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- <div class="head1">The Formal Systems of the λδ (\lambda\delta) Family</div>
- <div class="spacer">
- <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
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- <div xmlns:ld="http://lambdadelta.info/" class="text">
- <table cellpadding="4" cellspacing="0">
- <tbody>
- <tr>
- <td class="snns capitalize italic sky">
- <a href="http://lambdadelta.info/home.html">home</a>
- </td>
- <td class="snns capitalize italic magenta">
- <a href="http://lambdadelta.info/news.html">news</a>
- </td>
- <td class="snns capitalize italic white">
- <a href="http://lambdadelta.info/specification.html">specification</a>
- </td>
- <td class="snnn capitalize italic white">
- <br />
- </td>
- <td class="snnn capitalize italic white">
- <br />
- </td>
- <td class="snns capitalize italic orange">
- <a href="http://lambdadelta.info/documentation.html">documentation</a>
- </td>
- <td class="snns capitalize italic green">
- <a href="http://lambdadelta.info/implementation.html">implementation</a>
- </td>
- <td class="ssnn capitalize italic green">
- <br />
- </td>
- </tr>
- <tr>
- <td class="snns capitalize sky">
- <a href="http://lambdadelta.info/home.html#foreword">foreword</a>
- </td>
- <td class="snns capitalize magenta">
- <a href="http://lambdadelta.info/news.html#milestones">milestones</a>
- </td>
- <td class="snns capitalize white">
- <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
- </td>
- <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>
- <td class="snnn capitalize white">
- <br />
- </td>
- <td class="snns capitalize orange">
- <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
- </td>
- <td class="snns capitalize green">
- <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
- </td>
- <td class="ssnn capitalize green">
- <a href="http://lambdadelta.info/osn/">Open Symbolic Notation (OSN)</a>
- </td>
- </tr>
- <tr>
- <td class="snss capitalize sky">
- <a href="http://lambdadelta.info/home.html#citations">citations</a>
- </td>
- <td class="snss capitalize magenta">
- <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
- </td>
- <td class="snss capitalize white">
- <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
- </td>
- <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>
- <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
- <td class="snss capitalize orange">
- <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
- </td>
- <td class="snss capitalize green">
- <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
- </td>
- <td class="sssn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
- </tr>
- </tbody>
- </table>
- </div>
- <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" />
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">
- The systems of the λδ family are developed as machine-checked digital specifications,
- and are listed in the next table, which includes the major milestones.
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">
- The life cycle of a specification consists of four periods.
- <span class="emph alpha">Alpha:</span>
- the definitions are designed and the major propositions are proved,
- then the calculus is announced with a presentation.
- <span class="emph beta">Beta:</span>
- major changes and additions may occur before the calculus is released on paper.
- <span class="emph gamma">Gamma:</span>
- subsequent improvements occur until the specification is completed or superseded,
- while major changes and additions are announced and reported on paper.
- <span class="emph delta">Delta:</span>
- after its conclusion, the specification is modified just for maintenance.
