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- <meta content="Ferruccio Guidi" name="author">
- <meta content="The formal system λδ" name="description">
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-<h1>The Formal System λδ (\lambda\delta)<br>
-</h1>
-<h2>Towards the unification of terms, types, environments and contexts</h2>
-<img style="width: 95%; height: 4px;" alt="[Separator]"
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+ </a>
+ </div>
+ <div class="head1">The Formal System λδ (\lambda\delta)</div>
+ <div class="spacer">
+ <img class="rule" alt="[Spacer]" title="lambdadelta 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="text">
+ <table cellpadding="4" cellspacing="0">
+ <tbody>
+ <tr>
+ <td class="snns capitalize italic sky">
+ <a href="http://lambdadelta.info/index.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 orange">
+ <a href="http://lambdadelta.info/documentation.html">documentation</a>
+ </td>
+ <td class="snns capitalize italic green">
+ <a href="http://lambdadelta.info/specification.html">specification</a>
+ </td>
+ <td class="snnn capitalize italic green">
+ <br />
+ </td>
+ <td class="snnn capitalize italic green">
+ <br />
+ </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/index.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 orange">
+ <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
+ </td>
+ <td class="snns capitalize green">
+ <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
+ </td>
+ <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>
+ <td class="snnn capitalize green">
+ <br />
+ </td>
+ <td class="snns capitalize green">
+ <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
+ </td>
+ <td class="ssnn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
+ </tr>
+ <tr>
+ <td class="snss capitalize sky">
+ <a href="http://lambdadelta.info/index.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 orange">
+ <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
+ </td>
+ <td class="snss capitalize green">
+ <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
+ </td>
+ <td class="snsn capitalize green">(<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 green">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
+ <td class="snss capitalize green">
+ <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
+ </td>
+ <td class="sssn capitalize green">
+ <br />
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ </div>
+ <!-- ===================================================================== -->
+ <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="milestones">Milestones <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b3.png" />
+ </div>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph delta">January 2015.</span>
+ The specification of <a href="http://lambdadelta.info/specification.html#v1">λδ version 1</a>
+ is updated with backports from the abandoned specification of λδ version 2.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph gamma">December 2014.</span>
+ <a href="http://lambdadelta.info/implementation.html#v2">"Helena 0.8.2"</a> is released.
<ul>
- <li><a href="index.html">Foreword</a></li>
- </ul>
- <ul>
- <li>News</li>
- </ul>
- <ul>
- <li><a href="documentation.html">Papers</a></li>
- </ul>
- <ul>
- <li><a href="implementation.html">Resources</a><br>
- </li>
- </ul>
- </td>
- <td style="vertical-align: top; text-align: left;">
- <h3 style="text-align: right;">News <img
- style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
- src="images/b5.png"></h3>
- <ul>
- <li><span style="font-weight: bold;">June 2014.</span> <a
- href="documentation.html#ldt8">First communication on λδ version 2.</a><br>
- <span style="font-weight: bold;"></span></li>
- </ul>
- <ul>
- <li><span style="font-weight: bold;">December 2012.</span> The
-character "_" is removed from the denomination "lambda_delta". </li>
- </ul>
- <ul>
- <ul>
- <li>The denomination "\lambda\delta" is used in λδ-related
-texts.</li>
- <li>The denomination "lambdadelta" is used in λδ-related
-identifiers.</li>
- <li>Permanent λδ URL acquired: <a
- href="http://lambdadelta.info/">http://lambdadelta.info/</a>
-(pointing at this site). </li>
+ <li>
+ The corrected specification of Landau's "Grundlagen der Analysis"
+ is validated in λδ version 3.
+ </li>
</ul>
- </ul>
- <ul>
- <li><span style="font-weight: bold;">September 2011.</span> The
-denomination "lambda-delta" changes to "lambda_delta".
- <ul>
- <li>The character "-" is reserved in λδ textual syntax
-(recognized by <span style="font-style: italic;">Helena 0.8.1</span>).
- </li>
- <li>Eventually, the occurrences of the character "-" will
-be replaced by "_" in all λδ-related identifiers.</li>
- <li>In particular, this refactoring involves file names and
-path names.</li>
- </ul>
- </li>
- </ul>
- <ul>
- <li><span style="font-weight: bold;">April 2011.</span> The
-specification of λδ version 2 and related topics is restarted in <a
- href="http://matita.cs.unibo.it/">Matita 0.5</a>.
