">2011-09</span>).
282 <a href="http://helm.cs.unibo.it/">HELM</a> directory.
283 <span class="emph alpha">Notice: the HELM rendering engine is offline.</span>
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312 <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Fri, 16 Jan 2015 16:47:03 +0100</div>