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">
- <table cellpadding="4" cellspacing="0">
- <tbody>
- <tr>
- <td class="snns top capitalize italic gray">version</td>
- <td class="snnn top capitalize italic gray">name</td>
- <td class="snnn top capitalize italic gray">stage</td>
- <td class="snnn top capitalize italic gray">developed with</td>
- <td class="snnn top capitalize italic gray">started</td>
- <td class="snnn top capitalize italic gray">announced</td>
- <td class="snnn top capitalize italic gray">released</td>
- <td class="snnn top capitalize italic gray">concluded</td>
- <td class="ssnn top capitalize italic gray">references</td>
- </tr>
- <tr>
- <td class="snns top yellow">
- <a href="http://lambdadelta.info/specification.html#v3">Version 3</a>
- </td>
- <td class="snnn top yellow">"basic_3"</td>
- <td class="snnn top yellow" />
- <td class="snnn top yellow" />
- <td class="snnn top yellow" />
- <td class="snnn top yellow" />
- <td class="snnn top yellow" />
- <td class="snnn top yellow" />
- <td class="ssnn top yellow">
- <a href="http://lambdadelta.info/documentation.html#ldJ3a">J3a</a>
- </td>
- </tr>
- <tr>
- <td class="snns top orange">
- <a href="http://lambdadelta.info/specification.html#v2">Version 2</a>
- </td>
- <td class="snnn top orange">"basic_2"</td>
- <td class="snns top orange">"A2"</td>
- <td class="snnn top orange">
- <a href="http://matita.cs.unibo.it/">Matita 0.99.3</a>
- </td>
- <td class="snnn top orange">October 2015</td>
- <td class="snnn top orange" />
- <td class="snnn top orange" />
- <td class="snnn top orange" />
- <td class="ssnn top orange" />
- </tr>
- <tr>
- <td class="nnns top orange">
- <br />
- </td>
- <td class="nnnn top orange">
- <br />
- </td>
- <td class="snns top orange">"A1"</td>
- <td class="snnn top orange">
- <a href="http://matita.cs.unibo.it/">Matita 0.99.2</a>
- </td>
- <td class="snnn top orange">April 2011</td>
- <td class="snnn top orange">June 2014</td>
- <td class="snnn top orange">October 2014</td>
- <td class="snnn top orange">August 2015</td>
- <td class="ssnn top orange">
- <a href="http://lambdadelta.info/documentation.html#ldV2a">V2a</a>
- <a href="http://lambdadelta.info/documentation.html#ldR2c">R2c</a>
- </td>
- </tr>
- <tr>
- <td class="snns top orange">Abandoned</td>
- <td class="snnn top orange" />
- <td class="snnn top orange" />
- <td class="snnn top orange">
- <a href="http://coq.inria.fr/">Coq 7.3.1</a>
- </td>
- <td class="snnn top orange">March 2008</td>
- <td class="snnn top orange" />
- <td class="snnn top orange" />
- <td class="snnn top orange">February 2011</td>
- <td class="ssnn top orange" />
- </tr>
- <tr>
- <td class="snss top red">
- <a href="http://lambdadelta.info/specification.html#v1">Version 1</a>
- </td>
- <td class="snsn top red">"basic_1"</td>
- <td class="snsn top red" />
- <td class="snsn top red">
- <a href="http://coq.inria.fr/">Coq 7.3.1</a>
- </td>
- <td class="snsn top red">May 2004</td>
- <td class="snsn top red">December 2005</td>
- <td class="snsn top red">November 2006</td>
- <td class="snsn top red">May 2008</td>
- <td class="sssn top red">
- <a href="http://lambdadelta.info/documentation.html#ldV1a">V1a</a>
- <a href="http://lambdadelta.info/documentation.html#ldJ1a">J1a</a>
- </td>
- </tr>
- </tbody>
- </table>
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">
- Informational pages on the specifications are provided.
- </div>
- <ul xmlns:ld="http://lambdadelta.info/" id="notice1">
- <li>
- <span class="emph alpha">Notice on displayed numerical acounts:</span>
- nodes are counted according to the "intrinsic complexity measure"
- [F. Guidi: "Procedural Representation of CIC Proof Terms"
- Journal of Automated Reasoning 44(1-2), Springer (February 2010), pp. 53-78].
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/" id="notice2">
- <li>
- <span class="emph alpha">Notice on displayed logical structures:</span>
- from the logical standpoint, the source scripts are grouped in "planes"
- and these are grouped in "components";
- the notation for the relations or functions
- introduced in each script, is shown in parentheses (? are placeholders).
- </li>
- </ul>
- <!-- VERSION 3 =========================================================== -->
- <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v3">
- <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b8.png" /> λδ version 3 (proposed)</div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">
- The formal specification of λδ version 3
- is forthcoming.
- </div>
- <!-- VERSION 2 =========================================================== -->
- <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v2">
- <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png" /> λδ version 2 (active)</div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">
- The formal specification of λδ version 2
- is available in the following formats:
- </div>
- <ul xmlns:ld="http://lambdadelta.info/" id="source2">
- <li>
- <div class="text">
- <a href="http://lambdadelta.info/download/lambdadelta_2A1.tar.gz">lambdadelta_2A1 for Matita 0.99.2</a>
- (revised <span class="emph gamma">2014-10</span>).