- <ul>
- <li><a href="apps_2.html">Here</a> is a page about the
-topics related to the specification (Applications).</li>
- <li><a href="basic_2.html">Here</a> is a page about the
-specification (Core). </li>
- <li><a href="ground_2.html">Here</a> is a page about the
-background of the specification (Ground).</li>
- </ul>
- </li>
- </ul>
- <ul>
- <li><span style="font-weight: bold;">December 2010.</span>
-Transient λδ URL acquired: http://lambda-delta.info/
-(expires on December 2012). <br>
- <span style="font-weight: bold;"></span></li>
- </ul>
- <ul>
- <li><span style="font-weight: bold;">November 2010.</span> <span
- style="font-style: italic;">Helena 0.8.1</span> is released. <br>
- </li>
- </ul>
- <ul>
- <li><span style="font-weight: bold;">September 2009.</span> <span
- style="font-style: italic;">Helena 0.8.0</span> is released and the <a
- href="implementation.html#lddl">λδ Digital Library</a> is started.<br>
- <span style="font-weight: bold;"></span></li>
- </ul>
- <ul>
- <li><span style="font-weight: bold;">June 2009.</span> <span
- style="font-style: italic;">Helena</span>, a <a
- href="implementation.html#helena">validator for λδ version 2</a>, is
-available as a part of the <a href="http://helm.cs.unibo.it/">HELM</a>
-software. <br>
- </li>
- </ul>
- <span style="font-weight: bold;"></span>
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph gamma">October 2014.</span>
+ <a href="http://lambdadelta.info/documentation.html#ldJ2">λδ version 2A</a>
+ is released.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph beta">July 2014.</span>
+ A new version of this site is online.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph beta">June 2014.</span>
+ <a href="http://lambdadelta.info/documentation.html#ldP8">First communication on λδ version 2.</a>
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph alpha">December 2012.</span>
+ The character "_" is removed from the denomination "lambda_delta":
<ul>
- <li><span style="font-weight: bold;">September 2008.</span>
-This site is online.<br>
- </li>
- </ul>
- <span style="font-weight: bold;"></span>
- <ul>
- <li><span style="font-weight: bold;">July 2008.</span> <a
- href="documentation.html#ldp5">First journal paper on λδ</a> accepted
-for publication.</li>
- </ul>
- <ul>
- <li><span style="font-weight: bold;">July 2008.</span> First <a
- href="http://helm.cs.unibo.it/procedural/">procedural reconstruction</a>
-for <a href="http://matita.cs.unibo.it/">Matita 0.5</a> of the <a
- href="implementation.html#ldp1">λδ proof scripts for Coq 7.3.1</a>.<br>
- </li>
- </ul>
- <ul>
- <li><span style="font-weight: bold;">June 2008.</span> The <a
- href="implementation.html#static">HTML pages of the specification of
-λδ version 1 for Matita 0.5</a> are online.<br>
- <span style="font-weight: bold;"></span></li>
- </ul>
- <ul>
- <li><span style="font-weight: bold;">May 2008.</span> The
-specification of λδ version 1 is dismissed.<br>
- <span style="font-weight: bold;"></span></li>
- </ul>
- <ul>
- <li><span style="font-weight: bold;">March 2008.</span> The
-specification of λδ version 2 is started with Coq 7.3.1 (false start). </li>
- </ul>
-<!-- <ul>
- <li>native type assignment with new rules for application: <span
- style="font-style: italic;">nty</span> (it replaces <span
- style="font-style: italic;">ty3</span>);<br>
- </li>
- <li>parallel conversion on focalized terms: <span
- style="font-style: italic;">fpcs</span> (it replaces <span
- style="font-style: italic;"></span><span style="font-style: italic;">pc3</span>);
- <br>
- </li>
- <li>new weak parallel reduction on environments: <span
- style="font-style: italic;">wcpr</span> <span
- style="font-style: italic;"></span>(it is based on <span
- style="font-style: italic;">fpr</span> and replaces <span
- style="font-style: italic;">wcpr0</span>); <br>
- </li>
- <li>parallel reduction on focalized terms: <span
- style="font-style: italic;">fpr</span> and <span
- style="font-style: italic;">fprs</span> (they replace <span
- style="font-style: italic;"></span><span style="font-style: italic;"></span><span
- style="font-style: italic;">pr2</span>, <span
- style="font-style: italic;">pr3</span>); <br>
- </li>
- </ul>
- <ul>
- <li>new thinning relation: <span
- style="font-style: italic;">drop</span>
