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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 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="ssns capitalize italic green">
49 <a href="http://lambdadelta.info/implementation.html">implementation</a>
53 <td class="snns capitalize sky">
54 <a href="http://lambdadelta.info/index.html#foreword">foreword</a>
56 <td class="snns capitalize magenta">
57 <a href="http://lambdadelta.info/news.html#milestones">milestones</a>
59 <td class="snns capitalize orange">
60 <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
62 <td class="snns capitalize green">
63 <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
65 <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>
66 <td class="ssns capitalize green">
67 <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
71 <td class="snss capitalize sky">
72 <a href="http://lambdadelta.info/index.html#citations">citations</a>
74 <td class="snss capitalize magenta">
75 <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
77 <td class="snss capitalize orange">
78 <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
80 <td class="snss capitalize green">
81 <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
83 <td class="snsn capitalize green">
86 <td class="ssss capitalize green">
87 <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
94 <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" />
96 <div xmlns:ld="http://lambdadelta.info/" class="text">
97 λδ is developed as a machine-checked digital specification.
98 It comes in several versions listed in the next table,
99 which includes the major milestones.
101 <div xmlns:ld="http://lambdadelta.info/" class="text">
102 The life cycle of a specification consists of four periods.
103 <span class="emph alpha">Alpha:</span>
104 the definitions are designed and the major propositions are proved,
105 then the calculus is announced with a presentation.
106 <span class="emph beta">Beta:</span>
107 major changes and additions may occur before the calculus is released on paper.
108 <span class="emph gamma">Gamma:</span>
109 subsequent improvements occur until the specification is completed or superseded,
110 while major changes and additions are announced and reported on paper.
111 <span class="emph delta">Delta:</span>
112 after its conclusion, the specification is modified just for maintenance.
114 <div xmlns:ld="http://lambdadelta.info/" class="text">
115 <table cellpadding="4" cellspacing="0">
118 <td class="snns top capitalize italic gray">version</td>
119 <td class="snnn top capitalize italic gray">name</td>
120 <td class="snnn top capitalize italic gray">developed with</td>
121 <td class="snnn top capitalize italic gray">stage</td>
122 <td class="snnn top capitalize italic gray">started</td>
123 <td class="snnn top capitalize italic gray">announced</td>
124 <td class="snnn top capitalize italic gray">released</td>
125 <td class="ssnn top capitalize italic gray">concluded</td>
128 <td class="snns top orange">
129 <a href="http://lambdadelta.info/specification.html#v2">Version 2</a>
131 <td class="snnn top orange">"basic_2"</td>
132 <td class="snnn top orange">
133 <a href="http://matita.cs.unibo.it/">Matita 0.99.2</a>
135 <td class="snnn top orange">"A"</td>
136 <td class="snnn top orange">April 2011</td>
137 <td class="snnn top orange">June 2014</td>
138 <td class="snnn top orange">October 2014</td>
139 <td class="ssnn top orange" />
142 <td class="snns top orange">Abandoned</td>
143 <td class="snnn top orange" />
144 <td class="snnn top orange">
145 <a href="http://coq.inria.fr/">Coq 7.3.1</a>
147 <td class="snnn top orange" />
148 <td class="snnn top orange">March 2008</td>
149 <td class="snnn top orange" />
150 <td class="snnn top orange" />
151 <td class="ssnn top orange">February 2011</td>
154 <td class="snss top red">
155 <a href="http://lambdadelta.info/specification.html#v1">Version 1</a>
157 <td class="snsn top red">"basic_1"</td>
158 <td class="snsn top red">
159 <a href="http://coq.inria.fr/">Coq 7.3.1</a>
161 <td class="snsn top red" />
162 <td class="snsn top red">May 2004</td>
163 <td class="snsn top red">December 2005</td>
164 <td class="snsn top red">November 2006</td>
165 <td class="sssn top red">May 2008</td>
173 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v2">
174 <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b4.png" /> λδ version 2 (active)</div>
175 <div xmlns:ld="http://lambdadelta.info/" class="text">
176 The formal specification of λδ version 2
177 is available in the following formats:
180 <ul xmlns:ld="http://lambdadelta.info/" id="source2">
183 <a href="http://lambdadelta.info/download/lambdadelta_2.tar.gz">lambdadelta_2 for Matita 0.99.2</a>
184 (revised <span class="emph gamma">2014-10</span>).
188 The scripts are grouped in directories, first by part, then by component.
191 <span class="emph alpha">Notice:</span>
192 the scripts are checked by the latest version of Matita from
193 <a href="http://matita.cs.unibo.it/download.shtml">HELM Subversion repository</a>
194 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).
221 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v1">
222 <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b6.png" /> λδ version 1 (superseded)</div>
223 <div xmlns:ld="http://lambdadelta.info/" class="text">
224 The formal specification of λδ version 1
225 is available in the following formats:
228 <ul xmlns:ld="http://lambdadelta.info/" id="source1">
231 <a href="http://lambdadelta.info/download/lambdadelta_1.tar.gz">lambdadelta_1 for Coq 7.3.1</a>
232 (revised <span class="emph delta">2012-10</span>).
236 The scripts are grouped in directories, one for each part.
241 <ul xmlns:ld="http://lambdadelta.info/" id="static1">
243 <a href="http://lambdadelta.info/static/matita/lambdadelta/">lambdadelta_1 for Matita 0.5</a>
244 (revised <span class="emph delta">2011-09</span>).
245 Static HTML pages generated by the <a href="http://helm.cs.unibo.it/">HELM</a> rendering engine.
248 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/pr3/pr3/pr3_confluence.con.html">
249 Confluence of reduction</a>
250 (Church-Rosser property).
253 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_correct.con.html">
254 Correctness of types</a>.
257 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_unique.con.html">
258 Uniqueness of types up to conversion</a>.
261 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/pr3/ty3_sred_pr3.con.html">
262 Subject reduction of the type assignment</a>.
265 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/arity_props/ty3_sn3.con.html">
266 Strong normalization of the typed terms</a>.
269 <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/dec/ty3_inference.con.html">
270 Decidability of the type inference problem</a>.
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279 lambdadelta_1 for Matita 0.5</a>
280 (revised <span class="emph delta">2011-09</span>).
281 <a href="http://helm.cs.unibo.it/">HELM</a> directory.
282 <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: Tue, 04 Nov 2014 16:28:51 +0100</div>