- Source scripts [Svn revision: 12964].
- <a href="http://lambdadelta.info/documentation.html#ldR2c">Documentation (R2c)</a>.
- </div>
- <div class="text">
- The scripts are grouped in directories, first by part, then by component.
- </div>
- <div class="text">
- <span class="emph alpha">Notice:</span>
- the scripts are checked by the latest version of Matita from
- <a href="http://matita.cs.unibo.it/download.shtml">HELM Subversion repository</a>
- at path <trunk/matita/>.
- </div>
- </li>
- </ul>
- <div xmlns:ld="http://lambdadelta.info/" class="text">
- Informational pages on the parts of the specification:
- <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>.
- </div>
- <!-- VERSION 1 =========================================================== -->
- <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="v1">
- <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b6.png" /> λδ version 1 (superseded)</div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">
- The formal specification of λδ version 1
- is available in the following formats:
- </div>
- <ul xmlns:ld="http://lambdadelta.info/" id="source1">
- <li>
- <div class="text">
- <a href="http://lambdadelta.info/download/lambdadelta_1.tar.gz">lambdadelta_1 for Coq 7.3.1</a>
- (revised <span class="emph delta">2015-09</span>).
- Source scripts.
- <a href="http://lambdadelta.info/documentation.html#ldJ1a">Documentation (J1a)</a>.
- <ul>
- <li class="">
- <span class="emph delta">2015 January 15.</span>
- 17 new lemmas and former lemma "eq_nat_dec" renamed as "nat_dec_neg".
- </li>
- </ul>
- </div>
- <div class="text">
- The scripts are grouped in directories, one for each part.
- </div>
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/" id="static1">
- <li>
- <a href="http://lambdadelta.info/static/matita/lambdadelta/">lambdadelta_1 for Matita 0.5</a>
- (revised <span class="emph delta">2011-09</span>).
- Static HTML pages generated by the <a href="http://helm.cs.unibo.it/">HELM</a> rendering engine.
- <ul>
- <li class="">
- <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/pr3/pr3/pr3_confluence.con.html">
- Confluence of reduction</a>
- (Church-Rosser property).
- </li>
- <li class="">
- <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_correct.con.html">
- Correctness of types</a>.
- </li>
- <li class="">
- <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/props/ty3_unique.con.html">
- Uniqueness of types up to conversion</a>.
- </li>
- <li class="">
- <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/pr3/ty3_sred_pr3.con.html">
- Subject reduction of the type assignment</a>.
- </li>
- <li class="">
- <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/arity_props/ty3_sn3.con.html">
- Strong normalization of the typed terms</a>.
- </li>
- <li class="">
- <a href="http://lambdadelta.info/static/matita/lambdadelta/basic_1/ty3/dec/ty3_inference.con.html">
- Decidability of the type inference problem</a>.
- </li>
- </ul>
- </li>
- </ul>
- <ul xmlns:ld="http://lambdadelta.info/" id="dynamic1">
- <li>
- <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/">
- lambdadelta_1 for Matita 0.5</a>
- (revised <span class="emph delta">2011-09</span>).
- <a href="http://helm.cs.unibo.it/">HELM</a> directory.
- <span class="emph alpha">Notice: the HELM rendering engine is offline.</span>
- </li>
- </ul>
- <div xmlns:ld="http://lambdadelta.info/" class="text">
- Informational pages on the parts of the specification:
- <a href="http://lambdadelta.info/ground_1.html">Background</a>,
- <a href="http://lambdadelta.info/basic_1.html">Core</a>.
- </div>
- <div class="spacer">
- <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="spacer">
- <br />
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="spacer">
- <a href="http://validator.w3.org/check?uri=referer">
- <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
- </a>
- <a href="http://jigsaw.w3.org/css-validator/check/referer">
- <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
- </a>
- <a href="http://www.w3.org/XML/">
- <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
- </a>
- <a href="http://www.w3.org/Graphics/PNG/">
- <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
- </a>
- <a href="http://www.anybrowser.org/campaign/">
- <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
- </a>
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="spacer">
- <br />
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Fri, 24 Nov 2017 21:00:00 +0100</div>
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projects / helm.git / blobdiff