-(it replaces the old <span style="font-style: italic;">drop</span>, <span
- style="font-style: italic;">clear</span>, <span
- style="font-style: italic;">getl</span>, <span
- style="font-style: italic;">cimp</span>, <span
- style="font-style: italic;">drop1</span>);</li>
- <li>new shift function: <span style="font-style: italic;">shift</span>:
-(it
-replaces
-
- <span style="font-style: italic;">app1</span>);</li>
- <li>new length function for environments: <span
- style="font-style: italic;">clen</span>;<br>
- </li>
- <li>new relocation function: <span
- style="font-style: italic;">lift</span> (it replaces old <span
- style="font-style: italic;">lift</span>, <span
- style="font-style: italic;">lift1</span>);<br>
- </li>
- <li>new term structure with polarity indicators and no
-distinction between binding and flat items;</li>
- <li>new general theory of relocation (comprises new
-relocation functions: <span style="font-style: italic;">s</span>, <span
- style="font-style: italic;">r</span>);</li>
- <li>we removed context-free reduction and conversion (<span
- style="font-style: italic;">pr0</span>, <span
- style="font-style: italic;">pr1</span>, <span
- style="font-style: italic;">pc1</span>);<br>
- </li>
- <li>we removed greedy substitution (<span
- style="font-style: italic;"></span><span style="font-style: italic;">csubst0</span>,
- <span style="font-style: italic;">csubst1</span>, <span
- style="font-style: italic;">fsubst0</span>, <span
- style="font-style: italic;">subst0</span>, <span
- style="font-style: italic;">subst1</span>);<br>
- </li>
- <li>we removed level indicators on environments (<span
- style="font-style: italic;">cbk</span>).</li>
- </ul>
--->
- <ul>
- <li><span style="font-weight: bold;">September 2007.</span> The
- <a href="implementation.html#dynamic">specification of λδ
-version 1 for Matita 0.4</a> is online.</li>
- </ul>
- <ul>
- <li><span style="font-weight: bold;">November 2006.</span> <a
- href="documentation.html#ldp3">λδ version 1</a> is released.</li>
- </ul>
- <ul>
- <li><span style="font-weight: bold;">December 2005.</span> <a
- href="documentation.html#ldt1">First communication on λδ</a>.<br>
- </li>
- </ul>
- <ul>
- <li><span style="font-weight: bold;">May 2004.</span> The <a
- href="implementation.html#ldp1">specification of λδ version 1</a> is
-started with Coq 7.3.1.<br>
- </li>
- </ul>
- <h3 style="text-align: right;">Visibility <img
- style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly"
- src="images/b4.png"></h3>
- <ul>
- <li><span style="font-weight: bold;">June 2014.</span> The <a
- href="http://www.google.com/">Google</a> search for <span
- style="color: rgb(255, 0, 0);">formal system lambda delta</span> gives
-5 resources about λδ in the first 6 results.<br>
- </li>
- </ul>
+ <li>
+ The denomination "\lambda\delta" is used in λδ-related texts.
+ </li>
+ <li>
+ The denomination "lambdadelta" is used in λδ-related identifiers.
+ </li>
+ <li>
+ Permanent λδ URL acquired:
+ <a href="http://lambdadelta.info/">http://lambdadelta.info/</a>
+ (pointing at this site).
+ </li>
+ </ul>
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph alpha">September 2011.</span>
+ The denomination "lambda-delta" changes to "lambda_delta":
<ul>
- <li><span style="font-weight: bold;">June 2014.</span> The <a
- href="http://www.yahoo.com/">Yahoo</a> search <span
- style="color: rgb(255, 0, 0);">formal system lambda delta</span> gives
-4 resources about λδ in the first 5 results.</li>
- </ul>
- </td>
- </tr>
- </tbody>
-</table>
-<br>
-<a href="http://validator.w3.org/check?uri=referer"><img
- alt="[Valid HTML 4.01 Transitional]"
- title="Valid HTML 4.01
- Transitional"
- src="http://www.w3.org/Icons/valid-html401"
- style="border: 0px solid ; width: 88px; height: 31px;"></a> <a
- href="http://www.anybrowser.org/campaign/"><img
- alt="[Use Any
- Browser Here]" title="Use Any Browser Here"
- src="images/globe_trans.png"
- style="border: 0px solid ; width: 147px; height: 42px;"></a> <img
- style="width: 88px; height: 31px;" alt="[PNG Used Here]"
- title="PNG Used Here" src="images/PNGnow2.png"><br>
-<br>
-Last update 2014-06-19 by <a href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio
-Guidi</a><br>
-</div>
-</body>
+ <li>
+ The character "-" is reserved in λδ textual syntax
+ (recognized by "Helena 0.8.1").
+ </li>
+ <li>
+ Eventually, the occurrences of the character "-"
+ will be replaced by "_" in all λδ-related identifiers.
+ </li>
+ <li>
+ In particular, this refactoring involves file names and path names.
+ </li>
+ </ul>
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph alpha">April 2011.</span>
+ The specification of <a href="http://lambdadelta.info/specification.html#v2">λδ version 2</a>
+ and related topics is restarted in
+ <a href="http://matita.cs.unibo.it/">Matita 0.5</a>.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph delta">February 2011.</span>
+ The specification of λδ version 2 with Coq 7.3.1 is abandoned.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph alpha">December 2010.</span>
+ Transient λδ URL acquired: http://lambda-delta.info/ (expires on December 2012).
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph beta">November 2010.</span>
+ <a href="http://lambdadelta.info/implementation.html#v1">"Helena 0.8.1"</a> is released.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph beta">September 2009.</span>
+ <a href="http://lambdadelta.info/implementation.html#v0">"Helena 0.8.0"</a> is released and the
+ <a href="http://lambdadelta.info/implementation.html#lddl">λδ Digital Library</a> is started.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph alpha">June 2009.</span>
+ "Helena", a <a href="http://lambdadelta.info/implementation.html#helena">validator for λδ version 2</a>,
+ is available as a part of the <a href="http://helm.cs.unibo.it/">HELM</a> software.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph alpha">September 2008.</span>
+ This site is online.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph delta">July 2008.</span>
+ <a href="http://lambdadelta.info/documentation.html#ldJ1">First journal paper on λδ</a>
+ accepted for publication.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph delta">July 2008.</span>
+ First <a href="http://helm.cs.unibo.it/procedural/">procedural reconstruction</a>
+ for <a href="http://matita.cs.unibo.it/">Matita 0.5</a>
+ of the λδ version 1 for Coq 7.3.1.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph delta">June 2008.</span>
+ The <a href="http://lambdadelta.info/specification.html#static1">
+ HTML pages of the specification of λδ version 1 for Matita 0.5</a>
+ are online.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph delta">May 2008.</span>
+ The specification of λδ version 1 is concluded.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph alpha">March 2008.</span>
+ The specification of λδ version 2 is started with Coq 7.3.1 (false start).
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph gamma">September 2007.</span>
+ The <a href="http://lambdadelta.info/specification.html#dynamic1">
+ specification of λδ version 1 for Matita 0.4</a>
+ is online.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph gamma">November 2006.</span>
+ <a href="http://lambdadelta.info/documentation.html#ldR2">λδ version 1</a>
+ is released.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph beta">December 2005.</span>
+ <a href="http://lambdadelta.info/documentation.html#ldP1">First communication on λδ version 1</a>.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph alpha">May 2004.</span>
+ The specification of <a href="http://lambdadelta.info/specification.html#v1">λδ version 1</a>
+ is started with Coq 7.3.1.
+ </li>
+ </ul>
+ <!-- ===================================================================== -->
+ <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="visibility">Visibility <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b3.png" />
+ </div>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph alpha">June 2014.</span>
+ The <a href="http://www.google.com/">Google</a>
+ search for "formal system lambda delta" gives
+ 5 resources about λδ in the first 6 results.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="emph alpha">June 2014.</span>
+ The <a href="http://www.yahoo.com/">Yahoo</a>
+ search for "formal system lambda delta" gives
+ 4 resources about λδ in the first 5 results.
+ </li>
+ </ul>
+ <div class="spacer">
+ <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
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+ <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Wed, 21 Jan 2015 17:13:08 +0100</div>
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projects / helm.git / blobdiff